CN104731019B - Numerical control cam grinding contour error compensation control method based on Cycle to Cycle feedback control - Google Patents
Numerical control cam grinding contour error compensation control method based on Cycle to Cycle feedback control Download PDFInfo
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- G05B19/404—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form characterised by control arrangements for compensation, e.g. for backlash, overshoot, tool offset, tool wear, temperature, machine construction errors, load, inertia
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Abstract
The invention relates to a Cycle to Cycle feedback control compensation method for controlled system tracking errors with repeating movement features, in particular to a numerical control cam grinding contour error compensation control method based on Cycle to Cycle feedback control. The problem that according to a traditional numerical control cam grinding control method, only the information of a current grinding cycle is used, and the previous grinding cycle information is ignored is solved, and the contour accuracy of numerical control cam grinding is improved. According to CtC feedback control, between successive cyclic process control, the grinding information of a last cycle, namely a contour error is used for guiding the grinding process of a current cycle. Through system dynamic-state and steady-state characteristic analysis, CtC feedback controller parameters are optimized, so that grinding contour errors are controlled in an allowed range, and satisfied grinding accuracy is obtained. The Cycle to Cycle theory is introduced, the contour accuracy compensation method and the computing steps during the cam grinding process are provided, so that compensation has a theoretical foundation, and the current situation that current compensation is carried out by experience is changed.
Description
Technical Field
The invention relates to a contour error compensation control method in the field of numerical control, in particular to a numerical control cam grinding contour error compensation control method based on Cycle toCycle (CtC) feedback control.
Background
With the improvement of mechanical precision machining precision indexes, higher requirements are put forward on the servo control of a machine tool numerical control system, the contour precision becomes an important index of the machine tool numerical control system, and the machining quality of parts is directly influenced.
In the machining of the numerical control cam grinding, the machining of the cam piece belongs to mass production, and also means that the machining process of the same contour track is repeated. When machining a cam plate, the same path is required to be repeatedly taken, each repeated machining process is called a machining cycle, and the tool tracks the same expected path in each machining cycle. However, the current numerical control cam grinding technology can only measure the information about the cam piece after the period, and during the period, the correct measurement and control are often very expensive or complicated to be almost impossible. In addition, the dynamic control method of the systems reaches a certain height, and the improvement is difficult. Most of the numerical control cam grinding depends on the experience of technical workers to adjust, and waste of time and labor is inevitable.
For the problem of repetitive cycle control in numerical control grinding, Iterative Learning Control (ILC) is firstly proposed by Uchiyama in 1978, and the inventors propose to obtain an ideal actual reference input value by using iterative learning control (Chinese patent: CN 102323790B, a cascade iterative learning cross-coupling following error control method of a two-axis numerical control system) so as to improve the profile precision, but the method is not suitable for cam grinding with complex profile; in the document "a method for consistent error interaction in cam compensation" of dunghui, a contour error intelligent compensation method based on case inference (CBR) and rule inference (RBR) is proposed, but for different cam contour errors, the compensation method needs to continuously match the contour errors until the contour errors are suitable, and is relatively time-consuming; MIT Tsz-Sin Siu proposed Cycle to Cycle (CtC) feedback control in the production process in 2001, which is mainly applied to the control of plate bending and injection mold processes and obtains ideal effects. The idea is to use the effect of the last cycle to guide the production of the process. In a motion control system, the CtC idea can be used for compensating the profile error of the numerical control cam grinding.
Aiming at the problems, the invention provides a numerical control cam grinding profile error compensation control method based on Cycle to Cycle feedback control. The CtC control idea in process control is used for proposing a new CtC feedback control algorithm; a feedback control model is established CtC for the numerical control cam grinding system, and the controller is designed and optimized through analysis of stability, steady-state error and dynamic performance of the control model. The method solves the problem that the traditional control method for numerical control cam grinding only utilizes the information of the current motion period but not utilizes the information of the previous motion period, and obviously improves the cam profile precision.
