基于等效加工时间模型的机床退化过程建模

doi:10.13229/j.cnki.jdxbgxb20211087

Abstract

Abstract:

Performance degradation of machine tools affects machining quality and causes other problems. Machining parameters affect the degradation rate. Since the number of machining parameters is often larger than one， the degradation modelling involves multiple variables. A popular modelling method is regression analysis， which has two drawbacks：（a） the accuracy depends on the chosen mean degradation function， and （b） it does not produce the distribution of time to degradation limit. To address these issues， this paper proposes an equivalent processing time based modelling method. The proposed method views each of machining parameters as a stress， uses the product model to combine the machining parameters into a composite stress， and use an accelerated degradation model to combine the composite stress and actual processing time into an equivalent processing time. In such a way， the multivariable degradation modelling problem is simplified into a univariate degradation modelling problem. A real-world example that deals with tool wear is included to illustrate the superiority of the proposed method.

Key words: degradation of machine tools, machining parameters, composite stress, equivalent processing time, tool wear

CLC Number:

TH17

Ren-yan JIANG,Bin-bin XIONG. Modelling degradation processes of machine tools using an equivalent processing time model[J].Journal of Jilin University(Engineering and Technology Edition), 2022, 52(2): 483-490.

Figures/Tables 9

Table 1

Mean degradation function， shape and wear stage"

名称	μ（z）	形状类型	磨损阶段
指数^［31］	$a (e b z - 1)$	凹的	拐点前
幂率^［31］	$(z / a) b$	凹的或凸的	拐点前
对数^［31］	$a l n (1 + z / b)$	凸的	拐点前
线性-指数^{［31，32］}	$a z + b (1 - e - c z)$	增或减且渐近常数	磨耗前
线性-对数	$a z + b l n (1 + c z)$	凸的渐近线性	磨耗前
线性-指数^［31-33］	$a z b e c z$	反S形的	全过程
对数幂率^［34］	$a [l n (1 + z / b)] c$	S形的	不适用

