复合摆线少齿差行星传动的齿廓几何特性与啮合特性变化规律

Geometric Characteristics of Tooth Profile and Meshing Properties Changing Laws of Composite Cycloid Planetary Drive with Small Tooth Difference

针对摆线针轮少齿差行星传动的摆线针轮啮合角大、转臂轴承可靠性低与针齿均布位置精度要求高等问题,作者利用几何可控性较强的复合摆线构建少齿差行星内齿齿廓,提出一种新型高性能复合摆线内齿型少齿差行星齿轮副:基于传统摆线行星传动几何原理,提出复合摆线内齿齿廓曲线的几何设计方法,分析齿形调控参数c2对复合摆线内齿齿廓曲线几何形状与曲率变化的影响规律;基于齿轮啮合运动学共轭原理,建立复合摆线内齿齿廓方程、齿轮副共轭传动啮合方程、少齿差行星共轭齿廓方程与啮合线方程;利用参量转化法分析复合摆线内齿齿廓的啮合界限特性;根据共轭齿廓出现奇异点的几何原理,推导其不发生根切的判定方程;研究该新型齿轮副的啮合线、重合度、压力角、诱导法曲率与滑动率等啮合特性及其变化规律,提出诱导法曲率与滑动率的啮合区间敏感性分析方法。研究结果表明:复合摆线内齿齿廓存在啮合界限点,啮合界限特性与根切判定方程分别为新型齿轮副内齿齿根过渡曲线设计、共轭齿廓无根切设计提供了有效的理论方法;啮合线与重合度的分析表明该新型齿轮副具有多齿啮合特性;当新型齿轮副的齿数、偏心距、齿高和内齿分布圆半径确定后,c2是唯一影响压力角、诱导法曲率与滑动率的齿轮参数,行星轮压力角的最小值与平均值随c2减少而降低,在一个啮合周期内,c2对诱导法曲率与滑动率的影响存在着不敏感与敏感区间,可忽略c2对不敏感啮合区间诱导法曲率和滑动率的影响,敏感区间的诱导法曲率平均值、滑动率幅值与平均值均随着c2减少而降低。相对于同参数的传统摆线行星传动,新型齿轮副在压力角、诱导法曲率与滑动率等啮合特性方面具有传动优势,相应地,反应出其较好的多齿啮合特性、传力特性、润滑与承载特性及抗磨损特性,具有一定的工程应用价值。

Aimed at the problems of bigger engaging angle of cycloid-pin gear,lower reliability of turning ann bearing and higher uniform posi- tion precision of pinwheel,the composite cycloid,that has a relatively strong controllability in geometry,was utilized to establish the internal tooth profile of small tooth difference planetary drive （STDPD）,then a new high-performance STDPD with composite cycloid internal tooth profile （CCITP） was proposed.Based on the geometry principle of traditional cycloid pinwheel drive,the geometrical design method of CCITP was presented, and the impacts of c2 on geometrical shape and curvature were analyzed.Using kinematic conjugate theory of gear meshing,the profile equation of CCITP,the meshing equation of conjugate gear drive,the conjugate profile equation with small tooth difference and action line equa- tion were established.The analysis of meshing boundary properties based on parameter transformation was conducted.According to the mathemat- ic princple that singularity appeared on conjugate profile,the judgement equation for determining whether undercutting occurred or not was de- rived.Meshing properties including action line,contact ratio,pressure angle,induced normal curvature and sliding ratio of this new gear drive （TNGD） were investigated,sensitivity analysis methods on induced normal curvature and sliding ratio in certain meshing range were putforward.The results indicated that meshing boundary point existed on composite cycloid internal profile,furthermore the effective theoretical methods of both the transition-curve geometry design of internal tooth dedendum and the non-undercutting design of conjugate profile were provided on account of meshing boundary model and undercutting judgement equation.Meanwhile,the analysis result of action line and contact ra- tio showed that the multi-teeth meshing property of TNGD could be carried out.When the tooth number,eccentricity,tooth height and internal tooth distribution circle of TNGD were determined,c2 was the only gear parameter that really could impact the pressure angle,induced normal curvature and sliding ratio.The minimum and average of planet gear pressure angle decreased with c2,the impacts of c2 on induced normal curvature and sliding ratio were classified into non-sensitive and sensitive ranges in one meshing cycle.The impacts in non-sensitive range could be ignored,while both the average of induced normal curvature and the amplitude and average of sliding ratio in sensitive range were decreased with c2.Compared with the traditional cycloid drive having the same parameters,the advantages on pressure angle,induced normal curvature and sliding ratio of TNGD were shown.Accordingly,better meshing performances in multi-tooth meshing,force transmitting,lubrication,capacity and anti-wear were achieved.Therefore,a certain effect in engineering application of TNGD was showed.