基于工况的数控加工热误差与切削振动预测方法研究
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摘要
在高速高精加工过程中，由于数控机床力学特性、热学特性以及力热耦合特性的影响，机床热误差和切削振动已经成为制约加工质量和效率提高的主要因素。数控机床作为复杂的机电装备，是典型的非线性系统。本文以非线性系统辨识及控制为理论基础，综合运用赫兹接触理论、神经网络、有限差分理论和信号分析理论等方法，以数控机床进给系统和切削过程为对象，深入研究了加工过程中工况参数（主轴转速、进给量、轴向切深等）与进给轴热定位误差以及切削振动的关系模型，提出了基于工况参数调整的加工过程进给轴热定位误差以及切削振动优化方法。
以准高速进给系统实验平台为对象，分析了各种工况因素对进给系统支撑轴承的温度变化的影响。以叶轮铣削加工为对象，分析了切削参数（主轴转速、进给速度、切深等）对切削振动状态的影响。实验分析表明，数控加工过程中工况参数是机床动态特性的决定性因素。在此基础上，以NARMA-L2非线性系统辨识模型为理论依据，结合小波神经网络建模方法，提出了WNN-NARMAL2神经网络模型，建立了工况参数与机床动态特性的关系模型，实现了变工况条件下的数控机床动态特性预测。
针对数控机床进给系统中支撑滚动轴承由于滚动球体与内、外滚道之间的不完全接触而引起的接触热阻和摩擦发热问题，以赫兹接触理论为依据，研究了轴承内部载荷分布和椭圆接触区域参数的确定方法，结合半空间椭球坐标系Laplace温度分布方程，提出了滚动球体与内、外滚道之间接触热阻的理论计算方法；研究了接触区域滚动球体旋转和滑移摩擦力矩的计算方法，提出了滚动球体与内、外滚道之间的摩擦发热率理论计算方法；分析了不同工况参数对滚动球体与内、外滚道之间接触热阻及发热率的影响，并在自制准高速进给系统实验平台上进行了实验验证。
以准高速进给系统实验平台为对象，通过正交实验分析了工况参数对进给系统热源温升的影响，通过定义工况距离参数和进行聚类分析，建立了针对进给系统热源温升预测的工况规则库。在此基础上，以WNN-NARMAL2神经网络模型为依据，建立了工况参数与进给系统热源温升的关系模型，实现了基于工况参数的进给系统热源温升预测。
以两端支撑轴承温度、接触热阻和摩擦发热量以及丝杠螺母移动热源为边界条件，采用改进的分组显式有限差分方法对进给系统滚珠丝杠热传导方程进行数值求解，得到了不同工况条件下的滚珠丝杠温度场和热变形分布。在此基础上，建立了滚珠丝杠热变形与进给系统热误差的关系模型，实现了以工况参数为初始输入的进给系统热误差预测；以接触分析为理论依据，采用ANSYS参数化设计与分析语言建立了进给系统热分析有限元参数化模型，进行了进给系统温度场和滚珠丝杠热变形仿真求解,并与数值求解结果进行了比较。
以叶轮铣削加工为实例，以铣削过程动力学模型为基础，分析了切削过程中的振动频率；基于小波包分析理论，分析了切削状态变化时振动信号的频率转移特性和谐振信号幅值变化规律，提出了振动状态预先判别关键特征量的提取方法。在此基础上，基于WNN-NARMAL2神经网络模型，建立了工况参数与谐振信号幅值的关系模型，实现了基于工况参数的切削振动幅值实时预测。
以最小二乘支持向量机多分类算法为基础，以支撑轴承以及丝杠螺母温度信号的均值、方差、均方值和最大值作为特征量，对于数控加工过程中的进给轴热定位误差进行有效识别；基于振动信号的小波包分解，以振动倍频成分的相对小波包能量以及标准偏差作为特征量，对于加工过程失稳而引起的振动误差进行准确判别；以基于工况参数的进给系统热定位误差和切削振动实时预测为基础，结合粒子群多目标优化算法，提出了基于多目标优化Pareto最优解集的工况参数调整方法，实现了基于工况参数调整的加工过程中进给轴热定位误差和切削振动优化，并在叶轮铣削加工中进行了实验验证。
本文的研究为数控加工过程中进给轴热定位误差和切削振动判别、控制提供了一个有效途径，具有一定的理论意义和实际应用价值。
In high-speed precision machining, with the influences of mechanical characteristics,thermal characteristics and thermal-mechanical coupling characteristics of NC machine tools,thermal error and cutting vibration have become to be the key factors which prevent theimprovement of machining quality and efficiency. As complicated electromechanicalequipments, NC machine tools are considered to be typical nonlinear systems. In thisdissertation, based on the theory of nonlinear system identification and control, as well asHertzian contact theory, neural networks, finite differential theory and signal processing theory,the relationships between operation parameters (spindle speed, feed rate, and axial cuttingdepth) and thermal positioning error of feed system in NC machine tools are systematicallyinvestigated, so as the relationships between operation parameters and cutting vibration inmachining, and a control method to suppress thermal positioning error of feed system andcutting vibration by adjusting operation parameters is presented.
