Research Papers

Prediction of Comprehensive Thermal Error of a Preloaded Ball Screw on a Gantry Milling Machine

[+] Author and Article Information
Kuo Liu, Haibo Liu, Te Li

Key Laboratory for Precision and
Non-Traditional Machining Technology of
Ministry of Education,
Dalian University of Technology,
Dalian 116024, China

Yongqing Wang

Key Laboratory for Precision and
Non-Traditional Machining Technology of
Ministry of Education,
Dalian University of Technology,
Dalian 116024, China
e-mail: yqwang@dlut.edu.cn

Mingjia Sun, Yuliang Wu

State Key Laboratory,
Shenyang Machine Tool (Group) Co., Ltd.,
Shenyang 110142, China

1Corresponding author.

Manuscript received March 5, 2017; final manuscript received June 24, 2017; published online December 18, 2017. Assoc. Editor: Jaydeep Karandikar.

J. Manuf. Sci. Eng 140(2), 021004 (Dec 18, 2017) (9 pages) Paper No: MANU-17-1130; doi: 10.1115/1.4037236 History: Received March 05, 2017; Revised June 24, 2017

The conception of the comprehensive thermal error of servo axes is given. Thermal characteristics of a preloaded ball screw on a gantry milling machine is investigated, and the error and temperature data are obtained. The comprehensive thermal error is divided into two parts: thermal expansion error ((TEE) in the stroke range) and thermal drift error ((TDE) of origin). The thermal mechanism and thermal error variation of preloaded ball screw are expounded. Based on the generation, conduction, and convection theory of heat, the thermal field models of screw caused by friction of screw-nut pairs and bearing blocks are derived. The prediction for TEE is presented based on thermal fields of multiheat sources. Besides, the factors influencing TDE are analyzed, and the model of TDE is established based on the least square method. The predicted thermal field of the screw is analyzed. The simulation and experimental results indicate that high accuracy stability can be obtained using the proposed model. Moreover, high accuracy stability can still be achieved even if the moving state of servo axis changes randomly, the screw is preloaded, and the thermal deformation process is complex. Strong robustness of the model is verified.

Copyright © 2018 by ASME
Your Session has timed out. Please sign back in to continue.


