A hybrid finite element and analytical model for determining the mesh stiffness of internal gear pairs

Journal of Mechanical Science and Technology - This work developed an efficient model for calculating the mesh stiffness of spur/helical internal gear pairs by combining the finite element method...     

含间隙和时变啮合刚度齿轮传动系统的分岔和混沌

齿侧间隙和时变啮合刚度的存在,使齿轮传动系统中存在着丰富的非线性动力学行为。基于Poincare映射,建立了两自由度齿轮传动系统的数学模型,并通过数值仿真,说明了齿轮传动系统中存在着倍周期分岔、Hopf分岔和混沌等复杂的非线性现象。分析了系统参数对齿轮动力学行为的影响,进而为消除齿侧间隙和时变啮合刚度引起的非线性动力学行为指明了方向,为齿轮传动系统的优化设计奠定了基础。     

A semi-analytical method of time-varying mesh stiffness in concentric face gear split-torque transmission system

Concentric face gear split-torque transmission system (CFGSTTS) has great applied value in the field of aeronautical transmission due to the characteristic of high integration. Mesh stiffness, as one of the most primary sources of vibration, is vitally important for the dynamic performances of gear transmission system. The existing finite element method (FEM) and analytical method (AM) are not suitable for tackling the mesh stiffness calculation of closed-loop multi-branch system such as CFGSTTS. Thus, a semi-analytical method (SAM) is presented and verified, which combines the high precision of FEM with the high efficiency of AM. Additionally, the differences between the mesh stiffness of independent face gear drive and that of the same gear pair in CFGSTTS under accordant load is researched by applying SAM. The influence rules of distribution angle and load condition on the mesh stiffness of gear pairs considering system structure are also studied. Results demonstrate that the mesh stiffness of gear pairs in CFGSTTS is time-varying and tends to be consistent with each other by adjusting load parameters.     

Influences of friction and mesh misalignment on time-varying mesh stiffness of helical gears

As one of the most important excitation sources of vibration, time-varying mesh stiffness of helical gear pairs need accurately calculated. Compared with spur gears, friction in helical gears is significant. This work for the first time presents an improved calculation method for the mesh stiffness of helical gears with effect of friction incorporated. Firstly, helical gear is sliced into number of pieces along its axis direction and each piece could be regarded as spur gear. Then forces applied to each piece including friction force are analyzed. Potential energy method is employed to develop time-varying mesh stiffness of each piece pair of both kinds of helical gears with different transverse and axial contact ratios. Furthermore, influences of various working conditions and misalignment on mesh stiffness are also investigated. Results indicate that effect brought by friction on total mesh stiffness should be not neglected. The reduction amount of stiffness increases with lower speed, heavier load and rougher surface. The stiffness difference between cases with and without friction is affected by gear geometry and mounting parameters like module, helix angle and mounting misalignment. This work provides an essential tool for comprehensive dynamics analysis with consideration of the relationship between stiffness and working conditions.     

Experimental measurement of gear mesh stiffness of cracked spur gear by strain gauge technique

In this paper, an experimental technique based on strain gauge has been proposed to measure the gear mesh stiffness of healthy spur gear as well as of cracked spur gear pair system. Calculation of mesh stiffness of healthy and cracked spur gear tooth are based on strain energy and strain energy release rate respectively. The location of strain gauge plays an important role in calculation of strain energy stored in gear tooth. The locations of strain gauge on gear tooth are illustrated for healthy and cracked gear. Stress intensity factor (SIF) has been calculated by strain gauge technique for calculating the stiffness of cracked pinion tooth. The effect of crack length on mesh stiffness has been investigated by strain gauge technique and results are compared with the established analytical method.     

Influence of bearing stiffness on the static properties of a planetary gear system with manufacturing errors

Hybrid finite element analysis was used to analyze the influence of bearing stiffness on the static properties of a planetary gear system with manufacturing errors. The effects of changes in stiffness were similar for most of the manufacturing errors. State variables were most affected by the stiffness of the planet bearings. Floating either the sun or carrier helps to equal load sharing and minimizes the critical tooth stress. The effects of a floating sun and carrier are similar, but it is not recommended that both float, because this can induce greater critical tooth stress. Planet bearing stiffness should be optimized. Both load sharing and critical tooth stress should be considered to determine optimal bearing stiffness.     