Technical content
The invention provides a numerical control cam grinding profile error compensation control method based on Cycle to Cycle feedback control, aiming at controlling a numerical control cam grinding control system by using CtC feedback control of the invention, realizing error compensation of the previous processing Cycle by using information (deviation) of the previous processing Cycle, and finally realizing improvement of expected tracking accuracy.
To achieve the purpose, the invention establishes a CtC control model of the numerical control cam grinding control system based on an CtC feedback control idea of process control, and designs a corresponding controller. For a given cam lift, CtC feedback control is used for correcting the actual reference input quantity, so that the output signal gradually approaches the expected cam shape, the contour error tends to zero, and the precision of contour error control is improved.
The invention is described in detail below with reference to the accompanying drawings:
1) a CtC feedback compensation control strategy (see fig. 1) is established for the digitally controlled cam grinding process based on CtC feedback control, i.e., the grinding information, i.e., profile error, of the previous cycle is used to guide the grinding process of the present cycle between successive cycle process controls.
CtC the feedback compensation control strategy is as follows:
after the grinding process of one period is finished, measuring the profile error, wherein the measuring angle interval is 0.5 degrees, and the profile error compensation formula is as follows for 720 points in total:
ck＝Kk-1(1)
wherein, ckContour error values to be compensated for the kth period;k-1the maximum value of the measurement errors of the k-1 th period; k is the proportionality coefficient of the compensation.
2) A two-axis dynamic process model describing the numerical control cam grinding system is as follows:
wherein x isi,k(t) is a given value of the feed axis (X axis); x is the number ofo,k(t) is the actual reference input value for the feed axis (X-axis); c. Ci,k(t) is the given value of the rotation axis (C-axis); c. Co,k(t) is the actual reference input value of the rotation axis (C-axis); gxA closed loop transfer function for the X axis; gcIs a closed loop transfer function of the C-axis, k is 1,2,3 … n is the number of repeating cycles, t ∈ [1,2,3 … n]Is the cycle time length.
3) The two-input system of the numerical control cam grinding system is transformed into a single-input problem. That is, when a certain cam lobe lift is given, the relationship between the input values for the two shafts is fixed:
ci,k(t)＝f(xi,k(t)) (3)
xi,k(t)＝f-1(ci,k(t)) (4)
then, in the Z domain: c ═ F (X), X ═ F-1(C) In that respect Single input numerical control cam grindingThe control structure of the control system is shown in fig. 3.
4) Defining a new profile error, namely a profile error:
k＝xo,k(t)-f-1(co,k(t)) (5)
5) according to the control strategy, establishing a compensation control rule:
xo,k(t)＝Gx(xi,k-1(t)-Kk-1(t))
(6)
＝Gx(xi,k-1(t)-K(xo,k-1(t)-f-1(co,k-1(t))))
wherein K has the following values:
wherein,ois given an allowable error.
6) Analysis in the Z domain:
Xo＝Z-TGx(Xi-K(Xo-f-1(Co))) (8)
an CtC feedback control model of the numerically controlled cam grinding system can be obtained from equation (8), and a control block diagram refers to fig. 4.
7) And designing a controller K for the CTC feedback control model, and optimizing parameters of the CTC feedback controller through analysis of dynamic and steady-state characteristics of the system to control grinding profile errors within an allowable range so as to obtain satisfactory grinding precision.
Compared with the prior art, the control method of the invention has the following advantages:
1) the CTC feedback control model established by the invention is relatively complete and easy to understand, not only contains the information of the current motion period, but also fully utilizes the information of the previous motion period;
2) the invention converts the strong coupling control system into a single input control system, which is more beneficial to the analysis and the design of the controller;
3) the newly defined 'measurement error' simplifies the algorithm and can effectively reduce the real measurement error;
4) the CTC feedback control method has wide application range, is suitable for all controlled systems with periodic repetitive motion, and further improves the accuracy of the controlled systems with strong coupling of the periodic repetitive motion.
In conclusion, the numerical control cam grinding precision is effectively improved on the premise of not increasing any hardware.