Table 1

Table 2

Fig.1

Table 3

Fig.2

Table 4

Table 5

Table 6

Fig.3

References 36

1	许彬彬, 杨兆军, 陈菲, 等. 非齐次泊松过程的数控机床可靠性建模[J]. 吉林大学学报: 工学版, 2011, 41(2): 210-214.
	Xu Bin-bin, Yang Zhao-jun, Chen Fei, et al. Reliability model of CNC machine tools based on non-homogenous poisson process[J]. Journal of Jilin University(Engineering and Technology Edition), 2011, 41(2):210-214.
2	申桂香, 戚晓艳, 张英芝, 等. 基于等效样本法的系统组件运行可靠性建模[J]. 吉林大学学报: 工学版, 2020, 50(3):914-919.
	Shen Gui-xiang,Qi Xiao-yan,Zhang Ying-zhi, et al. Operational reliability modeling of system components based on equivalent sample method[J]. Journal of Jilin University(Engineering and Technology Edition), 2020, 50(3): 914-919.
3	Lad B K, Kulkarni M S. A parameter estimation method for machine tool reliability analysis using expert judgement[J]. International Journal of Data Analysis Techniques and Strategies, 2010, 2(2): 155-169.
4	Hu W, Yang Z, Chen C, et al. Reliability assessment of machine tools considerin[C]∥IOP Conference Series: Materials Science and Engineering. IOP Publishing, 2021: 032036.
5	Mikolajczyk T, Nowicki K, Bustillo A, et al. Predicting tool life in turning operations using neural networks and image processing[J]. Mechanical Systems and Signal Processing, 2018, 104: 503-513.
6	Lin Y, He S, Lai D, et al. Wear mechanism and tool life prediction of high-strength vermicular graphite cast iron tools for high-efficiency cutting[J]. Wear, 2020, 454: 203319.
7	王新刚, 张鑫垚, 杨禄杰, 等. 竞争失效条件下针对磨损退化数据的刀具可靠性分析[J]. 中国机械工程, 2020, 31(14): 1672-1677+1746.
	Wang Xin-gang, Zhang Xin-yao,Yang Lu-jie, et al. Tool reliability analysis for wear degradation data under competitive failure conditons[J]. China Mechanical Engineering, 2020, 31(14): 1672-1677+1746.
8	Ezugwu E O, Arthur S J, Hines E L. Tool-wear prediction using artificial neural networks[J]. Journal of Materials Processing Technology, 1995, 49(3): 255-264.
9	雷小宝, 廖文和, 谢峰, 等. 义齿用预烧结氧化锆高速铣削时刀具磨损及寿命预测[J]. 南京理工大学学报, 2013, 37(4): 567-572, 578.
	Lei Xiao-bao, Liao Wen-he, Xie Feng, et al. Predict on cutter wear and life in high-speed milling of pre-sintered zirconia used for denture[J]. Journal of Nanjing University of Science and Technology, 2013, 37(4): 567-572, 578.
10	Stephenson D A, Agapiou J S. Metal Cutting Theory and Practice[M].3rd ed. Boca Raton: CRC Press, 2016.
11	Alajmi M S, Almeshal A M. Estimation and optimization of tool wear in conventional turning of 709m40 alloy steel using support vector machine(SVM) with bayesian optimization[J]. Materials, 2021, 14(16): 3773.
12	Quiza R, Figueira L, Davim J P. Comparing statistical models and artificial neural networks on predicting the tool wear in hard machining D2 AISI steel[J]. International Journal of Advanced Manufacturing Technology, 2008, 37(7/8): 641-648.
13	Ramamoorthy K. Tool wear evaluation by stereo vision and prediction by artificial neural network[J]. Journal of Materials Processing Technology, 2001, 112(1): 43-52.
14	Xu L, Huang C, Li C, et al. Prediction of tool wear width size and optimization of cutting parameters in milling process using novel ANFIS-PSO method[J]. Proceedings of the Institution of Mechanical Engineers Part B Journal of Engineering Manufacture, 2020(3): 1-12.
15	Çelik Y H, Kilickap E, Güney M. Investigation of cutting parameters affecting on tool wear and surface roughness in dry turning of Ti-6Al-4V using CVD and PVD coated tools[J]. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 2017, 39(6): 2085-2093.
16	杨兆军, 陈传海, 陈菲, 等. 数控机床可靠性技术的研究进展[J]. 机械工程学报, 2013, 49(21): 130-139.
	Yang Zhao-jun, Chen Chuan-hai, Chen Fei, et al. Progress in the research of reliability technology of machine tools[J]. Journal of Mechanical Engineering, 2013, 49(21): 130-139.
17	Wu P, Wu J, Deng C. SVR-based degradation analysis and reliability assessment for CNC machine tools [C]∥Kota Kinabalu: Applied Computing,Computer Science, and Computer Engineering, Wuhan, 2011: 586-591.
