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1. input bias used for A const double FullBiasl T3 E T3 8 ms sms D 5396281073556299e4 2155285650187714e4 de 25 1081061271037377e4 2 1 1405546309460455e4 0092226745629825e4 3863482551199322e4 3776316084580969e4 8667949688335881e4 6486017651552007e4 1025011814584467e4 35677170884020387e4 1123058872867919e4 5031336101198693e4 9086499981718013e4 9976889065608717e4 1096013722954432e4 5389976478144561e4 1 Ol 10 0 I 1 Ol 1986270148644632e4 0684497872413800e4 5545079968154958e4 6416031669458668e4 4983425512452655e4 5797397367591479e4 1331556021774304e4 6358650232444849e4 4085567369344272e4 4701322032968340e4 1295955495436054e4 7 9 2995753942845081e4 5543556064397652e4 ODO ODO DODO OOO OOO OOO OOO OoOOoOoOoOoOOoO OOO ooo Cc OOOO DODO OOO CO COO OOO OOOO OoOOO OOOO oscsoo cC D po 3 p LS 3 Yo gx A O O OV TUO 762 C CO CO 0 CX Or 0 Od OOO DO COCO CO COCO OOOO 0 c OOrFROOF addition when direction input 70 0 2 0061702533473493e 1 9567626679904070e 9 7023646305029010e 1 0185475520917636e 1 6336552516527902e 5 3423886361010664e 1 4957998772309816e 5311024980801433e 3861709831682187e 8 6954486655705221e F2 2303031682519762e 8 8
2. ji li 0 500 1000 1500 2000 2500 3000 3186 Epochs Figure 5 8 Training results for the multi layer network The last network architecture closely examined was a combination of two networks This architecture was arrived at by considering the nature of the problem From the uncompensated positioning error results Figure 5 1 and Figure 5 2 the errors can be classified into two categories large or gross errors that occur over the range of motion and the cyclic error that occurs within the space of a single revolution of the leadscrew The large errors would include the general trend of the positioning error as the machine moved from linch to 40 inches and the backlash error as the machine changes direction of motion By considering and compensating for these problems separately two networks can be created One would be designed to address the large error issues and the other would focus solely on the cyclic error problem The system would be constructed so that just prior to applying the compensation to the control the network outputs would be added to make a single compensation value to be used The resulting networks were two single layer networks one with 30 neurons in the hidden layer and one with eight neurons in the hidden layer In both cases the network is as diagramed in Figure 5 5 only the number of hidden layer neurons would change The training results for the 30 layer network are shown in Figure 5
3. sesss 36 Figure 5 2 Single direction cyclic error 4c eie eda o 37 Figure 5 3 Bi directional leadscrew compensation results esses 38 Figure 5 4 Neural network error compensation results eese 39 Figure 5 5 Single hidden layer network eese 40 Figure 5 6 Training results for the single layer network esse 41 Figure 5 7 Multi layer network diagram id da 41 Figure 5 8 Training results for the multi layer network esee 42 Figure 5 9 Training result for large error network esee 43 Figure 5 10 Training result for cyclic error network eee 44 Figure A 1 Laser interferometer upper and lower apertures eese 48 Figure A 2 Close up of miobile reflector etnies teer Eee id 49 Figure A 3 Long axis leadscrew assembly edu cis ae ciate dep denies 50 Figure A4 Close up of balln t assemble ais 51 vi List of Tables Table 2 1 Key entries for software SEU ed heo RO OR RH Ree os op as eames otn die 9 Table 2 2 Part program entries for X axis motion 10 Table 2 3 Partial list of output data from 5 6 D laser system sees 12 Table 3 1 Error versus position compensation 2 00 eee eee ceeeeceeeeeeeeeceaeceseeeseeeeaeeesaeens 21 Table 3 2 Bi directional lead screw compensation values forward 22 Ta
4. dad 1 LDR esearch Methodology ti eene VR Deere Usa eae Cal NUR GUERRE 1 SS EUG CUEO cosi ds on acs Red Exito etcdtetutes a pondere o tome Sota ee S 2 Chapter 2 Backers 3 2 1 American Hustler Lathes cion anida sia e sine 3 2 2 Open Xrehlttecture COELI dea ase 4 23 Laser dIntetierome Let Sa dz 6 231 General INEO CMM ROUEN M ME 6 232 Physical Setup MR TER 7 2 3 3 Software Setup TE 8 2 3 4 Graphical Results and Output Dto ala 11 2 4 Artificial Neural Networks tia ici 13 2 5 MATLAB and the Neural Network Toolbox eene 17 Chapter 3 Related WOrkS eee eoo eoe seen oes rne eh aane ense reno a Rene ae eue eue eno Pee eer pua U Eb ea enn 20 3 1 Traditional Lead Screw Compensation sese 20 3 1 1 Uni Directional Compensation with Backlash esses 20 3 1 2 Bi Directional Lead Screw Compensation eee eee 22 3 2 Applications of Neural Neon ai 23 3 21 miellgon Control DAS AA A A udo Rt EM E d 23 3 2 2 Analysis of Vibration MAUI As 23 3 3 Positioning Error Correction with Neural Networks eere 24 Chapter 4 Experimental Setup o o ooosssss 25 4 1 Configuring Laser and Lathe Control eese 25 4 1 1 Laser Measurement System Setup eee ie e etie sene inen seat aa sena aan a asa aua 23 4 2 L the CONT OLDS D suis Asda leah opa 27 42 Data Coleco da AAN E 28 4 3 Neural Network Design and Training
5. 1 5201 000 0 001000 14 Position inch 40 000 File Name Machine Test Axis API5 6D S N Operator Test Date Test Time eval40MDSICompNew2 Air T Avg American Hustler Air P Avg 2 Material T Avg 4014 Humidity JFines Exp Caef 10 05 2000 Num of Runs 14 48 00 Window 69 5 F Max Avg Error 0 000885 in 28 8 in Hg Max Rev Err 0 000813 in 69 0 F Max Repeat 0 001098 in 50 96 6 7 ppm F 3 0 1000 in For Help press F1 Figure 5 3 Bi directional leadscrew compensation results The measurement runs that were used to test this compensation system were set to an interval of 0 52 for the range of 1 inch to 40 ionches This made for a much quicker check the umcompensated four passes took almost 20 hours to run and by setting the increment to a value that was not evenly divisible by the pitch of the leadscrew it still brought out the cyclic errors as the leadscrew stopped in different rotational positions As shown in Figure 5 3 the bi directional compensation system was able to correct for the majority of the errors The overall maximum average error was reduced to 0 000995 inches 17 8 of the uncompensated error Backlash as measured by the maximum reversal error has been reduced to 0 000813 inches 19 4 of the uncompensated value And while the cyclic error is clearly visible it has been reduced to approximately 0 0005 inches or less about 35 of the uncompensated value These
6. Hh layer weights for cyclic error net const double cyclicLW 8 3 4 x 2845598766206338e 002 7583290668195674e 001 9272704047420051e 001 2340609441792598e 001 3566978204302399e 003 72 1 9669801168724809e 002 3 5317654044065912e 003 1 6403797843778867e 002 bias layer 2 for cyclic error net const double cyclicBias2 3 7874518228170045e 001 KOR KK RK KR KR RR RR RR RR RR RR RR RR RK OK OK KK KKKKKKKKKKKKKKKKKKKKKKKKKKKK function calcz inputs K dir direction of motion 0 gt forward 1 gt reverse iS pos current position in inches ouputs ES returns comp value for position and direction in Z axis processing ES This does the feed forward portion of the neural networks It calculates the x transfer function of logsig for the hidden layer and a pure linear for the output neuron There are two networks one for a full length error function and one x that handles the details of the cyclic error in the screw KKEKKKKKKKKKK CC CC CK CC CC CC CK CK CC CK C CK CC CK C Ck S S E e KK E Kk AG KG X X X X KCKCKCKCKCKCKCKCKCKCKCKCKCKCkCkCk Ck Ck Ck Ck ckck ck ck Y double calcZ int dir double pos register int i double temp 30 double cyclicPos double fullResult 0 double cyclicResult 0 init the temp array dependent on direction of travel if dir 0 dir
7. V V 71 Tus cue bias val 2777120317224900e 002 2225148283068585e 002 const double FullBias2 input weights col const double cyclicIW2 0199735339014765e 1412266461437305e 4 1 2 6173165967393352e x 4 2 6 95 input weights col error net 5485150577054590e 7523812303695863e 6388036946666858e 4902852076295659e 7128378964014928e Lumn const double cyclicIW_B mu 4 7 FIS T3 D F3 E bias layer 1 for cycl const double cycl 3902984827427503e 8286945653885969e 7240626438899760e4 6338193323527328e4 7826837129765529e4 1199979350411143e4 8645326454024267e4 5064102092927918e4 icBiasl lue layer 2 OO ODO C9 629r 02 62 09 OD TOO DD uu DOE 9372202168215299e4 1473068913108277e4 1779003755671003e4 9534315151373125e4 0972641799667036e4 2932649248391974e4 5021445926326495e4 4 4508828942124801e4d OOOO ooo Oo lumn 1 V V V V N V V V N V OOo O00o0o00Q0c9nfb25 L5 A rar qa gg Ie LE 3 3526357495979814e 001 OOPOOOOO0 for cyclic error network if added to bias layer 1 for cyclic La GE Hi ic error net V V V V N V V V V 8 OOOrPooprpprp J
8. 2 2 is an extract of the key lines in the part program matching the setup illustrated in Figure 2 4 vb 1 1 Axis 1 X 2 Y 3 Z vb 3 7 Starting Position in Machine Coordinates vb 4 7 End Position in Machine Coordinates vb 5 0 14 Increment of motion between points vb 6 6 Dwell time at points vb 7 4 Number of complete runs vb 8 20 Feedrate for motion vb 9 1 Overshoot for backlash moves Table 2 2 Part program entries for X axis motion Close examination and comparison between the two shows one key difference the Dwell parameter on the machine is set for 6 seconds while the Dwell parameter on the 5 6 D Laser is set for 4 seconds After several runs of collecting data it was determined that these were the best real world settings for reliably collecting accurate data Attempting to too closely time the moves of the machine with reading the laser system sometimes leads to faulty readings and errors These settings are conservative and insure that the machine motion will settle before the laser system takes its reading and the machine will not begin motion to the next position until well after the laser system has completed the previous reading Figure 2 5 diagrams the relationship between the motion of the machine and the activity of the 5 6 D Laser system for taking measurements The key point here is that although there is no direct connection between the co
9. 83322 16756426421e 32907721902e 14055 00922 38634 37763 46309460455e 26745629825e 82551199322e 16084580969e 8667949688335881e 64860 102501 17651552007e 1814584467e 35677 11230 2 const double FullBiasl1 e T3 Ter 30313 90864 99768 10960 19862 06844 55450 64160 49834 70884020387e 58872867919e 36101198693e 99981718013e 89065608717e 13722954432e 5389976478144561e o 100 1 Ol 70148644632e 97872413800e 79968154958e 31669458668e 25512452655e co 599 T33415 97367591479e 56021774304e 6358650232444849e 40855 53962 231 552 47013 67369344272e 81073556299e 85650187714e 22032968340e 1295955495436054e 10810 61271037377Te 29957 55435 00617 53942845081e 56064397652e 02533473493e 9567626679904070e 7023646305029010e 01854 63365 34238 75520917636e 52516527902e OOOOOO OO COCO OOOO OO c0 cC OC Cc Coco OOO CO COO CO OOOO c c D oL 3 pa LS 4 soya e ER Ea E OS 86361010664e 4957998772309816e 53110 24980801433e 38617 69544 23030 84217 71255 09831682187e 86655705221e 31682519762e 53766822473e 62961409566e O CO 2 0 0 0 0 0 0 0 CX Or OO OVO OOO 00 CS O O 60 09 OOOO COCO OC C
10. 9 For the data presented this network was able to reduce the error measure as before the performance function was the SSE to under 4e 8 in less than 600 epochs The training time for this network was just under 42 seconds 42 Performance is 3 99749e 008 Goal is 4e 008 T T T 2 10 4 i 0 10 ft 7 1 he 1 re Oo 3 O 49 1 g a gt i 1 rat E 10 E a L I 1 i 6 10 Hi L I I L ia 8 10 i 0 100 200 300 400 500 558 Epochs Figure 5 9 Training result for large error network The training result for the eight neuron network is shown in Figure 5 10 This network was designed to address the cyclic errors seen in the data For this the network was able to reduce the SSE error measure to under 9e 9 in less than 300 epochs The training time for this network was under 15 seconds on the test computer 43 P Performance is 8 98224e 009 Goal is 9e 009 T T T 0 10 7 S 2 10 w o 9 1 c I n O Q4 5 10 H i S E 1 1 V 6 9 10 FA a Ni Ee Nm t ET 1 _ _ _ AAA a 0 50 100 150 200 250 273 Epochs Figure 5 10 Training result for cyclic error network By taking advantage of some pre training analysis it was possible to reduce the training time from over two hours to just a few minutes for the problem under study This was achieved while maintaining or improving the a
11. Laser Measurement System Setup The first step in configuring the laser interferometer system and the lathe for data collection is the physical alignment of the laser interferometer In Figure 4 1 the physical arrangement for collecting data on the Z long axis is shown In the lower right corner the laser head can be seen which houses the laser emitter beam splitter interferometer stationary reflector and measurement electronics Circled in the upper left is the mobile reflector mounted on a magnetic base to the tool turret The mobile reflector is mounted such that as closely as possible it accurately reflects the motion of the tool which is the point of greatest interest in this experiment 25 Figure 4 1 Laser alignment for Z axis Once the system components are arranged for the desired test they are precisely aligned horizontally and vertically parallel with the Z axis so that linear motion in the Z axis is accurately measured by the laser interferometer system This is readily determined by monitoring the beam strength of the laser as the machine is moved through its entire range of motion as long as the beam strength remains in an acceptable range throughout this motion the alignment is sufficient for correct measurement With the physical arrangement and alignment of the laser system complete the final step in configuring the system is to set the software parameters for the test to be conducted This is done on the Test
12. SINE SUE A ive TN Cancel name Figure 2 4 Setup screen for control of the 5 6 D laser system Entry Explanation of Selections Test Mode In a Bidirection test readings are taken in both directions of motion Therefore the machine is expected to move by the specified interval forward from the starting point and then in reverse from the ending point Mode In the Auto mode machine motion is controlled automatically by a part program The laser system is set to expect a specified sequence of moves and uses the Dwell Time and Window parameters to trigger readings Dwell Time Specifies the time in seconds for the laser to read at each position In Auto mode when the machine moves to within the Window parameter of the next position the laser system will begin its Dwell timer Halfway through the Dwell time the laser will begin taking its reading with the final reading at the end of the Dwell time This allows for the machine to complete the move to the next position and settle in place Window Specifies how close the machine has to be to the next position to start the Dwell timer Initial Position This is the starting point of the laser run For multiple Bidirectional runs the system expects the machine to incrementally move back to this position When the prior run is complete the machine is expected to move past this position outside the Windows distance and then return to the starting point for the first
13. Setup screen in the API 5 6 D laser system software While many tests were conducted with a variety of parameters the setup for the primary test for the Z axis is shown in Figure 4 2 The key parameter to note is that this was a bidirectional test with readings taken every 0 025 inches 40 readings per inch 26 Test Setup r 5D or BD Test 5 6D System Setup C 6D C 5D Vertical Units Environment Test Mode Linear inch Air Temp amp Pressure ov Bidirection Unidirection Straight inch Material Temp ov Mode Angle arc sec Air Humidity o 2 sut io pue quad paN az A E Manual ssyne ll o es Change seine eee 4 Machine Information Window n 0 01 Test Axis Axes Location Travel ini Pos foo oo oo foo oo Initial Position 1 Machine ID 51561 End Position jo Machine Name American Hustler Step Size oos CNC Program smauzvott Num of Runs EM ol Feedrate 20 Num of Positions E Operator fu Fines Laser amp Sensor Distance Comments z ee pa CO Ss Increase Decrease Plot Title Z Linear 1 40 40 step File Name c Program Files 4utomated Precision Incl4PI 5 6D Laser 51561 tsmallZv9_2 oad setup Troma eod Save setup amp give file Chncsl name Figure 4 2 Test setup for primary Z axis test 4 1 2 Lathe Control Setup Configuring the lathe control is accomplished by writing a part program that produces the patt
