凸轮轮廓NURBS重构与工作特性优化研究
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摘要
在自动机械中，凸轮机构主要用作传动、导向和控制元件，其运动、动力等工作特性对自动机械的精度、效率和速度有决定性影响。本文在全面分析国内外凸轮机构运动和动力特性研究的基础上，提出了一种新的凸轮机构设计和优化方法，该方法以非均匀有理B样条(non-uniform rational B-splines, NURBS)为工具，通过凸轮廓线、廓面NURBS重构，进一步改善和提高凸轮机构的运动和动力等工作特性，从而满足各类自动机械对高速、高精度工作的日益追求。
NURBS曲线曲面因其优良的全局表达性和强大的局部调控性，正逐渐引起工程界重视并在各领域得到应用。本文首先分析了NURBS曲线曲面的数学模型及其模型特性，设计了曲线曲面NURBS重构流程，重点研究了NURBS曲线曲面控制参量节点矢量、权因子及控制顶点等各项参数的几何意义、对曲线曲面形状的影响及计算方法。
其次，在研究NURBS曲线曲面重构方法的基础上，提出了凸轮廓面NURBS重构的设计方法。为提高空间凸轮廓面的建模和创成精度，利用直纹面和等距曲面理论分析了空间凸轮廓面的几何特性，基于单参数曲面包络理论，建立了空间凸轮廓面方程。利用空间分度凸轮廓面方程获取离散点云数据，实现了空间凸轮廓面NURBS重构，建立了空间凸轮参数化特征模型。基于该模型，进行空间凸轮分度机构运动特性优化与仿真，进而生成加工制造模型，实现空间凸轮NURBS廓面的仿真加工和四轴铣削NURBS高品质创成。
再次，针对高速工况下凸轮机构动态特性变差的问题，利用NURBS曲线设计和优化凸轮机构从动件运动规律，进行高速凸轮廓线NURBS重构。采用动态分析方法，建立高速凸轮机构单自由度动态特性模型，推导了高速凸轮机构输入和动态输出之间的关系，获得了系统残余振动评价指标，由此建立了高速凸轮机构多目标动态特性优化模型。设计了集成禁忌搜索策略和变参数二次寻优思想的改进人工鱼群多目标优化算法。通过该算法对高速凸轮机构多目标动态特性优化模型寻优，以获取优化模型的Pareto最优解，藉此重构高速凸轮NURBS廓线，研究NURBS廓线高速凸轮机构的主振和余振响应，以降低系统的振动和冲击。
最后，采用运动和动力性能集成优化方法，基于NURBS曲线进一步研究凸轮机构的动力接触特性。以摆动从动件固定凸轮机构为研究对象，分析了槽道凸轮残膜捡拾机构的工作特性，设计了适合机构的单停留修正正弦（Modifed Sine，MS）运动规律曲线，考虑运动副摩擦，建立槽道凸轮残膜捡拾机构的动力模型，根据赫兹接触理论得到槽道凸轮残膜捡拾机构的接触应力计算方程。采用NURBS曲线进行槽道凸轮残膜捡拾机构的运动特性设计，以接触应力和加速度为优化目标，利用改进人工鱼群算法进行多目标优化，优化结果和运动仿真表明：与单停留MS廓线相比，优化后NURBS廓线槽道凸轮残膜捡拾机构的加速度和接触应力较小，冲击和磨损较轻，提高了机构工作的可靠性和使用寿命。
本文的研究结果为凸轮机构的设计与制造提供了一个新的方法和思路，对于提升我国中高端凸轮机构的研发水平，实现高端产品的国产化具有一定的理论研究价值和工程应用前景。
Cam mechanism is mainly used for transmission, guidance and control components, andits kinematics and dynamics performance have a great influence on precision, efficiency,speed and other characteristics of automatic machine. By analyzing and reviewing theexisting related research achievements about cam mechanism at home and abroad, a newdesign and manufacturing method for cam mechanism was proposed. To improve thekinematics and dynamics of cam mechanism, profile of cam was reconstructed using non-uniform rational B-splines (NURBS) to meet all kinds of automatic machinery increasinglypursuit of high speed, high precision work.
