正交面齿轮传动的强度与动力学特性分析研究
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摘要
本文对正交面齿轮传动的啮合特性、强度特性和动力学特性进行了研究。其中，啮合特性包括面齿轮的齿面生成、齿宽设计、啮合轨迹分析以及重合度的计算；强度特性包括齿面接触应力、齿根弯曲应力以及齿面瞬时接触温升分析；动力学特性包括面齿轮传动系统的线性和非线性动力学特性分析。
在面齿轮传动的啮合特性研究中，推导了面齿轮的齿面方程，获得了面齿轮齿根根切和齿顶尖化的临界方程，及其相对应的最小内半径系数和最大外半径系数；对齿面上的接触轨迹进行了可视化仿真，分析了主要参数和安装误差对接触轨迹的影响；给出了高重合度面齿轮传动的实现方法，获得了重合度大于2的参数选择范围。
在面齿轮传动的齿面接触应力研究中，推导了圆柱齿轮和面齿轮的齿面曲率和点接触面齿轮传动中的诱导法曲率计算方程，分析了主要参数对齿面曲率的影响，获得了齿面曲率的变化规律；推导了齿面接触应力计算方程，获得了轴交角误差、轴交错误差和轴向偏移误差以及主要参数对齿面接触应力的影响规律。
在面齿轮传动的齿根弯曲应力研究中，根据面齿轮啮合传动的特点，提出了面齿轮计算几何模型的齿宽选择方法；采用正交试验法，确定了齿根弯曲应力计算几何模型的参数；采用有限元法，获得了齿根弯曲应力及其分布规律，提出了面齿轮传动的齿根最大弯曲应力计算的一种计算公式；进行了面齿轮传动中直齿圆柱齿轮齿根弯曲应力的试验，验证上述计算公式的正确性。
在面齿轮传动的齿面瞬时接触温升研究中，推导了齿面相对速度和齿面滑动速度方程，获得了齿面相对速度和齿面滑动速度的变化规律，分析了主要参数对齿面摩擦系数的影响；推导了点接触面齿轮传动的齿面瞬时接触温升计算方程，获得了轴交角误差、轴交错误差和轴向偏移误差以及主要参数对齿面瞬时接触温升的影响规律。
在面齿轮传动系统的动力学特性研究中，采用集中质量法建立了面齿轮传动系统的多自由度弯曲-扭转-轴向振动动力学模型；采用Runge-Kutta数值积分法对动力学微分方程进行了数值仿真分析，获得了面齿轮传动系统的线性动力学以及非线性动力学响应，分析了主要参数对动载荷系数、频率响应特性的影响；研究了面齿轮传动系统的非线性动力学分岔特性，获得了主要参数对系统动力学分岔特性的影响规律。
An investigation on meshing characteristics, strength and dynamic characteristics of theorthogonal face gear(FG) drives is made in this paper. Among them, the meshing characteristicsinclude the equations of FG tooth, tooth width design, contact path and the calculation of contactratio. The tooth contact stress, the bending stress and the scuffing of FG drives are included in theanalysis of the strength characteristics, and the linear and nonlinear dynamic responses are studied inthe investigation of dynamic characteristics of FG drives.
In the research on the meshing characteristics of FG drives, the equations of FG tooth, thelimiting equations of undercutting and pointing of FG are derived, and correspondingly the minimuminner radius and maximum outer radius coefficient is proposed. Visualizing contact path, and theeffect of transmission parameters and misalignment errors on the location of contact path is studied.The method to achieve high contact ratio of FG drives is analyzed, and parameter range is obtainedwith the contact ratio beyond two.
The principle curvatures of tooth surfaces and principle relative curvatures of FG drives in pointcontact are analyzed, and the distribution of these curvatures on tooth surface and their variation withtransmission parameters are obtained. Based on the Hertz theory, the formulae for calculating thetooth contact stress of FG drives is established，and the influences of transmission parameters andmisalignment errors for tooth contact stress is investigated, which includes shaft angle error, shaftcrossing error and axial shift error.
According to the meshing characteristics of FG drives, the tooth width of the three-teethgeometric model of FG is developed for calculating the bending stress. Using orthogonal experimentmethod, the design parameters is definited.The distribution of bending stress of FG and spur gear iscalculated by finite element mothod, and a expression of bending stress of FG drives is obtained. Thecorrectness of the expression of spur gear bending stress is testified by the experimentalinvestigations.
The tooth surface relative speed, tooth surface sliding speed and the friction coefficient arepresented, and their variation with transmission parameters is obtained in this paper. Based on the H.Blok’s theory, the formulae for calculating the transient contact temperature of a FG drive is presented.The influence of parameters on the transient contact temperature of a FG drive, including transmissionparameters, the shaft angle error, shaft crossing error and axial shift error, is analyed.