14. Z Linear 1 40 40 steps per inch Bi directional Linear Error Plot ANSI 0 007500 Linear Error inch 0 006250 0 005000 LU t itf P M E januam auteur eise T ARAM 0 003750 TTC 0 002500 0 001250 df 0 000000 0 001250 Position inch 1025 1 000 8 825 16 625 24 425 32 225 40 000 0 002500 1 y 1 f 1 File Name smallZv8 2 pos Air T Avg 69 0 F Max Avg Error 0 005582 in FW BW Rmi 0 Machine American Hustler Air P Avg 28 1 in Hg Max Rev Err 0 004181 in Rm2 c a Test Axis 2 Material T Avg 69 1 F Max Repeat 0 005570 in Rey on oe API5 8D S N 4014 Humidity 50 Run A Operator J Fines Exp Coef 6 7 ppm F c mo ccm Test Date 10 04 2000 Num of Runs 4 Rus cin os ad Test Time 13 15 29 Window 0 0100 in A me R B For Help press F1 Figure 5 1 Uncompensated positioning error average results The most glaring problem on this machine is the difference in positioning from between the forward and reverse motions commonly known as backlash As listed in the lower portion of the plot the maximum reversal error is 0 004181 inches This is the maximum error at any one measurement point between the two directions of motion The next problem is the general trend of the machine to position long as the desired position increases from 1 inch to 40 inches In the left side of the graph positioning errors are less than the errors on the right side of
15. directions of motion and these values are independently recorded These values would then be entered into the control as separate compensation values and the control would consider direction of motion when determining which value to use In this method of compensation there is no direct backlash value because that error is included in the bi directional measurements Once again the exact method of entering the compensation values is control specific but the contents would appear similar to Table 3 3 Error Amount A Linear Position Forward Motion Reverse Motion Figure 3 2 Error versus motion profile for bi directional compensation Forward Position inches Error inches 0 0 40 001 1 0 40 001 2 0 0 0 3 0 0 001 4 0 0 002 Table 3 2 Bi directional lead screw compensation values forward 22 Reverse Position Error 4 0 0 004 3 0 0 003 2 0 0 002 1 0 0 001 0 0 0 001 Table 3 3 Bi directional lead screw compensation values reverse 3 2 Applications of Neural Networks The applications of neural networks are many and varied The Matlab Neural Network Toolbox User s Guide Demth amp Beale lists a variety of applications in Finance Control Manufacturing and many others In Artificial Intelligence A Modern Approach Russell and Norvig briefly discuss three specific applications of neural networks pronunciation of written English text by a compu
16. i 0 i lt 8 i temp i 1 1 exp temp i calculate the vector multiplication of layerweights result of hidden layer for i 07 L 8 IE multiplication temp i cyclicLW i for i 0 i lt 8 i summing results cyclicResult temp i add the bias value for output neuron cyclicResult cyclicBias2 return fullResult cyclicResult end of calcZ 75
17. includes chapters on applications in control systems linear and adaptive filters and others Demuth and Beale There is a Graphical User Interface GUI for interacting with the routines in the toolbox or command line access for use in MATLAB s programming and scripting capability The Toolbox also includes an extensive set of built in transfer functions to use in defining the neurons of the network and many different training routines are included for use All of the neural 17 network development and implementation discussed in this thesis was done using MATLAB and the Neural Network Toolbox Utilizing the functionality of the Neural Network Toolbox referred to here as simply the toolbox defining a new neural network becomes a fairly simple series of one line commands with a few parameters to create train and simulate the specific characteristics and behavior of the network The toolbox has commands to create perceptrons radial basis networks competitive feed forward networks and many others Demuth and Beale For example creating a two input single neuron perceptron network where one input ranges from 0 to 2 and the second from 1 to 1 is accomplished by using the command net newp 0 2 1 1 1 A more complex and useful feed forward network with two inputs ranging from 0 to 1 and 1 to 40 with 30 neurons in the hidden layer with the logsig transfer function and a single linear neuron in the output layer can be cre
18. machine Chapter 6 is the conclusions section The discussion in the chapter is on the conclusions reached after examining the experimental results the limitations of the work conducted in this thesis and a discussion of future work The five appendices contain information that expands on the discussions in the main chapters Appendix A contains detailed photographs of the measurement equipment and the machines that highlight key features for this thesis Appendix B contains the complete listing of the Visual Basic macro and resultant machine control code that was used in the course of this thesis Appendix C is the complete listing of the Matlab m file script that was used to generate the artificial neural networks for this thesis Appendix D is the complete listing of the Matlab m file used for the extraction of key neural network paramaters required for integration into the machine tool control Appendix E is the listing for the C program that provides the necessary calculations to integration the artificial neural network into the machine tool control Chapter 2 Background The technological basis for this thesis lies in four areas Computer Numerically Controlled CNC machine tools Open Architecture Controls OACs for machine tools laser interferometry and artificial neural networks From the perspective of this thesis three of these areas were fully developed and available equipment and systems were used The CNC machine used is an Amer
19. net trainParam show 5 net trainParam epochs 1000 net trainParam goal 4e 8 for simplicity collect the inputs p and targets t p dir smallzv9 2ave 1 t smallzv9 2ave 2 oe train the network net train net p t 60 test the network on the first run zeros 1 1561 smallzv9_2 1 1561 1 am sim net Xm Ym bm ones 1 1561 smallzv9 2 1562 3122 1 sim net Ym plot the result figure 1 hold on plot smallzv9_2ave 1 1561 1 am b plot smallzv9_2ave 1562 3122 1 bm b save the resultant network for later use save net30 net 61 Appendix D M File for Extraction of Network Values The following Matlab m file script is a compete listing of the script used to extract and save the key parameters These values are written out to a text file in a form intended for ease of use as constant definitions in a C program o netvalues m gets the network values and outputs them in as useful a format as I can determine clear load netmean load netdet3 for each network I need inputWeights 2 multiplied by position input inputWeights 1 biasl equivalent to dir input 1 bias added to pos input IW 2 biasl used with dir input 0 either this or above is 9 added to pos input IW 2 layerWeights multiplied by result of layer 1 b
20. results represent what is generally achievable as state of the art in production machinery This machine is compensated at a very close interval typical for a machine this size is 1 inch intervals But the control system in use here allows for this and also allows for the large number of points that must be entered with this small interval 38 5 3 Neural Network Based Error Compensation A neural network based positioning error compensation system was constructed as previously described and the post compensation test was rerun with the same parameters as the bi directional leadscrew compensation was tested This allowed for a direct comparison of the results of the two methods The overall results can be seen in Figure 5 4 Figure 5 4 shows that the neural network error compensation routine was able to correct for the majority of the positioning errors in the machine The overall maximum average error was reduced to 0 000933 inches 16 7 of the uncompensated error The maximum reversal error was measured at 0 000614 inches showing a reduction of the backlash error to 14 7 of the uncompensated error Under close examination of the data plot the cyclic error can still be seen as peaks in the error measurements but it has been reduced to less than 0 0005 inches or about 35 of the uncompensated measurement The laser interferometer tests results are for the three compensation systems uncompensated errors bi directional leadscrew comp
21. shown in Figure 2 10 Figure 2 10 a shows the step function In this function the output is held at zero until the input reaches a threshold value At that point the output immediately steps to a fixed value normally one In Figure 2 10 Too T x 15 a step function a sigmoid function b the sigmoid function is illustrated While the sigmoid has the same general shape as the step function there are some key differences First it can take on values anywhere between zero and one where the step function is either zero or one Second the sigmoid function is differentiable This becomes an important issue in later discussions on training algorithms Once the transfer function of the neuron s has been defined determining the weights and bias values is the other portion of defining the functionality of the network Figure 2 10 Step and sigmoid function graphs Determining the values for the weights and bias for the neurons in a network is accomplished by the training process Haykin generalizes the training or learning process to three steps of stimulating the network changing the network parameters based on the stimulation and the network responding in a different manner due to the changes Haykin For example in error correction learning the network is stimulated by a set of training data in the form of input output pairs Each pair is a set of inputs combined with the desired output for this input The actual output
22. test computer the network was normally able to get the error measure down to a value of approximately 7 00e 7 as measured by the Sum Squared Error performance function With this level of performance a maximum error of 1 3498e 4 was reached for any single point in the range of operation The second network architecture that was closely studied consisted of two hidden layers between the inputs and outputs Both of these layers were made up of logsig 40 neurons with 30 neurons in the first layer and 10 neurons in the second layer The diagram of this network is shown in Figure 5 7 o Performance is 6 92861e 007 Goal is 4e 008 T T T T T Training Dash Goal Solid fi 0 1000 2000 3000 4000 5000 6000 7000 7636 Epochs Figure 5 6 Training results for the single layer network Figure 5 7 Multi layer network diagram The training results for this network were typically in the same range as the 40 neuron single layer network The training results are shown in Figure 5 8 As shown the network was able to achieve a comparable level of performance with the training time for this network taking about 2 5 hours about 25 longer than the single layer network but only 3200 epochs or less than half the single layer network 41 Performance is 2 88269e 007 Goal is 4e 008 4 10 T T T 2 10 7 0 10 7 2 10 4 E 1 1 Training Dash Goal Solid 10 o
23. the graph By analyzing the numerical measurements associated with this graph this contributes approximately 0 0012 inches to the overall error The last error is the most problematic and is very difficult to see in this plot Figure 5 2 is an expansion of the plot around measurements from a single direction of motion over a space of 2 5 inches from 1 inch to 3 5 inches This highlights the cyclic error on this machine 36 x 10 Single Direction Cyclic Error T T T T Measured Error Inches e Single Ballscrew Rotation 1 l 1 1 5 2 2 5 3 3 5 Linear Position Inches Figure 5 2 Single direction cyclic error The major mechanical contributor to linear positioning error on this machine is the leadscrew assembly Figure A 3 and Figure A 4 In this case the pitch of the leadscrew or the amount of linear motion generated by a single revolution of the leadscrew is 0 25 inches Examining Figure 5 2 the rather severe cyclic error can be seen for each revolution of the leadscrew It measures approximately 0 00145 inches peak to peak and has a double humped pattern for each turn of the screw This is what causes the forward and reverse runs in Figure 5 1 to appear as broad swipes across the graph instead of the expected single line of points As previously mentioned this contributes approximately 0 0
24. then used to determine the effectiveness of the compensation system as applied to the real world system Nos sk 34 Chapter 5 Results The results for this thesis are based on the laser interferometer data taken with the machine in three different states In the first state all positioning error compensation systems are turned off or removed from the control system This represents the basic mechanical condition of the machine and the data taken in this state is the starting point for any compensation system applied to the machine The second state the controls standard bi directional leadscrew compensation is applied as described in previously This represents the state of the art in machine tool positioning error compensation as normally seen on the shop floor today While there are more advanced methods of positioning error compensation they are normally not part of a commercially available control system and therefore are not often seen in a modern machine shop In the third state the results achieved by the neural network based positioning error compensation system are developed This includes a discussion of the various network architectures examined as part of this project 5 1 Uncompensated Positioning Errors Initial attempts at measuring the linear positioning error were made at the usual settings for a large machine tool Three repeated runs were made with measurements taken at one inch intervals over the full range of mot
25. tip This type of compensation is generally quicker to measure and apply than bi directional but it is limited in some ways It does work well for cases where the errors in motion are consistent in each direction and the amount of backlash is consistent throughout the range of motion Figure 3 1 illustrates an error motion profile that would be suited for uni directional with backlash compensation Note the consistent error profile the reverse motion plot looks like the forward motion plot shifted down a fixed amount There is no variation in the backlash across the range of motion 20 Error Amount A A Linear Position Ao o o o Forward Motion Reverse Motion Figure 3 1 Error versus motion profile for uni directional compensation Implementing uni directional compensation from this data is simply a matter of creating a table that provides the amount of error at each fixed point of measurement Each control has its own manner of entering the table but the basic contents are listed in Table 3 1 Note that in this table each error amount will be negated when entered as a compensation value For example if at position 1 0 inch there is an positioning error of 40 001 inches the compensation amount will be 0 001 inches The control will take this information and uses it any time an axis motion is programmed The compensation values for any points between the listed fixed intervals are normally calculated by line
26. 0005 inches Table 5 1 Positioning error summary 5 4 Network Training Results In the course of this project many different networks were tried and examined This trial phase quickly focused on three network architectures that produced reasonable and consistent results for the problem under study For all the networks the inputs consisted of the linear position of the machine a direction of motion indicator and a calculated value indicating where the machine was currently located within a single revolution of the leadscrew Also for all the networks the output was a single value of the currently required positioning error compensation value to be applied to the control system The variation between the networks was in the hidden layers of the network and the connectivity between the neurons The first network consisted of a single 40 neuron hidden layer between the inputs and outputs as diagrammed in Figure 5 5 the diagram is an extract from the view function in the Matlab Neural Network Toolbox graphical network editor nntool All the hidden layer neurons have the logsig transfer function with a single linear neuron in the output layer The network is fully connected from inputs to the hidden layer to the output layer Figure 5 5 Single hidden layer network Typical training results for the trials of this network are shown in Figure 5 6 After approximately 7500 epochs which took just over two hours on the