Fu, J. , and Chen, Z. , 2004, “ Research on Identification of Thermal Dynamics Characteristics Parameter of Precision Machine Based on Singular Value Decomposition,” J. Zhejiang Univ.: Eng. Sci., 38(4), pp. 474–476.
Ni, J. , 1997, “ CNC Machine Accuracy Enhancement Through Real-Time Error Compensation,” ASME J. Manuf. Sci. Eng., 119(4B), pp. 717–725. [CrossRef]
Han, Z. Y. , Jin, H. Y. , Liu, Y. L. , and Fu, H. Y. , 2013, “ A Review of Geometric Error Modeling and Error Detection for CNC Machine Tool,” Appl. Mech. Mater., 303–306, pp. 627–631. [CrossRef]
Wu, C. W. , Tang, C. H. , Chang, C. F. , and Shiao, Y. S. , 2011, “ Thermal Error Compensation Method for Machine Center,” Int. J. Adv. Manuf. Technol., 59(5–8), pp. 681–689.
Zhu, J. , Ni, J. , and Shih, A. J. , 2008, “ Robust Machine Tool Thermal Error Modeling Through Thermal Mode Concept,” ASME J. Manuf. Sci. Eng., 130(6), p. 061006. [CrossRef]
Pajor, M. , and Zapłata, J. , 2011, “ Compensation of Thermal Deformations of the Feed Screw in a CNC Machine Tool,” Adv. Manuf. Sci. Technol., 35(4), pp. 9–17. http://advancesmst.prz.edu.pl/pdfy/01a-Pajr-Zapala.pdf
Horejs, O. , Mares, M. , Kohut, P. , Barta, P. , and Hornych, J. , 2010, “ Compensation of Machine Tool Thermal Errors Based on Transfer Functions,” MM Sci. J., 3, pp. 162–165. https://www.researchgate.net/profile/Otakar_Horejs/publication/267202023_Compensation_of_machine_tool_thermal_errors_based_on_transfer_functions/links/566e8f5208ae62b05f0b546e.pdf?inViewer=0&pdfJsDownload=0&origin=publication_detail
Lin, W. , Fu, J. , Chen, Z. , and Xu, Y. , 2009, “ Modeling of NC Machine Tool Thermal Error Based on Adaptive Best-Fitting WLS-SVM,” J. Mech. Eng., 45(3), pp. 178–182. [CrossRef]
Miao, E. , Gong, Y. , Xu, Z. , and Zhou, X. , 2015, “ Comparative Analysis of Thermal Error Compensation Model Robustness of CNC Machine Tools,” J. Mech. Eng., 51(7), pp. 130–135. [CrossRef]
Zhang, Y. , and Yang, J. , 2011, “ Modeling for Machine Tool Thermal Error Based on Grey Model Preprocessing Neural Network,” J. Mech. Eng., 47(7), pp. 134–139. [CrossRef]
Li, Y. , and Yang, J. , 2006, “ Application of Grey System Model to Thermal Error Modeling on Machine Tools,” China Mech. Eng., 17(23), pp. 2439–2442.
Ozkan, M. T. , 2013, “ Experimental and Artificial Neural Network Study of Heat Formation Values of Drilling and Boring Operations on Al 7075 T6 Workpiece,” Indian J. Eng. Mater. Sci., 20(4), pp. 259–268. http://nopr.niscair.res.in/handle/123456789/20961
Jin, Z. F. , and Wang, P. , 2012, “ Neural Network–Based Thermal Error Modeling in Ball Screw,” Modular Machine Tool and Automatic Manufacturing Technique, 1, pp. 67–70.
Liu, G. , Zhang, H. , Cao, H. , Zhao, H. , and Yang, J. , 2005, “ Study on the Application of the Neural Network Theories in the NC Machine Tool Error Modeling,” Modern Manuf. Eng., 8(8), pp. 20–23.
Feng, W. L. , Li, Z. H. , Gu, Q. Y. , and Yang, J. G. , 2015, “ Thermally Induced Positioning Error Modeling and Compensation Based on Thermal Characteristic Analysis,” Int. J. Mach. Tool Manuf., 93, pp. 26–36. [CrossRef]
Liu, K. , Liu, Y. , Sun, M. , Wu, Y. , and Zhu, T. , 2015, “ Comprehensive Thermal Compensation of the Servo Axes of CNC Machine Tools,” Int. J. Adv. Manuf. Technol., 85(9), pp. 2715–2728.
Chen, C. , Qiu, Z. R. , Li, X. F. , Dong, C. J. , and Zhang, C. Y. , 2011, “ Temperature Field Model of Ball Screws Used in Servo Systems,” Opt. Precis. Eng., 19(5), pp. 1151–1158. [CrossRef]
Liu, K. , Sun, M. , Wu, Y. , and Zhu, T. , 2016, “ Comparison of Accuracy Stability Using a Thermal Compensator and Grating Ruler,” J. Braz. Soc. Mech. Sci. Eng., 38(8), pp. 1–9. [CrossRef]
Zhang, J. Z. , and Chang, H. P. , 2009, Heat Transfer, Science Press, Beijing, China.
Chen, C. , 2010, “ Structure Analysis and Research on Drive System Thermal Error Model of θFXZ Type CMMs,” Tianjin University, Tianjin, China.
Fraser, S. , Attia, M. , and Osman, M. , 1998, “ Modelling, Identification and Control of Thermal Deformation of Machine Tool Structures—Part I: Concept of Generalized Modelling,” ASME J. Manuf. Sci. Eng., 120(3), pp. 623–631. [CrossRef]
Horejs, O. , 2007, “ Thermo-Mechanical Model of Ball Screw With Non-Steady Heat Sources,” International Conference on Thermal Issues in Emerging Technologies: Theory and Application (THETA), Cairo, Egypt, Jan. 3–6, pp. 133–137.
Du, G. , Chen, J. , and Cao, R. J. , 2010, “ A Optimization Design Platform for Wind Turbine Airfoil Based on Isight,” Acta Energiae Sol. Sin., 31(7), pp. 891–895.
Liu, K. , Liu, Y. , Sun, M. , Li, X. , and Wu, Y. , 2016, “ Spindle Axial Thermal Growth Modeling and Compensation on CNC Turning Machines,” Int. J. Adv. Manuf. Technol., 87(5), pp. 2285–2292. [CrossRef]


Grahic Jump Location
Fig. 1

Thermal characteristics investigation using a laser interferometer

Grahic Jump Location
Fig. 2

Thermal errors and temperatures of Z-axis

Grahic Jump Location
Fig. 3

The decomposition diagram of comprehensive thermal errors

Grahic Jump Location
Fig. 4

The decomposed TEE and TDE

Grahic Jump Location
Fig. 5

(a) Thermal deformation process of screw: (1) before strain relief, (2) threshold of strain, (3) before thermal equilibrium, and (4) thermal equilibrium; (b) Thermal error variation of the final test point: (1) before strain relief, (2) threshold of strain, (3) before thermal equilibrium, (4) thermal equilibrium, and (5) cooling down

Grahic Jump Location
Fig. 6

Discretized screw: (1) heat production, (2) heat conduction, and (3) heat convection

Grahic Jump Location
Fig. 7

The predicted temperature fields in the range of stroke

Grahic Jump Location
Fig. 8

The temperature variation of screw after stopping

Grahic Jump Location
Fig. 9

Simulation results

Grahic Jump Location
Fig. 10

Diagram of thermal error compensation

Grahic Jump Location
Fig. 11

Experimental results




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In