According the fact of thermal contact resistance brought by the imperfect contact betweenrolling elements and raceway of the supporting bearings in feed system, a theoretical method tocalculate the thermal contact resistance is presented based on Hertzian contact theory andLaplace temperature distribution equation in ellipsoidal coordinates, and the internal loadingdistribution and elliptic contact area parameters are carefully studied. According the fact offriction heating brought by the contact friction between rolling elements and raceway of thesupporting bearings, a theoretical method to calculate the friction heating rate is presented withcareful consideration of the spinning and sliding friction torque in the elliptic contact area.Furthermore, the influences of operation parameters on the thermal contact resistance andfriction heating rate are analyzed, and experimental verifications were carried out on self-madequasi high-speed feed system.
Based on the orthogonal experiments carried out on the self-made quasi high-speed feedsystem, the influences of operation parameters on the temperature-rises of heat sources in feedsystem are analyzed, and an operation rule database is built by defining operation distance andclustering analysis. Furthermore, on the basis of nonlinear system identification modelNARMA-L2and wavelet neural network, the relation model for operation parameters andtemperature-rises of heat sources in feed system is obtained using improved particle swarmoptimization (PSO) as the training algorithm, and the temperature-rises of heat sources can bepredicted with operation parameters as the inputs.
With the temperatures, the thermal contact resistances and friction heating of supportingbearings and screw-nut as the boundary conditions, the heat conduction equation of ball screwin feed system is solved numerically using improved group explicit finite differential method, and the temperature and thermal deformation distribution of the ball screw under differentoperation parameters are obtained. Moreover, the thermal positioning error of the feed systemcan be predicted with operation parameters as the inputs by establishing the relationshipbetween the thermal deformation of the ball screw and thermal positioning error of the feedsystem. Based on contact analysis, the finite element parametric model is built using ANSYSparametric design and analysis language, and temperature and thermal deformation distributionof the feed system is solved.Finally, the results of numerical solution and simulation solutionare compared.
With impeller milling process as an example, the vibration frequencies in milling areanalyzed based on the dynamic model of milling process. Using wavelet packet analysis, thechanges of frequency transition and harmonic amplitude of vibration signal in different cuttingstates, and the key features for detecting vibration sates are presented. Furthermore, on the basisof nonlinear system identification model NARMA-L2and wavelet neural network, the relationmodel for operation parameters and cutting vibration in milling is obtained, and the cuttingvibration can be predicted with operation parameters as the inputs.
Using Multi-class Least Squares Support Vector Machines, the thermal positioning errorof the feed system is identified with the mean, variance, mean square value and maximum ofthe temperatures of supporting bearings and screw-nut as feature vector, and cutting vibrationstates in milling are detected with the relative wavelet packet energy and standard deviation ofthe multiple-frequency vibration as feature vector. Based on the prediction of thermalpositioning error of the feed system and cutting vibration, the adjusting strategies of operationparameters are presented according to the Pareto sets and Pareto Fronts of a multi-objectiveoptimization, and a experimental verification was carried out in impeller milling to suppress thethermal positioning error of feed system and the cutting vibration by adjusting operationparameters.