27. 0145 inches to the overall positioning error but more importantly is very difficult to compensate for in many control systems The data shown represents a machine with some significant mechanical flaws affecting its performance Any effort truly directed at improving its performance for example preparing it for use in a production environment would have to begin with mechanical repairs of these flaws However in its current state it is a good test of compensation systems that may be applied 5 2 Bi Directional Leadscrew Compensation Bi directional leadscrew compensation was applied as described previously The average error values recorded in the uncomped measurements were negated and input into the control system as leadscrew compensation values Since this compensation system requires that the values be at a fixed interval over the entire compensated range of 37 motion and in trying to make this work as well as possible compensation values were applied just as measured 0 025 inch interval from linch to 39 inches The overall results are displayed in Figure 5 3 5 6D Laser Measuring System eval40MDSICompNew2 pos E n x Z Ele Edt view Window Standards Tools Help x Pa 5 O 4 Rep iD Giese Lin Sir Ang x00 zoo 9 Z Linear 1 to 40 by 0 52 Bi directional Linear Error Plot ANSI 0 001000 0 000750 0 000500 0 000250 Linear Error inch 0 000250 0 000500 0 000750
28. 421753766822473e 1 7125562961409566e 6313926034840971e 1 7332421739865340e 5 9170950459425411e 1 0 pL DE OOO c COCO DODO CO O00 0 0 0c fea X A 3 pa pas ps pa V V V V V N V N V V V V N V V N V N V N V V oo H layer weights multiplied by result of layer 1 st double FullLW 30 1 9722090856230893e 3 3381213233866988e 3 5392149785856523e 2 2485102542564316e 2 1203505113612767e 1 6435067023459145e 2 8571235938803881 amp 8 1 7985204049942757e 2 8522718298553684e 1 6739422819069079e 6 698131573537643356 F5 1686224863966524e 1 2998730486961044e 2 5279135841123679e F5 5089960293835630e H2 0197341240874665e 3 0999957862638091e 1 5265730944106306e 5 8489218591469359e 1 9922873247891157e 1 0679026108750460e 4 2333059590505904e 2 1126715470884939e 71 3627218857791965e 3 717198915630692656 t4 6331692055082856e 6 3970870956342772e 1 6432927867145796e x OO O 0 00 10 00 CO CO O OO s E s OO O O 0 0 10 010 0 O N NAN UUN WWF CU Co PO YN DN NN WW WE V U V V V V V V V N V V V V V V V V V V V V V V V V V
29. 76295659e 3 7128378964014928e O c OQ C CO C 0 009 OOO c c5 c 0 COM Ne CREA qLA eq Bx EgEeg qa 67 const double cyclicIW_B 4 8 7 9 3 1 3 3902984827427503e 8286945653885969e 7240626438899760e 6338193323527328et 7826837129765529e 1199979350411143e 8645326454024267e 5064102092927918e const double cyclicBias 1 9372202168215299e 1473068913108277e 1779003755671003e 9534315151373125e 0972641799667036e 2932649248391974e 5021445926326495e 4508828942124801le const double cyclicLW 8 1 zi 2845598766206338e 7583290668195674e wis t4 x EE 1 9272704047420051e 2340609441792598e 3566978204302399e 9669801168724809e 5317654044065912e 64037978437778867e QQ O CO 1 Qc CC LIP const double cyclicBias2 OOO O00 0c OO0OPrPOoOoOOOOsJO0 O co OF QoQG M CO PO CO IS S pb P2 hi 3 7874518228170045e 001 68 Appendix E C Program for Network Calculation The following C program is the code for the calculation of the feed forward path of the neural network used in determining error compensation values This is the central part of the program that runs in the hard real time environment to interact with the lathe control system JE Oey i
30. BlockWriteVB block If ret lt gt mdsiMacro_Succeeded Then And ret lt gt mdsiMacro InJogMode Then failed to send block do error processing here fatal ret quit return the error code to OpenCNC Else ret mdsiMacroObj mdsiMsgWindowWriteVB Sendblock OK amp block End If End Sub 56 The following text is the resultant subroutine code after running the part program listed in Figure 4 3 G70 G01G59G90G94 Setting Machine Modals G53Z21 0F50 G5320 9F50 04F2 5321 0F50 00 Program Stop for Zero Laser Measurement run 1 5322 0 04F2 5843 0 04F2 5324 0 04F2 53 5 04F2 5326 0 04F2 532740 04F2 5321 1 04F2 5327 04F2 5326 0 04F2 53Z54 04F2 5324 04F2 5923 0 04F2 5322 04F2 DIA lg 04F2 01 End of Run 1 5320 9F50 04F2 5 C C C O O C 3421 0F50 4F2 Measurement run 2 5324220 04F2 G5323 0 MQAAAADAADAAANATAAAADAAAADAAAADAAANAAANAAAAANAAADQAAAAAAARDAAA FAA 57 04F2 04F2 04F2 04F2 04F2 04F2 04F2 04F2 04F2 04F2 04F2 04F2 04F2 C gt 4F2 4F2 4F2 4F2 4F2 4F2 4F2 4F2 4F2 00o000000 0 000 000 0 0 on0n0000 00000 0 0000 0 0000 0 0000 0 0000 OG O MOB O Ud O 0n Co Qn Q um OT O UT o Un c 4F2 5324 5325 5326 53Z2T 9327 S97 a 5326 5325 5324 5323 59224 5321 1 En 320 9F50 3439 324 325 326 3ZT 3ZT 3Z
31. Machine Tool Positioning Error Compensation Using Artificial Neural Networks By John M Fines B S Electrical Engineering University of Maryland College Park 1995 Submitted to the Department of Electrical Engineering and Computer Science and the faculty of the Graduate School of the University of Kansas in partial fulfillment of the requirements for the degree of Master of Science Dr Arvin Agah Committee Chair Dr Swapan Chakrabarti Committee Member Dr Frank Brown Committee Member Date of Acceptance Abstract This thesis is a study of the application of artificial neural networks to the problem of calculating error compensation values for axis positioning on a machine tool The primary focus is on the development of a neural network based system that could be implemented and integrated into the open architecture control system of an actual machine A number of neural network architectures were examined for applicability to the problem and one was selected and implemented on the machine Positioning error compensation capabilities were tested using industry standard equipment and procedures and the results obtained were compared with the capabilities of standard error compensation routines in machine tool controls 11 Acknowledgements I have to start out by acknowledging the people I work with and those who supported me in attending graduate school through the Technical Fellowship Program Specific
32. OO OOOO O OOOO OOOO OOO CO c AGE A cas as GE 66 1 6313926034840971e 001 1 7332421739865340e 000 5 9170950459425411e 000 const double FullLW 30 1 9722090856230893e 3 33812132338606988e 3 5392149785856523e 2 2485102542564316e 2 1203505113612767e 11 6435067023459145e 2 8571235938803881e 1 7985204049942757e 2 8522718298553684e 11 6739422819069079e 6 6813157353764335e 5 1686224863966524e 1 2998730486961044e 2 5279135841123679e 5 5089960293835630e 2 0197341240874665e 3 09999578620638091e 1 5265730944106306e 5 8489218591469359e 1 9922873247891157e 11 0679026108750460e 14 2333059590505904e 2 1126715470884939e 71 3627218857791965e 3 7719891563069265e 4 6331692055082856e 6 3970870956342772e 1 6432927867145796e 7 2777120317224900e 7 2225148283068585e ao WN WNN DN NH E C E E E E E E OO a O a AO O aa a a aar a O O a OO OOO c0 c NNN ON UUN UUWUWEPUVUWVUNUNNNUVUUWVUWVHHH b const double FullBias2 3 3526357495979814e 001 E const double cyclicIW2 4 0199735339014765e 1 1412266461437305e 2 6173165967393352e 3 5485150577054590e 4 7523812303695863e 2 6388036946666858e 6 49028520
33. T C C C C C C C d of Run 321 0F50 Measurement run 322 2 3 58 G lt 00000000 000 5326 04F2 5325 0 04F2 5324 0 04F2 5323 04F2 5322 0 04F2 5321 0 4F2 C C 1 En d of Run 3 59 Appendix C M File for Neural Network Generation The following Matlab m file script is the basic tool for generating a new neural network training it with test data and viewing the results of the new network preprocess m basic processing of the data to prepare for nn tasks 9 clear the workspace and load the data file clear load z plot the runs just cause I like to look at pictures plot smallzv9 2 1 3122 1 smallzv9 2 1 3122 3 r hold on plot smallzv9 2 3123 6244 1 smallzv9 2 3123 6244 3 g plot smallzv9 2 6245 9366 1 smallzv9 2 6245 93066 3 b plot smallzv9 2 9367 end 1 smallzv9 2 9367 end 3 c title Four Runs As Recorded By Laser Splot the averages for the same reason as above figure plot smallzv9 2ave 1 smallzv9 2ave 2 b title Averages vector indicating direction of motion 0 gt positive 1 gt negative dir zeros 1561 1 ones 1561 1 generate the network net newff 0 1 1 40 60 1 logsig purelin trainlm learngdm sse set constants for the network construction
34. ally I want to thank Jim Dycus and my manager Sam Allen for their support in getting me into the fellowship program and the continued support while I did school work instead of work work I also want to thank Rich Moreno and Ken Mitchell for their help in figuring out how to write part programs to run a lathe and how to operate the lathe safely and correctly Since I managed to get through the project without wrecking the machine and I still have all my fingers they must have done a good job Additionally I want to thank Mike King for his help in answering an endless series of questions about machine tool metrology and Lloyd Lazarus for the use of the machine in his department and another series of endless questions I want to thank Dr Arvin Agah for his patience in dealing with a part time student with a job and a family and his guidance and assistance in this project Also I would like to thank Dr Swapan Chakrabarti and Dr Frank Brown for consenting to be on my graduate committee Finally Pve got to thank my wife for her patience and support I finally got it done 111 Table of Contents List OE EISUFGS acess wasp sscecancsticeucusscuccesisicaucscecuces cx te VON M a d iE ter um ic un vi List of ADIOS i iacta gietoxpi eds ia dorus doi wee uY scacscaves ont susudscdcacetsdcuveadestedssjusdabeadacdeaessdcevsesisant vii Chapter 1 Introduction au eee er S NOI PP n iio SPI Um IM edd e Rd duis 1 1 1 MotivatiO MH
35. ar interpolation between the two adjacent fixed points The compensation table should cover the entire range of motion for the axis but if it does not the compensation values for points outside the table are often held stable as the value at the nearest fixed point Position Error 0 0 0 001 1 0 0 001 2 0 0 001 3 0 0 0 4 0 0 001 5 0 0 001 Table 3 1 Error versus position compensation Implementing the backlash amount is a matter of calculating the average backlash over the range of motion and entering this amount into the control system In Figure 3 1 the backlash is the difference between the two plots of forward and reverse motion This number would be determined from the data and entered as specified by the control The control would then use this value each time it reverses the direction of motion 21 3 1 2 Bi Directional Lead Screw Compensation In some situations uni directional compensation with backlash will not be capable of correctly compensating for the mechanical errors in the machine If the error associated with the motion profile were similar to Figure 3 2 the variations in the overall error profile and the variations in the amount of backlash over the range of motion would make this difficult to compensate using that method This would be a case for using bi directional lead screw compensation In this method positioning errors are measured in both
36. aser interferometer system the software must be setup to coordinate the reading of data from the system with the motion of the machine tool In this case the motion of the lathe was under automatic control of a part program written specifically for this purpose Setting up the Winner software for linear motion testing is done by filling in entries on the setup screen when it is presented as shown in Figure 2 4 The key entries for linear testing are explained in Table 2 1 Test Setup 5D or BD Test 5 6D System Setup C 6D 5Divertical Units Environment Test Mode Linear inch Air Temp amp Pressure Jon Bidirection Unidirection Straight inch Material Temp Jon Mode Angle arc sec Air Humidity 50 gt Auto CNC Manual Desd Pu hs Material Expan 6 67 C Remote Trigger C Manual C Sync Dwell Time sec 4 Window n 0 05 1 Avg Time sec Travel Initial Position 7 End Position ry Step Size ots Num of Runs EN aja Num of Positions Laser amp Sensor Distance C Increase Decrease Ud ATUS Change Machine Information Test Axis Axes Location Machine ID 51561 Machine Name American Hustler CNC Program newx bd Feedrate 20 Operator fu Fines Comments x Linear No Comp Plot Title 7X Linear 7 to by 07 File Name c Program Filesi4utomated Precision IncXAPI 5 BD Laser default Load set up from a file
37. asured by the Sum Squared Error SSE function In each of the tests the time to complete 1000 epochs or reach the training goal was tracked along with the final error reached The results of the test are summarized in Table 4 1 While the LM algorithms was the slowest of the four tested it was the only algorithm capable of reaching the training goal specified and it still completed in a reasonable amount of time The accuracy reached in each trial is shown in Figure 4 5 In this figure and noting that the accuracy level is plotted on a logarithmic scale it can be seen how much better the LM algorithm is at reaching a very small error level as required by this application 30 Average Time to 1000 Pa Final Error Measure Training Algorithm Epochs inches seconds TrainRP 23 4 4 67E 4 TrainSCG 44 9 3 67E 4 TrainBFG 54 3 1 23E 7 TrainLM 65 8 4 81E 8 Table 4 1 Comparison of training algorithms Comparison of Training Algorithms Trial Number 1 2 3 4 5 6 7 8 9 10 1 E 00 L fi L L L L fi L 1 E 01 o 1 E 02 acoso I a UT ced 2 W 1 E 03 S AAA RGENEREES 1 E 04 1 E 05 5 o 1 E 06 tc 1 E 07 EE C c E LEE eeo e 1 E 08 TrainLM TrainBFG TrainSCG gt TrainRP Figure 4 5 Comparison of training algorithm accuracy After reviewing the information on training algorithms and conductin
38. ated using the command net newff 0 les 1 40 30 1 logsig purelin 1 l e This network has a structure similar to the network shown in Figure 2 8 Training a newly created neural network can also be accomplished using a single command such as net train net p t where p is a set of input vectors and t is the set of associated target outputs for p This command would train the network for the toolbox default of 100 epochs one epoch is a single pass through all the inputs and targets utilizing the other toolbox default parameters for training function performance function and other parameters If desired or necessary all of the default parameters can be changed to meet the specific needs of the application under study Simulating network behavior when presented with a set of inputs is accomplished using the command sim net p which presents the network the inputs p and calculates the output of the network based on its current definition For example in the case of a single neuron perceptron with two inputs with the input weights defined as 1 2 a bias value of 0 5 inputs of 1 and 1 and using the hardlim transfer function in the neuron the function sim performs the following calcuation 1 a hard io 2 i os where a is the network output By utilizing the functions of the toolbox a network designer can quickly create train and test a neural network for the application of interest With some know
