journal article·2026-06-23Open access

Temperature-Induced Error Compensation Method for a Bearing Inner Diameter Measurement System Based on CNN-LSTM–Attention

Bohan Fu, Junjie Zong, Jiaming He, Daogong Rao, Zheng Ge

Applied Sciences· Volume 16· Issue 13

Abstract

The dimensional accuracy of the bearing inner ring is critical for the operational performance and reliability of high-end equipment. However, nonlinear deformation of the measurement mechanism caused by temperature variations and temperature drift of the sensor significantly affect the measurement accuracy. In this study, a novel online measurement system for bearing inner diameter was designed, which integrates a two-degree-of-freedom motion mechanism and an adaptive elastic measurement probe. To compensate for the measurement errors caused by temperature effects in the proposed system, an intelligent compensation method based on a CNN-LSTM–Attention hybrid model was proposed. The raw sensor signals and ambient temperature were used as the model inputs, and an end-to-end nonlinear mapping relationship for the actual bearing inner diameter deviation was established without the need to construct complex explicit physical equations. The experimental results show that, within the investigated temperature interval of 11–21 °C, the proposed method controls the measurement error within 1.87 μm, thereby satisfying the dimensional measurement requirement for P4-grade bearings with a tolerance of 0 to −6 μm.
Source: crossref · Quality: baseline

Research context

OpenAlex topics: Advanced Measurement and Metrology Techniques · Sensor Technology and Measurement Systems · Machine Fault Diagnosis Techniques

SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.

Affiliations

School of Information Science and Engineering (School of Cyber Science and Technology), Zhejiang Sci-Tech University, Hangzhou 310018, China

Chen Tong Bearing Company-Zhejiang, Quzhou 324299, China

Taizhou Institute of Zhejiang University, Taizhou 317600, China

Funding

The Key R&D projects of Science and Technology Department of Zhejiang Province · Zhejiang Provincial Natural Science Foundation

References (31)

Show source-provided references
1. Failure analysis of automobile engine pump shaft bearing10.1177/16878140211009411 ↗
2. Investigation on clinching assembly process of automobile wheel hub bearings10.1177/0954407020987912 ↗
3. Repeatability assessment of FBG-based strain measurements for bearing fault diagnostics10.1088/2515-7647/adec29 ↗
4. A novel temperature drift compensation method based on LSTM for NMR sensor10.1016/j.measurement.2024.115573 ↗
5. Cui, Y.X., Gao, P.F., Tang, W.C., Mo, G.W., and Yin, J.W. (2022). Adaptive thin film temperature sensor for bearing’s rolling elements temperature measurement. Sensors, 22.10.3390/s22082838 ↗
6. Methodological approach to the measurement of ball bearing grooves geometric parameters based on coordinate measuring machine10.24425/mms.2025.152776 ↗
7. Measurement of roundness on the bearing by varying probe length in CMM10.1016/j.matpr.2021.01.146 ↗
8. Accurate dimensional characterization of the textured inner surface of the bearing bushing by the mean of a new measurement instrument10.1016/j.measurement.2025.117068 ↗
9. Measurement techniques for complex surface based on a non-contact measuring machine10.1007/s00170-022-09803-y ↗
10. Application of a He3Ne infrared laser source for detection of geometrical dimensions of cracks and scratches on finished surfaces of metals10.1016/j.optlaseng.2013.05.002 ↗
11. Virtual wavefront calibration method based on ray tracing for alignment error compensation in the interferometric bearing ball measurement system10.1007/s00340-019-7156-5 ↗
12. A new continuous dynamic system for measuring the sphericity error of bearing balls10.1088/1361-6501/acb9ab ↗
13. Tan, Q.C., Kou, Y., Miao, J.W., Liu, S.Y., and Chai, B.S. (2021). A model of diameter measurement based on the machine vision. Symmetry, 13.10.3390/sym13020187 ↗
14. An improved method for film thickness measurement of cylindrical roller bearings based on a straight-beam probe10.1108/ILT-05-2022-0161 ↗
15. Deng, Y.S., Zhong, S.C., Lin, J.W., Zhang, Q.K., Nsengiyumva, W., Cheng, S.Y., Huang, Y., and Chen, Z.X. (2023). Thickness measurement of self-lubricating fabric liner of inner ring of sliding bearings using spectral-domain optical coherence tomography. Coatings, 13.10.3390/coatings13040708 ↗
16. Thermal error modelling and compensation of CNC lathe feed system based on positioning error measurement and decoupling10.1016/j.measurement.2024.114633 ↗
17. Lin, C.J., Su, X.Y., Hu, C.H., Jian, B.L., Wu, L.W., and Yau, H.T. (2020). A linear regression thermal displacement lathe spindle model. Energies, 13.10.3390/en13040949 ↗
18. Wei, X.Y., Ye, H.H., Zhou, J.H., Pan, S.J., and Qian, M.Y. (2023). A regularized regression thermal error modeling method for CNC machine tools under different ambient temperatures and spindle speeds. Sensors, 23.10.3390/s23104916 ↗
19. Deng, N.C., Zhang, H.T., Ning, F., and Tang, Z.Y. (2023). Research on the mechanical properties and temperature compensation of an intelligent pot bearing for a pipe-type welding strain gauge. Sensors, 23.10.3390/s23249648 ↗
20. Laubichler, C., Kiesling, C., Marques da Silva, M., Wimmer, A., and Hager, G. (2022). Data-driven sliding bearing temperature model for condition monitoring in internal combustion engines. Lubricants, 10.10.3390/lubricants10050103 ↗
21. Thermal error modeling of electric spindle based on particle swarm optimization-SVM neural network10.1007/s00170-022-09827-4 ↗
22. Thermal error prediction of machine tool spindle using segment fusion LSSVM10.1007/s00170-021-07066-7 ↗
23. Jia, H.K., Yu, L.D., Jiang, Y.Z., Zhao, H.N., and Cao, J.M. (2020). Compensation of rotary encoders using Fourier expansion-back propagation neural network optimized by genetic algorithm. Sensors, 20.10.3390/s20092603 ↗
24. Thermal error prediction and reliability sensitivity analysis of motorized spindle based on Kriging model10.1016/j.engfailanal.2021.105558 ↗
25. Precise compensation for positional accuracy of ultra-precision air-bearing motion stage based on the self-calibration method10.1007/s12541-021-00526-w ↗
26. Zhao, X.R., Hu, Z.W., Tang, J., and Chen, Z.L. (2025). Research on machine tool thermal error compensation based on an optimized LSTM model. Actuators, 14.10.3390/act14120567 ↗
27. Mu, S., Yu, C.P., Lin, K.L., Lu, C.J., Wang, X., Wang, T., and Fu, G.Q. (2025). A review of machine learning-based thermal error modeling methods for CNC machine tools. Machines, 13.10.3390/machines13020153 ↗
28. On the robustness and generalization of thermal error models for CNC machine tools10.1007/s00170-023-12685-3 ↗
29. An efficient thermal error prediction model using neural networks and key temperature points for gantry machining centers10.1093/jom/ufad042 ↗
30. Deep learning prediction for thermal error of CNC machine tools based on attention mechanism
31. (2017). Rolling Bearings—Radial Bearings—Geometrical Product Specifications (GPS) and Tolerance Values (Standard No. GB/T 307.1-2017).