数控机床热变形特性和热误差补偿研究
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摘要
数控机床在加工过程中，机床部件受到各种内部热源和外部热源的影响而产生不均匀的温度场，同时由于机床各部件的线膨胀系数不一致产生热应力和热变形，使机床上刀具和工件之间的正确位置遭到破坏，机床固有精度降低，导致工件加工过程中的热变形误差。在精密加工过程中由于工艺系统热变形引起的加工误差占总加工误差的40％～70％，其中机床的热变形误差占整个工件加工误差的60％～80％，机床热变形已经成为精密和超精密加工过程的主要误差来源。
本文以某立式加工中心为实验对象，通过大量的实验验证了主轴轴承的摩擦发热是主轴箱内的主要热源，是引起机床主轴热变形和热误差的主要原因；利用赫兹接触理论，分析了主轴轴承上钢球与滚道的接触变形和载荷分布；应用运动学理论分析了主轴轴承上钢球的运动及速度；将数学推导和经验公式相结合建立了主轴轴承运动过程中所产生的各种摩擦力矩及摩擦力的数学公式；在综合钢球的摩擦力矩和运动速度的基础上建立了机床主轴轴承摩擦热源的发热模型。
本文动态地分析了影响主轴轴承发热的工艺因素，并进行了相应的试验验证。利用热应力理论分析了主轴转速、轴承内外圈与主轴及轴套的配合过盈量对主轴热变形位移的影响规律。在对主轴轴承的装配工艺及配合过盈量进行有效改进的基础上，主轴箱测温点的温升和热位移达到很大的改善，验证了过盈量大小对主轴热位移的影响规律。
对数控机床进行热误差补偿时，补偿系统的信息输入是机床的温度场信息，为了最佳地把握机床的温度场信息，同时又降低温度测量的成本，本文结合模糊聚类和相关性分析理论来优化机床热关键点。在初步选定多个测温点的前提下，利用模糊聚类分析原理把测温点聚类分组，再从每组中选一个测温点，利用相关性分析，最终确定测温点的位置和数目。最后的补偿结果证明所选定的关键测温点能保证机床精度补偿的要求。
在确定测温点的前提下，需要建立测温点温升和热误差之间的关系模型。本文结合生产现场实际，应用多元线性回归模型对热误差建模，补偿结果表明初步收到良好的效果。在多元线性回归建模的基础上，应用分段线性回归模型进行建模，通过数据分析表明，进一步提高了热误差的精度。
利用径向基神经网络技术建立了测温点温升和热误差之间的关系模型，并应用该模型对某立式加工中心主轴箱上的测量数据进行了分析，结果表明径向基神经网络模型能够很好地逼近实际的热误差模型，从而降低热误差。
针对数控机床使用过程中的各种工况，在数控机床原有的机床坐标系和工件坐标系的基础上提出了热态坐标系和冷态坐标系的概念。应用热态坐标系和冷态坐标系的概念，对数控机床的各种工况进行了深入的分析，为工件数控加工过程中出现的各种意外情况提供了解决问题的思路。
When a NC machining tool is working, heat disturbances at internal and external thermal resource cause a non-even temperature field in the machining tool. At the same time, the coefficients of thermal expansion are different, the thermal stress and thermal deformation also emerge in parts of machining tool. The correct position relationship between tool and work is destroyed, and the accuracy of machining tools is come down, so the thermal error comes into being. In the process of precise machining, the thermal error of the mechanical process system covers 40-70% of the total machine error, the thermal error of machining tool covres 60-80% of thermal error. The thermal deformation has become the major error in precision and extra-precision machine.
In this thesis, a vertical machine centers is our research object. A large of tests state that friction heat of the spindle bearings is the major thermal resource. In spindle box ,it is also the major reason that leads to the thermal error of spindle. The contact deformation and load distribution between balls and rings have been researched with the theory of Hertz contact; Applying the kinematics principle, the ball motions have been analyzed, and formulas of the velocity have also been build. The formulas of friction force and torque have been build with mathematics inference and experiment. At last, on the basis of the friction torque and velocity, the thermal resource model of spindle bearings has been build.
The process factors that affect spindle bearing's friction heat have been analyzed, and many tests have done to verify the result. The regular that the interference between bearings and spindle and spindle sleeves affects the thermal deformation error has been researched according to the thermal stress theory. Afer improving the assemble technology and decreasing the interference, temperature raise in key point and thermal error all are cut down. These methods verify the regular correct.
Before thermal error compensates in a NC machining center, we must determine the key temperature measurement points. The points are more , the input information about the thermal character is more precise, but the cost for temperature measurement is more expensive, and the compensation system deal with the temperature information is more difficulty. So the least measurement points must be selected to express the thermal character information as full as possible. The fuzzy group and correlation analysis are made used of to optimizate the key points. At first some initia temperature measurement points in spindle box are selected as optimization base. Secondly these points are divided into several groups by fuzzy group theory. At last we select point from every group, them are accept or reject according to the result of correlation analysis. The error compensation has verified that the selected points are satisfied with the accuracy require of machining center.
The following thing is to model relationship between the thermal error and temperature raise of key points. In this thesis multiple linear regression is applied to build model, and the experimental test in the vertical machining center has already stated that the effect is very ideal. Based on multiple linear regression, the piecewise linear regression is lead into build the thermal error model. The simulation result states it can make thermal error further descend.
The thermal model based RBF(radial base function) neural netwoks has been built. The measurement data on the vertical machining center has been analysed. The result states that the model can be more closed to the real thermal model and reduce the effect of thermal error.
