对数螺旋锥齿轮啮合模型的建立及有限元分析的基本思想

Establishment of meshing model for logarithmic spiral bevel gear and basic idea with finite element analysis

对于一种新型锥齿轮—对数螺旋锥齿轮,研究其啮合模型在Pro/E中的建立方法。由于其齿向线是圆锥对数螺旋线,提出了一种新的建模方法,包括三个创新点:利用夹角为的两条圆锥对数螺旋线来确定齿廓曲线的空间位置,使渐开线得以精确定位;将盘绕在节锥曲面上的圆锥对数螺旋线作为扫引轨迹线,保证齿形的准确性;扫描混合截面建立在扫引线的法面内,使轮齿各点法面内的齿形均是标准齿形。在此基础上应用有限元理论的基本思想对啮合模型作了一些运算研究,进一步分析对数螺旋锥齿轮啮合传动过程中的相关特性,进而为该种新型锥齿轮的设计和应用提供理论依据。

For a new type of bevel gear-logarithmic spiral bevel gear,the establishing method of its meshing model in Pro/E is studied.Because its tooth curve is conical logarithmic spiral,one new modeling method is proposed in the article which includes three innovation spots.First,by utilizing two conical logarithmic spirals with an angle of 360/2Z the space position of tooth profile curve is determined in order to position the involute curve precisely.Second,the conical logarithmic spiral coiled around in the pitch cone surface is used as a sweeping trajectory so that tooth profile can be guaranteed accurately.Third,the scanning mix section is established in the normal plane of sweeping trajectory so that the tooth profile of each point normal plane for gear tooth is the standard tooth profile.Based on this,the computation for meshing model has be researched by applying basic philosophy of finite element theory in order to further analyze the related characteristic of meshing transmission process for logarithmic spiral bevel gear.Thus it may provide the theoretical basis for the design and the application of this kind of new bevel gear.