Dimensional Error Compensation Based on Data-Driven Sliding Mode Terminal Iterative Learning Control for CNC Batch Grinding
Abstract
:1. Introduction
2. Grinding Protocol and Problem Formulation
2.1. Grinding Model
2.2. Dimensional Error Analysis
2.3. Problem Formulation
3. Sliding Mode Terminal Iterative Learning Compensation Method
- 1.
- Define as the terminal dimensional error of the workpiece, which is shown as Equation (15):Here, is the terminal dimension of the workpiece, which is measurable by laser sensor. is the desired dimension of the workpiece. If is within the accepted error limit , the error compensation is ignored; otherwise, the compensation is operated.Substituting Equation (13) into Equation (15) yields Equation (16). Equation (16) is transformed as follows:
- 2.
- Introduce an iteration-dependent slide surface function and an index function [26], which are two common functions in sliding mode control. The Equations are shown as follows:Substituting Equation (16) and Equation (17) into Equation (18), the Equation (18) is transformed into Equation (19). The Equation (19) is shown as follows:In optimal conditions, the control input can be obtained in Equation (20), which is shown as follows:
- 3.
- In the upper part, the compensation control input is deduced, which is the function of the previous two-dimensional errors, the previous dimension, and the estimation parameter. In this part, the convergence analysis of the grinding system with the control input is derived.In combination with Equation (20) and Equation (13), in virtue of Equation (16), then Equation (21) can be deduced. It is shown as follows [26]:According to the above Equation (21), it is easy to derive the Equation (22),Therefore, for the sliding surface Equation (17), it can be derived Equation (23),Since , .Then =0. Since is bounded, is bounded. Therefore, the following Equation (24) can be derived.Therefore, the sliding surface will converge to 0.Substituting Equation (17) into Equation (24), =0. Then, Equation (25) can be deduced.Since , the following Equation (26) can be derived.Therefore, the terminal error will converge to 0.As mentioned above, the convergence analysis is made.
- 4.
- As it is mentioned in Section 2, the system input is constant of every cycle at an arbitrary sampling time for one batch and it is executed by X axis. The compensation is executed by the compensation module if it is necessary; the compensation input for the workpiece is computed as follows.
4. Simulation and Verification
4.1. Simulation
4.2. Experimental Investigation
5. Conclusions
- (1)
- Based on the theory of sliding mode terminal iterative learning control, the compensation method is presented. This method only needs to measure the terminal dimension using a touch probe, without using other sensors to detect all kinds of error sources. Moreover, there is no need of model information, which is data-driven;
- (2)
- Step and impulse input were introduced into the compensation module to simulate errors. Through many simulations, the values of compensation parameters were defined, and the simulation results showed that the compensation effectiveness was obvious;
- (3)
- In order to verify the compensation performance in an actual industrial environment, two groups of experiment were carried out on the machine tool. Based on the comparisons, the compensation parameters defined by simulation performed well and the performance effectiveness of this proposed compensation method was obvious. In the experiment, for 68 pieces of indexable inserts, the qualified rate increased from 48.5% to 95%.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Parameters | Value |
---|---|
diamond wheel | resin bonded, mesh #220, concentration 100% |
wheel diameter (mm) | 350 |
wheel rotation (mm/s) | 18 |
feed rate (mm/s) | 0.03–0.05 |
no spark time(s) | 3 |
coolant | water soluble |
temperature of coolant (°C) | 12–13 |
No. | Dimensions of the Group Workpieces without Compensation (mm) | Dimensions of the Group Workpieces with Compensation (mm) |
---|---|---|
1 | 9.422 | 9.422 |
2 | 9.424 | 9.434 |
3 | 9.428 | 9.438 |
4 | 9.428 | 9.434 |
5 | 9.43 | 9.436 |
6 | 9.43 | 9.436 |
7 | 9.428 | 9.434 |
8 | 9.428 | 9.434 |
9 | 9.428 | 9.434 |
10 | 9.428 | 9.434 |
11 | 9.432 | 9.438 |
12 | 9.432 | 9.434 |
13 | 9.436 | 9.438 |
14 | 9.434 | 9.432 |
15 | 9.432 | 9.431 |
16 | 9.432 | 9.436 |
17 | 9.428 | 9.432 |
18 | 9.428 | 9.436 |
19 | 9.43 | 9.438 |
20 | 9.434 | 9.442 |
21 | 9.436 | 9.436 |
22 | 9.434 | 9.434 |
23 | 9.438 | 9.438 |
24 | 9.434 | 9.434 |
25 | 9.434 | 9.434 |
26 | 9.434 | 9.434 |
27 | 9.434 | 9.434 |
28 | 9.434 | 9.434 |
29 | 9.434 | 9.434 |
30 | 9.434 | 9.434 |
31 | 9.434 | 9.434 |
32 | 9.434 | 9.434 |
33 | 9.438 | 9.438 |
34 | 9.436 | 9.436 |
35 | 9.436 | 9.436 |
36 | 9.436 | 9.436 |
37 | 9.436 | 9.436 |
38 | 9.436 | 9.436 |
39 | 9.436 | 9.436 |
40 | 9.434 | 9.434 |
41 | 9.436 | 9.436 |
42 | 9.438 | 9.438 |
43 | 9.44 | 9.439 |
44 | 9.446 | 9.440 |
45 | 9.448 | 9.436 |
46 | 9.446 | 9.434 |
47 | 9.446 | 9.434 |
48 | 9.448 | 9.436 |
49 | 9.45 | 9.438 |
50 | 9.452 | 9.436 |
51 | 9.448 | 9.432 |
52 | 9.45 | 9.434 |
53 | 9.454 | 9.438 |
54 | 9.452 | 9.432 |
55 | 9.45 | 9.431 |
56 | 9.452 | 9.438 |
57 | 9.452 | 9.438 |
58 | 9.45 | 9.436 |
59 | 9.45 | 9.436 |
60 | 9.446 | 9.432 |
61 | 9.446 | 9.436 |
62 | 9.444 | 9.434 |
63 | 9.442 | 9.432 |
64 | 9.444 | 9.438 |
65 | 9.444 | 9.438 |
66 | 9.444 | 9.438 |
67 | 9.444 | 9.438 |
68 | 9.44 | 9.434 |
Number of workpieces within the dimensional error tolerance 0.005 mm | 33 | 65 |
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Chen, T.; Tian, X. Dimensional Error Compensation Based on Data-Driven Sliding Mode Terminal Iterative Learning Control for CNC Batch Grinding. Appl. Sci. 2023, 13, 1822. https://doi.org/10.3390/app13031822
Chen T, Tian X. Dimensional Error Compensation Based on Data-Driven Sliding Mode Terminal Iterative Learning Control for CNC Batch Grinding. Applied Sciences. 2023; 13(3):1822. https://doi.org/10.3390/app13031822
Chicago/Turabian StyleChen, Tiantian, and Xincheng Tian. 2023. "Dimensional Error Compensation Based on Data-Driven Sliding Mode Terminal Iterative Learning Control for CNC Batch Grinding" Applied Sciences 13, no. 3: 1822. https://doi.org/10.3390/app13031822
APA StyleChen, T., & Tian, X. (2023). Dimensional Error Compensation Based on Data-Driven Sliding Mode Terminal Iterative Learning Control for CNC Batch Grinding. Applied Sciences, 13(3), 1822. https://doi.org/10.3390/app13031822