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Highlights • The thermal boundary conditions of ball screw feed drive system are optimized. • The method is extended to predict thermal boundary conditions at different feed rates. • The thermal contact resistance is essential for thermal characteristics modeling. • Thermal characteristics of the ball-screw feed drive system is analyzed. • The thermal deformation of feed drive system is closely related to supporting mode. Abstract To improve the simulation accuracy of the traditional transient thermal characteristics analysis model (TCAM) of the ball screw feed drive system (BSFDS), the optimization method of the thermal boundary conditions (TBCs), including the thermal loads, the convective heat transfer coefficient and the thermal contact resistance (TCR), was proposed. A multi-objective and multi-parameter optimization model was established based on the hybrid response surface (HRS) and a multi-objective genetic algorithm (MOGA) was developed to optimize the above TBCs. To simulate the thermal characteristics of the BSFDS under different working conditions, the generality of the method was extended to predict the TBCs under different feed rates. To validate the effectiveness of the method, the thermal characteristic experiments of BSFDS were conducted. The results showed that the simulation error for the temperature field was reduced from 25% to 10% and that the simulation error for the thermal elongation was reduced from 30% to 11%. [ABSTRACT FROM AUTHOR]

Highlights • A method to predict contact stiffness of spindle/tool holder interface was proposed. • The modeling method of contact stiffness took the micro morphology into consideration. • The surface contact coefficient was introduced to correct the contact stiffness. • The modeling model was useful for fast identification of contact stiffness. Abstract The contact stiffness of the spindle/tool holder is essential for the cutting stability of the spindle system because the elastic connection of the spindle/tool holder interface determines the dynamic characteristics of the spindle system. To predict the dynamic characteristics of the spindle system at the design stage, an analytical model of the contact stiffness of the spindle/tool holder interface was proposed based on the fractal theory and the multi-scale contact mechanics model to consider the combined effect of the cutting force and drawbar force on the contact stiffness. The fractal theory was used to characterize the micro-morphology of rough surfaces and the fractal parameters were identified by the power spectrum method. For the contact of two rough curved surfaces, the surface contact coefficient was introduced into the multi-scale contact mechanics model to correct the contact stiffness, the actual contact area and the contact stress. To verify the validity of the method, the experiments were conducted and the results showed that the modeling error of the contact stiffness was reduced from 25.13% to 4.72% by the proposed method. Finally, the effect of such factors as the cutting force, the mean roughness, the material properties, the preload and the temperature variation on the contact stiffness was discussed. The contact stiffness of spindle/tool holder interface increased with the cutting force and the drawbar force and that the contact stiffness decreased with the mean roughness. Moreover, the shear contact stiffness increased with the equivalent elastic modulus, the interference fit and the temperature. The conclusion was drawn that the model can be used to predict the contact stiffness of the spindle/tool holder interface at the design stage. [ABSTRACT FROM AUTHOR]

