非等模数非等压力角行星齿轮传动系统设计与动力学特性研究
发布时间：2018-12-06 12:04
【摘要】：本文对非等模数非等压力角行星齿轮传动系统的设计和动力学特性进行了研究,主要包括:非等模数非等压力角行星齿轮传动系统的几何参数计算及其优化设计、齿轮强度的计算与分析、系统的均载特性分析和试验验证、系统的非线性动力学建模型及其动力学特性分析。论文主要研究内容有:(1)推导了非等模数非等压力角齿轮副无侧隙啮合计算方程,给出了实际中心距、齿顶高变动系数等齿轮副几何参数的计算方法,并将它们应用到行星齿轮传动系统的参数计算中;建立了非等模数非等压力角齿轮副的接触应力计算方程,分析比较了内外啮合副在齿轮模数比不同时,齿轮副的接触强度、弯曲强度和胶合强度安全系数的变化趋势;建立了以体积最小和行星轮个数最优为目标函数的行星齿轮传动系统优化设计模型并求解运算,获得理想的设计方案,发挥了非等模数非等压力角齿轮副啮合性能。(2)考虑齿轮的偏心误差、齿频误差以及齿轮副的平均啮合刚度等,建立了非等模数非等压力角行星齿轮传动系统的静力学和动力学模型;分别运用力学平衡法和傅里叶级数法对力学方程进行数值仿真分析,获得了该系统的静力学和动力学响应;分析比较了非等模数非等压力角和等模数等压力角以及齿轮副压力角不同时的系统均载特性,获得了齿轮主要参数对系统均载性能的影响规律;开发了行星齿轮传动系统的均载特性分析软件;开展了均载性能试验验证测试,验证上述计算方法的正确性。(3)考虑到齿轮副齿侧间隙、时变啮合刚度和齿轮副综合误差,采用集中质量法建立了非等模数非等压力角行星齿轮传动系统的弯曲-扭转振动的非线性动力学模型;推导出多间隙、变参数的多自由度非等模数非等压力角行星齿轮传动系统的非线性无量纲化微分方程组。(4)利用谐波平衡法对动力学微分方程进行数值仿真,获得了系统的非线性动力学频域响应,分析了考虑齿侧间隙时该系统出现幅值跳跃现象的典型非线性特征;对非线性系统和线性系统、非等模数非等压力角系统和等模数等压力角系统进行了动态响应对比分析;研究了阻尼系数、啮合刚度变动系数和误差幅值对该系统动态特性的影响,获得了与线性系统响应不一致的非线性系统的变化规律。(5)利用龙格库塔法对非等模数非等压力角行星齿轮传动系统的动力学微分方程进行数值仿真,获得了不同激励频率下的系统非线性动态特性;研究了该系统的动力学分岔特性,获得了阻尼系数不同时系统随激励频率变化、激励频率不同时系统随着齿侧间隙变化时的分岔规律;研究了非线性模型下的行星齿轮传动系统功率分流均载特点,获得了齿轮副模数和齿侧间隙对系统均载性能的影响规律。
[Abstract]:In this paper, the design and dynamic characteristics of the non-constant modulus and unequal pressure angle planetary gear transmission system are studied. The main contents are as follows: the geometric parameter calculation and the optimization design of the non-equal modulus and non-equal pressure angle planetary gear transmission system. The calculation and analysis of gear strength, the analysis and verification of the system's average load characteristics, the establishment of nonlinear dynamic model and the analysis of its dynamic characteristics are presented. The main contents of this paper are as follows: (1) the calculation equation of non-equal modulus and unequal pressure angle gear pair is derived, and the calculation method of geometric parameters of gear pair, such as actual center distance, change coefficient of tooth top height and so on, is given. They are applied to the parameter calculation of planetary gear transmission system. The calculation equation of contact stress of non-equal modulus and unequal pressure angle gear pair is established, and the change trend of contact strength, bending strength and safety factor of adhesive strength of internal and external meshing pair is analyzed and compared with the difference of gear modulus ratio. The optimal design model of planetary gear transmission system with the minimum volume and the optimal number of planetary gears as the objective function is established and solved, and the ideal design scheme is obtained. The meshing performance of non-equal modulus, non-equal pressure angle gear pair is brought into play. (2) considering the gear eccentricity error, tooth frequency error and the average meshing stiffness of gear pair, etc. The statics and dynamics models of the planetary gear transmission system with non-constant modulus and unequal pressure angle are established. The static and dynamic responses of the system are obtained by numerical simulation and analysis of the mechanical equations by using the mechanical equilibrium method and the Fourier series method respectively. The load sharing characteristics of the system with different pressure angles of unequal modulus and equal modulus and pressure angle of gear pair are analyzed and compared, and the influence of main parameters of gear on the load sharing performance of the system is obtained. A software for the analysis of the load sharing characteristics of planetary gear transmission system is developed. The load sharing performance test was carried out to verify the correctness of the above calculation methods. (3) considering the gear pair side clearance, the time-varying meshing stiffness and the gear pair comprehensive error, The nonlinear dynamic model of the bending torsional vibration of the non-constant modulus and unequal pressure angle planetary gear transmission system is established by means of the lumped mass method. The nonlinear dimensionless differential equations of multi-degree-of-freedom, non-constant pressure angle planetary gear transmission systems with multiple clearances and variable parameters are derived. (4) the dynamic differential equations are numerically simulated by using harmonic balance method. The nonlinear dynamic frequency domain response of the system is obtained, and the typical nonlinear characteristics of the amplitude jump phenomenon are analyzed when the tooth side clearance is considered. The dynamic response of nonlinear system, linear system, non-equal modulus non-equal pressure angle system and equal modulus equal pressure angle system are compared and analyzed. The effects of damping coefficient, meshing stiffness variation coefficient and error amplitude on the dynamic characteristics of the system are studied. The variation law of nonlinear system which is inconsistent with the response of linear system is obtained. (5) the dynamic differential equation of the non-isodal non-isobaric angle planetary gear transmission system is numerically simulated by the Runge-Kutta method. The nonlinear dynamic characteristics of the system with different excitation frequencies are obtained. The dynamic bifurcation characteristics of the system are studied, and the bifurcation law is obtained when the damping coefficient varies with the excitation frequency and the excitation frequency varies with the tooth clearance. In this paper, the power distribution and load sharing characteristics of planetary gear transmission system under nonlinear model are studied, and the influence of gear pair modulus and tooth side clearance on the load sharing performance of the system is obtained.