Drawings
The invention will be further elucidated, by way of example, with reference to the following drawings:
FIG. 1 is a diagram of an error pre-compensation strategy;
FIG. 2 is a flow chart of a numerical control cam grinding profile error compensation control method based on CtC feedback control;
FIG. 3 is a control structure diagram of a single input numerically controlled cam grinding control system;
FIG. 4 is a control model of an CtC feedback numerically controlled cam grinding control system;
FIG. 5 is a cam profile shape;
FIG. 6 is a comparison of profile error before and after the addition CtC of feedback control.
Detailed Description
The following further illustrates the details of the present invention and its embodiments:
the invention provides a numerical control cam grinding profile error compensation control method based on Cycle to Cycle feedback control, which is characterized in that the compensation strategy is shown in figure 1, and a flow chart is shown in figure 2. The specific implementation steps are as follows:
1) a two-axis dynamic process model describing the numerical control cam grinding system is as follows:
wherein x isi,k(t) is a given value of the feed axis (X axis); x is the number ofo,k(t) is the actual reference input value for the feed axis (X-axis); c. Ci,k(t) is the given value of the rotation axis (C-axis); c. Co,k(t) is the actual reference input value of the rotation axis (C-axis); gxA closed loop transfer function for the X axis; gcIs a closed loop transfer function of the C-axis, k is 1,2,3 … n is the number of repeating cycles, t ∈ [1,2,3 … n]Is the cycle time length.
The experiment is built on a Simens 840D numerical control system platform. The mechanical transmission mechanism of the X axis adopts a DIK6310-8 series ball screw of a feeding system of a numerical control camshaft grinding machine of the Japan THK company, wherein a grinding wheel feeding motor adopts a 1FT6105-8AC7 type natural air cooling servo motor; the C shaft adopts an MHM95-6 type coupling produced by German Flender company, and the C shaft rotating shaft adopts a 1FT6102-8AB7 type natural air cooling servo motor. Through multiple reference data, the accurate parameters of each transmission mechanism and each motor can be obtained. The control of the two shafts adopts three-loop control, namely a current loop, a speed loop and a position loop from inside to outside. And respectively building a two-axis control system model by using a Simulink tool box and an LTI Viewer tool box and setting parameters of the two-axis control system model.
When designing a controller for an CtC feedback control system, a low-order model is usually used to simplify the controller design instead of a high-order model. Based on the requirement of error control, a two-order system model is selected to replace a dynamic process model of two shafts of numerical control cam grinding through a theoretical derivation and simulation verification method. Through consulting the concrete parameters of the test equipment and calculating the transmission function of each axis, the closed-loop transmission function of the whole dynamic process of the two axes can be simplified as follows:
in the Z-frequency domain:
CtC the feedback control depends on the error of the last period to continuously correct the actual reference input quantity, so that the output profile shape can be further close to the given value.
2) The two-input system of the numerical control cam grinding system is transformed into a single-input problem. That is, when a certain cam lobe lift (see table 1) is given, the profile shape (see fig. 5), the relationship between the input values of the two axes is fixed:
ci,k(t)＝f(xi,k(t)) (4)
xi,k(t)＝f-1(ci,k(t)) (5)
then, in the Z domain: c ═ F (X), X ═ F-1(C) In that respect The control structure of the single input numerically controlled cam grinding control system is shown in fig. 3.
3) For a numerically controlled cam grinding dynamic system with strong coupling, the improvement of the controller can reduce the tracking error, but cannot completely eliminate the tracking error, and the measurement error always exists, so that the aim is locked to reduce the measurement error. Defining a new measurement error, namely a profile error:
k＝xo,k(t)-f-1(co,k(t)) (6)
4) according to the control strategy, establishing a compensation control rule:
xo,k(t)＝Gx(xi,k-1(t)-Kk-1(t))
(7)
＝Gx(xi,k-1(t)-K(xo,k-1(t)-f-1(co,k-1(t))))
wherein k has the following values:
wherein,ois that given the allowed error that is to be given,o＝0.01mm。
5) analysis in the Z-frequency domain:
Xo＝Z-TGx(Xi-K(Xo-f-1(Co))) (9)
the control model of the numerical control cam grinding control system fed back by CtC can be obtained by equation (9) (see fig. 4).