Dynamic behavior of the spur gear system with time varying stiffness by gear positions in the backlash

Gear backlash is a nonlinear effect of the gear system. In a spur gear system with the backlash, the initial position of gears with the backlash affects the impact force. This work conducted a dynamic analysis of the spur gear system with time-varying mesh stiffness and bearing stiffness with a focus on the initial gear position within the backlash. For this purpose, the time-varying stiffness of the gears and rolling bearings were calculated. Mesh force with the time-varying stiffness and the gear backlash was applied to four DOF equations of motion. The equations of motion were solved using the Newmark beta method and Newton-Raphson method. The dynamic characteristics of the spur gear system by the initial position of gears within the backlash were investigated along with the magnitude of the backlash. The results showed that as the backlash increased, the mesh and bearing forces increased as well. The mesh and bearing forces were highly dependent on the initial gear position within the backlash. Significant initial mesh and bearing forces by the initial gear position within the backlash can lead to cumulative damages to the gear system.     

一种分析行星齿轮变速器的新方法

提出了一种利用波尔(Boo1ean)参数对行星齿轮变速器进行分析的新方法，由于它能将变速器的运动学和动力学方程用一组含波尔参数的代数方程表示，因而，既能使分析过程简化，又特别适用于此类变速器的设计。     

斜齿轮参数化设计系统开发

采用UG自带的二次开发工具UG/Open,结合标准斜齿轮的设计流程,开发了一种基于程序的斜齿轮参数化设计系统。首先运用Visual C++中的MFC类库设计系统数据库的界面,使用COM组件完成访问和修改数据库中的设计参数,并通过UG/Open API将得到的参数回传给主程序,然后调用UG/Open Grip编写的斜齿轮参数化设计程序,最终实现了标准渐开线斜齿轮的精确建模;该系统实现了知识重用,提高了斜齿轮三维数字模型的造型精度和设计效率,创建的模型能够很好的满足后续的CAE分析的要求。     

斜齿轮插削加工的CNC系统

基于实现斜齿轮插削加工CNC控制的思想，提出了运用同步锁相保证工件主轴与刀具主轴的同步跟踪，用电子差动合成来实现刀具主轴附加转动与圆周进给运动的合成，进而驱动伺服系统实现斜齿轮插削加工的数字化控制。     

汽车自动变速行星齿轮系统的动力学仿真

采用键合图理论和方法，建立一种汽车自动变速行星齿轮系统的动态模型，并进行动力学仿真，仿真结果具有明显的规律性，从而为该系统的动力学研究提供一种正确的数值分析方法。     

齿轮传动噪声测量系统的研究

为实现通过测量齿轮传动噪声来分析齿轮加工工艺的目标,开发了一套齿轮传动噪声测量系统.利用硬件系统现场采集与分析处理齿轮噪声,并实时显示噪声信号的处理结果;为了对噪声信号做进一步对比分析,利用硬件系统的USB模块与上位机进行数据通讯,通过上位机信号处理软件对齿轮传动噪声信号做FFT分析和细化谱分析,并对处理结果进行实时显...     

粉末冶金斜齿轮传动效率研究

研究了粉末冶金斜齿轮的传动效率特性,与38CrMoAl斜齿轮的传动效率进行对比,分析了材料因素对齿轮传动效率的影响.设计了齿轮传动效率测量方案、步骤.试验结果表明,在相同工况下,粉末冶金斜齿轮的传动效率比相应的38CrMoAl斜齿轮要高,传动更加平稳,啮合过程中润滑性能更好、磨损小,因而具有广阔的应用前景.     