39. ature of the machine under test This data is collected from sensors attached to the 5 6 D laser system and is used in internal laser wavelength and material temperature compensation algorithms Automated Precision Inc Position LasRead LinearError Status AirTemp AirPress Mat Temp 7 00000 0 000004 0 000004 0 73 76 29 33 74 65 6 86000 0 139901 0 000099 0 73 76 29 33 74 65 6 72000 0 279949 0 000051 0 73 76 29 34 74 65 6 58000 0 419945 0 000055 0 73 76 29 34 74 65 6 44000 0 559952 0 000048 0 73 76 29 34 74 65 6 30000 0 699888 0 000112 0 73 76 29 34 74 65 Table 2 3 Partial list of output data from 5 6 D laser system The resulting data from a complete 5 6 D laser system run may also be graphically displayed using APInc s Winner v1 3 1 software Figure 2 7 displays the 12 results of the example laser run This screen is a complete display of operating parameters of the recorded run a plot of all collected data points and calculated error values for the entire run For a perfect machine all the data points would lie directly on the 0 000000 line in the middle of the plot Variation from this line is the error in the actual motion of the machine from the commanded motion In Figure 2 7 the lower curve is the data from the forward motion of the machine while the upper curve is the data from reverse motion The difference between the two curves is a result of the mechanical backlash of the machine that occurs when the lead
40. bility of the system to approximate the function as necessary to generate the compensation values This multi network architecture was the network architecture that was implemented and tested 44 Chapter 6 Conclusions 6 1 Contributions In the course of this project it was shown that a neural network is a viable technology for calculating compensation values for positioning errors in a machine tool By treating this as a function approximation problem and designing and training a network to approximate the function that describes the mechanical errors in the machine a system was constructed that successfully corrected for the majority of the positioning errors in the machine The system designed was not simulated but was actually implemented on a real machine tool in an industrial environment Uncompensated errors were measured the neural network system was designed and integrated into the real time deterministic level of the machine control system The results were measured using industry standard test equipment and procedures The final results achieved were as good as or slightly better than the current state of the art in machine tool positioning error compensation capabilities in commercially available control systems Three different network architectures were closely studied and it was demonstrated that any of the three were able to achieve final results sufficient to meet the machine requirements However it was shown that w
41. ble 3 3 Bi directional lead screw compensation values reverse 23 Table 4 1 Comparison of training algorithms serene 31 Table 5 1 Positioning error summary 3 tet ro ceded seed ieee 40 vil Chapter 1 Introduction 1 1 Motivation In a modern high precision industrial machining environment there is a general push to constantly produce better and better parts by reducing the dimensional errors of the machined parts A large portion of the dimensional errors in these parts is caused by positioning errors in the axes of motion on a machine tool Efforts to reduce these positioning errors have been on going for many years Much of the work has gone into making the machine tool itself more accurately At installation the technicians will spend many hours ensuring and correcting the structural alignment of the machine parts to reduce geometric errors such as perpendicularity of axes in a milling machine or concentricity of a spindle and axis on a lathe But no matter how much work is put into making an accurate machine it is impossible to make it perfect And if the dimensional tolerances required are fine enough the basic mechanical errors in machine motion will impact the quality of the parts that are produced In the continuing effort to improve the performance of machining tools control routines to compensate for uncorrected positioning errors have been developed Machine errors are meas
42. block return to start position block G53 amp AxisLetter amp Format StartPos 0 0 amp F amp Format Feedrate Print 1 block 54 If LaserZero Then block GO4F amp Format Dwell Print 1 block Else block M00 Program Stop for Zero Laser Print 1 block LaserZero True End If clear the comment line block Measurement run amp CStr RunCount amp Print 1 block loop for motion in positive direction CurrentPos StartPos Increment Do block G53 amp AxisLetter amp Format CurrentPos 0 0 Print 1 block block GO4F amp Format Dwell Print 1 block CurrentPos CurrentPos Increment Loop Until CurrentPos gt EndPos NearZero make the end backlash move block G53 amp AxisLetter amp Format EndPos Backlash 0 0 Print 1 block block GO4F amp Format Dwell Print 1 block loop for return pass CurrentPos EndPos Do block G53 amp AxisLetter amp Format CurrentPos 0 0 Print 1 block block GO4F amp Format Dwell Print 1 block CurrentPos CurrentPos Increment Loop Until CurrentPos lt StartPos NearZero block MOI End of Run amp CStr RunCount amp Print 1 block Next E ret mdsiMacroObj mdsiMsgWindowWriteVB End of requested runs exiting macro End If Set mdsiMacroObj Nothing Close 1 End Sub mai
43. cise measurement system it will actually be at 3 9980 inch thus an error of 0 002 inches in axis positioning The normal method of compensation is accomplished by creating a table of these positioning errors for a set of points at fixed intervals For a large machine this might be at every even inch for the entire range of travel Other machines may have other intervals or the end user might be able to choose an interval that best meets the requirements Giddings amp Lewis and MDSI Variable Dictionary include the details for methods of implementing lead screw compensation There are two basic types of lead screw error compensation the first is uni directional with backlash compensation and the second is bi directional compensation 3 1 1 Uni Directional Compensation with Backlash In uni directional compensation with backlash the error measurements are all taken with the machine moving in only one direction with no direction reversals while taking the error measurements Measurements taken with the machine moving in the other direction are only used to determine an average backlash value Backlash is the error induced by mechanical looseness or other mechanical slop that occurs when the machine reverses direction of motion In other words it is the amount that the motor will move to drive the machine in the opposite direction before the motion is observed at the point of interest In a machine tool this is usually at the cutting tool
44. collects the resultant data At the conclusion of the test the laser system writes out the data files that contain all of the data collected along with some analytical results Figure 4 4 is an extract of one laser data file with a few sample lines of data Figure 4 4 Laser data example The raw data collected by the laser measurement system include the commanded Position LasRead LinearError Status AirTempAirPress MatTemp 1 00000 0 000010 0 000010 O 70 37 29 25 71 49 2 00000 0 999691 0 000309 O 70 36 29 25 71 49 3 00000 1 999600 0 000400 0 35 29 25 71 49 4 00000 2 000554 N NNN444 0 7035 2095 71 49 position laser reading calculated linear error status air temperature air pressure and material temperature This data can be taken off line for analysis or reviewed in some detail on the laser measurement system 4 3 Neural Network Design and Training As all of the neural network design and training was done using Matlab and its associated Neural Network Toolbox this portion of the experiment centers on the use of various Matlab functions to accomplish specific tasks After the data have been collected from the laser measurement system they are taken off line for processing The data file would contain two sets of data The first is the raw data collected during the entire test The second in the case of a multiple run test would contain the average of the error value at each individual data point over all of the run
45. control functions Examples of applications created using API Level 2 are thermal compensation routines such as monitoring machine temperature and adjusting for positioning errors induced by thermal expansion or other machine error compensation routines MDSI API Datasheet While the software development tools used for both levels of the API are standard tools there are restrictions on the functions available for use when developing API Level 2 applications These are based on the list of functions supported by the VentureCom RTX in the C Run Time Library Supported API VCI 2 3 Laser Interferometers The laser interferometers have been around for many years and today are commonly used to make extremely accurate measurements of linear displacement The basic theory for laser interferometers dates back to the early 1900s with the Michelson Interferometer being one of the earliest devices to demonstrate interferometric measurements of length Jenkins and White Modern interferometers are highly portable devices that are relatively easy to set up and use They are normally computer controlled devices that offer an array of analysis and recording capabilities 2 3 1 General Theory A laser interferometer uses a laser source that emits a very focused monochromatic light beam In its simplest form the normal set up for a laser interferometer uses a stationary light source a beam splitter a stationary reference reflective target and a mobile
46. croObj mdsiMsgWindowWriteVB ERROR Not enough travel to make backlash move from ret mdsiMacroObj mdsiMsgWindowWriteVB ERROR Not enough travel to make backlash move from ending position Format Feedrate Else made it past all the error checks so run the machine LaserZero False open the subroutine file for writing Open OpenCNC Subroutines laserSub txt For Output Shared As 1 set machine initial conditions if there is a diameter type axis i e a lathe do the G07 ret mdsiMacroObj mdsiVariableReadByNameVB axDiameterType v nValues If ret lt gt mdsiMacro_Succeeded Then fatal ret quit return the error code to OpenCNC End If If v AxisNumber lt gt 0 Then block GO7 Print 1 block End If set to inch mode block G amp CStr defGInchMode Print 1 block Feedrate moves Inch mode work coord offsets off absolute mode IPM block G01G59G90G94 Setting Machine Modals Print 1 block move to starting position I m using G53 to make sure offsets are not a factor necessary block G53 amp AxisLetter amp Format StartPos 0 0 amp F amp Format Feedrate Print 1 block start to loop through motion For RunCount To NumRuns make the backlash move block G53 amp AxisLetter amp Format StartPos Backlash 0 0 amp E amp Print 1 block block GO4F amp Format Dwell Print 1
47. cturing Data Systems Inc MDSI OpenCNC Plus Pro V6 2 Datasheet 2002 13 June 2002 lt http www mdsi2 com images DataS 6 2 20Plus zPro pdf gt Manufacturing Data Systems Inc MDSI OpenCNC 6 0 API Manual Ann Arbor n p 2000 Manufacturing Data Systems Inc MDSD OpenCNC 6 0 Variable Dictionary Ann Arbor n p 2000 Microsoft Corporation Product Information 2003 12 March 2003 lt http www microsoft com ntworkstation ProductInformation default asp gt Open Modular Architecture Controls OMAC User s Group Business Justification of Open Architecture Control White Paper Version 1 0 8 Apr 1999 13 June 2002 lt http www arcweb com omac Deliverables default htm gt Russell Stuart and Peter Norvig Artificial Intelligence A Modern Approach Upper Saddle River Prentice Hall 1995 United States Patent and Trademark Office USPTO United States Patent 5 523 953 Method and apparatus for correcting positioning errors on a machine tool Araie Ichiro and Osamu Akemura inventors June 1996 9 July 2002 lt http patft uspto gov netahtml srchnum htm gt VenturCom Inc VCI RTX 5 0 Reference Guide Cambridge n p 2000 47 Appendix A Detail Photographs Figure A 1 Laser interferometer upper and lower apertures Figure A 1 shows the upper and lower apertures of the interferometer The laser beam is emitted from the lower aperture and is reflected back to the upper aperture from the mobil
48. e reflector In this photo the beam is intentionally misaligned to be visible to the side of the upper aperture 48 _ Figure A 2 Close up of mobile reflector Figure A 2 shows a close up view of the mobile reflector It is mounted on a magnetic base and its position is adjusted by sliding or rotating the shafts used to mount it As shown it is positioned as close as possible to the tool turret and its height matches the height of cutting tools mounted in the turret In this position the motion of the mobile reflector closely matches the motion of the cutting tool 49 Figure A 3 Long axis leadscrew assembly The machine depicted in Figure A 3 similar to the American Hustler lathe used in the experiments As shown it has been partially disassembled for major maintenance leaving the leadscrew exposed and viewable The long axis leadscrew is visible in the lower portion of the figure running the entire length of the machine The leadscrew and its corresponding ballnut is used to convert the rotary motion of the servo motor to the linear motion required by the machine It is fixed at both ends with bearings and rotating it causes the cross slide to move along the guide ways for the long axis This can be seen in greater detail in Figure A 4 50 fa Hi s sek yeaah Ae mS M i EL c e Figure A 4 Close up of ballnut assembly Figure A 4 shows the leadscrew ballnut assembly for the long axis on a lathe Motion a
49. ection input 0 gt zeros out the input weights for G 0 uias IFF temp i FullBias1 i else direction input 1 gt includes dir input weights 73 for da Ue i lt 30 dug temp i FullIW_Bl i calculate position input input weights and add to temp E for 1 0 i lt 30 1 temp i pos FullIW2 i calculate the logsig function for each element for i 0 i lt 30 i temp i 1 1 exp temp i calculate the vector multiplication of layerweights result of hidden layer for L S108 E lt 30 EE multiplication temp i FullLW i for 1 0 i lt 30 1 summing results fullResult temp i add the bias value for output neuron fullResult FullBias2 now calculate the value for the cyclic error compensation cyclicPos fmod pos 0 25 init the temp array dependent on direction of travel if dir 0 direction input 0 gt zeros out the input weights for i 0 i lt 8 i temp i cyclicBiasl i else direction input input weights includes dir ll ll V for i 0 i lt 8 i temp i cyclicIW_B1l i calculate position input input weights and add to temp A Por i 0 i lt 8 i temp i cyclicPos cyclicIW2 i 74 calculate the logsig function for each element for
50. ensation and neural network based compensation are summarized in Table 5 1 Briefly it can be seen that either compensation system made vast improvements in the accuracy of the machine and the results of the two systems are comparable 5 6D Laser Measuring System evalMyCompNew3 pos n x a File Edit View Window Standards Tools Help ice x Pa 6 E O V 7 kep ID tm O 63 sin str ang 00 yo 9 Z Linear 1 to 40 by 0 52 Bi directional Linear Error Plot ANSI 0 001000 Linear Error inch 0 000750 1 f 0 000500 0 000250 Mg 0 000000 y 0 000250 4 0 000500 4 0 000750 4 Position inch 1 5201 000 40 000 0 001000 L4 File Name evalMyCompNew3 poAir T Avg B8 5F Max Avg Error 0 000933 in Machine American Hustler Air P Avg 29 9 in Hg Max Rev Err 0 000614 in Test Axis Z Material T Avg 70 5 F Max Repeat 0 001043 in API5 6D S N 4014 Humidity 50 96 Operator JFines Exp Coef 8 7 ppm F oe oe Test Date 10 19 2000 Num of Runs 3 E iar Re Test Time 13 11 22 Window 0 1000 in For Help press F1 Figure 5 4 Neural network error compensation results Error Measured Uncompensated Bi Directional Neural Network Max Average Error 0 005582 0 000995 0 000933 39 inches Max Reversal Error 0 004181 0 000813 0 000614 inches Max Repeat 0 005570 0 001098 0 001043 inches Cyclic Error 0 00145 0 0005 0
51. ern of motion expected by the laser measurement system For this experiment OpenCNC s VB Macro feature was used for the required programming In this setup a small part program was written in which the key test parameters were defined The program then called a VB macro to error check the input parameters and produce a subroutine that contained the G amp M code required to produce the desired pattern of motion Finally the program called the subroutine to run This allowed for major changes in test parameters with only quick minor edits to the basic part program the macro would then be recalled to regenerate all of the necessary code instead of rewriting all of the code each time a test needed to be changed 27 Figure 4 3 contains the part program used for control of the lathe under test The first nine lines establish the parameters for the desired test The macrofile line calls the VB macro and passes in the test parameters for processing The M200 is a part program syncing command in this control and the subfile line calls the subroutine produced by the VB macro Finally M30 is the end of program command Figure 4 3 The part program for lathe control vb 1 Axis 1 X 2 Y 3 Z vb 3 1 Starting Position in Machine Coordinates vb 4 End Position in Machine Coordinates vb 5 ik Increment of motion between point vb 6 Dwell time at points vb 7 Number of complete runs vb 8 Feedrate
