拓扑修形齿轮附加径向运动成形磨削中的砂轮廓形优化方法.pdf

第47卷第11期
机械工程学报
Vo1.47No.11
2011年6月
JOURNAL OF MECHANICAL ENGINEERING
2011
DOI:10.3901/ME.2011.11.155
拓扑修形齿轮附加径向运动成形磨削中的
砂轮廓形优化方法
李国龙李先广2刘飞孙孟辉
(1.重庆大学机械传动国家重点实验室重庆4000
2.重庆机床(集团)有限责任公司重庆40005
摘要:拓扑修形齿轮附加径向运动成形磨削时,砂轮与齿轮的接触线随时在变,基于齿轮任一截面齿形计算出的砂轮廓形都
会引起较大的磨削误差,为此,提出一种减小磨削误差的砂轮廓形优化方法。依据空间啮合原理,采用抛物线附加径向运动
轨迹,建立成形砂轮廓形求解数学模型;平行于齿轮端面等距截出多个平面齿廓,求解出以点表示的不同齿廓对应的砂轮廓
形,再将各砂轮廓形投影到同一平面生成点云,通过区间划分,采用最小二乘法求解出每个区间点云的拟合点,连接各拟合
点形成优化的砂轮廓形。为验证砂轮磨削效果,由砂轮与齿轮的啮合条件,建立由砂轮廓形求解齿轮齿形的反算数学模型,
给出实际齿形与设计齿形的偏差计算公式。以一种齿向修形齿轮为例,进行成形磨轮廓形计算及优化,磨削误差分析结果表
明该方法有效,可用于修形齿轮的成形磨轮廓形计算,并可有效降低修形齿轮的成形磨削误差
关键词:渐开线齿轮拓扑修形成形磨削成形秒轮磨削误差优化
中图分类号:TG701
Method of Profile Optimization of a Form Grinding Wheel for grinding
with Additional Radial Motion of Topologically Modified Gear
LI Guolong LI Xianguang""LIU Fei SUN Menghui
(1. State Key Laboratory of Mechanical Transmission, Chongqing University, Chongqing 400030
2. Chongqing Machine Tool(Group)Co, Ltd, Chongqing 400055)
Abstract: Since the contact lines between grinding wheel and gear are dynamically changing for form grinding with additional radial
motion of topologically modified gear, the calculated wheel profile based on any cross-section of gear will cause a larger grindi
error. For reducing grinding error, a method to optimize the profile of grinding wheel is proposed. Firstly, the mathematical models to
solve the profile of grinding wheel with additional radial parabolic trajectory is established based on the space engagement theory
Secondly, multiple equidistant plane is used to intercept the gear and to obtain a number of cross-sections for solving the wheel
profiles represented with points corresponding to the cross-sections of gear; then a cloud of points is formed by projecting the wheel
profiles to a plane, the fitting points of each interval obtained by dividing the cloud into equal intervals is solved based on the least
square method, and connecting all the fitting points to form an optimal wheel profiie. Given a formula of deviation between actual
tooth profile and ideal profile, a mathematical model of ear ooth profile is established based on the meshing condition between
wheel and gear to verify the grinding effect of grinding wheel. As an example of axial modified gear, wheel profile both the
un-optimized and optimized are calculated, and the results show that the method can be used in the profile calculation of form
grinding wheel and effectively reduce the grinding errors of topologically modified gear.
Key words: Involute gear Topologically modified Form grinding Grinding wheel Grinding error Optimization
防止边缘接触,减少振动和噪声,延长齿轮的工作寿
0前
命。目前,几乎所有的高速、重载、薄壁结构的精密
齿轮都需要进行拓扑修形。 LIVN等采用了一个拓
拓扑修形可以较好地改善齿面啮合状态,有效扑修形齿轮来减少传动误差, WAGAJ等叫研究了齿
形修形对斜齿轮耐用性的影响, KAHIRAMAN等
*中央高校基本科硏业务费资助项目( CDJZR1011005)020101011收到
初稿,20110425收到修改稿
建立了一个修形齿轮的磨损模型。修形齿轮精加工