滚珠型弧面凸轮分度系统动力学建模与分析
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摘要
弧面分度凸轮副是各种自动机械的关键功能部件,随着生产率的提高,机械的运转速度越来越高,本文提出了一种新型的基于钢球滚子的点啮合弧面分度凸轮副的结构,同其他形式滚子的弧面分度凸轮机构相比具有适应性强、传动效率好、高速性能优越、精度高、发热少、磨损小等优点,其“旋转—旋转”滚动传动副在目前数控机床等大型设备上还未见普及应用。对该新机构的研究,对于我国凸轮理论研究水平的提升和装备制造业的发展有着重要的实际意义。本课题在对钢球滚子弧面分度凸轮机构进行了建模与动力学方面的分析,主要工作集中在以下几个方面：
1.分析了钢球滚子弧面分度凸轮机构的约束类型和运动规律的特征值,对其常用的运动规律进行了比较分析,给出了分度凸轮运动规律选取的一般原则。
2.对钢球滚子弧面分度凸轮进行了啮合理论方面的分析,以空间回转变换张量和空间微分几何理论作为数学工具,采用回转运动群和圆矢量函数等数学表达方法,建立了工作滚道截形为双圆弧的弧面分度凸轮的数学模型,该模型通过控制滚道与钢球滚子的接触角,真正实现了分度盘从动件滚子与凸轮之间的点啮合传动。随后在Pro／e环境下建立了系统的三维几何模型,并对其压力角进行了分析,为后续的动力学分析奠定了基础。
3.在几何建模的基础上,分析给出了钢球滚子弧面分度凸轮机构的弹性动力学模型,应用拉格朗日方程研究了各个部位的动力学特性,建立了系统的整体动力学方程,并应用振型叠加法对其进行了解耦与求解分析,将结果与线啮合圆柱弧面分度凸轮进行了对比分析,阐述其优越性所在。
4.对弧面凸轮工作曲面进行了曲率分析,对比分析了修正正弦加速度、修正等速、修正梯形加速度三种运动规律的工作曲面曲率变化情况,应用Hertz接触模型对钢球滚子弧面凸轮机构进行了接触应力与接触变形分析,分析了影响接触应力与接触应变的因素。
Globoidal indexing cam mechanism is a key functional part of all kinds of automatic machines. With the promotion of produce efficiency, the rotational speed of machines goes higher and higher. A new type of Globoidal indexing cam mechanism based on steel balls which is engaged with the cam at one single point is presented. Compared with other types of indexing cam, it has an advantage in wide applicability, high transmission efficiency and precision, minor abrasion, superiority in performance of high rotational speed and better heat quality. The "rotation to rotation" transmission mechanism is rarely used in good-sized numerical control machines at present. It is of vital meaning that studying at the new mechanism to promote the cam academic level and advance the manufacturing. This academic dissertation establishes the model of the cam mechanism and analyses the dynamics response of the cam mechanism, the main work is listed as follows:
1. The constraint form and the motion law's characteristic value of the Globoidal indexing cam are analyzed, and the motion laws which are most widely used are compared and studied, the principle of how to select the cam mechanism motion law is presented.
2. The engage theory of the Globoidal indexing cam is studied based on the mathematic means of spatial rotation transformation tensor and space differential geometry theory. The mathematic model of the Globoidal indexing cam with double-arc cross-sectional shape working raceway is established by mathematic methods of rotary motion group and round vendor functions. This model genuinely achieves the point engagement transmission between the cam and indexing plate by controlling the contact angle of raceway and the steel balls. In addition, the geometric model is set up in Pro/e and the stress angle is analyzed, which provides a foundation for the followed dynamics studies.
3. Based on the geometric model, this dissertation has studied and build the elastodynamics model of the Globoidal indexing cam, analyzed the dynamics characteristic of every component by means of Lagrange equation., and established the dynamics equation of the whole system, solved the equation using the modal superposition method. Finally, the result is compared with the line engagement indexing cam, the superiority is presented.