52. ese are usually known as layer weights the bias values applied to hidden neurons and the transfer functions of all the neurons in the network Since the design and training of the network were accomplished within the Matlab environment these parameters are all stored as properties of the network object created in Matlab As is often the case the easiest method of repeatedly accomplishing a task in Matlab is to write an m file script to do the work For example within Matlab if there exists a neural network object named net it will have properties referred to as net IW 1 which contains the matrix of input weights for the network Other properties are net b 1 net b 2 and net LW 2 which are the bias values for layer one bias values for layer two and the layer weights applied to inputs to layer two respectively The script included as Appendix D was used to extract the parameters of the networks Also included in Appendix D is the results of running the script which shows the output of the m file This output was formatted to be as close as possible to the text necessary to define constants in a C program which is how the values were used in programming the calculations 4 4 2 Calculation of Compensation Values Determining the compensation values to be used in the system control is done by calculating the feed forward action of the neural network defined previously This calculation must be designed to meet the constraints o
53. eseesees 69 List of Figures Figure 2 1 The Hustler lathe by American Tool Inc eese 4 Figure 2 2 Simplified block diagram for laser interferometer esses 6 Figure 2 5 Physical setup of laser interferometer tina d Figure 2 4 Setup screen for control of the 5 6 D laser system sees 8 Figure 2 5 Machine motion laser timing diagram essere 11 Figure 2 6 5 6 D laser system in progress screen ceeeeeceenceceseececeeceececeecseeeeceteeeenaeees 12 Figure 2 7 Graphical display of 5 6 D laser system data esse 13 Figure 2 8 Neural network interconnections nenas eid in 14 Figure 2 9 Single neurom Network pipi tt 15 Figure 2 10 Step and sigmoid function graphs sese 16 Figure 3 1 Error versus motion profile for uni directional compensation 21 Figure 3 2 Error versus motion profile for bi directional compensation 22 Figure 4 1 Laser alignment for 252318 us ao 26 Figure 4 2 Test setup for primary Z axis ee do 27 Figure 4 3 The part program for lathe control eee 28 Figure 4 4 Laser data camp 5s b E ets A ISAE 28 Figure 4 5 Comparison of training algorithm accuracy eee 31 Figure 4 6 Neural network with weights and biases eene 33 Figure 5 1 Uncompensated positioning error average results
54. essing for netdet inputWeights netdet IW 1 biasl netdet b 1 bias2 netdet b 2 layerWeights netdet LW 2 9 output input weights column 2 fprintf fid const double cyclicIW2 d r n length inputWeights for i 1 length inputWeights 1 fprintf fid 2 16e r n inputWeights i 2 end fprintf fid 2 16e t r n r n inputWeights i 1 2 output input weights column 1 bias 1 fprintf fid const double cyclicIW Bl d r n length inputWeights for i 1 length inputWeights 1 fprintf fid 2 16e NrMn inputWeights i 1 biasl i end fprintf fid 2 16e t r n r n inputWeights 1 1 1 bias1 1 1 o output bias values for layer 1 fprintf fid const double cyclicBiasl d r n length bias1 for i 1 length bias1 1 63 fprintf fid 2 16e r n bias1 i end fprintf fid 2 16e t r n r n biasl 1 1 output layer weights fprintf fid const double cyclicLW d r n length layerWeights for i 1 length layerWeights 1 fprintf fid 2 16e r n layerWeights i end fprintf fid 2 16e t r n r n layerWeights it 1 9 output the bias value for layer 2 fprintf fid const double cyclicBias2 fprintf fid 2 16e r n r n bias2 fclose fid 64 The following text file is the result of running the previous m file on one of the neural netw
55. eural networks In particular neural networks are designed to model the behavior of the human brain Russell and Norvig For this thesis the key characteristics of interest are the ability of a 13 network to be trained on a problem and its ability to learn or to improve its performance as it is presented with more data The fundamental structure of a neural network is that of a massively interconnected collection of simple computing elements neurons operating in parallel to produce an output or set of outputs in response to a set of inputs Figure 2 8 illustrates the interconnections of a small fully connected neural network In this figure each of the input neurons feeds information to each of the neurons in the next layer and each of those neurons feed information to the output neuron Neurons 4 Inputs d RC N SN i Figure 2 8 Neural network interconnections It is this characteristic of having every neuron in each layer connected to every neuron in the next layer that defines this network as being fully connected If some of the connections were missing the network would be defined as partially connected Haykin The computational elements of the neural network are in two areas The first is in the interconnections themselves Each of these interconnections has a weight assigned to it The weight assigned to the interconnection becomes part of the information pa
56. f the tools used it must use only functions supported by the VentureCom SDK VCI and must be simple and quick enough to meet the timing constraints established in the machine control In the case of this system the control was queried for inputs and new compensation values were calculated and returned every 10 milliseconds As an example one network structure that was used in this system was made up of two simple networks Figure 4 6 includes a diagram of the network structure with weights and bias points where Il and I2 are input neurons IIWI I1Wn and 12W1 12Wn are input weights H1 Hn are the hidden neurons bH1 bHn are the bias values for these neurons LW1 LWn are the layer weights Ol is the output neuron and bO1 is the bias value for that neuron The first network had two input neurons an eight neuron hidden layer using the logsig transfer function and a single output neuron with a linear transfer function The second network also had two input neurons a 30 neuron hidden layer using the logsig transfer function and a single linear output neuron The outputs from the two simple networks were added to make the final compensation value to be returned to the control 32 LWI i LW2 WM UM A O1 bO1 A Hn bHn Figure 4 6 Neural network with weights and biases Following the diagram in Figure 4 6 the complete calculation of the feed forward path of the network can be written as log
57. for motion vb 9 Overshoot for backlash moves macrofile LaserMotion A 1 S 3 E 44 I 5 T 6 N 7 F 8 B 9 D 0 M200 When the listed part program is run and the macro is called the first function it performs is to error check the input parameters The macro looks for errors in requested axis of motion requested limits of travel and requested increment of motion along with others The first part of Appendix B includes a complete listing of the macro source code After the input parameters have been checked the G amp M code is generated and is output to a specified filename and location The second part of Appendix B contains a complete listing of the output from running the part program listed in Figure 4 3 After the macro has generated all of the necessary code it exits and returns control back to the part program which then calls the subroutine file to control machine motion 4 2 Data Collection The data collection step of the experiment is a fairly simple process Once the laser and lathe controls are configured correctly the lathe is put into an AUTO mode This is where the control of the lathe is passed to the part program currently loaded When the control s CYCLE START function is activated the lathe proceeds along the programmed pattern of motion The laser control observes this motion and based on the parameters entered for the test automatically takes measurements and
58. g the test discussed above on actual data from this experiment it was concluded that the Levenberg Marquardt was the best training algorithm to use for this application All further network development and training for this experiment were done using the LM algorithm 4 4 Programming Real Time Calculations Programming the real time calculations for integration into the lathe control system is accomplished using the capabilities provided by MDSI s Application Programming Interface API for hard real time program development MDSI API Manual The programming was done in Microsoft Visual C and referenced libraries provided as part of VentureCom s Software Development Kit VenturCom Programming the real time calculations first required the extraction of the key network 3l parameters from the network developed in Matlab described in the previous step Then those parameters had to be coded into the program that produced the actual calculations of compensation values to integrate into the control 4 4 1 Extraction of Network Parameters At the point where the real time calculation is being programmed the structure of the neural network has been designed and all of the values within the network have been determined by the training process These key parameters are the weights applied to the inputs the bias values applied to the input neurons the weights applied to any values passed to neurons in the hidden layers of the network th
59. h B arguments msDebugMode D setup default values parse the incoming command line arguments argCount mdsiMacroObj mdsiParseMacroArgsVB arguments retArgs errorPosition If argCount mdsiMacro Succeeded Then fatal argCount quit return the parse error code to OpenCNC End If assign argument variables Axis retArgs mvAxis StartPos retArgs mvStartPos EndPos retArgs mvEndPos Increment retArgs mvIncrement Dwell retArgs mvDwell NumRuns retArgs mvNumRuns Feedrate retArgs mvFeedrate Backlash retArgs mvBacklash DebugMode retArgs mvDebugMode End Function Call fatal when you want to quit with an error code Public Sub fatal exitCode As Long Dim o As Object cleanup all objects we know about mdsiMacroObj unInitialize Set mdsiMacroObj Nothing For Each o In Forms Unload o Next o close all open files Reset ExitProcess exitCode End Sub This is a wrapper function for mdsiBlockWrite It checks the return code and calls fatal on an error other than mdsiMacro_InJogMode Note A caveat about using this function mdsiBlockWriteVB returns t the error code mdsiMacro InJogMode if OpenCNC is in Jog mode i This is not considered a fatal error here The property y runMode may be checked to determine if OpenCNC is in Jog mode Public Sub SendBlock block As String Dim ret As mdsiMacroReturnTypes send the block to the parser ret mdsiMacroObj mdsi
60. here is certainly much more work to be done Addressing the limitations discussed would be a high priority This would involve several areas of integration One would be the integration of the control of the laser 45 interferometer system and the machine tool motion This would eliminate the dual set up required and it would facilitate development of more advanced motion routines For example variable increments of motion over the range of motion versus the current requirement for a fixed interval across the entire range of motion can be examined Development of a widely applicable network architecture would greatly improve the usability of this technology in the industrial environment Development of a universal architecture would also facilitate development of a more universal real time calculation routine that would not have to be independently implemented for each individual machine Other areas of future work would focus on expansion of the capabilities of the system For example including more variables into the compensation calculation This would allow the system to account for errors induced by thermal changes or by errors caused by the interaction between machine axes or by fundamental geometric errors in the machine A common geometric error is an out of square condition where the axes of motion are not exactly perpendicular In this case the motion of one axis would induce a positioning error in the other axes 46 References A
61. ias2 added to result of above fid fopen netvalues txt w o begin processing for netmean inputWeights netmean IW 1 biasl netmean b 1 bias2 netmean b 2 layerWeights netmean LW 2 o output input weights column 2 fprintf fid const double FullIW2 d NrMn length inputWeights for i 1 length inputWeights 1 fprintf fid 2 16e r n inputWeights i 2 end fprintf fid 2 16e t r n r n inputWeights it1 2 output input weights column 1 bias 1 fprintf fid const double FullIW Bl d r n length inputWeights for i 1 length inputWeights 1 fprintf fid 2 16e r n inputWeights i 1 biasl i end fprintf fid 2 16e t r n r n inputWeights 1 1 1 biasl1 1 1 9 output bias values for layer 1 62 fprintf fid const double FullBiasl d r n length bias1 for i 1 length bias1 1 fprintf fid 2 16e r n biasl i end fprintf fid 2 16e t r n r n biasl 1 1 output layer weights fprintf fid const double FullLW d r n length layerWeights for i 1 length layerWeights 1 fprintf fid 2 16e r n layerWeights i end fprintf fid 2 16e t r n r n layerWeights i 1 o output the bias value for layer 2 fprintf fid const double FullBias2 fprintf fid 2 16e r n r n bias2 9 begin proc
62. ican Hustler lathe American Tool the OAC on the lathe is OpenCNC from Manufacturing Data Systems Inc MDSI V6 2 Datasheet and the laser interferometer is a 5 6 D Laser Measuring System from Automated Precision Inc Automated Precision This thesis focuses on the application of neural networks to the problem of compensating for positioning errors in the axes of motion on machine tools 2 1 American Hustler Lathe The American Hustler lathe is a standard single spindle two axis CNC lathe as shown in Figure 2 1 The two axes are labeled X and Z with the X axis being the cross slide which moves perpendicular to the spindle center line and the Z axis being the major carriage axis which moves parallel to the spindle center line American Tool In most operations control of the lathe is handled by the automatic control system as programmed by the operator In other words a predetermined sequence of operations is programmed into the control using standard G and M code programming The control is then set into the Automatic mode and a Cycle Start is initiated It will then step through the pre programmed sequence of operations with no further intervention by the operator The basic operations available to the operator are control of axis motion direction and rate of travel control of the spindle direction and rate of rotation and control of other machine functions such as use of coolant or selection of cutting tools More ad
63. iof x Command Setup View DataAnalysis Back Help i l x E RIS TIR O ells Unitinch Linear 2 939919 Air Temperature 175 17 F Material Temp Air Pressure 29 37 inHg Material Coef 6 7 ppm F Humidity 50 0 Setup Ini Position 7 Test Type Bidirection Dwell sec 4 End Position Test Mode Auto Window 0 05 feo 0 14000 4000 Direction Deceased BunsNum BN Test Status Target Position File Name C Program Filest utomated Precision Inc 4PI 5 6D Laser 5 S N 4014 For Help press F1 Figure 2 6 5 6 D laser system in progress screen After all runs of the current test are completed the 5 6 D laser system closes the ASCII text data file for this run This file contains all of the data collected for this run and other summary data from the 5 6 D laser system Table 2 3 is a partial list of results from the 5 6 D laser system run used as an example in the previous screens As seen in the table the system records the current position laser reading and the calculated linear error The position and laser reading are different because the system is zeroed at the starting point of the run therefore in this case a position of 7 00000 inches is equivalent to a laser reading of 0 00000 inch Since the laser reading was 0 000004 inches the calculated error is 0 000004 inches The system also records the current air temperature and pressure and the current material temper