On the basis of the machining tool coordinate system and work coordinate system, the thermal coordinate system and cool coordinate have put forward. All cases in machine process are deeply analyzed with these concepts. The methods that solve all questions in most abnormal cases also are list.
本文以某立式加工中心为实验对象，通过大量的实验验证了主轴轴承的摩擦发热是主轴箱内的主要热源，是引起机床主轴热变形和热误差的主要原因；利用赫兹接触理论，分析了主轴轴承上钢球与滚道的接触变形和载荷分布；应用运动学理论分析了主轴轴承上钢球的运动及速度；将数学推导和经验公式相结合建立了主轴轴承运动过程中所产生的各种摩擦力矩及摩擦力的数学公式；在综合钢球的摩擦力矩和运动速度的基础上建立了机床主轴轴承摩擦热源的发热模型。
本文动态地分析了影响主轴轴承发热的工艺因素，并进行了相应的试验验证。利用热应力理论分析了主轴转速、轴承内外圈与主轴及轴套的配合过盈量对主轴热变形位移的影响规律。在对主轴轴承的装配工艺及配合过盈量进行有效改进的基础上，主轴箱测温点的温升和热位移达到很大的改善，验证了过盈量大小对主轴热位移的影响规律。
对数控机床进行热误差补偿时，补偿系统的信息输入是机床的温度场信息，为了最佳地把握机床的温度场信息，同时又降低温度测量的成本，本文结合模糊聚类和相关性分析理论来优化机床热关键点。在初步选定多个测温点的前提下，利用模糊聚类分析原理把测温点聚类分组，再从每组中选一个测温点，利用相关性分析，最终确定测温点的位置和数目。最后的补偿结果证明所选定的关键测温点能保证机床精度补偿的要求。
在确定测温点的前提下，需要建立测温点温升和热误差之间的关系模型。本文结合生产现场实际，应用多元线性回归模型对热误差建模，补偿结果表明初步收到良好的效果。在多元线性回归建模的基础上，应用分段线性回归模型进行建模，通过数据分析表明，进一步提高了热误差的精度。
利用径向基神经网络技术建立了测温点温升和热误差之间的关系模型，并应用该模型对某立式加工中心主轴箱上的测量数据进行了分析，结果表明径向基神经网络模型能够很好地逼近实际的热误差模型，从而降低热误差。
针对数控机床使用过程中的各种工况，在数控机床原有的机床坐标系和工件坐标系的基础上提出了热态坐标系和冷态坐标系的概念。应用热态坐标系和冷态坐标系的概念，对数控机床的各种工况进行了深入的分析，为工件数控加工过程中出现的各种意外情况提供了解决问题的思路。
When a NC machining tool is working, heat disturbances at internal and external thermal resource cause a non-even temperature field in the machining tool. At the same time, the coefficients of thermal expansion are different, the thermal stress and thermal deformation also emerge in parts of machining tool. The correct position relationship between tool and work is destroyed, and the accuracy of machining tools is come down, so the thermal error comes into being. In the process of precise machining, the thermal error of the mechanical process system covers 40-70% of the total machine error, the thermal error of machining tool covres 60-80% of thermal error. The thermal deformation has become the major error in precision and extra-precision machine.
In this thesis, a vertical machine centers is our research object. A large of tests state that friction heat of the spindle bearings is the major thermal resource. In spindle box ,it is also the major reason that leads to the thermal error of spindle. The contact deformation and load distribution between balls and rings have been researched with the theory of Hertz contact; Applying the kinematics principle, the ball motions have been analyzed, and formulas of the velocity have also been build. The formulas of friction force and torque have been build with mathematics inference and experiment. At last, on the basis of the friction torque and velocity, the thermal resource model of spindle bearings has been build.
The process factors that affect spindle bearing's friction heat have been analyzed, and many tests have done to verify the result. The regular that the interference between bearings and spindle and spindle sleeves affects the thermal deformation error has been researched according to the thermal stress theory. Afer improving the assemble technology and decreasing the interference, temperature raise in key point and thermal error all are cut down. These methods verify the regular correct.
Before thermal error compensates in a NC machining center, we must determine the key temperature measurement points. The points are more , the input information about the thermal character is more precise, but the cost for temperature measurement is more expensive, and the compensation system deal with the temperature information is more difficulty. So the least measurement points must be selected to express the thermal character information as full as possible. The fuzzy group and correlation analysis are made used of to optimizate the key points. At first some initia temperature measurement points in spindle box are selected as optimization base. Secondly these points are divided into several groups by fuzzy group theory. At last we select point from every group, them are accept or reject according to the result of correlation analysis. The error compensation has verified that the selected points are satisfied with the accuracy require of machining center.
The following thing is to model relationship between the thermal error and temperature raise of key points. In this thesis multiple linear regression is applied to build model, and the experimental test in the vertical machining center has already stated that the effect is very ideal. Based on multiple linear regression, the piecewise linear regression is lead into build the thermal error model. The simulation result states it can make thermal error further descend.
The thermal model based RBF(radial base function) neural netwoks has been built. The measurement data on the vertical machining center has been analysed. The result states that the model can be more closed to the real thermal model and reduce the effect of thermal error.
On the basis of the machining tool coordinate system and work coordinate system, the thermal coordinate system and cool coordinate have put forward. All cases in machine process are deeply analyzed with these concepts. The methods that solve all questions in most abnormal cases also are list.
引文
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