基于目标约束的NURBS方法凸轮曲线寻优创成设计
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摘要
针对凸轮机构的设计优化问题,提出了一种通用的NURBS(Non Uniform Rational B-Splines)凸轮曲线寻优创成设计方法,即采用NURBS曲线实现凸轮从动件位移、速度、以及加速度的表达。在约束条件及目标函数的双重限制下,通过数值迭代优化算法对NURBS曲线的控制顶点及权因子进行同步整定以实现凸轮曲线的优化设计与创成,使其满足设计所要求的运动学约束、几何约束、压力角约束、运动不失真条件等综合性能指标。特别地,此方法不仅能够实现优化水平的整体控制,还能够对凸轮运动曲线的局部形状实现自适应调整,使其具有最佳的性能特征。以一DRD(Dwell-RiseDwell)型直动从动件盘型凸轮机构的凸轮曲线设计为例,验证了NURBS凸轮曲线寻优创成设计方法的有效性。应用实例表明,与传统的凸轮曲线设计方法相比,基于目标约束的NURBS方法凸轮曲线寻优创成设计能够在强耦合的约束关系之间,获得目标设计参数最优的凸轮曲线形状表达。
A general searching method is presented for the optimum generative design of a cam curve.This method involves the use of Non Uniform Rational B- Splines( NURBS) outputs for representing the follower motions,namely as displacement,velocity and acceleration. Using a numerical iterative approach optimized in a constraint and objective function set,the optimum design is obtained by simultaneously adjusting the multiple control points and weights of the NURBS parameters. The results yield to a generative motion that satisfy the prescribed terminal conditions that include performance criteria related to kinematic,geometry,pressure angle as well as undercutting property of the system. Particularly,this method can control not only the level but also the local shape of the motion curves to better performance property. The effectiveness of the approach is illustrated by comparing the results between the present method and the conventional curves for a disk cam- follower mechanism specified in Dwell- Rise- Dwell( DRD) follower motion type. Example shows that the obtained cam profile provide a good solution for the strong coupling constraints in the cam optimization design.
A general searching method is presented for the optimum generative design of a cam curve.This method involves the use of Non Uniform Rational B- Splines( NURBS) outputs for representing the follower motions,namely as displacement,velocity and acceleration. Using a numerical iterative approach optimized in a constraint and objective function set,the optimum design is obtained by simultaneously adjusting the multiple control points and weights of the NURBS parameters. The results yield to a generative motion that satisfy the prescribed terminal conditions that include performance criteria related to kinematic,geometry,pressure angle as well as undercutting property of the system. Particularly,this method can control not only the level but also the local shape of the motion curves to better performance property. The effectiveness of the approach is illustrated by comparing the results between the present method and the conventional curves for a disk cam- follower mechanism specified in Dwell- Rise- Dwell( DRD) follower motion type. Example shows that the obtained cam profile provide a good solution for the strong coupling constraints in the cam optimization design.
引文
[1]葛荣雨.基于NURBS的空间分度凸轮廓面创成与品质评价技术研究[D].济南:山东大学,2008:1-18.
[2]Berzak N.Optimization of Cam-follower systems with kinematic and dynamic constraints[J].Journal of Mechanical Design,1982,104(1):29-38.
[3]Rothbart H A,Klipp D L.Cam design handbook[M].New York:Mc Graw-Hill,2004:27-76.
[4]Qiu H,Lin C J,Li Z Y,et al.A universal optimal approach to cam curve design and its applications[J].Mechanism and Machine Theory,2005,40(6):669-692.
[5]Mandal M,Naskar T K.Introduction of control points in splines for synthesis of optimized cam motion program[J].Mechanism and Machine Theory,2009,44(1):255-271.
[6]Carra S,Garziera R,Pellegrini M.Synthesis of cams with negative radius follower and evaluation of the pressure angle[J].Mechanism and Machine Theory,2004,39(10):1017-1032.
[7]龙连春,黄金运.内燃机配气机构几何凸轮优化设计[J].柴油机,1997(1):20-24.
[8]周世才,杨玉虎,沈煜,等.新型分度机构的动力学建模与优化设计[J].机械工程学报,2010,46(19):9-16.
[9]Piegl L,Tiller W.The NURBS book[M].London:Springer,1997:117-138.
[10]Nguyen V T,Kim D J.Flexible cam profile synthesis method using smoothing spline curves[J].Mechanism and Machine Theory,2007,42(7):825-838.
[11]孙树峰,周以齐.基于非均匀有理B样条的空间凸轮设计[J].机械工程学报,2009,45(8):125-129.
[2]Berzak N.Optimization of Cam-follower systems with kinematic and dynamic constraints[J].Journal of Mechanical Design,1982,104(1):29-38.
[3]Rothbart H A,Klipp D L.Cam design handbook[M].New York:Mc Graw-Hill,2004:27-76.
[4]Qiu H,Lin C J,Li Z Y,et al.A universal optimal approach to cam curve design and its applications[J].Mechanism and Machine Theory,2005,40(6):669-692.
[5]Mandal M,Naskar T K.Introduction of control points in splines for synthesis of optimized cam motion program[J].Mechanism and Machine Theory,2009,44(1):255-271.
[6]Carra S,Garziera R,Pellegrini M.Synthesis of cams with negative radius follower and evaluation of the pressure angle[J].Mechanism and Machine Theory,2004,39(10):1017-1032.
[7]龙连春,黄金运.内燃机配气机构几何凸轮优化设计[J].柴油机,1997(1):20-24.
[8]周世才,杨玉虎,沈煜,等.新型分度机构的动力学建模与优化设计[J].机械工程学报,2010,46(19):9-16.
[9]Piegl L,Tiller W.The NURBS book[M].London:Springer,1997:117-138.
[10]Nguyen V T,Kim D J.Flexible cam profile synthesis method using smoothing spline curves[J].Mechanism and Machine Theory,2007,42(7):825-838.
[11]孙树峰,周以齐.基于非均匀有理B样条的空间凸轮设计[J].机械工程学报,2009,45(8):125-129.