Study On Robust Modeling And Compensation Of Thermal Error For NC Gear Grinding Machine Tool

The machining accuracy and quality of gears directly determine the gear transmission performance.CNC gear grinding machine is the key equipment for machining high-precision gears,while thermal error is one of the essential factors affecting its machining accuracy.Thermal error compensation technology has turned into the main means to solve the thermal error of machine tools due to its economic efficiency.However,as the robustness of the compensation model under different operating conditions affects the engineering application of this technology,it is of great significance to study the thermal error robust modeling technology of CNC gear grinding machine under variable operating conditions.Aiming at CNC grinding machine tool with grinding wheel,this paper studies the layout methods of temperature measure points,the optimization of modeling variables,as well as the thermal error robust modeling technology of the machine tool feed system,workpiece spindle and grinding wheel spindle.The main research contents can be summarized as follows.(1)It proposes an optimization method of temperature characteristic variables based on virtual construction method of measure points and feature extraction algorithm.The ball screw in the feed system is simplified into one-dimensional rod.Based on the heat transfer principle and the thermos-elastic motion equation,this paper analyzes the correlation between the thermal deformation and the temperature of each measure point;seeks optimal measure point with linear relationship between the thermal deformation and temperature;establishes the mathematical description of the thermal deformation and optimal temperature measure point;and reveals the influencing factors and changing rules of the change of optimal measure point and the change of robustness when operating conditions vary.Furthermore,based on the principle of isotropic temperature transfer of metal materials,it plans the layout strategy of the temperature sensor in the feed system;and puts forward the optimization method of temperature characteristic variables on the basis of virtual construction of linear measure points and feature extraction algorithm,which reduces the instability of linear relationship between thermal deformation and measure point temperature as well as the influence of multicollinearity on model robustness and prediction accuracy.Experiments on gear grinding machine verify the correctness of the above theoretical methods.(2)A Bayesian network-based thermal error classification modeling method for gear grinding machine feed system is proposed.In view of the problem that variable operating conditions affect the robustness and accuracy of the model,based on Bayesian theory,the network structure of the classifier is determined by expert knowledge,and the conditional probability density between the parent and child nodes is determined by the solution of posterior probability distribution,thereby constructing the temperature classifier to realize the classification of temperatures under various operating conditions.According to the error separation principle of the feed system,the thermal error and geometric error models are constructed by linear and polynomial fitting methods,while the error synthesis model is constructed by linear superposition of the two fitting models.The variable operating condition test on the CNC gear grinding machine indicates that the proposed method effectively improves the prediction accuracy and robustness of the model,and provides reference for thermal error modeling under multiple operating conditions.(3)A classification modeling method of workpiece spindle without temperature sensor of CNC grinding machine tool is proposed.In view of the optimal layout of temperature sensor influenced by cutting fluid and the problem of multi-collinearity between measure points that may be caused by sensor information modeling in the actual machining process,through the structural analysis of workpiece spindle of CNC gear grinding machine,the overall heat equation of the spindle is established on the basis of the heat loss of the motor and the friction heat of the bearing.According to the difference of convective heat transfer coefficient,air kinematic viscosity and other parameters of the spindle in the ascending and descending temperature process,the initial theoretical model of temperature ascending and descending is constructed respectively by combining with the overall heat equation;based on the spindle geometric structure analysis and the differential equation of thermal deformation,it establishes the initial theoretical model of thermal deformation at ascending and descending temperature,and the above theoretical model is modified by combining the temperature and thermal error information of actual operating conditions.The verification on the gear grinding machine implies that the proposed method can effectively predict the evolution of temperature and thermal deformation during the process of temperature rise and fall.The physical meaning of this method is relatively clear,which lays a foundation for the analysis of the thermal error mechanism of machine tools and has practical value in engineering.(4)The data-driven thermal error modeling method for the grinding wheel spindle of CNC grinding machine tools is proposed.Traditional modeling methods based on model control theories and methods can hardly avoid problems such as“poor robustness”and“unmodeled dynamics”due to changes in operating conditions.Based on the data-driven theory,the general nonlinear thermal error system is defined,and the variation range of temperature and thermal error is determined through the thermal error offline data.On the basis,the author defines the tight form dynamic linearization model,derives the data-driven model free adaptive control law formula,and modifies the model online to track the thermal deformation dynamics with the real-time data generated in machining.Experiments on the grinding wheel spindle of gear grinding machine has proved the high robustness of the data-driven model and its rapid adaptability to“unmodeled dynamics”.The methods proposed have initially explored the application of big data in thermal error modeling.