双滚轮-导轨式渐开线测量仪的空间几何误差补偿方法

A compensation method for spatial geometric error of double roller-rail involute measuring instrument

为解决1级齿轮渐开线样板的精密测量难题,提出了一种基于双滚轮-导轨式渐开线测量仪的空间几何误差补偿新方法。首先,建立了空间几何误差与渐开线齿廓偏差之间映射关系的数学模型;然后,基于该模型对齿轮渐开线样板、基圆盘与芯轴的综合安装误差和基圆盘的圆度误差进行了具体分析;最后,通过改变渐开线展开长度对应的基圆盘使用圆弧段、综合安装偏心量及相位等参数,实测了齿轮渐开线样板的齿廓偏差,并得出以下结论:基圆盘的圆度误差引起的齿廓偏差实测值与理论值之差不大于0.04μm;以偏心量e为3.46μm为例,纯滚动组件按照最大齿廓倾斜偏差相位(λ_(1)=λ_(2)=λ_(3)=70°)装配时,齿廓倾斜偏差f;的实测值与理论值相差-0.16μm,相对误差约为4%;按照最大齿廓形状偏差相位(λ_(1)=λ_(2)=λ_(3)=160°)装配时,齿廓形状偏差f;的实测值与理论值相差0.01μm,相对误差约为2%。实验结果证明了空间几何误差补偿方法的有效性,该补偿方法为实现1级齿轮渐开线样板的制造提供了测量手段。

To solve the difficult problem of precision measurements of class-1 gear involute artefacts,this paper proposes a new method of spatial geometric error compensation of a double roller-rail involute measuring instrument.First,a mathematical model of the mapping relationship between the spatial geometric error and involute tooth profile deviation is established.Subsequently,the comprehensive installation error of the gear involute artefact,the base discs,and the mandrel,and the roundness error of the base discs are analyzed based on the established model.Finally,the tooth profile deviations of the gear involute artefact are measured by changing parameters such as the arc segment of base discs corresponding to the roll path length of involute,the comprehensive installation eccentricity,and phase.The following conclusions are drawn.The difference between the measured and theoretical values of the tooth profile deviation caused by the roundness error of the base discs is no more than 0.04μm.Considering the eccentricity e of 3.46μm as an example,when the pure rolling component is assembled according to the maximum profile slope deviation phase(λ_(1)=λ_(2)=λ_(3)=70°),the measured value of the profile slope deviation differs from the theoretical value by-0.16μm,and the relative error is about 4%.When assembled according to the maximum profile form deviation phase(λ_(1)=λ_(2)=λ_(3)=160°),the difference between the measured and theoretical values of the profile form deviation is 0.01μm,and the relative error is about 2%.The experimental results demonstrate the effectiveness of the spatial geometric error compensation method,which provides measurement means for realizing the high-precision manufacturing of class-1 gear involute artefact.