64. ion of the Z axis of the machine However after getting some inconsistent results and taking a closer look at the condition of the machine the final measurements were made as a set of four repeated runs with the measurement interval set to 0 025 inches 40 readings per inch The range of measurements was reduced to 39 inches from the inch point to the 40 inch point This was done to reduce the time involved in taking the measurements The results of these measurements are shown in Figure 5 1 In Figure 5 1 each data point was measured in the forward and reverse directions The individual data points were averaged and presented From these values the maximum average error is calculated to be 0 005582 inches This is the difference between the highest average value and the lowest average value across the entire range of measured motion The lower set of values are those taken while the machine was moving in the forward direction stated position was increasing in value The upper set of values are those measured while the machine was moving in the reverse direction The data plot graphically illustrates the three major issues that any positioning error compensation system must address to improve the performance of the machine 35 5 6D Laser Measuring System small2v9_2 pos ol x IL Ele Edit view Window Standards Tools Help l x Pal 53 6 O O V lt Rep ED C Eos Lin Str Ang xo0 x00 Y
65. ith some analysis of the problem prior to network design an architecture could be created that was well tailored to the application This architecture was able to meet system requirements with much less training time 6 2 Limitations The limitations of this work are in two areas The first is in the highly manual nature of the work required to implement the system Data is manually moved from the laser interferometer system to the network design and training system Results are then manually moved to the real time calculation programming system and imbedded in the code The end result is then manually moved to the control system and installed In working on this project the ability of each of these systems to take the information and data from other systems was proven but no real effort was made to truly integrate these systems The second limiting area was in designing the neural network to perform the function approximation As it was implemented there was no generic or universal solution that could be used to solve a wide range of problems For example applying the neural network based positioning error compensation system to another machine tool would likely require the re examining of the network architecture and redesigning it to solve the new function approximation problem a new set of error data 6 3 Future Work While this project was successful in demonstrating the application of neural networks to the positioning error problem t
66. lathe was chosen as a test machine and the machine errors were measured using a laser interferometer system already available in the factory for this purpose The lathe was chosen because it had recently been retrofitted with a PC based open architecture control system which allowed for the integration of external error compensation routines The neural network design and development was done using Matlab and it s associated Neural Network Toolbox from The MathWorks Inc Demuth and Beale The programming required to implement the system was accomplished with standard PC programming tools In the course of this thesis several different neural network architectures were examined with three being closely studied for their application to this problem For reasons of training speed and the ability to reduce the errors to an absolute minimum one of the networks was selected and finally implemented in the live machine A small set of learning algorithms for the networks was examined with a determination of one as best suited for the problem at hand The neural network based system was implemented in its most basic form and tested for its ability to compensate for the mechanical errors of the lathe The resulting error compensation system was shown to be as good as the current state of the art in commercially available machine tool control systems This was based on its ability to reduce the positioning errors as measured by the laser interferometer sy
67. ledge of neural networks and some study of the toolbox User s Guide the designer can rapidly get into very complex networks and customize the details of the network structure as desired while taking for granted the lowest level details of network implementation in a software simulation environment Where logsig is defined as 18 19 Chapter 3 Related Works Since the primary goal of this thesis was to implement a neural network based error compensation capability for a machine tool the related works falls into three areas The first area is the traditional methods of machine tool error compensation JThe second is a brief survey of other applications of neural networks The third area is a review of available material on attempts to use a neural network based error compensation routine for machine positioning errors 3 1 Traditional Lead Screw Compensation Any modern machine tool control will contain some capability to compensate for linear axis positioning errors This is often referred to as lead screw error compensation so named because the major cause of positioning errors is often the lead screw mechanism that drives the motion Figure A 3 and Figure A 4 illustrate the detailed views The errors occur when usually due to mechanical variations or wear the machine does not exactly reach the commanded position For example the X axis of a lathe may be commanded to move to the 4 inch position but if measured with a very pre
68. lguindigue Israel E Anna Loskiewicz Buczak and Robert E Uhrig Clustering and Classification Techniques for the Analysis of Vibration Signatures Applications of Artificial Neural Networks III SPIE Vol 1709 1992 American Tool Inc Operator s Instruction Service and Repair Parts Manual for the American Tool The Hustler N C Turning Center Cincinnati n p 1975 Automated Precision Inc User Manual for the 5 6 D Laser Measuring System V3 0 Gaithersburg n p n d Baumann Bernd Giorgio Rizzoni and Gregory Washington Intelligent Control of Hybrid Vehicles Using Neural Networks and Fuzzy Logic SAE Technical Paper Series 981061 1998 Demuth Howard and Mark Beale Neural Network Toolbox User s Guide Natick The Mathworks Inc 2000 Giddings amp Lewis Inc Orion 2200 2300 Machining Centers Electrical Service Manual With the NumeriPath 8000B Computer Numerical Control Fond du Lac n p 1999 Hagan Martin T Howard B Demuth and Mark H Beale Neural Network Design Boston MA PWS Publishing Company 1996 Haykin Simon Neural Networks A Comprehensive Foundation 2 ed Upper Saddle River Prentice Hall 1999 Jenkins Francis A and Harvey E White Fundamentals of Optics 4 ed New York McGraw Hill 1976 Manufacturing Data Systems Inc MDSI OpenCNC Application Programming Interface DataSheet n d 13 June 2002 lt http www mdsi2 com images DataS 5 0 20API pdf gt Manufa
69. long this axis is generated by a servo motor rotating the leadscrew Since the leadscrew is fixed in position by bearings at each end rotating it causes the ballnut assembly to move linearly along its length The ballnut is of course fixed to the cross slide which then slides along the long axis of the machine guided by the guide ways seen at the top of the figure 51 Appendix B Visual Basic Macro Code and Subroutine Result The following text is the main module from the Visual Basic VB macro that error checks the input parameters and generates the G amp M code subroutine to run the machine under test Attribute VB_Name Modulel ee kk koc kk ee ee ee ee ee ee ck ckockck LaserMotion VB Macro to make motion for laser checks By John M Fines This assumes that we have either a XZ lathe or XYZ mill and only does bidirectional runs VKKKKKKKKKKKKKKKKKKKKKKKKKK ck ck ck ck ck ck ck ck ck cec ck ck kk ck ck ck ck ck ck kk AAA KAR kk ck kk ck ck kc kc k ck kckck kk ckok Ensure that all variables must be declared Option Explicit macro specific constants ms gt index to argument name mv gt index to argument value Public Enum macroArgs msAxis 0 mvAxis Axis of motion X 1 Y 2 Z 3 msStartPos mvStartPos Starting point of motion msEndPos mvEndPos Ending point of motion msIncrement mvIncrement Motion increment msDwell mvDwell Dwell time at each point msNumRuns mvNumRuns Number of com
70. machine is equiped with thermal sensors and accurate measurements of the thermal deformations of the machine are taken while the temperature at each sensor is recorded This data is prepared and presented to the network as training data Once the trained network is completed it then becomes a part of the machine controller During operation the thermal sensors are constantly monitored by the neural network and its output is routed to the machine control as an error signal to be included in the control of the axes of motion of the machine 24 Chapter 4 Experimental Setup The setup of the experiments consisted of five major steps 1 Configuring the laser interferometer system and the lathe control to measure the positioning accuracy of the axis under examination 2 Running the lathe and laser system to collect the measurement data 3 Designing the neural network and training it with the measured data 4 Extracting the key network parameters and programming the real time calculations for integration into the control 5 Repeating the measurement test to determine real world performance of the system 4 1 Configuring Laser and Lathe Control The configuration of the laser and the lathe control is determined by the desired test data While these are two separate systems their configurations must match for a successful test The lathe control must be set up to produce the pattern of motions expected by the laser measurement system 4 1 1
71. modular and scalable OMAC The key characteristic applied to this thesis was that of being open OMAC presents a definition of an open control as allowing the integration of off the shelf hardware and software components into a controller infrastructure that supports a de facto standard environment OMAC It is the ability to integrate external software components into the controller that makes it possible to write custom error compensation routines and use them in real time In the case of the lathe used in this project the control system was OpenCNC from Manufacturing Data Systems Inc MDSI OpenCNC is an open architecture software based CNC control system MDSI V6 2_Datasheet suitable for use on most typical CNC controlled machines OpenCNC runs on the Microsoft Windows NT Microsoft operating system and uses the add on Real Time Extensions from VentureCom Inc VenturCom to give it the hard real time deterministic response required to maintain control of the machine tool Since OpenCNC uses a standard PC operating system it runs on generic PC hardware It also has a published Application Programming Interface API that allows the control designer to develop external software routines and interface them with the control system using standard PC software development tools The internal architecture of OpenCNC is centered around its Real Time Database MDSI API Datasheet This database contains all the system variables f
72. n This function checks for EndPos StartPos Increment evenly within value of NearZero By looping through there are numerical problems with int Public Function CheckIncrement E As Double S As Double I As Double local variables Dim x As Double CheckIncrement True default to success xX 28 Do XXI Loop Until Abs E x lt NearZero Or x gt E If x E And Abs E x NearZero Then CheckIncrement False Else X 7 X I Loop Until Abs S x NearZero Or x S If x S And Abs S x gt NearZero Then CheckIncrement False End If End If End Function CheckIncrement This subroutine does the initialization and command line parsing Public Function Initialize generic macro variables Dim arguments maxArguments 10 As Variant Dim retArgs As Variant Dim ret As mdsiMacroReturnTypes Dim argCount As mdsiMacroReturnTypes Dim errorPosition As Long 35 As Boolean MDSI initialization this section of code must not be deleted Set mdsiMacroObj CreateObject mdsiMacroSupport clsMdsiMacroSupport ret mdsiMacroObj Initialize Command If ret lt gt mdsiMacro_Succeeded Then fatal ret quit return the error code to OpenCNC End If setup argument names arguments msAxis A arguments msStartPos S arguments msEndPos E arguments msIncrement I arguments msDwell T arguments msNumRuns N arguments msFeedrate F arguments msBacklas
73. nclude lt math h gt input weights column 2 for mulitply by position input EJ const double FullIW2 30 3 5299591828609689e 0 2 9772889998702345e 0 6 4793260461973534e 0 5 4195020390193360e 0 9 7106115496384826e 0 6 1905741094569089e 0 7 7323968706067736e 0 1 9677546910613436e 0 7 5903727601389914e 0 1 0715500354505123e 0 7 4182768355941786e 0 8 3897565665597562e 0 6 2476996136658969e 0 6 2602614925206490e 0 2 4024212111154136e 0 8 1848186292315062e 4 0822195177470089e 7 1626070157100863e 8 9921491040980839e 1 2928512211754312e 8 2383751470809030e 8 3874484365466773e 3 7197208002594834e 7 0063070389361926e 7 4830770954720938e 2 5576441880935413e 5 7884559271706870e 5 1772547956387849e 2 8298441045876910e 3 9568791198859837e OOD DO O O ODO COCO OOOO OOO OO ccc OOO OOO OO c E ee ppp Es Es ps ps pa 3 pa L3 pa 3 qma Aa y input weights column 1 added to input bias used for addtion when direction input 1 const double FullIW B1 30 7 0470049377939930e 000 69 4097100862194786e4 8789253140934623e4 7455579099105591e4 1396950984946812e4 0504336719678323e4 4603634074333058e4 9485358741831220e4 5169577723346919e4 3935073610259401e4 e 6541715543130792e4 3470121353454136e4 769411 8332232907721902e4 675642642164
74. ne net newff 0 1 1 40 40 20 1 logsig logsig purelin trainlm learngdm sse will generate a three layer network a 40 neuron logsig a 20 neuron logsig and a single linear neuron The last few lines in the script plot the results of testing the new network on the same figure as the original test data This provides a pictorial view of the results for evaluation of network performance After evaluating the network performance and finding a suitable network for the problem the network structure is saved to allow for extracting the key parameters to use in programming the real time calculations 4 3 1 Matlab Implemented Training Algorithms Training a neural network in the Matlab environment is normally accomplished using one of the built in training functions that are included in the Neural Network Toolbox There are sixteen different training functions implemented and included as part of the toolbox Demuth and Beale While each of the training algorithms could be used 29 on any problem they are each more suited for certain classes of problems and network architectures One of the issues was to determine early on which algorithm was best suited for the problem at hand and the network architectures under investigation For feed forward backpropagation networks the default training algorithm is the Levenberg Marquardt algorithm According to Demuth and Beale this algorithm is well suited to function approximation pr
