齿轮动力学模型建立—葛银明1. 齿轮模型发展历史• From the 1920s to 1930s of the last century, a primary goal of engineers is to analyze the engaging dynamic problems in order to quantify the entity of teeth loadings by means of both analytical and experimental methodologies.• From the 1950s, very simplified lumped parameters systems (as mass-spring systems) have been set up to study dynamic effects on gears, becoming more and more sophisticated. • During the 1970s and 1980s, lumped parameters models may include complex effects as the tridimensional stiffness of teeth, nonlinearities of the system, damping and friction parameters.1. 齿轮模型发展历史• Nowadays, reference models available take the peculiarity into account global dynamic phenomena as torsion, flexural and axial vibrations, allowing to obtain both transitory and operating responses, also if different typologies of engaging errors are considered. • Aim of the present work is to set up a combined multibody/FEM numerical technique, on the basis of a commercial code, in order to simulate the engaging phenomenon in aerospace gears, whose peculiarity is a high flexibility of the body gear with respect teeth ring• The last one is probably the best way to analyze the gear dynamics, but the computational effort required is very high, so in the present paper, the RFLEX approachs implemented. All the flexibility features of bodies are derived using FE approach.• Full Rigid Model (FRM)（1） the RecurdynToolkit Gear（2） the stiffness value of the teeth is computed using an analytical approach based on the Hertzian formulation or FEA2.1 直齿轮刚体动力学模型• Flex Teeth Model (FTM) （1）a Bushing Force element sets the stiffness values of the three torsional springs that link the tooth. （2） the QFBGeartool of Recurdyn （3）the tooth compliance parameter in the Bushing Forces is computed imposing a torque to a gear sector and measuring the deflection of each tooth2.1 直齿轮刚体动力学模型斜齿轮斜齿轮弯一扭一轴祸合分析模型2.2 斜齿轮动力学模型2.2 斜齿轮动力学模型•（1）模态分析阻尼C=0及激励P=0时进行模态分析•（2）响应求解方法结构复杂，解析方法求解困难，多用数值方法求解。
常见的数值求解方法：逐步积分法（Newmark法，Wilson—θ，中央差分法）和精细积分法2.2 斜齿轮动力学模型2.3 圆锥齿轮动力学模型2.3 圆锥齿轮动力学模型3. 齿轮柔体动力学• The conventional finite element analyses require a prohibitively refined mesh to address these problems when one seeks dynamic response.• The semi-analytical finite element analysesContact parameters solved by using the analytical method ，and substituted into the FEM • Flexibility of bodies could be considered in two different ways, using the modal superposition (RFLEX, reduced flexibility model) or considering the overall body flexibility by means of the discretized mass and stiffness matrices of the body (FFLEX, full flexibility model).• Full Flexible Model (FFM)The flexibility of the gears is computed by means of a reduced FE model. （ reduced stiffness and mass matrices – compute modal properties and mode shapes —a metafile - Recurdyn）3. 齿轮柔体动力学。