Thermal Error Robust Modeling for High-Speed Motorized Spindle

2012 ◽  
Vol 466-467 ◽  
pp. 961-965 ◽  
Author(s):  
Chun Li Lei ◽  
Zhi Yuan Rui ◽  
Jun Liu ◽  
Li Na Ren
Keyword(s):  
High Speed ◽  
Thermal Error ◽  
Least Square Method ◽  
Information Criterion ◽  
Least Square ◽  
Proposed Model ◽  
Nc Machine ◽  
Input Variables ◽  
Thermal Error Model ◽  
Multivariate Autoregressive

To improve the manufacturing accuracy of NC machine tool, the thermal error model based on multivariate autoregressive method for a motorized high speed spindle is developed. The proposed model takes into account influences of the previous temperature rise and thermal deformation (input variables) on the thermal error (output variables). The linear trends of observed series are eliminated by the first difference. The order of multivariate autoregressive (MVAR) model is selected by using Akaike information criterion. The coefficients of the MVAR model are determined by the least square method. The established MVAR model is then used to forecast the thermal error and the experimental results have shown the validity and robustness of this model.

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

2017 ◽  
Vol 140 (2) ◽  
Author(s):  
Kuo Liu ◽  
Haibo Liu ◽  
Te Li ◽  
Yongqing Wang ◽  
Mingjia Sun ◽  
...  
Keyword(s):  
Thermal Field ◽  
Thermal Characteristics ◽  
Thermal Error ◽  
Least Square Method ◽  
High Accuracy ◽  
Least Square ◽  
Ball Screw ◽  
Milling Machine ◽  
Thermal Fields ◽  
Proposed Model

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.

Thermal Error Compensation and Modeling for CNC Boring and Milling Center

2014 ◽  
Vol 945-949 ◽  
pp. 1665-1668
Author(s):  
Jun Sun ◽  
Yan Ping Xu ◽  
Xing Liu
Keyword(s):  
Error Compensation ◽  
Structural Characteristics ◽  
Thermal Error ◽  
Least Square Method ◽  
Measured Data ◽  
Least Square ◽  
Model Parameters ◽  
Heat Sources ◽  
Thermal Error Model ◽  
Thermal Error Compensation

The thermal error compensation and modeling is an effective way to improve the machining tool precision. This article took the CNC boring and milling center for example. Firstly, this article made analysis and research on the heat sources by analyzing the structural characteristics of CNC boring and milling center, and then on the basis of the previously measured data of selected critical temperature points, established the thermal error model using a method of multiple linear regression based on least square method. The model parameters were solved by MATLAB software. Finally, thermal error compensation model was tested.

scholarly journals Forming a Hierarchical Choquet Integral with a GA-Based Heuristic Least Square Method

Mathematics ◽  
2019 ◽  
Vol 7 (12) ◽  
pp. 1155
Author(s):  
Chen ◽  
Huang
Keyword(s):  
Choquet Integral ◽  
Least Square Method ◽  
Least Square ◽  
Integral Model ◽  
Fuzzy Measures ◽  
Proposed Model ◽  
Choquet Integrals ◽  
The Mean ◽  
Input Variables ◽  
Least Mean Squares Algorithm

: Identifying the fuzzy measures of the Choquet integral model is an important component in resolving complicated multi-criteria decision-making (MCDM) problems. Previous papers solved the above problem by using various mathematical programming models and regression-based methods. However, when considering complicated MCDM problems (e.g., 10 criteria), the presence of too many parameters might result in unavailable or inconsistent solutions. While k-additive or p-symmetric measures are provided to reduce the number of fuzzy measures, they cannot prevent the problem of identifying the fuzzy measures in a high-dimension situation. Therefore, Sugeno and his colleagues proposed a hierarchical Choquet integral model to overcome the problem, but it required the partition information of the criteria, which usually cannot be obtained in practice. In this paper, we proposed a GA-based heuristic least mean-squares algorithm (HLMS) to construct the hierarchical Choquet integral and overcame the above problems. The genetic algorithm (GA) was used here to determine the input variables of the sub-Choquet integrals automatically, according to the objective of the mean square error (MSE), and calculated the fuzzy measures with the HLMS. Then, we summed these sub-Choquet integrals into the final Choquet integral for the purpose of regression or classification. In addition, we tested our method with four datasets and compared these results with the conventional Choquet integral, logit model, and neural network. On the basis of the results, the proposed model was competitive with respect to other models.

Cutting Force Empirical Model of High-Speed Precision Hard Cutting GCr15

2009 ◽  
Vol 69-70 ◽  
pp. 301-305
Author(s):  
Jing Shu Hu ◽  
Yuan Sheng Zhai ◽  
Fu Gang Yan ◽  
Yu Fu Li ◽  
Xian Li Liu
Keyword(s):  
Cutting Force ◽  
Empirical Model ◽  
High Speed ◽  
Orthogonal Design ◽  
Cutting Speed ◽  
Least Square Method ◽  
Cutting Parameters ◽  
Least Square ◽  
Physical Parameters ◽  
Hard Cutting

In the cutting process, cutting force is one of the important physical parameters, which affects the generation of cutting heat, tool life and surface precision of workpiece directly. In this paper an orthogonal design of experiment and subsequent data is analyzed using high speed finish hard cutting GCr15 whose hardness is 65HRC. Cutting speed is 200-400m/min, to study the influence of cutting parameters on cutting force, cutting force empirical model has obtained from least square method.