75. ntrol of the laser system and the lathe motion the laser expects a specific series of moves to be made and the lathe is programmed to make those exact moves 10 Laser Dwell 1 2 Laser Dwell Laser Dwell time ends time begins time Reading final reading recorded begins Machine reaches desired position and stops Machine Dwell time begins Machine Dwell time ends next move begins Machine motion reaches Window edge Machine Begins Move Figure 2 5 Machine motion laser timing diagram 2 3 4 Graphical Results and Output Data The results of a successful laser interferometer run are presented using three methods During the run a screen is displayed on the controlling laptop that shows the current state and activity of the system After the run is complete an ASCII test data file is produced which can be manually analyzed or opened from within the 5 6 D laser system for a graphical display of the results While a run of the 5 6 D laser system is in progress the screen shown in Figure 2 6 is displayed This shows the current reading of the laser distance measurement in the upper left block A graphical display of the results collected in this run is plotted in the upper right block Operating parameters of the current run are displayed in the lower left area with the bottom right blocks showing the current status target position and run number 11 5 6D Laser Measuring System Linear Test2
76. oblems with networks of moderate size and number of parameters It is also well suited to problems that require the approximation to be very accurate Other algorithms that were considered to work well in function approximation problems are the Scaled Conjugate Gradient and the BFGS Quasi Newton algorithms Demuth and Beale Demuth and Beale present a discussion on speed and memory comparisons of the various training algorithms for a set of sample problems This discussion supports the conclusion that the Levenberg Marquardt LM algorithm is the best available in this toolbox for the class of problems that are function approximation problems on small to moderate sized networks As the problem under study fits that description these recommendations were considered and the conclusions on the actual data for this problem were validated The work in this thesis included a function approximation problem that required the final error to be reduced to a very small value and in general the networks were of moderate size A series of ten tests each were conducted on four of the training algorithms where a newly created network was trained against the data collected from the laser interferometer measurements of the lathe In each of the tests the entire network was newly created and randomly initialized in the default manner of the toolbox The training parameters were set to train for 1000 epochs and the goal of reducing the error to 4 x 10 was set as me
77. of the network is compared to the desired and an error value is produced This error value is then used to adjust the network parameters such that it will produce an output that is closer to the desired 16 Mathematically referring to the single neuron model in Figure 2 9 where Z is the input vector W is the weight vector and O is the output of the neuron and adding D as the desired output from the training data and the factor n the learning rule can be stated as W W nele D O From this equation the following points can be made 1 The new weight values are not totally new values but rather modifications of the previous values after some incremental adjustment 2 Since D is the desired output and O is the actual if D O is positive the output O is increased in the next iteration and if D O is negative the output is decreased in the next iteration Since each individual input contributes Wel to the total input the error D O is multiplied by each individual input in the adjustment factor This way if this input is positive its associated weight is greater giving it more influence on the total input to increase it If the input is negative the associated weight is decreased reducing this input s influence on the total input also increasing it 3 The factor n is known as the learning rate It is used to adjust the learning rule for a balance between stability and speed of convergence A large learning rate will make
78. oooocccnnoccnonocanononcnonononananononnnncnnnononnncncnneninnnos 29 4 3 1 Matlab Implemented Training Algorithms esee 29 4 4 Programming Real Time Calculations eese eene 31 4 4 1 Extraction of Network POrameters anita iia 32 4 4 2 Calculation of Compensation Values i ases a aa ab 32 4 4 3 Control Integration and Measurement Testing eese 34 Chapter 5 Retina 35 5 1 Uncompensated Positioning Errors essere eere nere 35 5 2 Bi Directional Leadscrew Compensation eese 37 iv 5 3 Neural Network Based Error Compensation esee 39 5 4 Network Training Results eurer eee e nai NT Nas deuda ede es adn ta ie aun PR ETE A 40 Chapter EX cdi me ienest 45 A dude tentare tu tes ch unclean 45 0 2 Bic TE aS 45 0 3 Future WW OU Restos ons stot a cats it ODE un ud uides Goes named ERU Donc Eas debu o QUERN 45 ROPE RENICOS Mese E ic AA ARAS RIA AAA AAA 47 Appendix A Detail Photograpbs oooommmsmsss 48 Appendix B Visual Basic Macro Code and Subroutine Result 52 Appendix C M File for Neural Network Generation sccsccccscessssscsseseceseeees 60 Appendix D M File for Extraction of Network Values scccsscssscssssessseseeeeees 62 Appendix E C Program for Network Calculation sccsscsssscsscsscssssscsec
79. or the control These system variables contain the current state of the machine under control and define all of the control characteristics Literally every function of the machine and the control are defined and represented in the system variables As part of the database there are system variables for the location velocity and direction of motion of each of the axes on the machine along with any error compensation values that should be applied to the positioning of the axis The API that is available with OpenCNC provides functionality at two levels The API Level 1 provides access to the system variables in the database It is often used to develop additional user interfaces to the control or to add functionality such as e mail notices or system monitoring capability However the API Level 1 is used for non real time applications and does not have the functionality to create scheduled deterministic hard real time applications Applications created using the API Level 1 run with the same priority and scheduling scheme as any other application running on the Windows NT operating system OpenCNC s API Level 2 is used to develop those applications that require deterministic hard real time response It also provides access to the system variables in the database and additionally provides the ability to schedule the execution of processes at predetermined time intervals and set the priority of processes to levels normally reserved for internal
80. orks developed It is the output of netvalues m const double FullIW2 30 3 5299591828609689e 2 9772889998702345e 6 4793260461973534e 5 4195020390193360e 9 7106115496384826e 6 1905741094569089e 7 7323968706067736e 1 9677546910613436e 7 5903727601389914e 1 0715500354505123e 7 4182768355941786e 8 38975656655977562e 6 2476996136658969e 6 2602614925206490e 2 4024212111154136e 8 1848186292315062e 4 0822195177470089e 7 1626070157100863e 8 9921491040980839e 1 2928512211754312e 8 2383751470809030e 8 3874484365466773e 3 7197208002594834e 7 0063070389361926e 7 4830770954720938e 2 5576441880935413e 5 7884559271706870e 5 1772547956387849e 2 8298441045876910e 3 9568791198859837e C OC Or DO C2 C5 C C C9 C CD CO CO 00 CD CD CD C2 C CO CO CO QOO CC O VO O O QC CCCo OOO OO COCO OOO COCO OO COO OOOO OOO OO c PA EA OA pe ee pet ed eae A a 3 pa L3 pa Y LX EA E qn const double FullIW B1 7 0470049377939930et 1 4097100862194786e 1 8789253140934623e 9 745557909910559le 2 1396950984946812e 1 0504336719678323e 8 4603634074333058e 4 9485358741831220e 8 5169577723346919e 1 3935073610259401le 1 6541715543130792e 1 3470121353454136e CO Co Or OOO Ok CO CO C G9 OO cc c cc coc ccc c La 65 76941
81. plete runs msFeedrate mvFeedrate Feedrate for moves msBacklash mvBacklash distant for backlash overshoot moves msDebugMode mvDebugMode Debug mode for program 0 No messages NonZero messages maxArguments End Enum Declare any global constants for use Const NearZero As Double 0 0001 Declare the win32 API function that let s us return an error code Private Declare Function ExitProcess Lib kernel32 ByVal exitCode As Long As Long this needs to be global so we can clean it up on a fatal error Dim mdsiMacroObj As IMdsiMacroSupport declare argument variables Dim Axis As Double Dim StartPos As Double Dim EndPos As Double Dim Increment As Double Dim Dwell As Double Dim NumRuns As Double Dim Feedrate As Double Dim Backlash As Double Dim DebugMode As Double Public Sub Main generic macro variables Dim ret As mdsiMacroReturnTypes Dim block As String Dim nValues As Long macro application specific variables for example 32 3 Dim x As Double y As Double Dim index As Integer Dim defAxisLetters As Variant defGInchMode As Variant defDecimalShift As Variant Dim AxisLetter As String Dim AxisNumber As Integer Dim AxMin As Double AxMax As Double Dim v As Variant Dim CurrentPos As Double Dim LaserZero As Boolean Dim RunCount As Integer open and clear the subroutine file Open OpenCNC Subroutines laserSub txt For Output As 1 Print 1 Error in processing input see message window Clo
82. r defAxisLetters AxisLetter 1 Then ret mdsiMacroObj mdsiMsgWindowWriteVB ERROR Invalid Axis specified ret mdsiMacroObj mdsiMsgWindowWriteVB ERROR Start Position must be less than End ElseIf StartPos lt AxMin Or StartPos gt AxMax Then ret mdsiMacroObj mdsiMsgWindowWriteVB ERROR Invalid Start Position must be between ret mdsiMacroObj mdsiMsgWindowWriteVB ERROR Invalid End Position must be between Start ElseIf Increment lt NearZero Or Increment gt EndPos StartPos Then ret mdsiMacroObj mdsiMsgWindowWriteVB ERROR Invalid Increment spec d too small or too ElseIf Not CheckIncrement EndPos StartPos Increment Then ret mdsiMacroObj mdsiMsgWindowWriteVB ERROR Increment does not divide evenly ret mdsiMacroObj mdsiMsgWindowWriteVB ERROR Invalid Dwell spec d must be between 1 and 99 ElseIf NumRuns lt 1 Or NumRuns gt 99 Then ret mdsiMacroObj mdsiMsgWindowWriteVB ERROR Invalid Number of Runs spec d must be between 1 and 99 ElseIf Feedrate lt 0 1 Or Feedrate gt 50 Then ret mdsiMacroObj mdsiMsgWindowWriteVB ERROR Invalid Feedrate spec d must be between 0 1 and 50 IPM ElseIf Backlash lt 0 Or Backlash gt 1 Then ret mdsiMacroObj mdsiMsgWindowWriteVB ERROR Invalid Backlash move spec d must be between 0 and 1 starting position ElseIf StartPos Backlash lt AxMin Then ElseIf EndPos Backlash gt AxMax Then ret mdsiMa
83. reading of the next run End Position This is the ending point of the laser run For a Bidirectional run the system expects the machine to incrementally move to this position in the forward direction then move past it outside the Window distance and then return to this position for the first reading in the reverse direction Step Size This is the distance between measurement points Num of Runs This is the number of complete runs to measure A Bidirectional run is complete when the machine has moved from the starting point to the ending point and back to the starting point for a final reading Table 2 1 Key entries for software setup The other entries on the setup screen are for general system parameters and labeling the results with name title comments etc Just as the 5 6 D Laser system requires setup to correctly measure the motion of the lathe the lathe itself requires programming so that it would make the expected sequence of moves for correct measurement The required machine programming is accomplished by a Visual Basic macro that produces the G and M code commands for the machine This macro is called by a small part program that establishes the parameters for the test being run Changing this program for a different series of moves i e moving a different interval or a different axis of motion is accomplished by editing the values of the variables in the first several lines of the program Table
84. reflective target as illustrated in Figure 2 2 The emitted beam is projected through the beam splitter which results in two separate beams of light that start out with matching phases These beams are then projected onto the two targets and reflected back to the beam splitter which combines them into a single beam again The resultant combined beam is then examined for fringes created by a mismatch in the phase relationship between the two returned beams By counting these fringes as the mobile target is moved the interferometer system can determine linear displacement as a function of the wavelength of the light beam Beam Splitter Measurement Mobile Beam Retroreflector Emitted Beam Combined Beam Phase Detector Direction of Motion Measurement MS Electronics Reference Beam EM V o Output to Stationary Comp ter Retroreflector Figure 2 2 Simplified block diagram for laser interferometer Since the measurement of distances with an interferometer is accomplished by comparing phase relationships between the reference beam and the measurement beam the accuracy of the system is dependent on the wavelength of light used and the system s ability to distinguish fringes created by phase mismatches The 5 6 D Laser system used for this thesis is a Helium Neon laser with a waveleng
85. rol Integration and Measurement Testing Integration into the control requires the installation of the compiled program onto the machine under test and editing the control system s configuration files to include this program in the startup of the machine control The exact details are specific to MDSI s OpenCNC product and can be found in the OpenCNC 6 0 API Manual and the sample programs provided with the OpenCNC API The program was configured to run on a strict timing cycle of 10 milliseconds In each cycle the following actions take place Control variables are read to determine the current axis position Direction of motion is determined from previous position to current position Current position is recorded for motion comparison in the next cycle Input values are scaled and applied to the compensation calculations Compensation values are calculated based on the inputs presented Compensation value is returned to the control for immediate application to the system 7 Wait for the next timing mark to repeat cycle The complete routine is programmed to run as an infinite loop Once the loop is entered the cycle will be repeated on each timing mark forever or until the process is killed by shutting down the control system Once the compensation routine is installed in the control system and the control is restarted the measurement test outlined previously is repeated under the exact same setup conditions The results from this test are
86. s in the test Using Matlab s internal File Import Data functionality all of the data is manually imported into two matrices one of raw data the other of averages These matrices would become the basis for neural network training and testing The average values were used to train the network and the raw data were used to test the resultant network Generating and training a neural network and displaying the results of test data was accomplished using Matlab s m file scripting capability As this process turned out to be highly repetitive in trying and testing different network structures numbers of neurons numbers of layers etc using a script allowed for quickly editing a few key lines and rerunning the script to test an entirely different network Appendix C includes the complete script The key line in the script generates a new network and specifies the network architecture in terms of the number of layers neurons in each layer and the transfer function to be used in each layer It also defines what training function is to be used and the evaluation function used in training and measuring performance For example the script line net newff 0 1 1 40 60 1 logsig purelin trainlm learngdm sse generates a new network with two layers One layer will be made up of 60 neurons with the logsig transfer function and the second layer will be a single neuron with a linear transfer function Once edited the script li
