基于共轭修形的大模数摆线齿锥齿轮齿面建模及承载性能分析

Tooth Surface Modeling and Load Performance Analysis of Large Modulus Cycloidal Bevel Gear Based on Conjugate Modification

针对大模数摆线齿锥齿轮在专用铣齿机上难以加工的问题,提出一种面向加工中心的摆线齿锥齿轮齿面模型构建方法。基于摆线齿锥齿轮加工原理,根据刀具与大轮之间的几何位置关系,建立大轮切齿参数计算方法;根据大轮切齿加工数学模型,推导大轮理论齿面,并通过齿面离散方法获得大轮数值齿面;基于齿轮啮合数学模型推导出与大轮完全共轭的小轮齿面,通过在完全共轭小轮齿面法线方向上构建二阶修形差曲面并进行叠加,获得与大轮齿面呈局部共轭的小轮数值齿面。最后,建立有限元齿面加载接触分析流程,以一对矿用减速器大模数摆线齿锥齿轮副为例,利用ABAQUS软件进行齿轮三维建模和有限元加载接触仿真。结果表明:在实际加载工况下,通过共轭修形构建的小轮齿面与大轮齿面呈局部内对角接触,并且加载接触区受啮合错位影响在大轮齿面内部移动,未脱离齿面产生边缘接触,齿面接触区满足工程需要。仿真结果验证了共轭齿面修形建模方法的可行性。

Aiming at the problem that large modulus cycloidal bevel gear is difficult to be machined on dedicated gear milling machine,a method of constructing the tooth surface model of cycloidal bevel gear suitable for machining centers was proposed.Based on the processing principle of cycloidal bevel gear and the geometric relationship between the cutter head and the gear,a calculation method of gear processing parameters was established.The gear theoretical tooth surface was deduced according to the mathematical model of the gear cutting tooth processing,and the gear numerical tooth surface was obtained through the tooth surface discretization method.Based on the gear meshing mathematical model,the pinion tooth surface which was completely conjugated with the gear tooth surface was derived.By constructing a second-order modification difference surface in the normal direction of the fully conjugated pinion tooth surface and superimposing it,the pinion numerical tooth surface which was partially conjugated with the gear tooth surface was obtained.Finally,the loaded tooth contact analysis flow with finite element was established.Taking a pair of large modulus cycloidal bevel gear applied to the mine reducers as an example,the gear 3D modeling and loaded tooth contact simulation with finite element were conducted using ABAQUS software.The results show that under actual loading conditions,the pinion tooth surface constructed by conjugate modification is in local internal diagonal contact with the gear tooth surface,and the loaded contact area moves inside the gear tooth surface due to meshing dislocation,and it does not leave the tooth surface to produce edge contact,so the tooth contact area can meet the engineering need.The simulation results verify the feasibility of modeling method of conjugate tooth surface modification.