Research On Quasi Static Error Measurement,Modeling And Compensation Of Worm Wheel Gear Grinding Machine

The worm wheel grinding machine tool is used for gear batch processing with small and medium modulus.The quasi-static error is composed of geometric error and thermal error,which determines the processing quality of gears to a great extent.The spatial structure of the worm wheel gear grinding machine is similar with the 5-axis horizontal machining center,but the high-precision motorized spindle needs to be linked with other moving axes at high speed in the grinding process.Therefore,the gear grinding machine is essentially a 6-axis machine tool,which makes the volumetric error model and decoupling compensation more complex than common 5-axis machine tools.The geometric errors consisting of the volumetric errors are up to 41 items,and most of them are difficult to detect directly,and the special structure different from the conventional machine tools increases the difficulty of measuring and identifying many geometric errors.In addition,the causes of the thermal error are complex.The temperature changing of linear axis,spindle and worktable can all lead to the thermal errors.Recognizing the thermal deformation principle of each functional component is an important premise to guarantee the actual machining accuracy.In this paper,the research on quasi-static error measurement,modeling and compensation of worm wheel gear grinding machine tool is carried out.The main research contents are as follows:(1)The forward modeling and reverse decoupling method of volumetric error model of the grinding machine are studied.Based on the screw theory,the kinematics model of6-axis grinding machine and the forward volumetric error model considering 41 geometric errors are established,and the Jacobian matrix of the volumetric error model is deduced through the product of exponential formula.The nonlinear relationship between the volumetric posture of the tool relative to the workpiece and the amount of moving axis is transformed into the linear relationship between the volumetric posture error and the compensation value of the moving axis,so as to realize the accurate correction of the volumetric posture error.At the same time,aiming at the poor compensation effect with incomplete degrees of freedom under the compensation motion constraints,a step-by-step Jacobian matrix decoupling compensation method is proposed.Based on the principle of pose before position,the posture matrix and position vector of the volumetric error model are decoupled successively,and the maximum compensation of position vector deviation is realized on the basis of posture matrix deviation compensation.Compared with the numerical decoupling method,the proposed decoupling method is approximate analytical and more accuracy,which provides a theoretical support for volumetric error compensation.(2)The measurement,identification and modeling methods of geometric error elements of the grinding machine are studied.A general identification model of positiondependent geometric errors of rotary axis with single axis driven is proposed.The model supports the construction of identification patterns according to the specific structure of the machine tool and the rotary axis,and the feasibility of the identification patterns is judged by calculating the rank of identification matrix.In addition,the existing positionindependent geometric error identification methods are optimized,and a multi-height circular trajectory measurement pattern is proposed to realize the stable identification of position-independent geometric error.The methods are applied to the identification of 10position-dependent geometric errors and 8 position-independent geometric errors of Aaxis and C-axis of the grinding machine.Using XM60 multi beam laser interferometer,18 position-dependent geometric errors of three linear axes are measured directly.Finally,the position-dependent geometric errors of axis rotary axes and linear axes are modeled with sum of sin functions and polynomial functions respectively.The measured and identified errors provide the data support for the volumetric error model.(3)The thermal error measurement and modeling method of the grinding machine are studied.A series of thermal characteristic experiments were carried out for the functional components including the X-axis,spindle and worktable leading the radial error of gear grinding machine.For the thermal error of X-axis,a step-by-step modeling method is proposed.The positioning error is decomposed into slope parameters representing the thermal expansion and intercept parameters representing the thermal drift.The two models are built step by step,and then the thermal error model of X-axis is constructed comprehensively.For the thermal error of spindle,worktable and the gear Mvalue,the regression models between the thermal error and the temperature are directly established based on multiple linear regression and support vector machine algorithm,and the accuracy and robustness of these models are verified by group prediction.Aiming at the poor prediction accuracy of the spindle thermal error model under complex working conditions,a temperature range index for evaluating the applicability of the thermal error model is proposed.The relationship between the temperature change range of the prediction group and the modeling group is quantitatively calculated,and the applicability of the current thermal error model is evaluated to realize the optimization of the thermal error model or the modeling temperature point.The experimental results show the usability of the proposed index.(4)The error compensation method of the worm grinding wheel gear grinding machine is studied.For the error of single axis,the methods of pitch error compensation and NC code modification are adopted for direct compensation.For the volumetric error,combined with the geometric error measured and identified,the proposed Jacobian matrix decoupling method based on product of exponential is applied to calculate the compensation motion command and realize the compensation of volumetric error.Aiming at the failure of volumetric error compensation under the limitation of compensation motion,the step-by-step Jacobian matrix decoupling method is modified,and the compensation with incomplete degrees of freedom is realized by considering the coordinates of specific points.For the thermal error,the compensation software is developed based on the secondary development human-machine interfaces software supported by the Siemens CNC system.Combined with the established spindle thermal error model and the M-value error model,the thermal errors of spindle and M-value error are compensated,and the maximum error of spindle and M-value after compensation is3.3 μm and 7.3 μm respectively.The experimental results show the effectiveness of the compensation method.