The ball screw system is one of the most core components of CNC machine tool, and its thermal positioning error directly affects the machining accuracy of parts. Establishing a data-based thermal error model is currently a popular method to predict this thermal error. Uncertain disturbances are unavoidable in reality. However, most of the existing thermal error models are deterministic, which cannot consider the uncertainty and generally can only provide the predictive value. To quantify the uncertainty of thermal error from the ball screw system, this paper proposes an interval prediction method, in which gated recurrent unit (GRU) neural network is embedded into the model and prediction interval (PI) evaluation indexes are used to determine the model parameters. Both the temporal and spatial characteristics of thermal error in the ball screw system are taken into account by the proposed method. The experimental data has verified that the proposed method can effectively generate PIs for the thermal error of ball screw system.
MayrJJedrzejewskiJUhlmannE, et al. Thermal issues in machine tools. CIRP Ann Manuf Technol2012; 61(2): 771–791.
2.
JuXLuJJinH.Study on heat transfer characteristics and thermal error suppression method of cylindrical giant magnetostrictive actuator for ball screw preload. Proc IMechE, Part B: J Engineering Manufacture2020; 235(5): 782–794.
3.
SpurGHoffmannEPaluncicZ, et al. Thermal behaviour optimization of machine tools. CIRP Ann Manuf Technol1988; 37(1): 401–405.
4.
HuangSC.Analysis of a model to forecast thermal deformation of ball screw feed drive systems. Int J Mach Tools Manuf1995; 35(8): 1099–1104.
5.
YangJZhangDMeiX, et al. Thermal error simulation and compensation in a jig-boring machine equipped with a dual-drive servo feed system. Proc IMechE, Part B: J Engineering Manufacture2015; 229(1): 43–63.
6.
ZhangJLiBZhouC, et al. Positioning error prediction and compensation of ball screw feed drive system with different mounting conditions. Proc IMechE, Part B: J Engineering Manufacture2016; 230(12): 2307–2311.
7.
GaoXZhangKZhangZ, et al. XGBoost-based thermal error prediction and compensation of ball screws. Proc IMechE, Part B: J Engineering Manufacture2024; 238(1–2): 151–163.
8.
LiuJMaCGuiH, et al. Thermally-induced error compensation of spindle system based on long short term memory neural networks. Appl Soft Comput2021; 102: 107094.
9.
YangJYuanJNiJ.Thermal error mode analysis and robust modeling for error compensation on a CNC turning center. Int J Mach Tools Manuf1999; 39(9): 1367–1381.
10.
MayrJBlaserPRyserA, et al. An adaptive self-learning compensation approach for thermal error on 5-axis machine tools handling an arbitrary set of sample rates. CIRP Ann Manuf Technol2018; 67(1): 551–554.
11.
FengWLiZGuQ, et al. Thermally induced positioning error modelling and compensation based on thermal characteristic analysis. Int J Mach Tools Manuf2015; 93: 26–36.
12.
LiTZhaoCZhangY.Prediction method of thermal errors of the screw system in lathes based on moving thermal network. Precis Eng2019; 59: 166–173.
13.
CaoLParkCChungS.Real-time thermal error prediction and compensation of ball screw feed systems via model order reduction and hybrid boundary condition update. Precis Eng2022; 77: 227–240.
14.
AbdulshahedAMLongstaffAPFletcherS, et al. Thermal error modelling of a gantry-type 5-axis machine tool using a Grey Neural Network Model. J Manuf Syst2016; 41: 130–142.
15.
YangHXingRDuF.Thermal error modelling for a high-precision feed system in varying conditions based on an improved Elman network. Int J Adv Manuf Tech2020; 106: 279–288.
16.
ShiHJiangCYanZ, et al. Bayesian neural network-based thermal error modeling of feed drive system of CNC machine tool. Int J Adv Manuf Tech2020; 108: 3031–3044.
17.
GaoXGuoYHansonDA, et al. Thermal error prediction of ball screws based on PSO-LSTM. Int J Adv Manuf Tech2021; 116: 1721–1735.