One-dimensional model for axial thermal error in a micro high-speed spindle

2017 ◽  
Vol 232 (20) ◽  
pp. 3781-3793
Author(s):  
Van-The Than ◽  
Jin H Huang ◽  
Thi-Thao Ngo ◽  
Chi-Chang Wang
Keyword(s):  
High Speed ◽  
Thermal Error ◽  
Axial Direction ◽  
Transfer Model ◽  
Measured Temperature ◽  
One Dimensional ◽  
Thermal Errors ◽  
Short Processing Time ◽  
Thermal Error Model ◽  
Effective Integration

This article proposes a robust and accurate axial thermal error model for a micro high-speed spindle. With measured temperatures, an inverse method is applied to obtain the heat source and temperature field in the spindle for demonstrating that there exists a uniform temperature distribution along the axial direction within the motor range. Hence, a simple one-dimensional heat transfer model is established to acquire the temperature and resulting thermal errors using only one measured temperature on housing surface. Jumped displacement when the spindle starts and stops and the nonlinear deformation on the bearings are satisfactorily treated in the model. The results show that the estimated thermal errors agree with the measured data for both constant and various speeds. In addition, the results reveal that spindle speed significantly affects the maximum thermal error. A short processing time is an advantage of the proposed method. The model promises effective integration in machine tools for compensating thermal errors.

Thermal Error Modeling and Compensating of Motorized Spindle Based on Improved Neural Network

2010 ◽  
Vol 129-131 ◽  
pp. 556-560 ◽  
Author(s):  
Chun Li Lei ◽  
Zhi Yuan Rui
Keyword(s):  
Neural Network ◽  
High Speed ◽  
Thermal Deformation ◽  
Influence Factors ◽  
Thermal Error ◽  
Error Modeling ◽  
Motorized Spindle ◽  
Key Factor ◽  
Manufacturing Accuracy ◽  
Thermal Error Model

In a lot of factors, thermal deformation of motorized high-speed spindle is a key factor affecting the manufacturing accuracy of machine tool. In order to reduce the thermal errors, the reasons and influence factors are analyzed. A thermal error model, that considers the effect of thermodynamics and speed on the thermal deformation, is proposed by using genetic algorithm-based radial basis function neural network. The improved neural network has been trained and tested, then a thermal error compensation system based on this model is established to compensate thermal deformation. The experiment results show that there is a 79% decrease in motorized spindle errors and this model has high accuracy.

scholarly journals Research on Thermal Error Modeling of Motorized Spindle Based on BP Neural Network Optimized by Beetle Antennae Search Algorithm

Machines ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 286
Author(s):  
Zhaolong Li ◽  
Bo Zhu ◽  
Ye Dai ◽  
Wenming Zhu ◽  
Qinghai Wang ◽  
...  
Keyword(s):  
Neural Network ◽  
Prediction Model ◽  
Bp Neural Network ◽  
High Speed ◽  
Search Algorithm ◽  
Thermal Error ◽  
Error Prediction ◽  
Machining Accuracy ◽  
Motorized Spindle ◽  
Thermal Error Model

High-speed motorized spindle heating will produce thermal error, which is an important factor affecting the machining accuracy of machine tools. The thermal error model of high-speed motorized spindles can compensate for thermal error and improve machining accuracy effectively. In order to confirm the high precision thermal error model, Beetle antennae search algorithm (BAS) is proposed to optimize the thermal error prediction model of motorized spindle based on BP neural network. Through the thermal characteristic experiment, the A02 motorized spindle is used as the research object to obtain the temperature and axial thermal drift data of the motorized spindle at different speeds. Using fuzzy clustering and grey relational analysis to screen temperature-sensitive points. Beetle antennae search algorithm (BAS) is used to optimize the weights and thresholds of the BP neural network. Finally, the BAS-BP thermal error prediction model is established. Compared with BP and GA-BP models, the results show that BAS-BP has higher prediction accuracy than BP and GA-BP models at different speeds. Therefore, the BAS-BP model is suitable for prediction and compensation of spindle thermal error.

scholarly journals Thermal Error Prediction of Ball Screws Based on PSO-LSTM

2021 ◽  
Author(s):  
Xiangsheng Gao ◽  
Yueyang Guo ◽  
Dzonu Ambrose Hanson ◽  
Zhihao Liu ◽  
Min Wang ◽  
...  
Keyword(s):  
Neural Network ◽  
Time Series ◽  
High Speed ◽  
Thermal Characteristic ◽  
Thermal Error ◽  
Error Model ◽  
Cnc Machine Tools ◽  
Error Prediction ◽  
Model Based ◽  
Thermal Error Model

Abstract Thermal error of ball screws seriously affects the machining precision of CNC machine tools especially in high speed and precision machining. Compensation technology is one of the most effective methods to address the thermal issue, and the effect of compensation depends on the accuracy and robustness of the thermal error model. Traditional modeling approaches have major challenges in time-series thermal error prediction. In this paper, a novel thermal error model based on Long Short-Term Memory (LSTM) neural network and Particle Swarm Optimization (PSO) algorithm is proposed. A data-driven model based on LSTM neural network is established according to the time-series collected data. The hyperparameters of LSTM neural network are optimized by PSO and then a PSO-LSTM model is established to precisely predict the thermal error of ball screws. In order to verify the effectiveness and robustness of the proposed model, two thermal characteristic experiments based on step and random speed are conducted on a self-designed test bench. The results show that the PSO-LSTM model has higher accuracy compared with the RBF model and BP model with high robustness. The proposed method can be implemented to predict the thermal error of ball screws, and provide a foundation for thermal error compensation.

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