【学位授予单位】：南京航空航天大学
【学位级别】：博士
【学位授予年份】：2014
【分类号】：TH132.41
本文编号：2365996
[Abstract]:In this paper, the design and dynamic characteristics of the non-constant modulus and unequal pressure angle planetary gear transmission system are studied. The main contents are as follows: the geometric parameter calculation and the optimization design of the non-equal modulus and non-equal pressure angle planetary gear transmission system. The calculation and analysis of gear strength, the analysis and verification of the system's average load characteristics, the establishment of nonlinear dynamic model and the analysis of its dynamic characteristics are presented. The main contents of this paper are as follows: (1) the calculation equation of non-equal modulus and unequal pressure angle gear pair is derived, and the calculation method of geometric parameters of gear pair, such as actual center distance, change coefficient of tooth top height and so on, is given. They are applied to the parameter calculation of planetary gear transmission system. The calculation equation of contact stress of non-equal modulus and unequal pressure angle gear pair is established, and the change trend of contact strength, bending strength and safety factor of adhesive strength of internal and external meshing pair is analyzed and compared with the difference of gear modulus ratio. The optimal design model of planetary gear transmission system with the minimum volume and the optimal number of planetary gears as the objective function is established and solved, and the ideal design scheme is obtained. The meshing performance of non-equal modulus, non-equal pressure angle gear pair is brought into play. (2) considering the gear eccentricity error, tooth frequency error and the average meshing stiffness of gear pair, etc. The statics and dynamics models of the planetary gear transmission system with non-constant modulus and unequal pressure angle are established. The static and dynamic responses of the system are obtained by numerical simulation and analysis of the mechanical equations by using the mechanical equilibrium method and the Fourier series method respectively. The load sharing characteristics of the system with different pressure angles of unequal modulus and equal modulus and pressure angle of gear pair are analyzed and compared, and the influence of main parameters of gear on the load sharing performance of the system is obtained. A software for the analysis of the load sharing characteristics of planetary gear transmission system is developed. The load sharing performance test was carried out to verify the correctness of the above calculation methods. (3) considering the gear pair side clearance, the time-varying meshing stiffness and the gear pair comprehensive error, The nonlinear dynamic model of the bending torsional vibration of the non-constant modulus and unequal pressure angle planetary gear transmission system is established by means of the lumped mass method. The nonlinear dimensionless differential equations of multi-degree-of-freedom, non-constant pressure angle planetary gear transmission systems with multiple clearances and variable parameters are derived. (4) the dynamic differential equations are numerically simulated by using harmonic balance method. The nonlinear dynamic frequency domain response of the system is obtained, and the typical nonlinear characteristics of the amplitude jump phenomenon are analyzed when the tooth side clearance is considered. The dynamic response of nonlinear system, linear system, non-equal modulus non-equal pressure angle system and equal modulus equal pressure angle system are compared and analyzed. The effects of damping coefficient, meshing stiffness variation coefficient and error amplitude on the dynamic characteristics of the system are studied. The variation law of nonlinear system which is inconsistent with the response of linear system is obtained. (5) the dynamic differential equation of the non-isodal non-isobaric angle planetary gear transmission system is numerically simulated by the Runge-Kutta method. The nonlinear dynamic characteristics of the system with different excitation frequencies are obtained. The dynamic bifurcation characteristics of the system are studied, and the bifurcation law is obtained when the damping coefficient varies with the excitation frequency and the excitation frequency varies with the tooth clearance. In this paper, the power distribution and load sharing characteristics of planetary gear transmission system under nonlinear model are studied, and the influence of gear pair modulus and tooth side clearance on the load sharing performance of the system is obtained.
【学位授予单位】：南京航空航天大学
【学位级别】：博士
【学位授予年份】：2014
【分类号】：TH132.41
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