任意转角位置的双渐开线齿轮的齿面数学模型

MATHEMATICAL MODEL OF TEETH SURFACES OF DOUBLE INVOLUTES GEAR WITH LADDER SHAPE OF TOOTH ON ANY ROTARY ANGLE

运用渐开线展开和曲线包络原理,建立了双渐开线齿轮端面齿廓数学模型,用数据验证了模型的准确性。在端面齿廓数学模型基础上建立了任意转角位置的双渐开线齿轮齿面数学模型,使用该模型获得了三种典型刀具齿顶圆弧半径的双渐开线齿轮三维仿真图形,并进行了啮合仿真,从而验证了齿面数学模型的正确性和可行性。该齿面数学模型表述简单,使用时无须坐标变换,能快速、真实地描述双渐开线齿轮任一轮齿在任意转角位置时齿面上的任一点。为双渐开线齿轮三维数字化设计、制造,啮合干涉、运动学和动力学分析提供了简捷的新理论依据。

The outspread principle of involute and enveloping principle of curve is applied to build the model of double involutes gear contrate profile, the veracity is verified by the data. On the base of the mathematical model of double involutes gear contrate profile, the mathematical model of double involutes gear teeth surfaces is built, which is on any rotary angle. The 3D simulation pictures of double involutes gear of three typical cut tooth top＇s circular arc radius and simulation of mesh are obtained by mathematical model of double involutes gear teeth surfaces, the correctness and feasibility of model is validated. The expression is very simple and coordinate is not translated by using, the any point of double involutes gear teeth surfaces is fast and truly described on any rotary angle, the simple and speedily new theory gist is offered for 3D numerical design, manufacture and the analysis of mesh, kinematics and dynamics of double involutes gears.