【作者】 李蕾；

【导师】 冯显英；

【作者基本信息】 山东大学 ， 机械电子工程， 2011， 博士

【摘要】 空间分度凸轮机构作为实现“连续输入-间歇输出”功能的关键组件,广泛应用于各种自动机械、生产线和加工中心中。根据点啮合化处理技术,本文在球面包络弧面分度凸轮机构的基础上提出了滚珠型弧面分度凸轮机构,并围绕此机构展开了几何特性、静力学、运动学及动力学方面的研究。本文的主要研究内容如下：提出滚珠型弧面分度凸轮机构,对机构的几何特性进行了分析。在球面包络弧面分度凸轮机构的基础上,对凸轮廓面滚道及分度盘球座进行改进设计,分析滚珠型弧面分度凸轮机构的结构特点。利用回转变换张量法及空间啮合原理推导双圆弧滚道弧面凸轮的廓面方程；计算双圆弧滚道弧面凸轮的压力角,并对机构中心距、分度盘回转半径以及分度盘凸轮角速度比值对压力角的影响进行分析,提出了降低压力角的措施；给出螺旋升角的计算公式,并分析了凸轮廓面的曲率,得到了凸轮廓面与滚珠曲面在啮合点处的诱导主曲率。几何特性分析是机构其它方面分析研究的基础,并为结构设计提供了依据。对滚珠型弧面分度凸轮机构中的滚珠运动及机构静力学进行了研究。滚珠型弧面分度凸轮机构的滚珠能够沿任意方向转动,滚珠的转动对润滑性能影响很大。对滚珠运动分析得到滚珠与凸轮啮合点处相对滑动速度及其在各坐标轴上的分速度随分度盘转角变化的曲线,并对滚珠的回转运动进行了分析。在滚珠运动分析的基础上对机构进行受力分析,分别得到滚珠、分度盘及凸轮的受力状况。分析滚珠与凸轮啮合时的接触特性,对接触应力进行计算,得到结构参数对接触特性的影响,为改善接触特性提供了依据。对机构建立三维模型并进行运动仿真,验证模型建立的正确性。对滚珠型弧面分度凸轮机构的动力学进行了研究。为了得到高速高精度的弧面分度凸轮机构必须研究机构的动力学特性。论文主要采用集中质量法对滚珠型弧面分度凸轮机构进行动力学分析。首先建立机构扭转动力学模型,建立了凸轮与分度盘之间的等效接触刚度,分析广义坐标微小变动量间的几何位移关系,应用拉格朗日方程建立扭转动力学方程。在扭转动力学模型的基础上,进一步考虑输入输出轴的横向振动及轴向振动,得到机构更为精细的动力学模型,并建立其动力学方程。求解动力学方程得到机构多阶固有频率、低阶振型及机构的速度、加速度响应。分析了凸轮轴与分度盘的扭转变形以及刚度变化对动力学特性的影响。考虑电机因素,以永磁同步电机为驱动电机,对整个系统进行了动力学分析。建立系统机电耦合动力学模型,通过系统力学方程和电压方程得到机电耦合动力学方程。对机电耦合动力学方程进行求解,得到电机转速、电流以及分度盘与载荷盘的加速度变化曲线,并且得到了电机转速及负载变化对机电耦合振动特性的影响。机电耦合动力学模型的分析揭示了电机与机构动力学特性间的相互联系。引入控制算法后得到系统动力学响应,首先加入PI控制,得到分度盘和载荷盘的加速度曲线,系统动态特性得到改善。通过Simulink分别对PI控制及模糊PI控制下的机电耦合动力学模型进行仿真,得到了电机速度、电流及载荷盘的加速度曲线,仿真结果与理论结果变化趋势一致。通过不同控制算法下的结果对比,发现模糊PI控制下的机构动态性能更好。对滚珠型弧面分度凸轮机构进行动力学响应实验研究。首先介绍滚珠型弧面分度凸轮机构结构的主要几何参数,然后对机构进行了固有频率和动态特性测试实验,得到不同输入转速下载荷盘的加速度响应和机构在不同啮合位置时的固有频率,为修正动力学模型及验证理论计算结果提供了实验数据。本文的工作为滚珠型弧面分度凸轮机构的进一步研究奠定了基础,并为其它点接触弧面分度凸轮机构提供了借鉴,有助于实现弧面分度凸轮机构的高质量运行。更多还原