Optimization of helix angle for helical gear system

A method is presented to optimize the helix angle of a helical gear from the viewpoint of the transmission error, which is the deflection of the teeth due to the transmitted load. The deflection of the gear teeth is calculated by using the bending and shear influence function, which is formulated from the common formula for deflection obtained from FEM, and the contact influence function based on Hertzian contact theory. Tooth contact analysis is performed to calculate the contact lines of the helical gear, where the deflection of the tooth is measured. A numerical example is presented to explain a method to optimize the helix angle of a helical gear system. The relation between the contact ratio and transmission error is investigated through calculations of the variation in the transmission error with the helix angle. This paper was recommended for publication in revised form by Associate Editor Hong Hee Yoo     

PHEV行星齿轮传动系统设计及仿真

分析了并联式混合动力电动汽车(PHEV)行星齿轮传动系统的设计条件,针对条件要求进行了配齿计算,选择了齿轮的主要参数.在并联式混合动力电动汽车启动加速阶段,利用Simulink软件建立了系统的转速关系、输出扭矩和功率的仿真模型,仿真得出系统的输出转速特性、功率分配特性和扭矩输出特性曲线.结果表明:设计的行星齿轮系统符合PHEV启动加速工作模式的动力分配性要求.     

Comparisons of gear dynamic responses with rectangular mesh stiffness and its approximate form

The mesh stiffness is close to rectangular stiffness, and the first harmonic approximate term of rectangular stiffness is generally adopted in the nonlinear gear dynamic analysis. The differences between the rectangular stiffness and its approximate form are analyzed in detail. The frequency response and dynamic factor are calculated by a numerical method, to illustrate the dynamic characteristics of the gear nonlinear system with different mesh stiffness forms. The results show that: The trends of frequency response of gear dynamic system with rectangular stiffness and its approximate form are identical. The jump phenomena are detected in both cases. Without the effect of static transmission error, the dynamic factor with rectangular mesh stiffness is larger than that with approximate mesh stiffness. Under design power and speed condition, the result with approximate mesh stiffness function may deduce reasonless suggestions for a designer. The static transmission error will enlarge the vibration amplitude and dynamic factor when the approximate mesh stiffness is adopted, but the effects on the response of gear system with rectangular mesh stiffness are fractional. The mesh stiffness may excite the odd subharmonic resonance, and the static transmission error may excite the even sub-harmonic resonance respectively.     

An analytical determining the internal ring gear rim stiffness for practical purpose

Journal of Mechanical Science and Technology - Internal ring gears have a wide application in planetary gearboxes and transmission systems. The mesh stiffness of planetary gearboxes is an essential...     

利用UG对渐开线斜齿圆柱齿轮参数化设计

渐开线斜齿圆柱齿轮是机械传动中常用零件,由于齿形轮廓复杂,其参数化设计困难.利用三维软件UG-NX3对斜齿圆柱齿轮进行三维建模,首先利用模型模块中的规律曲线、扫描、缝合、休整和抽取等运算,建立齿槽轮廓,经布尔运算形成齿槽轮廓体,对其特征阵列,生成斜齿圆柱齿轮三维模型.同时以齿数41为界,对两种齿轮建模方法不同之处进行介绍.该方法实现了改变斜齿圆柱齿轮的齿数、法向模数和螺旋角等参数,立即得到相应的渐开线斜齿圆柱齿轮三维模型的参数化设计.对其他具有复杂表面形状的形体参数化设计具有参考价值.     

行星齿轮传动系统的可靠性优化设计

利用机械优化设计和可靠性设计方法,结合传统行星齿轮减速器实例,探索机械可靠性优化设计的新方法。     

粉末冶金斜齿轮系统模态分析

使用温压成形技术制造的粉末冶金斜齿轮耐磨性好、成本低。利用有限元法建立包含齿轮副、传动轴、轴承和箱体的粉末冶金斜齿轮系统完整的动力学模型,分析斜齿轮系统的固有频率和主要振型类型,通过试验模态分析方法验证有限元分析模型的计算结果。该模型反映了斜齿轮系统的动力学性能,为齿轮系统动态性能分析提供了依据。