摘要
系统地建立了高次方修形直廓环面蜗杆传动的数学模型,用微分几何和啮合理论等理论推导了蜗杆副的曲率参数,啮合函数以及曲率干涉界线函数.证明了直廓环面蜗杆的齿面为不可展的直纹面,这与其蜗杆的齿面形成原理相吻合.利用最小二乘法拟合无量纲化的修形数据得到普适型高次方修形曲线,基于此曲线推导出工艺传动比的计算公式,得到高次方修形蜗杆传动.根据不同次修形曲线修形的数值算例分析表明,高次方修形可消除原始型直廓环面蜗杆齿面的常接触线,有效的增大了蜗杆副齿面的共轭区面积,修形后蜗杆全长可被利用,承载能力强.但高次方修形后的蜗杆副齿面存在曲率干涉界线,有可能导致蜗杆副发生根切.
The mathematical model of globoidal worm drive with high-order modification is established systematically.The curvature parameters,meshing function and curvature interference boundary function of worm pair are derived by differential geometry and meshing theory.It is proved that the tooth surface of globoidal worm is an undevelopable ruled surface,which is consistent with the principle of tooth surface formation.The least squares method is used to fit the dimensionless modification data to obtain a universal high-order modification curve.Based on the curve,the calculation formula of the process transmission ratio is derived,and the high-order modification worm transmission is obtained.According to the numerical examples of different modification curves,the analysis shows that the high-order modification can eliminate the constant contact line of the tooth surface of the original globoidal worm,and effectively increase the conjugate area of the tooth surface of the worm pair.After the modification,the full length of the worm can be used and the bearing capacity is strong.However,there is a curvature interference line on the tooth surface of the worm pair after high-order modification,which may lead to undercutting of the worm pair.
作者
赵亚平
李帅
陈新元
李公法
ZHAO Yaping;LI Shuai;CHEN Xinyuan;LI Gongfa(School of Mechanical and Automotive Engineering,Northeastern University,Shenyang 110819,China;Hubei Key Laboratory of Mechanical Transmission and Manufacturing Engineering,Wuhan University of Science and Technology,Wuhan 430081,China;Key Laboratory of Metallurgical Equipment and Control Technology of Ministry of Education,Wuhan University of Science and Technology,Wuhan 430081,China)
出处
《湖南大学学报（自然科学版）》
EI
CAS
CSCD
北大核心
2022年第2期20-30,共11页
Journal of Hunan University:Natural Sciences
基金
国家自然科学基金资助项目(52075083)
武汉科技大学冶金装备与控制教育部重点实验室开放基金项目(MECOF2021B02,MECOF2020B03)。
关键词
蜗轮
啮合理论
修形
曲率干涉
传动比
worm gear
gear geometry
modification
curvature interference
transmission ratio
