机械变速器换档的接合过程建模及特性分析

Modeling and characteristic analysis of engaging process during gear shifting of mechanical transmissions

接合套和接合齿圈的接合过程是影响机械变速器换档品质的关键阶段。针对在接合过程中,当接合套和接合齿圈在齿端倒角处接触时碰撞发生,其相对速度会发生突变,相应的耦合关系及动力学方程也会发生改变的现象,为了得到机械变速器整个接合过程的精确数学模型和特性,运用多体动力学理论和混杂系统方法建立了描述接合过程的混杂自动机模型。在该模型中,用3个微分方程组描述接合过程中接合套和接合齿圈在不同耦合关系下的动力学特性;引入泊松恢复系数,建立了4个差分方程组描述碰撞过程接合齿圈转速、接合套轴向运动速度和转速产生的突变。基于该混杂自动机模型,在MATLAB环境下进行了仿真分析,得到了接合过程中接合套和接合齿圈的轨迹、接合时间和最大冲击,分析了换档力、接合套相对接合齿圈的初始转速和位置对接合性能(时间和最大冲击)的影响。研究结果表明:接合套和接合齿圈的相对位置对接合时间和冲击有显著影响;当接合套和接合齿圈的转速差在一定范围内时,接合时间较短,过大的转速差则会使接合时间呈指数上升;接合套和接合齿圈的转速差越大,冲击越大;增大换档力可缩短接合时间,但会增大冲击。在设计机械式自动变速器的控制系统时,应根据机械变速器换档过程的特性,选取最佳的换档力、相对转速、相对位置作为控制参数,进而缩短动力中断时间,减小换档冲击。

The engaging process of engaging sleeve and clutch gear is the key phase influencing the gear shifting performance of mechanical transmissions. During an engaging process, collision occurred when engaging sleeve and clutch gear contacted at the end of the tooth chamfer, their relative speed suddenly changed, and their coupling relationship and dynamic equations also changed. In order to obtain an accurate mathematical model and characteristics of the engaging process of mechanical transmission, a hybrid automaton model was built to describe the engaging process through multi-body dynamics theory and hybrid system methodology. In this model, three sets of differential equations were built to describe the dynamic characteristics of engaging sleeve and clutch gear under different coupling relationships during an engaging process. Poisson recovery coefficient was introduced to build four sets of difference equations to describe the rotational speed of clutch gear, the axial movement speed of engaging sleeve and the sudden change of rotational speed during the collision process. Based on the hybrid automaton model, simulation analysis was carried out in the MATLAB environment. The trajectories, the engaging duration and the maximum impact of engaging sleeve and clutch gear during their engaging process were obtained. The effects of the shifting force and the initial rotational speed and position of engaging sleeve relative to clutch gear on engaging performance were analyzed. The results show that the relative position of engaging sleeve and clutch gear has significant effect on the engaging duration and the maximum impact. If the rotational speed difference of engaging sleeve and clutch gear is within limit, the engaging duration is relatively short, and a big rotational speed difference will cause an exponential rise of engaging duration, a bigger rotational speed difference of engaging sleeve and clutch gear will cause a bigger engaging impact. When increasing the shifting force, the engaging duration will shorten but the impact will increase. When designing the control system of automated mechanical transmission, the optimal shifting force, relative rotational speed and position should be adopted as control parameters to shorten power interruption time and reduce shifting impact according to the gear shifting characteristics of mechanical transmission. 1 tab, 7 figs, 25 refs.