Considering its excellent global expression and powerful local regulation, NURBS hasaroused the attention in engineering field and has been applied in various fields. Firstly,Thispaper analyzed the mathematical model and the model characteristics of NURBS curve andsurface, and designed the NURBS curve and surface reconstruction process. The studyfocused on the geometric meaning and calculation method of control parameter node vector,power factor and control points, which affect the shape of curve and surface.
Secondly, based on the study of NURBS curve and surface reconstruction method, a newdesign method was presented to reconstruct cam profile with NURBS. In order to improvethe spatial cam surfaces modeling and machining precision, the geometric characteristics ofspace cam were analyzed with ruled surface and offset surface theory. Applying the singleparametric curve enveloping theory, the profile equation of spatial cam was established anddiscrete point cloud data were obtained. Non-uniform rational B-splines has been adopted toreconstruct the profile of spatial cam. Based on the parametric feature model, the spatial camindexing mechanism was set up to perform kinematics simulation, and then the anufacturingmodel was generated to simulate the spatial cam NC machining.
Thirdly, To improve dynamic characteristics of high-speed cam mechanisms，Non-uniform rational B-Spline was used to fit a modified-sine curve． Based on the SDOFelastic dynamic theory，a multi-objective dynamic optimization model for NURBS profilewas designed here． The multi-objective dynamic model was optimized to search a Paretooptimal solution with an improved artificial fish swarm algorithm，the optimized NURBS profile was acquired． The dynamic responses of a high-speed cam mechanism underNURBS profile and modified sine profile were analyzed and compared． The resultsshowed that the improved artificial fish swarm algorithm can effectively solve the multi-objective optimization problem. The optimized NURBS profile keeps the modified sineprofile's fine kinematic characteristics，and the residual vibration is reduced. The high-speed cam mechanism designed by using this method has advantages of stable transmissionand lower noise．
Finally, kinematic design was proposed for grooved cam plastic film collector using non-uniform rational B-splines. By considering Joint friction, a dynamic model of plastic filmcollector was established and the equation for calculating the contact stress was deducedusing Hertz contact theory. Taking the minimum contact stress and the minimumacceleration as the optimal objective, integrated design model for respective kinematic anddynamic design approaches was set up and optimized with an improved artificial fish swarmalgorithm. The results show NURBS profile has better kinematic and dynamic performances.The impact of the plastic film collector is reduced and wear characteristics are improved.The research results of this paper provide a new method for the design and manufacturingof cam mechanism, which promote cam mechanism research and development level in ourcountry, and has theoretical research value and application prospect in engineering.
NURBS曲线曲面因其优良的全局表达性和强大的局部调控性，正逐渐引起工程界重视并在各领域得到应用。本文首先分析了NURBS曲线曲面的数学模型及其模型特性，设计了曲线曲面NURBS重构流程，重点研究了NURBS曲线曲面控制参量节点矢量、权因子及控制顶点等各项参数的几何意义、对曲线曲面形状的影响及计算方法。
其次，在研究NURBS曲线曲面重构方法的基础上，提出了凸轮廓面NURBS重构的设计方法。为提高空间凸轮廓面的建模和创成精度，利用直纹面和等距曲面理论分析了空间凸轮廓面的几何特性，基于单参数曲面包络理论，建立了空间凸轮廓面方程。利用空间分度凸轮廓面方程获取离散点云数据，实现了空间凸轮廓面NURBS重构，建立了空间凸轮参数化特征模型。基于该模型，进行空间凸轮分度机构运动特性优化与仿真，进而生成加工制造模型，实现空间凸轮NURBS廓面的仿真加工和四轴铣削NURBS高品质创成。
再次，针对高速工况下凸轮机构动态特性变差的问题，利用NURBS曲线设计和优化凸轮机构从动件运动规律，进行高速凸轮廓线NURBS重构。采用动态分析方法，建立高速凸轮机构单自由度动态特性模型，推导了高速凸轮机构输入和动态输出之间的关系，获得了系统残余振动评价指标，由此建立了高速凸轮机构多目标动态特性优化模型。设计了集成禁忌搜索策略和变参数二次寻优思想的改进人工鱼群多目标优化算法。通过该算法对高速凸轮机构多目标动态特性优化模型寻优，以获取优化模型的Pareto最优解，藉此重构高速凸轮NURBS廓线，研究NURBS廓线高速凸轮机构的主振和余振响应，以降低系统的振动和冲击。
最后，采用运动和动力性能集成优化方法，基于NURBS曲线进一步研究凸轮机构的动力接触特性。以摆动从动件固定凸轮机构为研究对象，分析了槽道凸轮残膜捡拾机构的工作特性，设计了适合机构的单停留修正正弦（Modifed Sine，MS）运动规律曲线，考虑运动副摩擦，建立槽道凸轮残膜捡拾机构的动力模型，根据赫兹接触理论得到槽道凸轮残膜捡拾机构的接触应力计算方程。采用NURBS曲线进行槽道凸轮残膜捡拾机构的运动特性设计，以接触应力和加速度为优化目标，利用改进人工鱼群算法进行多目标优化，优化结果和运动仿真表明：与单停留MS廓线相比，优化后NURBS廓线槽道凸轮残膜捡拾机构的加速度和接触应力较小，冲击和磨损较轻，提高了机构工作的可靠性和使用寿命。
