受激并车弧齿锥齿轮系统两参量平面上解域界结构  

Solution domain structures of power combining spiral bevel gear system under excitations in two-parameter plane

作　　者：林何 洪灵[3] 江俊[3] 胥光申[1,2] LIN He;HONG Ling;JIANG Jun;XU Guang-shen(School of Mechanical and Electrical Engineering,Xi'an Polytechnic University,Xi'an 710048,China;Xi'an Key Laboratory of Modern Intelligent Textile Equipment,Xi'an Polytechnic University,Xi'an 710048,China;State Key Laboratory for Strength and Vibration of Mechanical Structures,Xi'an Jiaotong University,Xi'an 710049,China)

机构地区：[1]西安工程大学机电工程学院,陕西西安710048 [2]西安工程大学西安市现代智能纺织装备重点实验室,陕西西安710048 [3]西安交通大学机械结构强度与振动国家重点实验室,陕西西安710049

出　　处：《振动工程学报》2021年第5期1020-1026,共7页Journal of Vibration Engineering

基　　金：国家自然科学基金资助项目(51805402,11972274);陕西省自然科学基础研究计划项目(2019JQ-851);西安市现代智能纺织装备重点实验室(2019220614SYS021CG043)。

摘　　要：为掌握齿轮系统激振参数对系统动态特性的影响规律,建立了考虑多种激励的并车弧齿锥齿轮系统非线性动力学模型。应用胞映射(CMM)与区域离散分解技术(DDM)构建并数值求解了多组两参量平面上的解域界结构,算法基于吸引子在Poincaré截面上的点映射准则。通过分岔图和最大Lyapunov指数等分析了系统稳态特性,结果表明,啮合频率分岔路径上外加误差激励可使分岔中的部分周期分支收缩和转变。求解了阻尼比和综合传动误差分别与其他参数配置下的解域界演变,解析出周期域、混沌带与边界胞等分布特征,确定了目标参数域中周期分岔全局覆盖性态,通过最大Lyapunov指数和Poincaré映射验证了解域界算法中各态子域胞集的有效性。To explore the basic conduction between parameters and dynamic characteristics of gear system,a nonlinear dynamical model of power combining spiral bevel gear system(SBGs)with multiple excitations are formulated.Some groups of two-dimensional parameterized solution domain structure are investigated and numerical calculated by cell mapping method(CMM)and domain decomposition method(DDM),the algorithm is based on the point mapping criterion of attractor on Poincarésection.With the bifurcation diagram and maximum Lyapunov exponent(MLE),the stable state characteristic is inspected,the result demonstrates that additional transmission error excitation can alter partial branch of period trajectory to shrink and transform on the path of meshing frequency bifurcation.The evolution of solution domains is solved when the comprehensive transmission error as well as damping ratio is combined with other parameters respectively,the responses such as periodic domains,chaotic bands and even cells on boundary zone are computed,the global behavior of periodic bifurcation inside the parameter domain is analyzed,and the distribution of variety subdomains in the solution domain structure is verified by applying MLE and Poincarésection.

关 键 词：非线性振动 并车弧齿锥齿轮 胞映射 区域离散分解 解域界 

分 类 号：O322[理学—一般力学与力学基础] TH113.1[理学—力学]