6) And (3) stability analysis:
by closed loop transfer function
A closed-loop characteristic equation can be obtained:
z2+(81KTe-9T-2e-9T)z+(e-9T)2＝0 (12)
the essential condition for the stability of the linear steady discrete system is as follows: the moduli of the feature roots are all less than 1. With a period T of 3.6, we can obtain:
K≤1 (13)
considering that the compensation coefficient K is a variable value, the controller K is designed through experimental simulation until the contour error is within an allowable range, and finally K is selected to be 0.6 through simulation experiment debugging and the dynamic response effect of the contour error.
7) Given the controller, the actual reference input value is obtained. Experimental simulation comparison is carried out, a whole-course profile error graph can be obtained, and is compared with a profile error without adding CtC feedback control loops (see figure 6), and a simulation curve of figure 6 shows that the maximum profile error is reduced from 0.023mm to 0.015mm, the control precision is greatly improved, and the attenuation speed of the profile error is more stable.
Table 1: data of cam lift meter provided by numerical control grinding machine of certain model
| Angle (°) | Lift (mm) | Angle (°) | Lift (mm) | Angle (°) | Lift (mm) | Angle (°) | Lift (mm) |
| 1 | 0.0000 | 63 | 17.0000 | 125 | 12.4640 | 187 | 3.6545 |
| 2 | 0.0069 | 64 | 17.0000 | 126 | 12.3230 | 188 | 3.5397 |
| 3 | 0.0276 | 65 | 17.0000 | 127 | 12.1820 | 189 | 3.4265 |
| 4 | 0.0622 | 66 | 17.0000 | 128 | 12.0400 | 190 | 3.3149 |
| 5 | 0.1108 | 67 | 17.0000 | 129 | 11.8960 | 191 | 3.2048 |
| 6 | 0.1735 | 68 | 17.0000 | 130 | 11.7520 | 192 | 3.0965 |
| 7 | 0.2501 | 69 | 16.9980 | 131 | 11.6070 | 193 | 2.9898 |
| 8 | 0.3422 | 70 | 16.9940 | 132 | 11.4610 | 194 | 2.8847 |
| 9 | 0.4487 | 71 | 16.9860 | 133 | 11.3140 | 195 | 2.7814 |
| 10 | 0.5705 | 72 | 16.9740 | 134 | 11.1660 | 196 | 2.6798 |
| 11 | 0.7080 | 73 | 16.9610 | 135 | 11.0180 | 197 | 2.5798 |
| 12 | 0.8616 | 74 | 16.9430 | 136 | 10.8690 | 198 | 2.4817 |
| 13 | 1.0320 | 75 | 16.9230 | 137 | 10.7190 | 199 | 2.3853 |
| 14 | 1.2196 | 76 | 16.8990 | 138 | 10.5700 | 200 | 2.2907 |
| 15 | 1.4253 | 77 | 16.8720 | 139 | 10.4190 | 201 | 2.1978 |
| 16 | 1.6499 | 78 | 16.8430 | 140 | 10.2680 | 202 | 2.1068 |
| 17 | 1.8942 | 79 | 16.8090 | 141 | 10.1170 | 203 | 2.0175 |
| 18 | 2.1592 | 80 | 16.7740 | 142 | 9.9659 | 204 | 1.9301 |
| 19 | 2.4462 | 81 | 16.7350 | 143 | 9.8143 | 205 | 1.8446 |
| 20 | 2.7564 | 82 | 16.6930 | 144 | 9.6626 | 206 | 1.7608 |
| 21 | 3.0914 | 83 | 16.6470 | 145 | 9.5107 | 207 | 1.6790 |