87. screw ballnut assembly reverses its direction of motion This value is also calculated and displayed as Max Rev Err maximum reversal error The two horizontal dotted lines are the high and low points of the average error values for in this case the four runs This value is calculated and displayed as Max Avg Error maximum average error These are the two key values that give an indication of the mechanical condition of the machine Compensation routines discussed elsewhere are directed at reducing these values to acceptable levels 5 6D Laser Measuring System newX pos Iof x TJ File Edit View Window Standards Tools Help l x Pa 5 6 E o Vv VAGA ta ses sin se ese x00 zo 2 7X Linear 7 to by 0 14 Bi directional Linear Error Plot ANSI 0003009 Linear Error inch 0 001500 Pa 0 001000 0 000500 0 000500 0 001000 0 001500 6 860 7 000 0 002000 File Name newX pos Air T Avg Max Avg Error 0 003173 in American HustleAir P Avg 29 3 in Hg Max Rev Err 0 002054 in 09 Material T Avg 75 0F Max Repeat 0 002357 in 4014 Hurnidity 50 96 JFines Exp Coef 6 7 ppmiF 02 1 3 2001 Num of Runs 4 10 35 40 Window 0 0500 in For Help press F1 Figure 2 7 Graphical display of 5 6 D laser system data 2 4 Artificial Neural Networks As one of the forms of artificial intelligence artificial neural networks are an attempt to mimic the behavior and capabilities of biological n
88. se 1 Initialize and parse the command line arguments Initialize first check the axis selection if bad bail out this allows me to set up initial values based on axis selection it might not be the right axis but at least it s not total garbage If Axis 1 Or Axis 3 Then ret mdsiMacroObj mdsiMsgWindowWriteVB ERROR Invalid Axis selected must be between 1 and fatal ret End If Set up initial values go get the axis letters for this machine ret mdsiMacroObj mdsiVariableReadByNameVB defAxisLetters defAxisLetters nValues If ret mdsiMacro Succeeded Then fatal ret quit return the error code to OpenCNC End If If DebugMode lt gt 0 Then ret mdsiMacroObj mdsiMsgWindowWriteVB DEBUG Axis letters CStr defAxisLetters End If AxisLetter Choose Axis X Y Z select letter based on numeric input from user If Axis 3 Then if X or Y then axis number is 0 or 1 respectively AxisNumber Int Axis 1 ElseIf Axis 3 And InStr CStr defAxisLetters Y gt 0 Then AxisNumber 2 if selected Z and Y exists then axis number is 2 Else AxisNumber 1 if selected Z and no Y then axis number is 1 End If get the decimal shift value for location calculations ret mdsiMacroObj mdsiVariableReadByNameVB defDecimalShift defDecimalShift nValues If ret mdsiMacro Succeeded Then fatal ret quit return the error code to OpenCNC End If go get the absolute minimum coord for
89. selected axis ret mdsiMacroObj mdsiVariableReadByNameVB axLocAbsMin v nValues If ret mdsiMacro Succeeded Then fatal ret quit return the error code to OpenCNC Else AxMin v AxisNumber 2540000 10 defDecimalShift End If If DebugMode lt gt 0 Then ret mdsiMacroObj mdsiMsgWindowWriteVB DEBUG Axis Minimum CStr AxMin End If go get the absolute max coordinate for selected axis ret mdsiMacroObj mdsiVariableReadByNameVB axLocAbsMax v nValues If ret mdsiMacro Succeeded Then fatal ret quit return the error code to OpenCNC Else AxMax v AxisNumber 2540000 10 defDecimalShift End If If DebugMode lt gt 0 Then ret mdsiMacroObj mdsiMsgWindowWriteVB DEBUG Axis Maximum CStr AxMax End If go get the inch mode G code for this machine ret mdsiMacroObj mdsiVariableReadByNameVB defGInchMode defGInchMode nValues If ret mdsiMacro Succeeded Then fatal ret quit return the error code to OpenCNC End If If DebugMode lt gt 0 Then ret mdsiMacroObj mdsiMsgWindowWriteVB DEBUG Inch Mode G Code CStr defGInchMode 53 End as Error checks see imbedded messages for individual purpose If E Position CStr AxMin and End Position Elself EndPos lt AxMin Or EndPos gt AxMax Then Position and CStr AxMax large ra Self StartPos EndPos Then self Dwell 1 Or Dwell 99 Then nStr CSt
90. sifying vibration signatures for rolling element bearings in analyzing the bearings for defects The idea is based on the fact that a real mechanical system in operation generates vibration The amplitude and frequency spectra of the vibration changes as the mechanical system changes due to wear or mechanical defects By analyzing the resulting vibration signatures likely defects can be determined In this application neural networks were used for compression of the spectral signatures and for classification of the compressed signature For the compression phase of the system the authors described using a recirculation network Compressing the 23 vibration signature results in mapping the spectra into a smaller dimensional space This results in the network acting as a feature extractor which highlights the notable features of the data while reducing the noise present in the signal For the classification phase of the system a backpropagation network was used to classify the signal into one of eight possible patterns one indicating no fault and the rest indicating one or a combination of predefined fault signatures 3 3 Positioning Error Correction with Neural Networks One example of using a neural network to correct for positioning errors in a machine tool is described in U S Patent 5 523 953 USPTO In it the inventors outline a method of correcting for errors induced by temperature changes in the machine during its operation The
91. sig I1e IIW1 I2 e I2W1 bH1 e LW1 log sig I1e 11W2 12 12W2 bH2 e LW2 log sig I1 e IIWn 12 I2Wn bHn e LWn bOl or more succinctly as Y log sig I1e I1Wj 12 e I2Wj bHj e LWj bOl j l where n is the number of neurons in the hidden layer and the transfer function logsig x is defined as 1 l e However by taking advantage of prior knowledge of the inputs this can be simplified In the case of this system the first input I1 is either 0 or 1 indicating forward or reverse motion respectively In the case of forward motion where I1 is O the calculation can be reduced to 33 Y log sig I2 I2Wj bHj e LWj bOl j l In the case of reverse motion where I1 is 1 and noting that the input weights and bias values are predetermined the calculation can be reduced to Y log sig DWHj I2 e I2Wj e LWj bOl q where b WH is the predetermined value of I IW bHj The complete C program code for this calculation is included as Appendix E By reviewing that code it can be seen how all of the calculations were accomplished using simple mathematical functions and basic looping structures These were required to stay within the supported functions of the VentureCom SDK It can also be seen how all required values from the network and any additional constants that could be derived from those basic values were predetermined and loaded into the program code as constants to be used in the calculations 4 4 3 Cont
92. ssed to the connected neuron The second computational element of the network is the transfer 14 function of each neuron The transfer function is used to generate the output of each neuron based on the complete set of inputs to that individual neuron In its simplest form a neural network would consist of a single input to a single neuron which outputs a single output A more useful form of this single neuron network is diagrammed in Figure 2 9 In this case a single neuron with several inputs generates a single output The figure illustrates the network consisting of a set of inputs I weighted connections W a single neuron with transfer function T and output O It also adds the concept of an applied bias B Where B is used to offset or bias the output of the neuron B is also sometimes viewed as another weighted connection to a fixed input value of 1 A mathematical description of the single neuron network is O T I W 1 W B The transfer function of the neuron is determined when the network is initially designed and created Determination of the transfer function is one of the basic issues the network designer has to address Figure 2 9 Single neuron network There are many different types of transfer functions used in neural networks but a few examples are commonly presented in the literature including the step or threshold function and the sigmoid function Simple graphical illustrations of these two functions are
93. stem to a level slightly below that of the controls standard error compensation capability 1 3 Thesis Structure This thesis is organized into six chapters and five appendices Chapter 1 is the introduction which discusses the motivation for the thesis and the basic methodology for the experiments conducted This chapter highlights the desire for improving the performance of machine tools and how that will be attempted by improving the machine tools ability to compensate for positioning errors in the axes of motion Chapter 2 is the background information for the thesis In it is discussed the equipment machinery and systems used in the experiments and a very basic discussion of artificial neural networks Chapter 3 is the related works section of the thesis In it is discussed the current methods of positioning error compensation and some applications of artificial neural networks that exist in the literature Chapter 4 is the experimental setup discussion This chapter presents the measurement system used to evaluate positioning error on the machine tool how the artificial neural networks were designed and implemented and how the resulting neural network was integrated into the machine tool control Chapter 5 is the experimental results In 1t is discussed the numerical results achieved by the artificial neural network positioning error compensation system and a comparison with the results achieved by traditional methods of compensation on the same
94. ter recognition of handwritten characters and driving a vehicle along a single lane highway 3 2 1 Intelligent Control One common area of application for neural networks is in intelligent control Bauman et al present an intelligent control for load balancing the internal combustion engine ICE and the electric machine EM of a hybrid vehicle In their problem the ICE and the EM were mechanically connected in parallel to drive the vehicle The goal of the controller was to distribute the load across the ICE and the EM to achieve maximum efficiency for the entire system The authors present a discussion of the controller that uses a combination of neural networks and fuzzy logic to achieve the goals In their discussion of the controller approach they list five properties of the controller which make it appropriate for their application a model free approach adaptability fault tolerance nonlinearity and real time operation These properties were highly advantageous in their application which had the characteristics of being highly complex and difficult to mathematically model experienced a high degree of variability and system noise in operation was fundamentally nonlinear in its behavior and required the ability to handle constant transient operations 3 2 2 Analysis of Vibration Signatures Another area of application for neural networks is in data analysis and classification or grouping Alguindigue ef al present a method of clas
95. th of 0 6329 microns The system is able to count fringes in 1 4 fringe increments This leads to a resolution of 0 6329 x 1 4 0 1582 microns or approximately 6 23 microinches Automated Precision Inc 2 3 2 Physical Setup The physical set up of the laser interferometer consists of arranging the stationary and mobile components of the system so that the relative motion between these components accurately reflects the motion of the machine under measurement Mounting of the mobile reflector is normally done with a magnetic base and it is mounted as closely as possible to mimic the motion of the cutting tool of the machine The stationary components are mounted off the machine on a tripod to insulate them from vibration of the machine in motion For a linear measurement as in this case they are aligned so that the emitted beam leaves the interferometer from the lower aperture and is returned from the mobile reflector to the upper aperture throughout the entire range of motion to be measured Figure 2 3 shows a view of the physical setup and Figure A 1 and Figure A 2 illustrate detailed views of the components Figure 2 3 Physical setup of laser interferometer 2 3 3 Software Setup The 5 6 D Laser system is controlled by software on a standard laptop computer connected via an RS 232 serial connection For this project the APInc s Winner v1 3 1 package was used Automated Precision To successfully collect information from the l
96. the system converge more quickly to an acceptable state reducing the error to acceptable limits but too large of a learning rate may make the system unstable by causing the learning rule to over correct for small errors causing it to oscillate around the desired weight values The rules stated above are often presented in neural network texts as the initial starting point for a study of learning rules or training algorithms and complete coverage can be found in Russell Hagan and Haykin 2 5 MATLAB and the Neural Network Toolbox There are two primary methods of implementing a neural network system One is in dedicated hardware and the other is to simulate the network on a digital computer Because of the obvious cost and flexibility concerns the latter is the most common method Also because of the programming complexities of implementing the various types of networks it is often advantageous to use a commercially available packaged set of routines to design and develop a neural network system One such package is the Neural Network Toolbox from The Mathworks Inc Demuth and Beale This package runs under The Mathworks MATLAB program and extends its capability to include many of the functions necessary to design and implement a neural network system MATLAB and the Neural Network Toolbox provide the capability to design many different types of neural network systems for a variety of applications The Neural Network Toolbox User s Guide
97. ured with some type of a high precision device such as a laser interferometer system This information is then entered into the control system of the machine tool and it is used to correct for known errors in the machine For example if a machine consistently falls 0 002 inches short of the desired position when moving an axis the control system will command a move 0 002 inches longer than desired to compensate for the expected error Using this method modern machine tools have been able to reduce positioning errors to a level lower than the mechanical accuracy of the machine Typical positioning error compensation routines in modern machine tool control systems have one basic characteristic in common They allow for a limited number of compensation values to be entered and the values must be at fixed intervals of motion Some systems will allow the user to pick the interval and in some systems this value is determined at design time by the machine tool builder With the advent of open architecture control systems which allow for the integration of external control routines into the basic function of the control system there is now interest in more advanced and flexible error compensation routines 1 2 Research Methodology The focus of this thesis is the design and implementation of a neural network based positioning error compensation system for an actual machine tool in an industrial environment A large standard configuration two axis
98. vanced functions are available for capabilities such as interpolation of arcs and thread cutting operations American Tool Since the motions studied were single axis and linear the programming of the lathe was restricted to only those commands required to produce these movements The normal pattern Figure 2 1 The Hustler lathe by American Tool Inc of motion could be accomplished by repeating these two commands GOLX 1F 2 GO4F 3 Where G01 is the G code command for single axis controlled feedrate motion The first line would command the X axis to move to position 1 at feedrate 2 normally inches per minute G04 is the command for a program dwell Therefore the second line would command a program dwell for 3 seconds at the current position An example of the complete command lines is G01X3 5 F20 GO4F6 These two lines would command the X axis to move to the 3 5 inch position at 20 inches per minute then dwell at this point for 6 seconds The entire program would be constructed by a series of these moves either specifically listed out in the program or some type of looping structure would be used in the program while setting the values to 1 2 and 3 2 2 Open Architecture Control According to the Open Modular Architecture Controls User s Group OMAC a CNC control is generally considered to be an Open Architecture Control OAC if it has the characteristics of being open economical maintainable

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