【Abstract】 Spatial indexing cam mechanism is widely used in automatic machines, production lines and machining centers as the key component to realize the function from continuous input to intermittent output. According to point engagement processing technology, based on spherical envelope indexing cam mechanism this paper puts forward globoidal indexing cam mechanism with steel ball and makes research on geometric features, statics, kinematics and dynamics. Main tasks are as follows:Globoidal indexing cam mechanism with steel ball was proposed, and structural characteristics of the mechanism were analyzed. Cam profile raceway and indexing plate ball seat were modified based on spherical envelope indexing cam mechanism, and the structural characteristics of globoidal indexing cam mechanism with steel ball were analyzed. Profile equation of globoidal cam with double-circular-arc raceway was derived based on the rotation tensor transformation method and the spatial engagement principle. Pressure angle of globoidal cam was calculated; analysis of influences on pressure angles exerted by the center distance of mechanism, the radius of gyration of the indexing plate and the angular velocity ratio between cam and indexing plate was made; measures as to how to reduce pressure angles were come up with; the calculation formula of helix angle was given and the curvature of cam surface was analyzed, and then the induced main curvature at engaging point between cam profile and ball surface could be obtained. Geometric characteristic was the foundation of mechanism analysis, which could provide basis for structural design.Ball motion of globoidal indexing cam mechanism and mechanism statics were studied. Steel ball in globoidal indexing cam mechanism could rotate in any direction, and the rotation of steel ball had great influence on lubrication performance. Through analysis on the movement of steel ball can relative sliding velocity at engaging point between steel ball and cam and the curve of component velocity of steel ball with the rotation angle in each coordinate axis were obtained, and the redundant rotary motion of steel ball was also researched. Based on the analysis of steel ball motion to analyze the force of mechanism could get the force of cam, indexing plate and ball respectively. Analysis of the contact characteristics between cam and steel ball at the engaging point was carried out. contact stress was calculated, and the influence of structure parameters on contact characteristics was analyzed which could be improved by the conclusions. Based of three-dimensional model of the mechanism kinematics simulation was conducted, and simulation results could provide proof of accuracy of the model.Dynamics of globoidal indexing cam mechanism with steel ball was studied. To get the globoidal indexing cam mechanism with high speed and high accuracy, dynamic characteristics of mechanism must be researched. This dissertation mainly used lumped mass method to analyze the dynamic characteristics of the mechanism. Torsional dynamic model of the mechanism was firstly established, equivalent contact stiffness between cam and indexing plate was built, geometric displacement relation of minimal variation quantity of generalized coordinates was analyzed, and finally the torsional dynamic equation was established by using Lagrange equation. Based on torsional dynamic model, a more precise dynamic model of the mechanism can be obtained with further consideration of transverse and axial vibration of the input and output shaft, then the dynamic equations were established. Through solving the dynamic equation multiple natural frequencies, low-order vibration mode and velocity and acceleration response of mechanism were obtained. Torsional deformation of cam shaft and indexing plate and the influence of stiffness change on dynamic characteristics were analyzed.Motor factors considered, taking the permanent magnet synchronous motor as driving motor, dynamic analysis of the whole system was analyzed. Electromechanical coupling dynamic model of system was established. Through establishment of mechanics equations and voltage equations of system electromechanical coupling dynamic equations were obtained. Through solving the electromechanical coupling dynamic equations motor speed, current, and acceleration curve of indexing plate and load plate were obtained, and the influence of motor speed and load change on electromechanical coupling vibration characteristic was also obtained. Analysis on electromechanical coupling dynamic model can reveal the relationship between motor characteristic and dynamic characteristic of mechanism. By introducing PI control acceleration curves of indexing plate and load plate of the system were reached, and the dynamic characteristic of the system could be improved. Based on Simulink simulations of electromechanical coupling dynamic model based on PI control and fuzzy PI control respectively motor speed, current and the acceleration curve load plate were obtained, and the simulation results and the theoretical results were consistent. Results contrast of different control algorithms proved that the dynamic performance under fuzzy PI control was better.Experimental research of dynamic response of globoidal indexing cam mechanism with steel ball was conducted. Main geometric parameters of globoidal indexing cam mechanism with steel ball were introduced; test experiments of natural frequency and dynamic characteristics of mechanism were conducted to obtain both the acceleration response of load plate at different input speed and the natural frequency of mechanism at different engaging positions, which provided experimental data for modifying dynamic model and verifying the theoretical results.The present study lays foundations for further research on globoidal indexing cam mechanism with steel ball, and provides reference for point engagement globoidal indexing cam mechanism. The research in this dissertation is helpful to realizing a high-quality performance of globoidal indexing cam mechanism.更多还原