摆动从动件空间凸轮设计及非等径加工研究
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摘要
空间凸轮机构已被广泛应用于机械设备的各个领域,但常用的空间凸轮平面展开法在设计过程中错误地用从动件轴线偏离空间凸轮主母线的直线距离取代了对应的空间凸轮上圆弧的展开长度,产生了较大的设计误差。而HSIEH等用解析法得出的解析式有较高的精度,却又过于复杂,无法实际应用。针对常用空间凸轮轮廓线在展开过程中产生的误差,本课题提出了用附加偏离角的方法对空间凸轮轮廓线的展开进行了修正,消除了现有设计中存在的误差；应用从动件运动轨迹的3D展开的新方法,构建了空间凸轮从动件运动轨迹的三维表达式,并依据空间凸轮的空间几何关系,推导了空间凸轮轮廓展开线的平面极坐标曲线方程；在此基础上对按正弦加速规律变化的空间凸轮机构轮廓线进行实例设计,根据极坐标曲线方程及运动规律函数表达式,用MATLAB软件求解曲线方程的坐标值,在AutoCAD软件中生成空间凸轮轮廓展开线,可得到满足运动规律要求的轮廓线在直角坐标系的展开图。本方法是一种设计过程简洁、直观,易于实现,易于掌握,且能避免传统设计误差的高精度摆动从动件空间凸轮轮廓展开线设计的新方法。
空间凸轮凹槽的加工也是个难题,特别是摆动从动件空间凸轮的非等径加工更是难以实现。通过对摆动从动件空间凸轮工作过程的分析,指出常用的平面展开及偏距加工法存在的问题。对空间凸轮的摆动从动件运动过程进行分解,提出从件运动轨迹的3D展开法,并在此基础上创造性地提出了一套摆动从动件空间凸轮非等径加工的“仿摆线”加工法,有效地解决了摆动从动件空间凸轮非等径加工的难题。
Spatial cam mechanism has been widely used in machinery and equipment in all areas. However, the commonly used planar expansion methods for the design of spatial cam contour produce significant errors, because these methods incorrectly use the distance from the axis of the follower to the main spatial cam to replace the corresponding arc length on the spatial cam. HSIEH, et al and others used analytical methods to achieve higher accuracy, but these analytical methods have their own drawbacks since these methods are too complicated for practical use. Through the analysis of the errors created during the generation of spatial cam contour using the existing expansion methods, this paper proposes to include diverge angle in the calculation of spatial cam rotation angle in the equation of spatial cam contour expansion. This correction eliminates the error generated by the commonly used methods. Based on the expression of the follower's 3D trajectory and the spatial geometry of spatial cam, this paper has deduced the planar polar curve equation for determining polar coordinates for the curve of planar expansion outline. Furthermore, this paper provides an example of spatial cam contour design based on sinusoidal acceleration variation. According to polar coordinates and the movement of curve equation function expression, this paper applies MATLAB software to solve coordinates for the cam expansion curve and use AutoCAD software to generate spatial cam expansion contour that meets the requirement of the law of motion. This method provides a design process that is simple, intuitive and easy to master and implement. It also avoids the design error in the traditional methods for generating contour of spatial cam with oscillating follower that requires high precision.
However, non-equalization machining for spatial cam trough remains to be a difficult problem. This paper focuses on the analysis of running conditions and machining processes of spatial cam with oscillating follower. We point out the common errors in the biased distance cutting. By analyzing the motion of oscillating follower of spatial cam, we present a new 3D curve expansion model of spatial cam trough-outline. Based on this model, we have proposed a machining method for trochoidal milling with non-equalization diameter cutter. This new method has led to a creative and effective way for non-equalization diameter machining for spatial cam with oscillating follower.
空间凸轮凹槽的加工也是个难题,特别是摆动从动件空间凸轮的非等径加工更是难以实现。通过对摆动从动件空间凸轮工作过程的分析,指出常用的平面展开及偏距加工法存在的问题。对空间凸轮的摆动从动件运动过程进行分解,提出从件运动轨迹的3D展开法,并在此基础上创造性地提出了一套摆动从动件空间凸轮非等径加工的“仿摆线”加工法,有效地解决了摆动从动件空间凸轮非等径加工的难题。
Spatial cam mechanism has been widely used in machinery and equipment in all areas. However, the commonly used planar expansion methods for the design of spatial cam contour produce significant errors, because these methods incorrectly use the distance from the axis of the follower to the main spatial cam to replace the corresponding arc length on the spatial cam. HSIEH, et al and others used analytical methods to achieve higher accuracy, but these analytical methods have their own drawbacks since these methods are too complicated for practical use. Through the analysis of the errors created during the generation of spatial cam contour using the existing expansion methods, this paper proposes to include diverge angle in the calculation of spatial cam rotation angle in the equation of spatial cam contour expansion. This correction eliminates the error generated by the commonly used methods. Based on the expression of the follower's 3D trajectory and the spatial geometry of spatial cam, this paper has deduced the planar polar curve equation for determining polar coordinates for the curve of planar expansion outline. Furthermore, this paper provides an example of spatial cam contour design based on sinusoidal acceleration variation. According to polar coordinates and the movement of curve equation function expression, this paper applies MATLAB software to solve coordinates for the cam expansion curve and use AutoCAD software to generate spatial cam expansion contour that meets the requirement of the law of motion. This method provides a design process that is simple, intuitive and easy to master and implement. It also avoids the design error in the traditional methods for generating contour of spatial cam with oscillating follower that requires high precision.
However, non-equalization machining for spatial cam trough remains to be a difficult problem. This paper focuses on the analysis of running conditions and machining processes of spatial cam with oscillating follower. We point out the common errors in the biased distance cutting. By analyzing the motion of oscillating follower of spatial cam, we present a new 3D curve expansion model of spatial cam trough-outline. Based on this model, we have proposed a machining method for trochoidal milling with non-equalization diameter cutter. This new method has led to a creative and effective way for non-equalization diameter machining for spatial cam with oscillating follower.
引文
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