螺旋运动系数对弧齿锥齿轮齿形的影响规律  

Effect of Helical Motion Coefficient on Tooth Profile of Spiral Bevel Gear

作　　者：段志宏 王志永[1] 张竹 张宇[1] DUAN Zhihong;WANG Zhiyong;ZHANG Zhu;ZHANG Yu(School of Mechanical and Electrical Engineering,Central South University of Forestry and Technology,Changsha 410004,China)

机构地区：[1]中南林业科技大学机电工程学院,长沙410004

出　　处：《组合机床与自动化加工技术》2023年第11期159-162,共4页Modular Machine Tool & Automatic Manufacturing Technique

基　　金：国家自然科学基金企业创新发展联合基金项目(U22B2084);湖南省教育厅资助科研项目(20A527)。

摘　　要：为探究螺旋运动系数对弧齿锥齿轮齿形的影响规律,充分发挥数控机床的万能运动特性,使齿轮设计人员及机床调整人员更好地运用高阶运动实现齿面的修形以及齿面接触区的调整,基于弧齿锥齿轮加工原理,通过引入一至六阶螺旋运动系数,建立了齿面数学模型。基于齿面数学模型,采用矢量运算与二元迭代的方法,计算了实际齿面相对于理论齿面在其各离散点法线方向上的齿面误差。分析了各阶螺旋运动系数的改变对弧齿锥齿轮齿面形状的影响规律,以图像的方式表示了实际齿面相对于理论齿面的偏离方向以及误差值的大小。采用最小二乘法,计算了弧齿锥齿轮轮齿齿面在各阶螺旋运动系数改变下的敏感系数,分析了各阶螺旋运动系数对齿面形状的影响类型和程度。通过实际的磨齿加工和测量验证,结果表明各阶螺旋运动系数对齿面形状的实际影响与理论分析结果一致。In order to explore the influence law of helical motion coefficient on the tooth profile of spiral bevel gear,give full play to the universal motion characteristics of NC machine tool,and make gear designers and machine tool adjuster better use of high order motion to achieve tooth surface modification and tooth surface contact area adjustment,based on the machining principle of spiral bevel gear,by introducing the first to sixth order helical motion coefficient,the mathematical model of tooth surface was established.Based on the mathematical model of the tooth surface,the tooth surface errors of the actual tooth surface relative to the theoretical tooth surface in the normal direction of each discrete point were calculated by using vector operation and binary iteration method.The influence of the change of helical motion coefficients on the shape of spiral bevel gear tooth surface was analyzed.The deviation direction of the actual tooth surface from the theoretical tooth surface and the size of the error value were represented by image.By using the least square method,the sensitivity coefficients of spiral bevel gear tooth surface under the change of helical motion coefficients were calculated,and the influence type and degree of helical motion coefficients on the shape of tooth surface were analyzed.The results show that the effect of helical motion coefficients on the shape of tooth surface is consistent with the theoretical analysis results.

关 键 词：螺旋运动系数 弧齿锥齿轮 齿面误差 影响规律 

分 类 号：TH161[机械工程—机械制造及自动化] TG54[金属学及工艺—金属切削加工及机床]