| 22 | 3.4527 | 84 | 16.5990 | 146 | 9.3588 | 208 | 1.5990 |
| 23 | 3.8424 | 85 | 16.5480 | 147 | 9.2069 | 209 | 1.5208 |
| 24 | 4.2626 | 86 | 16.4940 | 148 | 9.0550 | 210 | 1.4446 |
| 25 | 4.7052 | 87 | 16.4370 | 149 | 8.9032 | 211 | 1.3703 |
| 26 | 5.1508 | 88 | 16.3770 | 150 | 8.7516 | 212 | 1.2978 |
| 27 | 5.5986 | 89 | 16.3150 | 151 | 8.6000 | 213 | 1.2273 |
| 28 | 6.0484 | 90 | 16.2490 | 152 | 8.4490 | 214 | 1.1587 |
| 29 | 6.5000 | 91 | 16.1810 | 153 | 8.2981 | 215 | 1.0920 |
| 30 | 6.9532 | 92 | 16.1100 | 154 | 8.1476 | 216 | 1.0271 |
| 31 | 7.4077 | 93 | 16.0360 | 155 | 7.9975 | 217 | 0.9644 |
| 32 | 7.8632 | 94 | 15.9590 | 156 | 7.8478 | 218 | 0.9035 |
| 33 | 8.3194 | 95 | 15.8800 | 157 | 7.6986 | 219 | 0.8446 |
| 34 | 8.7761 | 96 | 15.7980 | 158 | 7.5499 | 220 | 0.7876 |
| 35 | 9.2331 | 97 | 15.7130 | 159 | 7.4019 | 221 | 0.7326 |
| 36 | 9.6900 | 98 | 15.6260 | 160 | 7.2545 | 222 | 0.6795 |
| 37 | 10.1470 | 99 | 15.5360 | 161 | 7.1078 | 223 | 0.6284 |
| 38 | 10.6030 | 100 | 15.4440 | 162 | 6.9617 | 224 | 0.5793 |
| 39 | 11.0580 | 101 | 15.3490 | 163 | 6.8165 | 225 | 0.5322 |
| 40 | 11.5120 | 102 | 15.2520 | 164 | 6.6720 | 226 | 0.4870 |
| 41 | 11.9650 | 103 | 15.1530 | 165 | 6.5284 | 227 | 0.4439 |
| 42 | 12.4160 | 104 | 15.0510 | 166 | 6.3856 | 228 | 0.4027 |
| 43 | 12.8650 | 105 | 14.9470 | 167 | 6.2438 | 229 | 0.3635 |
| 44 | 13.3120 | 106 | 14.8410 | 168 | 6.1030 | 230 | 0.3263 |
| 45 | 13.7470 | 107 | 14.7320 | 169 | 5.9631 | 231 | 0.2911 |
| 46 | 14.1530 | 108 | 14.6220 | 170 | 5.8243 | 232 | 0.2579 |
| 47 | 14.5290 | 109 | 14.5090 | 171 | 5.6865 | 233 | 0.2267 |
| 48 | 14.8790 | 110 | 14.3940 | 172 | 5.5499 | 234 | 0.1975 |
| 49 | 15.1990 | 111 | 14.2780 | 173 | 5.4144 | 235 | 0.1703 |
| 50 | 15.4930 | 112 | 14.1590 | 174 | 5.2801 | 236 | 0.1452 |
| 51 | 15.7600 | 113 | 14.0380 | 175 | 5.1470 | 237 | 0.1220 |
| 52 | 16.0000 | 114 | 13.9160 | 176 | 5.0151 | 238 | 0.1008 |
| 53 | 16.2140 | 115 | 13.7920 | 177 | 4.8845 | 239 | 0.0817 |
| 54 | 16.4020 | 116 | 13.6660 | 178 | 4.7552 | 240 | 0.0645 |
| 55 | 16.5640 | 117 | 13.5380 | 179 | 4.6272 | 241 | 0.0494 |
| 56 | 16.7000 | 118 | 13.4090 | 180 | 4.5006 | 242 | 0.0363 |
| 57 | 16.8110 | 119 | 13.2780 | 181 | 4.3753 | 243 | 0.0252 |
| 58 | 16.8960 | 120 | 13.1460 | 182 | 4.2515 | 244 | 0.0161 |
| 59 | 16.9560 | 121 | 13.0120 | 183 | 4.1292 | 245 | 0.0091 |
| 60 | 16.9900 | 122 | 12.8770 | 184 | 4.0082 | 246 | 0.0040 |
| 61 | 17.0000 | 123 | 12.7410 | 185 | 3.8888 | 247 | 0.0010 |
| 62 | 17.0000 | 124 | 12.6030 | 186 | 3.7709 | 248 | 0.0000 |
Note: since the cam rotation angle is between 249-360 degrees and the lift is 0mm, it is not listed in the table.