The achievements of this dissertation provide an effective approach to detect and controlthe thermal positioning error of feed system and the cutting vibration in NC machining process,which is proved to have both theoretical significance and practical application value.
以准高速进给系统实验平台为对象，分析了各种工况因素对进给系统支撑轴承的温度变化的影响。以叶轮铣削加工为对象，分析了切削参数（主轴转速、进给速度、切深等）对切削振动状态的影响。实验分析表明，数控加工过程中工况参数是机床动态特性的决定性因素。在此基础上，以NARMA-L2非线性系统辨识模型为理论依据，结合小波神经网络建模方法，提出了WNN-NARMAL2神经网络模型，建立了工况参数与机床动态特性的关系模型，实现了变工况条件下的数控机床动态特性预测。
针对数控机床进给系统中支撑滚动轴承由于滚动球体与内、外滚道之间的不完全接触而引起的接触热阻和摩擦发热问题，以赫兹接触理论为依据，研究了轴承内部载荷分布和椭圆接触区域参数的确定方法，结合半空间椭球坐标系Laplace温度分布方程，提出了滚动球体与内、外滚道之间接触热阻的理论计算方法；研究了接触区域滚动球体旋转和滑移摩擦力矩的计算方法，提出了滚动球体与内、外滚道之间的摩擦发热率理论计算方法；分析了不同工况参数对滚动球体与内、外滚道之间接触热阻及发热率的影响，并在自制准高速进给系统实验平台上进行了实验验证。
以准高速进给系统实验平台为对象，通过正交实验分析了工况参数对进给系统热源温升的影响，通过定义工况距离参数和进行聚类分析，建立了针对进给系统热源温升预测的工况规则库。在此基础上，以WNN-NARMAL2神经网络模型为依据，建立了工况参数与进给系统热源温升的关系模型，实现了基于工况参数的进给系统热源温升预测。
以两端支撑轴承温度、接触热阻和摩擦发热量以及丝杠螺母移动热源为边界条件，采用改进的分组显式有限差分方法对进给系统滚珠丝杠热传导方程进行数值求解，得到了不同工况条件下的滚珠丝杠温度场和热变形分布。在此基础上，建立了滚珠丝杠热变形与进给系统热误差的关系模型，实现了以工况参数为初始输入的进给系统热误差预测；以接触分析为理论依据，采用ANSYS参数化设计与分析语言建立了进给系统热分析有限元参数化模型，进行了进给系统温度场和滚珠丝杠热变形仿真求解,并与数值求解结果进行了比较。
以叶轮铣削加工为实例，以铣削过程动力学模型为基础，分析了切削过程中的振动频率；基于小波包分析理论，分析了切削状态变化时振动信号的频率转移特性和谐振信号幅值变化规律，提出了振动状态预先判别关键特征量的提取方法。在此基础上，基于WNN-NARMAL2神经网络模型，建立了工况参数与谐振信号幅值的关系模型，实现了基于工况参数的切削振动幅值实时预测。
以最小二乘支持向量机多分类算法为基础，以支撑轴承以及丝杠螺母温度信号的均值、方差、均方值和最大值作为特征量，对于数控加工过程中的进给轴热定位误差进行有效识别；基于振动信号的小波包分解，以振动倍频成分的相对小波包能量以及标准偏差作为特征量，对于加工过程失稳而引起的振动误差进行准确判别；以基于工况参数的进给系统热定位误差和切削振动实时预测为基础，结合粒子群多目标优化算法，提出了基于多目标优化Pareto最优解集的工况参数调整方法，实现了基于工况参数调整的加工过程中进给轴热定位误差和切削振动优化，并在叶轮铣削加工中进行了实验验证。
本文的研究为数控加工过程中进给轴热定位误差和切削振动判别、控制提供了一个有效途径，具有一定的理论意义和实际应用价值。
In high-speed precision machining, with the influences of mechanical characteristics,thermal characteristics and thermal-mechanical coupling characteristics of NC machine tools,thermal error and cutting vibration have become to be the key factors which prevent theimprovement of machining quality and efficiency. As complicated electromechanicalequipments, NC machine tools are considered to be typical nonlinear systems. In thisdissertation, based on the theory of nonlinear system identification and control, as well asHertzian contact theory, neural networks, finite differential theory and signal processing theory,the relationships between operation parameters (spindle speed, feed rate, and axial cuttingdepth) and thermal positioning error of feed system in NC machine tools are systematicallyinvestigated, so as the relationships between operation parameters and cutting vibration inmachining, and a control method to suppress thermal positioning error of feed system andcutting vibration by adjusting operation parameters is presented.