18	Sun B, Xu B, He J, et al. Application of inverse gaussian model in mechanical product degradation model [C]∥2nd International Conference on System Reliability and Safety, Milan, 2017: 238-242.
19	Li S, Ran Y, Zhang G, et al. Accuracy degradation model and residual accuracy life prediction of CNC machine tools based on wiener process [C]∥2nd International Conference on Robotics and Mechantronics, Shaanxi, 2021: 032039.
20	杨志伟, 任工昌, 孟勃敏. 基于性能退化数据的加工中心的可靠性评估[J]. 陕西科技大学学报: 自然科学版, 2011, 29(6): 43-46.
	Yang Zhi-wei, Ren Gong-chang, Meng Bo-min. Reliability evaluation on machining center based on performance degradation data[J]. Journal of Shaanxi University of Science and Technology(Natural Science Edition), 2011, 29(6): 43-46.
21	邓超, 钱有胜, 吴军, 等. BP网络在进给系统定位误差预测中的运用[J]. 振动、测试与诊断, 2017, 37(3): 449-455.
	Deng Chao, Qian You-sheng, Wu Jun, et al. A forecasting method of positioning acurracy for CNC machine tools feed system based on BP neural network[J]. Journal of Vibration, Measurement and Diagnosis, 2017, 37(3): 449-455.
22	Duan C, Deng C, Li N. Reliability assessment for CNC equipment based on degradation data[J]. The International Journal of Advanced Manufacturing Technology, 2019, 100(1-4): 421-434.
23	Peng W, Li Y F, Yang Y J, et al. Bivariate analysis of incomplete degradation observations based on inverse gaussian processes and copulas[J]. IEEE Transactions on Reliability, 2016, 65(2): 624-639.
24	王刚, 陈捷, 洪荣晶, 等. 基于HMM和优化的PF的数控转台精度衰退模型[J]. 振动与冲击, 2018, 37(6): 7-13.
	Wang Gang, Chen Jie, Hong Rong-jing, et al. Model for the positional accuracy degradation of NC rotary tables based on the hidden Markov model and optimized particle fitering[J]. Journal of Vibration and Shock, 2018, 37(6): 7-13.
25	张云, 姜楠, 王立平. 基于Wiener过程的数控转台极小子样可靠性分析[J]. 清华大学学报: 自然科学版, 2019, 59(2): 91-95.
	Zhang Yun, Jiang Nan, Wang Li-ping. Relibility analysis of NC rotary table based on a wiener process for extremely small samples[J]. Journal of Tsinghua University(Science and Technology), 2019, 59(2): 91-95.
26	Guo J, Zheng H, Li B, et al. A bayesian approach for degradation analysis with individual differences [J]. IEEE Access, 2019, 7: 175033-175040.
27	Li Z, Wang Y, Wang K. A data-driven method based on deep belief networks for backlash error prediction in machining centers[J]. Journal of Intelligent Manufacturing, 2017(4): 1-13.
28	Wen J, Gao H, Liu Q, et al. A new method for identifying the ball screw degradation level based on the multiple classifier system[J]. Measurement, 2018, 130: 118-127.
29	Jiang R. A general proportional model and modelling procedure[J]. Quality and Reliability Engineering International, 2012, 28(6): 634-647.
30	Jiang R. Introduction to Quality and Reliability Engineering[M]. Beijing:Science Press and Springer, 2015.
31	Guida M, Pulcini G. The inverse Gamma process: a family of continuous stochastic models for describing state-dependent deterioration phenomena[J]. Reliability Engineering and System Safety, 2013, 120: 72-79.
32	Jiang R. An extended log-linear model for modeling wear processes[C]∥9th IMA International Conference on Modelling in Industrial Maintenance and Reliability, London, 2016: 84-89.
33	Jiang R, Jardine A. Health state evaluation of an item: a general framework and graphical representation[J]. Reliability Engineering and System Safety, 2008, 93(1): 89-99.
34	Jiang R. A new NHPP model for modeling failure process with S-shaped mean cumulative function[C]∥the Proceedings of 2016 11th International Conference on Reliability Maintainability and Safety, Hangzhou, 2016: 17209315.
35	Akaike H T. A new look at the statistical model identification[J]. Automatic Control IEEE Transactions on, 1974, 19(6): 716-723.
36	Jiang R. A trade off BX life and its applications[J]. Reliability Engineering and System Safety, 2013, 113: 1-6.

