齿轮齿条直线运动的线性测量与分析

Linear Measurement and Analysis of Linear Movement of Gear Rack

摘要:

在齿轮传动机构的直线运动研究中,为了测量直线误差,设计了齿轮齿条的测量平台；采用伺服电机直接驱动齿轮在齿条上运动,并以基于运动控制点位运动模式来实现测量间距和待机等控制要求；在齿轮齿条传动机构直线运动的过程中,用激光干涉仪对与齿轮同轴运动的工作台实际运动位置测量,获得测量数据；用最小二乘法求解线性矛盾方程的方法来构造拟合函数,并将其推广至任意次和任意多个变量的拟合函数,使用MATLAB编程求解,获得与设计数据曲线对应的实际数据曲线,得出齿轮齿条的线性定位精度和重复精度；这项技术可以推广到对大多数的直线运动机构来进行线性测量及数据分析；也能成为直线运动控制中线性参数自动补偿算法的依据。

Abstract:

In the research of the linear motion of the gear drive mechanism, the measuring platform of the gear rack is designed in order to measure the linear error. using servo motor directly drives the gears on the rack. and is based on the motion control PT point mode to realize the measurement of the Measuring distance and standby control requirements etc.In the process of the linear motion of the gear and rack drive mechanism, the measuring data is obtained by using the laser interferometer to measure the position of the actual movement of the gear axis. Using the least square method to solve the linear equations of contradiction, and to extend it to any number of times and arbitrary number of fitting functions, using MATLAB programming to obtain the actual data curve corresponds with design data curve,and the linear positioning accuracy and repeatability of gear and rack。This technology can be extended to linear measurement and data analysis of the majority of linear motion mechanism. It can also be used as the basis for the automatic compensation algorithm of linear motion control.