According the fact of thermal contact resistance brought by the imperfect contact betweenrolling elements and raceway of the supporting bearings in feed system, a theoretical method tocalculate the thermal contact resistance is presented based on Hertzian contact theory andLaplace temperature distribution equation in ellipsoidal coordinates, and the internal loadingdistribution and elliptic contact area parameters are carefully studied. According the fact offriction heating brought by the contact friction between rolling elements and raceway of thesupporting bearings, a theoretical method to calculate the friction heating rate is presented withcareful consideration of the spinning and sliding friction torque in the elliptic contact area.Furthermore, the influences of operation parameters on the thermal contact resistance andfriction heating rate are analyzed, and experimental verifications were carried out on self-madequasi high-speed feed system.
Based on the orthogonal experiments carried out on the self-made quasi high-speed feedsystem, the influences of operation parameters on the temperature-rises of heat sources in feedsystem are analyzed, and an operation rule database is built by defining operation distance andclustering analysis. Furthermore, on the basis of nonlinear system identification modelNARMA-L2and wavelet neural network, the relation model for operation parameters andtemperature-rises of heat sources in feed system is obtained using improved particle swarmoptimization (PSO) as the training algorithm, and the temperature-rises of heat sources can bepredicted with operation parameters as the inputs.
With the temperatures, the thermal contact resistances and friction heating of supportingbearings and screw-nut as the boundary conditions, the heat conduction equation of ball screwin feed system is solved numerically using improved group explicit finite differential method, and the temperature and thermal deformation distribution of the ball screw under differentoperation parameters are obtained. Moreover, the thermal positioning error of the feed systemcan be predicted with operation parameters as the inputs by establishing the relationshipbetween the thermal deformation of the ball screw and thermal positioning error of the feedsystem. Based on contact analysis, the finite element parametric model is built using ANSYSparametric design and analysis language, and temperature and thermal deformation distributionof the feed system is solved.Finally, the results of numerical solution and simulation solutionare compared.
With impeller milling process as an example, the vibration frequencies in milling areanalyzed based on the dynamic model of milling process. Using wavelet packet analysis, thechanges of frequency transition and harmonic amplitude of vibration signal in different cuttingstates, and the key features for detecting vibration sates are presented. Furthermore, on the basisof nonlinear system identification model NARMA-L2and wavelet neural network, the relationmodel for operation parameters and cutting vibration in milling is obtained, and the cuttingvibration can be predicted with operation parameters as the inputs.
Using Multi-class Least Squares Support Vector Machines, the thermal positioning errorof the feed system is identified with the mean, variance, mean square value and maximum ofthe temperatures of supporting bearings and screw-nut as feature vector, and cutting vibrationstates in milling are detected with the relative wavelet packet energy and standard deviation ofthe multiple-frequency vibration as feature vector. Based on the prediction of thermalpositioning error of the feed system and cutting vibration, the adjusting strategies of operationparameters are presented according to the Pareto sets and Pareto Fronts of a multi-objectiveoptimization, and a experimental verification was carried out in impeller milling to suppress thethermal positioning error of feed system and the cutting vibration by adjusting operationparameters.
The achievements of this dissertation provide an effective approach to detect and controlthe thermal positioning error of feed system and the cutting vibration in NC machining process,which is proved to have both theoretical significance and practical application value.
引文
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