4. This dissertation has analyzed the curvature of working surface of the Globoidal indexing cam, compared and studied curvature of three motion laws of revised isokinetic, revised trapezoidal acceleration and revised sine acceleration. In addition, this topic studied the contact stress and deformation of the Globoidal indexing cam using Hertz theory, presented the factors influencing the contact stress and deformation.
1.分析了钢球滚子弧面分度凸轮机构的约束类型和运动规律的特征值,对其常用的运动规律进行了比较分析,给出了分度凸轮运动规律选取的一般原则。
2.对钢球滚子弧面分度凸轮进行了啮合理论方面的分析,以空间回转变换张量和空间微分几何理论作为数学工具,采用回转运动群和圆矢量函数等数学表达方法,建立了工作滚道截形为双圆弧的弧面分度凸轮的数学模型,该模型通过控制滚道与钢球滚子的接触角,真正实现了分度盘从动件滚子与凸轮之间的点啮合传动。随后在Pro／e环境下建立了系统的三维几何模型,并对其压力角进行了分析,为后续的动力学分析奠定了基础。
3.在几何建模的基础上,分析给出了钢球滚子弧面分度凸轮机构的弹性动力学模型,应用拉格朗日方程研究了各个部位的动力学特性,建立了系统的整体动力学方程,并应用振型叠加法对其进行了解耦与求解分析,将结果与线啮合圆柱弧面分度凸轮进行了对比分析,阐述其优越性所在。
4.对弧面凸轮工作曲面进行了曲率分析,对比分析了修正正弦加速度、修正等速、修正梯形加速度三种运动规律的工作曲面曲率变化情况,应用Hertz接触模型对钢球滚子弧面凸轮机构进行了接触应力与接触变形分析,分析了影响接触应力与接触应变的因素。
Globoidal indexing cam mechanism is a key functional part of all kinds of automatic machines. With the promotion of produce efficiency, the rotational speed of machines goes higher and higher. A new type of Globoidal indexing cam mechanism based on steel balls which is engaged with the cam at one single point is presented. Compared with other types of indexing cam, it has an advantage in wide applicability, high transmission efficiency and precision, minor abrasion, superiority in performance of high rotational speed and better heat quality. The "rotation to rotation" transmission mechanism is rarely used in good-sized numerical control machines at present. It is of vital meaning that studying at the new mechanism to promote the cam academic level and advance the manufacturing. This academic dissertation establishes the model of the cam mechanism and analyses the dynamics response of the cam mechanism, the main work is listed as follows:
1. The constraint form and the motion law's characteristic value of the Globoidal indexing cam are analyzed, and the motion laws which are most widely used are compared and studied, the principle of how to select the cam mechanism motion law is presented.
2. The engage theory of the Globoidal indexing cam is studied based on the mathematic means of spatial rotation transformation tensor and space differential geometry theory. The mathematic model of the Globoidal indexing cam with double-arc cross-sectional shape working raceway is established by mathematic methods of rotary motion group and round vendor functions. This model genuinely achieves the point engagement transmission between the cam and indexing plate by controlling the contact angle of raceway and the steel balls. In addition, the geometric model is set up in Pro/e and the stress angle is analyzed, which provides a foundation for the followed dynamics studies.
3. Based on the geometric model, this dissertation has studied and build the elastodynamics model of the Globoidal indexing cam, analyzed the dynamics characteristic of every component by means of Lagrange equation., and established the dynamics equation of the whole system, solved the equation using the modal superposition method. Finally, the result is compared with the line engagement indexing cam, the superiority is presented.
4. This dissertation has analyzed the curvature of working surface of the Globoidal indexing cam, compared and studied curvature of three motion laws of revised isokinetic, revised trapezoidal acceleration and revised sine acceleration. In addition, this topic studied the contact stress and deformation of the Globoidal indexing cam using Hertz theory, presented the factors influencing the contact stress and deformation.
引文
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