[Display omitted] • Machine learning platform is proposed for error prediction and control. • Spatial-temporal behaviors are revealed with energy conservation equation. • GGC is proposed for the first time to mine spatial behavior of thermal errors. • S-GRU fuse temporal information and spatial information. • ST-Attention is designed to retain long-term spatial–temporal information. • STFGCN is proposed for spatial–temporal prediction of thermal errors. The big data platform, which has a high control accuracy and efficiency, is expected to realize the high-accuracy prediction and real-time control of the thermal error (TE) for the ball screw system. But the TE of a ball screw system has significant dynamic spatial–temporal behaviors. The TE model, which fully captures its dynamic spatial–temporal behaviors, has not been reported so far. Moreover, the embedding of the TE model into the big data platform is extremely difficult, and the deployment of the big data platform is time-consuming and relies on the expert knowledge, and the cloud computing used in the big data platform also faces a limited bandwidth pressure of the industrial Internet, leading to the failure of the real-time control. To overcome the above limitations, a novel machine learning application platform (MLAP) is designed based on the cloud-terminal architecture. Moreover, the spatial–temporal fusion graph convolutional network (STFGCN) is proposed for the first time to fully capture of the dynamic spatial–temporal behaviors, and the proposed STFGCN is embedded into the designed MLAP to expedite the training process of the STFGCN model and reduce the bandwidth pressure on the industrial Internet. The prediction performance and robustness of the proposed STFGCN model are compared with that of the traditional multiple linear regression (MLR), long short-term memory (LSTM), gated recurrent unit (GRU), convolutional neural network-long short-term memory (CNN-LSTM), temporal-graph convolutional network (T-GCN), hypergraph neural network (HGNN), spatial–temporal graph convolutional network (STGCN), and attention-based spatial–temporal graph convolutional network (ASTGCN). The results suggest that the evaluation metrics R2 of the MLR, LSTM, GRU, CNN-LSTM, T-GCN, HGNN, STGCN, ASTGCN, and STFGCN are 0.8039, 0.9500, 0.9441, 0.9414, 0.9571, 0.9512, 0.9689, 0.9712, and 0.9812 to show the prediction performance, respectively. Moreover, the training rate is improved by adding the number of the virtual machine nodes on the MLAP. The reduction rate of the machining error is the ratio of the machining error reduction to the original machining error. The positioning error and its fluctuation range of the ball screw system are reduced effectively, and the machining errors with the implementation of the MLAP are decreased by more than 33% and 72% compared with that with the pitch error control and without the TE control, respectively. [ABSTRACT FROM AUTHOR]

[Display omitted] • Mist-edge-fog-cloud system architecture for error control is designed. • ONT-GCN thermal error model is proposed. • Mapping model of tooth surface error/geometric-thermal errors is proposed. • Spatial-temporal behavior demonstrates applicability of ONT-GCN model. • A sensor network is designed to capture spatial information. The geometric precision of worm gears (WGs) determines the service performance and life of precision machine tools, indexing turntables and other equipment. The machining accuracy of worm gear machine tools (WGMTs) is the core to guarantee the geometric precision of WGs, and is greatly affected by the thermal and geometric errors. To improve the machining accuracy of WGMTs, the thermal and geometric errors should be controlled and compensated. But the control system has a poor real-time performance, and the synchronous control of the geometric and thermal errors cannot be currently achieved, and the thermal error model has a low prediction accuracy and low robustness. To make up for the above gap, a mist-edge-fog-cloud computing system is designed for the error prediction and compensation to relieve the bandwidth pressure of the industrial Internet. Moreover, a sensor network composed of multiple sensors is constructed to obtain the thermal information, and then the ordered neuron temporal-graph convolutional network (ONT-GCN) is proposed based on the ordered neuron-long short term memory network (ON-LSTMN) and graph convolutional network (GCN) for the first time to conduct the spatial and temporal modeling of the thermal error data. The interaction among multiple sensors is explicitly considered, and the dependence of the temporal information of the thermal error data on and spatial information of sensors is taken into account. Besides, to realize the error control, the mapping relationship between the tooth surface error and geometric-thermal errors is established. The error mapping model converts 51 geometric errors and 4 thermal errors into the spatial errors of the hob. Moreover, the sensitivity of errors is analyzed, and then the key error items that affect the geometric precision of the tooth surface are identified and compensated. The results show that the ONT-GCN is superior to traditional time-series modeling methods and that the mist-edge-fog-cloud computing system can effectively shorten the executing time compared with other system frameworks, and can improve the machining accuracy of WGMTs. [ABSTRACT FROM AUTHOR]