本文的研究结果为凸轮机构的设计与制造提供了一个新的方法和思路，对于提升我国中高端凸轮机构的研发水平，实现高端产品的国产化具有一定的理论研究价值和工程应用前景。
Cam mechanism is mainly used for transmission, guidance and control components, andits kinematics and dynamics performance have a great influence on precision, efficiency,speed and other characteristics of automatic machine. By analyzing and reviewing theexisting related research achievements about cam mechanism at home and abroad, a newdesign and manufacturing method for cam mechanism was proposed. To improve thekinematics and dynamics of cam mechanism, profile of cam was reconstructed using non-uniform rational B-splines (NURBS) to meet all kinds of automatic machinery increasinglypursuit of high speed, high precision work.
Considering its excellent global expression and powerful local regulation, NURBS hasaroused the attention in engineering field and has been applied in various fields. Firstly,Thispaper analyzed the mathematical model and the model characteristics of NURBS curve andsurface, and designed the NURBS curve and surface reconstruction process. The studyfocused on the geometric meaning and calculation method of control parameter node vector,power factor and control points, which affect the shape of curve and surface.
Secondly, based on the study of NURBS curve and surface reconstruction method, a newdesign method was presented to reconstruct cam profile with NURBS. In order to improvethe spatial cam surfaces modeling and machining precision, the geometric characteristics ofspace cam were analyzed with ruled surface and offset surface theory. Applying the singleparametric curve enveloping theory, the profile equation of spatial cam was established anddiscrete point cloud data were obtained. Non-uniform rational B-splines has been adopted toreconstruct the profile of spatial cam. Based on the parametric feature model, the spatial camindexing mechanism was set up to perform kinematics simulation, and then the anufacturingmodel was generated to simulate the spatial cam NC machining.
Thirdly, To improve dynamic characteristics of high-speed cam mechanisms，Non-uniform rational B-Spline was used to fit a modified-sine curve． Based on the SDOFelastic dynamic theory，a multi-objective dynamic optimization model for NURBS profilewas designed here． The multi-objective dynamic model was optimized to search a Paretooptimal solution with an improved artificial fish swarm algorithm，the optimized NURBS profile was acquired． The dynamic responses of a high-speed cam mechanism underNURBS profile and modified sine profile were analyzed and compared． The resultsshowed that the improved artificial fish swarm algorithm can effectively solve the multi-objective optimization problem. The optimized NURBS profile keeps the modified sineprofile's fine kinematic characteristics，and the residual vibration is reduced. The high-speed cam mechanism designed by using this method has advantages of stable transmissionand lower noise．
Finally, kinematic design was proposed for grooved cam plastic film collector using non-uniform rational B-splines. By considering Joint friction, a dynamic model of plastic filmcollector was established and the equation for calculating the contact stress was deducedusing Hertz contact theory. Taking the minimum contact stress and the minimumacceleration as the optimal objective, integrated design model for respective kinematic anddynamic design approaches was set up and optimized with an improved artificial fish swarmalgorithm. The results show NURBS profile has better kinematic and dynamic performances.The impact of the plastic film collector is reduced and wear characteristics are improved.The research results of this paper provide a new method for the design and manufacturingof cam mechanism, which promote cam mechanism research and development level in ourcountry, and has theoretical research value and application prospect in engineering.
引文
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