18.
ChenYChenJXuG.A data-driven model for thermal error prediction considering thermoelasticity with gated recurrent unit attention. Measurement2021; 184: 109891.
19.
LiTSunTZhangY, et al. Dynamic memory intelligent algorithm used for prediction of thermal error reliability of ball screw system. Appl Soft Comput2022; 125: 109183.
20.
GuiHLiuJMaC, et al. New machine learning application platform for spatial-temporal thermal error prediction and control with STFGCN for ball screw system. Mech Syst Signal Process2023; 192: 110240.
21.
LiMMaCLiuJ, et al. Thermal error prediction of precision boring machine tools based on extreme gradient boosting algorithm-improved sailed fish optimizer-bi-directional ordered neurons-long short-term memory neural network model and physical-edge-cloud system. Eng Appl Artif Intel2024; 127: 107278.
22.
LiTYuanJZhangY, et al. Time-varying reliability prediction modeling of positioning accuracy influenced by frictional heat of ball-screw systems for CNC machine tools. Precis Eng2020; 64: 147–156.
23.
LiuKWuJLiuH, et al. Reliability analysis of thermal error model based on DBN and Monte Carlo method. Mech Syst Signal Process2021; 146: 107020.
24.
WuCHKungYT.Thermal analysis for the feed drive system of a CNC machine center. Int J Mach Tools Manuf2003; 43: 1521–1528.
25.
KhosraviANahavandiSCreightonD.Construction of optimal prediction intervals for load forecasting problems. IEEE Trans Power Syst2010; 25(3): 1496–503.
26.
KhosraviANahavandiSCreightonD.A prediction interval-based approach to determine optimal structures of neural network metamodels. Expert Syst Appl2010; 37(3): 2377–2387.
27.
KhosraviANahavandiSCreightonD, et al. Lower upper bound estimation method for construction of neural network-based prediction intervals. IEEE Trans Neural Netw2011; 22(3): 337–346.
28.
KhosraviANahavandiSCreightonD, et al. Comprehensive review of neural network-based prediction intervals and new advances. IEEE Trans Neural Netw2011; 22(9): 1341–1356.
29.
KhosraviAMazloumiENahavandiS, et al. A genetic algorithm-based method for improving quality of travel time prediction intervals. Transp Res Part C Emerg Technol2011; 19(6): 1364–1376.
30.
ChoKvan MerriënboerBGulcehreC, et al. Learning phrase representations using RNN encoder-decoder for statistical machine translation. In: Proceedings of the 2014 conference on empirical methods in natural language processing (EMNLP), Doha, Qatar, 25–29 October 2014.
31.
QinQLiLZhaoG, et al. Uncertainty quantification for spindle axial thermal error of CNC machine tools considering hysteresis effect. Precis Eng2023; 83: 159–169.
32.
LiZTanZChenY, et al. Thermal error prediction of ball screw feed system based on inverse heat transfer analysis. Int J Adv Manuf Tech2022; 122: 2607–2624.
33.
TangJLiuGPanQ.A review on representative swarm intelligence algorithms for solving optimization problems: applications and trends. IEEE CAA J Autom Sinica2021; 8(10): 1627–1643.
34.
EberhartRKennedyJ.A new optimizer using particle swarm theory. In: Proceedings of the sixth international symposium on micro machine and human science, Nagoya, Japan, 4–6 October 1995, pp.39–43. New York: IEEE.
35.
ShiYEberhartR.A modified particle swarm optimizer. In: Proceedings of IEEE international conference on evolutionary computation, Anchorage, AK, USA, 4–9 May 1998, pp.69–73. New York: IEEE.
36.
PassinoKM.Biomimicry of bacterial foraging for distributed optimization and control. IEEE Control Syst Mag2002; 22(3): 52–67.
37.
DorigoMManiezzoVColorniA.Ant system: optimization by a colony of cooperating agents. IEEE Trans Syst Man Cybern B Cybern1996; 26(1): 29–41.