[Display omitted] • Four-terminal-architecture CEDTS is proposed for thermal error control. • Hyper-parameters of ILSTM network are optimized by ISOA. • Comprehensive machining error model is constructed according to HCT theory. • Data services, including clustering analysis, status monitoring, and data funsion, are provided. • GPU-based cloud computing layer is used to expedite executing process. Production lines are important for the high-accuracy and efficient machining of parts. The thermal error of key machining equipment in production lines has a significant effect on the geometric accuracy of machined parts. To improve the geometric accuracy of machined parts, the thermal error of key machining equipment in a production line should be controlled. Then the collection, storage, analysis, and calculation of the large-volume manufacturing data are essential. But the processing involving the large-volume manufacturing data is time-consuming and challenging, which leads to low executing efficiency. To solve the problem that the system is inefficient in the processing of the large-volume manufacturing data, a four-terminal-architecture cloud-edge-based digital twin system (CEDTS) is proposed with a reasonable functional division of four terminals, and thus the executing efficiency of CEDTS is expedited. Then the error mechanism is studied to prove the long-term memorizing behavior, and an improved seagull optimization algorithm (ISOA) is proposed based on the chaos thought to optimize the weights, thresholds, and the number of iterations of an improved long short term memory (ILSTM) network with the attention mechanism. The ISOA-ILSTM error model is embedded into the intelligent decision-making terminal of CEDTS to predict the thermal error. Moreover, a comprehensive machining error model is proposed and embedded into the intelligent decision-making terminal of CEDTS to control the thermal error. Finally, the effectiveness of CEDTS is verified on a production line. The results show that the reduction of the large-volume manufacturing data for the collection, storage, analysis, and calculation is significant. With the implementation of CEDTS, the fluctuation range of geometric errors of machined parts is reduced significantly. The executing time is reduced by more than half by CEDTS with the GPU acceleration. [ABSTRACT FROM AUTHOR]

• The data-driven compensation method of the 5-axis machine tools is proposed. • The relationship between the thermal error and positioning error is explored. A novel thermal error is proposed for feed drive systems. • The regression analysis is effective to establish the thermal error model. • The pre-stretch can improve the positioning accuracy. The data-driven thermal error compensation method of high-speed and precision five-axis machine tools was proposed based on the homogeneous transformation. The compensation component was obtained by analyzing the error transmission chain of machine tools and was expressed as the transmission matrix consisting of thermal error terms of linear axes and spindle system according to the differential movement of the compensation axis. From the view of thermal error generation mechanism, the thermal error of the linear axis was formulated as the product of the polynomial function with time as its independent variable and the polynomial function with position as its independent variable. Then the thermal errors of the linear axes were decomposed and identified from the measured positioning error. The thermal error of the spindle system was identified by the thermal characteristic experiments. The compensation component in each direction is calculated by substituting the identified thermal error terms of the linear axes and spindle system into the data-driven thermal error model. Finally, to demonstrate the effectiveness of the proposed method, the thermal error at a new working condition was predicted, and then the error compensation and actual machining were carried out. The results show that the machining error is reduced by more than 85% and 37% with the present error compensation compared with that without compensation and that without traditional error compensation, respectively. This research sheds new light on both the generation mechanism and the compensation method of the thermally-induced error of five-axis machine tools. [ABSTRACT FROM AUTHOR]

• A precision loss model is proposed with the effect of rough curved surfaces. • An effective contact coefficient is introduced into the precision loss model. • The precision loss model is modified with multiscale contact mechanics model. • The contact mechanics model between two rough curved surfaces is established. • A surface contact coefficient is introduced to modify the contact parameters. A precision loss modeling method of the ball screw pair was proposed by introducing an effective contact coefficient to consider the intermittent contact between the balls and screw grooves and the parameter in the precision loss model was modified by establishing a multiscale contact mechanics model. The multiscale contact mechanics model between two rough curved surfaces was established by considering the elastic, elastic-plastic, and plastic deformations of contacting asperities to compute such contact parameters as the total actual contact area and contact load. A surface contact coefficient was introduced into the multiscale contact mechanics model to modify the contact parameters by taking the rough curved surfaces of balls and screw grooves into account. The microtopographies of rough surfaces of screw grooves and balls were characterized by the fractal geometry theory, and then the characterization of the microtopography of screw groove surfaces and the multiscale contact mechanics model were unified in the precision loss modeling. Then the relative sliding distance was calculated according to the kinematic analysis of the ball screw. Finally, the precision loss model of the ball screw pair was established by the above analysis. To verify the effectiveness of the precision loss model, the wear test was conducted on a dual-drive ball screw feed drive system under different working conditions. The predicted results agree well with the experimental data in the stable wear stage and the predictive accuracy of the model is much higher than that of previous studies. The effects of such parameters as the axial load and the feed rate on the precision loss were discussed. It is shown that the precision loss increases with the axial load and the feed rate. [ABSTRACT FROM AUTHOR]