齿轮系统动力学刚体模型

1、齿轮系统动力学刚体模型第1页，共14页，2022年，5月20日，2点4分，星期五齿轮动力学模型建立葛银明第2页，共14页，2022年，5月20日，2点4分，星期五1. 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 experimen

2、tal methodologies.From the 1950s, very simplied 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

3、 of teeth, nonlinearities of the system, damping and friction parameters.第3页，共14页，2022年，5月20日，2点4分，星期五1. 齿轮模型发展历史Nowadays, reference models available take the peculiarity into account global dynamic phenomena as torsion, exural and axial vibrations, allowing to obtain both transitory and operating r

4、esponses, 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 exibility of the

5、 body gear with respect teeth ring第4页，共14页，2022年，5月20日，2点4分，星期五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 exibility features of bodies are derived using FE a

6、pproach.第5页，共14页，2022年，5月20日，2点4分，星期五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 FEA 2.1 直齿轮刚体动力学模型第6页，共14页，2022年，5月20日，2点4分，星期五Flex Teeth Model (FTM)（1）a Bushing Force element

7、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 deection of each tooth2.1 直齿轮刚体动力学模型第7页，共14页，2022年，5月20日，2点4分，星期五斜齿轮斜齿轮

8、弯一扭一轴祸合分析模型2.2 斜齿轮动力学模型第8页，共14页，2022年，5月20日，2点4分，星期五2.2 斜齿轮动力学模型第9页，共14页，2022年，5月20日，2点4分，星期五（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，中央差分法）和精细积分法2.2 斜齿轮动力学模型第10页，共14页，2022年，5月20日，2点4分，星期五2.3 圆锥齿轮动力学模型第11页，共14页，2022年，5月20日，2点4分，星期五2.3 圆锥齿轮动力学模型第12页，

9、共14页，2022年，5月20日，2点4分，星期五3. 齿轮柔体动力学The conventional nite element analyses require a prohibitively rened mesh to address these problems when one seeks dynamic response.The semi-analytical nite element analyses Contact parameters solved by using the analytical method，and substituted into the FEM Flexi

10、bility of bodies could be considered in two different ways, using the modal superposition (RFLEX, reduced exibility model) or considering the overall body exibility by means of the discretized mass and stiffness matrices of the body (FFLEX, full exibility model). 第13页，共14页，2022年，5月20日，2点4分，星期五Full Flexible Model (FFM) The exibility of the gears is computed by means o