The transmission efficiency is an aggregative indicator that directly reflects the overall performance of the ball screw. While most researches focus on calculating transmission efficiency under different working conditions, few of them investigate the influencing factors that lead to the transmission efficiency change. To this end, this paper proposed a new analysis method to acquire the changing transmission efficiency with running revolution based on wear volume calculation considering lubrication. The fractal theory is introduced to describe the surface roughness, through which the modified expression of the wear volume between the balls and raceway is proposed. By submitting the wear volume into the transmission efficiency analysis model, the change of the transmission efficiency is obtained. From the experimental results, two obvious stages are shown: the rising stage with the increase of the wear volume and a steady stage as the initial preload vanishes. For higher transmission efficiency for the preloaded ball screw of the same type, the ratio of 0.75, which compares the initial preload to the external load, has some certain reference for the practical application.
HuJWangMZanT. The kinematics of ball-screw mechanisms via the slide–roll ratio. Mech Mach Theory2014; 79: 158–172.
2.
LinMCVelinskySARavaniB. Design of the ball screw mechanism for optimal efficiency. J Mech Des1994; 116: 856–861.
3.
WeiCCLiouWLLaiRS. Wear analysis of the offset type preloaded ball–screw operating at high speed. Wear2012; 292: 111–123.
4.
Xu XHWang YHXuD. Wear prediction of ball screw based on adhesive wear. Applied Mechanics & Materials2014; 635–637: 261–265.
5.
LiuXMaoXHeY, et al.A new approach to identify the ball screw wear based on feed motor current. In: proceedings of the international conference on artificial intelligence and robotics and the international conference on automation. Control and Robotics Engineering2016: 1–5. https://doi.org/10.1145/2952744.2956682
6.
PichlerKKlinglmayrJPichler-SchederM. Detecting wear in a ball screw using a data-driven approach. In: 2018 IEEE International Conference on Systems, Man, and Cybernetics (SMC), IEEE, 2018, 3123–3128.
7.
Zhou CGZhou HXFeng HT. Experimental analysis of the wear coefficient of double-nut ball screws. Wear2020; 446: 203201.
8.
MajumdarATien CL. Fractal characterization and simulation of rough surfaces. Wear1990; 136: 313–327.
9.
ZhouGYLeuMCBlackmoreD. Fractal geometry model for wear prediction. Wear1993; 170: 1–14.
10.
ShirongGGouanC. Fractal prediction models of sliding wear during the running-in process. Wear1999; 231: 249–255.
11.
LiouJLLinJF. A modified fractal microcontact model developed for asperity heights with variable morphology parameters. Wear2010; 268: 133–144.
12.
YinXKomvopoulosK. An adhesive wear model of fractal surfaces in normal contact. Int J Solids Struct2010; 47: 912–921.
13.
LiuZXuMZhangH, et al.Nonlinear dynamic analysis of variable lead preloaded single nut ball screw considering the variation of working parameters. Nonlinear Dyn2022: 1–26. https://doi.org/10.1007/s11071-022-07223-x
14.
ZhaoJLinMSongX, et al.Analysis of the precision sustainability of the preload double-nut ball screw with consideration of the raceway wear. Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology2020; 234: 1530–1546.
15.
OyangurenALarranagaJUlaciaI. Thermo-mechanical modelling of ball screw preload force variation in different working conditions. The International Journal of Advanced Manufacturing Technology2018; 97: 723–739.
16.
HuangYCKaoCHChenSJ. Diagnosis of the hollow ball screw preload classification using machine learning. Applied Sciences2018; 8: 1072.
17.
LiFJiangYLiT, et al.An improved dynamic model of preloaded ball screw drives considering torque transmission and its application to frequency analysis. Advances in Mechanical Engineering2017; 9: 1687814017710580.
18.
Zhou HXZhou CGWang XY, et al.Degradation reliability modeling for two-stage degradation ball screws. Prec Eng2022; 73: 347–362.
19.
Zhou CGFeng HTOuY. A new model for predicting the mechanical efficiency of ball screws based on the empirical equations for the friction torque of rolling bearings. Advances in Mechanical Engineering2018; 10: 1687814018800173.
20.
Berry MVLewis ZVNye JF. On the weierstrass-mandelbrot fractal function. Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences1980; 370: 459–484.
21.
MajumdarABhushanB. Fractal model of elastic-plastic contact between rough surfaces. J Tribol1991; 113(1): 1–11.
22.
LiuJMaCWangS, et al.Contact stiffness of spindle-tool holder based on fractal theory and multi-scale contact mechanics model. Mech Syst Signal Process2019; 119: 363–379.
23.
HamrockBJDowsonD. Isothermal elastohydrodynamic lubrication of point contacts: part III—fully flooded results. Lubr Technol1977; 92(2): 264–275.
24.
CaoSMischlerS. A lubricated tribocorrosion model incorporating surface roughness. Biotribology2021; 26: 100181.
25.
LiuJMaCWangS. Precision loss modeling method of ball screw pair. Mech Syst Signal Process2020; 135: 106397.
26.
ZhouCGXieJLFengHT. Investigation of the decompression condition of double-nut ball screws considering the influence of the geometry error and additional elastic unit. Mech Mach Theory2020; 156: 104164.
27.
LiuJFengHZhouC. Static load distribution and axial static contact stiffness of a preloaded double-nut ball screw considering geometric errors. Mech Mach Theory2022; 167: 104460.
28.
ZhouHXZhouCGFengHT, et al.Theoretical and experimental analysis of the preload degradation of double-nut ball screws. Prec Eng2020; 65: 72–90.
29.
YokoyamaKTohyamaASuzukiT. Evaluation of friction torque of rolling bearing. Journal of the Japan Society for Precision Engineering1996; 62: 210–214.
30.
HamrockBJDowsonD. Ball bearing lubrication: the elastohydrodynamics of elliptical contacts. J Lubr Technol1981. https://doi.org/10.1115/1.3253193
31.
HarrisTAKotzalasMN. Rolling Bearing Analysis 2 Volume Set. 2006.
32.
ZhangLCZhouCG. Experimental study on the coefficient of friction of the ball screw. J Tribol2021; 144: 1–18.