Metrics

Viewed

Full text

Abstract

Cited

Shared

Discussed

Comments

Recommended 0

No Suggested Reading articles found!

序号	V/（m·min^-1）	f/（mm·tooth^-1）	d/mm	y（t）/μm
序号	V/（m·min^-1）	f/（mm·tooth^-1）	d/mm	t=5	t=10	t=15	t=20	t=25
1	170	0.13	0.2	62	68	81	109	130
2	170	0.23	0.6	48	59	83	94	113
3	170	0.33	1.0	40	70	80	93	99
4	370	0.13	0.6	75	104	131	173	237
5	370	0.23	1.0	75	92	105	153	226
6	370	0.33	0.2	66	70	88	90	94
7	570	0.13	0.6	67	104	134	197	266
8	570	0.23	0.2	58	68	104	149	195
9	570	0.33	1.0	53	79	100	144	171

试验序号	s₁	s₂	s₃	s
1	1.000	1.000	1	1.0000
2	1.000	1.769	3	0.9213
3	1.000	2.538	5	0.8521
4	2.176	1.000	3	1.5900
5	2.176	1.769	5	1.3470
6	2.176	2.538	1	0.9206
7	3.350	1.000	3	1.8860
8	3.350	1.769	1	1.2700
9	3.350	2.538	5	1.3740

项目	初始估计	更新的估计
b₁	0.501 60	0.3947
b₂	-0.548 80	-0.4183
b₃	0.104 10	0.1427
a	34.400 00	38.6000
b	0.212 90	0.1155
c	0.025 78	0.0337
σ	1.257 00	1.1347
ln（L）	-177.454 00	-172.9840

项目	a₀	a₁	a₂	a₃	a₄
系数值	0.6871	0.3171	-0.3869	0.1112	0.6033
p值	0.0307	0.0000	0.0000	0.0033	0.0000

项目	本文模型		回归模型
项目	ε_A	ε_max	ε_A	ε_max
t=5	0.1431	0.2422	0.1618	0.5013
t=10	0.0817	0.1454	0.1066	0.2279
t=15	0.0451	0.0904	0.0846	0.1545
t=20	0.0586	0.1288	0.0670	0.1135
t=25	0.1159	0.2537	0.1751	0.4157
SSR/N	165.5	-	363.8	-
k	6	-	5	-
AIC	241.9	-	275.3	-

Modelling degradation processes of machine tools using an equivalent processing time model

RICH HTML

PDF (PC)

Abstract

Cite this article

share this article

Figures/Tables 9

References 36

Related Articles 8

Metrics

Comments

Recommended 0

[1]	Fei-yue DENG, LYUHao-yang,Xiao-hui GU,Ru-jiang HAO. Fault diagnosis of high⁃speed train axle bearing based on a lightweight neural network Shuffle⁃SENet [J]. Journal of Jilin University(Engineering and Technology Edition), 2022, 52(2): 474-482.
[2]	Hong-xun ZHAO,Zhao-jun YANG,Chuan-hai CHEN,Hai-long TIAN,Li-ping WANG. Optimal design of acceleration test of motorized spindle of numerical control Machine Tool considering parameter weight [J]. Journal of Jilin University(Engineering and Technology Edition), 2022, 52(2): 409-416.
[3]	Li-juan YU,Ang LIU,Zhao-jun YANG,Hai-long TIAN,Chuan-hai CHEN,Jing-wen GAO. Reliability analysis of numerical control machine tools based on analytic network process and date enevalopment analys [J]. Journal of Jilin University(Engineering and Technology Edition), 2022, 52(2): 400-408.
[4]	Shao-jiang DONG,Peng ZHU,Xue-wu PEI,Yang LI,Xiao-lin HU. Fault diagnosis of rolling bearing under variable operating conditions based on subdomain adaptation [J]. Journal of Jilin University(Engineering and Technology Edition), 2022, 52(2): 288-295.
[5]	Guo-fa LI,Yan-bo WANG,Jia-long HE,Ji-li WANG. Research progress and development trend of health assessment of electromechanical equipment [J]. Journal of Jilin University(Engineering and Technology Edition), 2022, 52(2): 267-279.
[6]	Gen-bao ZHANG,Hao LI,Yan RAN,Qiu-jin LI. A transfer learning model for bearing fault diagnosis [J]. Journal of Jilin University(Engineering and Technology Edition), 2020, 50(5): 1617-1626.
[7]	WANG Qian, ZHAO Ding-xuan, ZHAO Ying, CHEN Na. Dynamic analysis of carrier helicopter on complex deck [J]. 吉林大学学报(工学版), 2017, 47(4): 1109-1113.
[8]	ZHANG Biao，ZHAO Ke-ding，LI Ge-qiang . Nonlinear control of friction in passive force servo system [J]. 吉林大学学报(工学版), 2008, 38(06): 1348-1353.