Claims (2)
1. The numerical control cam grinding profile error compensation control method based on Cycle to Cycle feedback control is characterized by comprising the following steps of:
step one, based on CtC feedback control, namely guiding the grinding process of the period by using the grinding information of the previous period, namely the profile error, between successive cycle process control, establishing CtC feedback compensation control strategy for the numerical control cam grinding process:
after the grinding process of one period is finished, measuring the profile error of the grinding wheel according to a certain angle interval, wherein the angle interval can be 0.5 degrees, 1.0 degree and 2.0 degrees; the selection principle is that the larger the cam is, the smaller the angle interval is to ensure the density of the measuring points on the cam profile, the specific numerical value can refer to the angle interval in the cam lift table, and the profile error compensation formula is described by the measuring angle interval of 0.5 degrees and 720 points in total as follows:
ck＝Kk-1(1)
wherein, ckContour error values to be compensated for the kth period;k-1the maximum value of the measurement errors of the k-1 th period; k is a proportional coefficient of compensation, wherein the value law of the proportional coefficient of compensation K is as follows:
wherein,ois a given tolerance;
step two, establishing an CtC feedback control model for the coupled numerical control cam grinding system;
and step three, designing a controller for the CTC feedback control model, and optimizing parameters of the CTC feedback controller through analysis of dynamic and steady-state characteristics of the system to control grinding profile errors within an allowable range and obtain satisfactory grinding precision.
2. The numerical control cam grinding profile error compensation control method based on Cycle to Cycle feedback control as claimed in claim 1, wherein the step two of establishing CtC feedback control model for the coupled numerical control cam grinding system specifically comprises:
(1) a two-axis dynamic process model describing the numerical control cam grinding system is as follows:
wherein x isi,k(t) is a given value of the feed axis (X axis); x is the number ofo,k(t) is the actual reference input value for the feed axis (X-axis); c. Ci,k(t) is the given value of the rotation axis (C-axis); c. Co,k(t) as a practical reference for the axis of rotation (C-axis)Inputting a value; gxA closed loop transfer function for the X axis; gcIs a closed loop transfer function of the C-axis, k is 1,2,3 … n is the number of repeating cycles, t ∈ [1,2,3 … n]Is the cycle time length;
(2) the two-input system of the numerical control cam grinding system is transformed into a single-input problem, namely when a certain cam piece lift is given, the relationship between input values of two shafts is fixed:
ci,k(t)＝f(xi,k(t)) (4)
xi,k(t)＝f-1(ci,k(t)) (5)
then, in the Z-frequency domain: c ═ F (X), X ═ F-1(C)；
(3) Defining a new profile error, namely a profile error:
k＝xo,k(t)-f-1(co,k(t)) (6)
(4) according to the control strategy, establishing a compensation control rule:
(5) in the numerical control grinding control system, the input values of two shafts are discrete sequence values, so that the analysis in a Z domain is as follows:
Xo＝Z-TGx(Xi-K(Xo-f-1(Co))) (8)。
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| CN101653921A (en) * | 2009-09-11 | 2010-02-24 | 湖南大学 | Error compensation method of numerical control grinding contour of camshaft |
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