Based on the theory of the concentrated parameter, a three-dimensional dynamic model with multiple degrees of freedom for the FG transmission system is developed. Using the Runge-Kuttanumerical integral method, the linear and nonlinear dynamic responses of the FG transmission systemis obtained, and the dynamic behavior of FG transmission system including kinetic load modulus,frequency response characteristics and dynamical bifurcation, is analyzed with main parameters.
在面齿轮传动的啮合特性研究中，推导了面齿轮的齿面方程，获得了面齿轮齿根根切和齿顶尖化的临界方程，及其相对应的最小内半径系数和最大外半径系数；对齿面上的接触轨迹进行了可视化仿真，分析了主要参数和安装误差对接触轨迹的影响；给出了高重合度面齿轮传动的实现方法，获得了重合度大于2的参数选择范围。
在面齿轮传动的齿面接触应力研究中，推导了圆柱齿轮和面齿轮的齿面曲率和点接触面齿轮传动中的诱导法曲率计算方程，分析了主要参数对齿面曲率的影响，获得了齿面曲率的变化规律；推导了齿面接触应力计算方程，获得了轴交角误差、轴交错误差和轴向偏移误差以及主要参数对齿面接触应力的影响规律。
在面齿轮传动的齿根弯曲应力研究中，根据面齿轮啮合传动的特点，提出了面齿轮计算几何模型的齿宽选择方法；采用正交试验法，确定了齿根弯曲应力计算几何模型的参数；采用有限元法，获得了齿根弯曲应力及其分布规律，提出了面齿轮传动的齿根最大弯曲应力计算的一种计算公式；进行了面齿轮传动中直齿圆柱齿轮齿根弯曲应力的试验，验证上述计算公式的正确性。
在面齿轮传动的齿面瞬时接触温升研究中，推导了齿面相对速度和齿面滑动速度方程，获得了齿面相对速度和齿面滑动速度的变化规律，分析了主要参数对齿面摩擦系数的影响；推导了点接触面齿轮传动的齿面瞬时接触温升计算方程，获得了轴交角误差、轴交错误差和轴向偏移误差以及主要参数对齿面瞬时接触温升的影响规律。
在面齿轮传动系统的动力学特性研究中，采用集中质量法建立了面齿轮传动系统的多自由度弯曲-扭转-轴向振动动力学模型；采用Runge-Kutta数值积分法对动力学微分方程进行了数值仿真分析，获得了面齿轮传动系统的线性动力学以及非线性动力学响应，分析了主要参数对动载荷系数、频率响应特性的影响；研究了面齿轮传动系统的非线性动力学分岔特性，获得了主要参数对系统动力学分岔特性的影响规律。
An investigation on meshing characteristics, strength and dynamic characteristics of theorthogonal face gear(FG) drives is made in this paper. Among them, the meshing characteristicsinclude the equations of FG tooth, tooth width design, contact path and the calculation of contactratio. The tooth contact stress, the bending stress and the scuffing of FG drives are included in theanalysis of the strength characteristics, and the linear and nonlinear dynamic responses are studied inthe investigation of dynamic characteristics of FG drives.
In the research on the meshing characteristics of FG drives, the equations of FG tooth, thelimiting equations of undercutting and pointing of FG are derived, and correspondingly the minimuminner radius and maximum outer radius coefficient is proposed. Visualizing contact path, and theeffect of transmission parameters and misalignment errors on the location of contact path is studied.The method to achieve high contact ratio of FG drives is analyzed, and parameter range is obtainedwith the contact ratio beyond two.
The principle curvatures of tooth surfaces and principle relative curvatures of FG drives in pointcontact are analyzed, and the distribution of these curvatures on tooth surface and their variation withtransmission parameters are obtained. Based on the Hertz theory, the formulae for calculating thetooth contact stress of FG drives is established，and the influences of transmission parameters andmisalignment errors for tooth contact stress is investigated, which includes shaft angle error, shaftcrossing error and axial shift error.
According to the meshing characteristics of FG drives, the tooth width of the three-teethgeometric model of FG is developed for calculating the bending stress. Using orthogonal experimentmethod, the design parameters is definited.The distribution of bending stress of FG and spur gear iscalculated by finite element mothod, and a expression of bending stress of FG drives is obtained. Thecorrectness of the expression of spur gear bending stress is testified by the experimentalinvestigations.
The tooth surface relative speed, tooth surface sliding speed and the friction coefficient arepresented, and their variation with transmission parameters is obtained in this paper. Based on the H.Blok’s theory, the formulae for calculating the transient contact temperature of a FG drive is presented.The influence of parameters on the transient contact temperature of a FG drive, including transmissionparameters, the shaft angle error, shaft crossing error and axial shift error, is analyed.
Based on the theory of the concentrated parameter, a three-dimensional dynamic model with multiple degrees of freedom for the FG transmission system is developed. Using the Runge-Kuttanumerical integral method, the linear and nonlinear dynamic responses of the FG transmission systemis obtained, and the dynamic behavior of FG transmission system including kinetic load modulus,frequency response characteristics and dynamical bifurcation, is analyzed with main parameters.
引文
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