Determination of static tooth stresses in nonstandard spur gears cut by pinion cutter

This paper is a continuation of the paper entitled “Determination of Pinion-Cutter Offsets Required to Produce Nonstandard Spur Gears with Teeth of Equal Strength.” Sample charts are presented for determining how closely the static bending stress in the pinion teeth and gear teeth are balanced when gears are designed using the cutter offsets determined from the previous paper. These charts are plots of stress factors for the pinion or gear versus gear ratio for changes in center distance and for a particular diametral pitch and pitch diameter of cutter. This paper also presents a set of sample calculations for the determination of the stresses in the pinion teeth and gear teeth.     

Some studies on hypoid face gears

Some of the geometric characteristics of a hypoid face gear in mesh with an involute spur pinion are analysed. These geometric characteristics include (a) the maximum diameter of the hypoid gear to avoid pointing of the teeth, (b) the minimum diameter for avoiding undercutting, (c) the contact ratio, (d) the field of contact and (e) the variation of the pressure angle along the face of the pinion. The variations of the above quantities with different parameters such as number of teeth of the pinion, transmission ratio, amount of offset and the pressure angle of the cutter are given.     

数控端铣弧齿锥齿轮的刀背与轮齿干涉避免方法

在五轴数控机床上端铣加工弧齿锥齿轮时,为了避免中凹盘铣刀背锥面与对侧齿面发生干涉,提出了基于刀具和齿轮结构的干涉避免方法。通过确定加工轨迹上刀背圆锥面最突出母线与对侧齿面的位置关系,保证刀具背锥面沿进给方向的法曲率小于对侧齿面法曲率,优化确定刀具边缘厚度和背锥角,实现了端铣齿面时刀背不干涉对侧齿面。最后,以一对弧齿锥齿轮副的小轮为例,通过比较虚拟加工模型和理论模型,验证了所提干涉避免方法的有效性。     

Kinematic errors on helical gear of triple circular-arc teeth

Two imaginary skew rack cutter curves with stepped triple circular-arc teeth are presented in this paper. A helical gear pair that includes the gear and pinion surfaces was generated by using two matched imaginary skew rack cutter surfaces. The mathematical models of the helical gear pair with stepped triple circular-arc teeth were developed based on theory of gearing. With the use of these models, the analysis of kinematic errors can be illustrated and evaluated by computer programming and tooth contact analysis (TCA). The assembly errors used had several kinds: ideal assembly errors, vertical misalignment angles, horizontal misalignment angles, manufacturing errors of helical angles, and center distance deviation. TCA revealed that the sensitivity of horizontal misalignment angles was lower than that of manufacturing errors of helix angles but higher than that of vertical misalignment angles.     

斜齿特形插齿技术的研究

发展了斜齿特形插齿刀设计制造新方法。利用数值模拟法根据插齿刀齿形计算铲磨砂轮廓形,并能进行逆运算以验证计算结果的正确性。试验证明该方法用于斜齿特形插齿是可行的。     

锥基波形前刀面硬齿面插齿刀构形方法与构形理论的研究

在深入剖析现有硬齿面插齿刀构形方法利弊的基础上,论述了锥基波形前刀面硬齿面插齿刀的构形方法与构形理论及其优越性。研究表明:新构形方法插齿刀较现有插齿刀构形精度可提高一倍以上,刀具主剖面负前角绝对值可提高2～5倍,刀具抗崩刃能力和整体寿命大幅度提高,完全满足高精度硬齿面插齿加工的需要。     

基于UG的弧齿锥齿轮建模新方法的研究

介绍了一种基于UG的接触区主动控制的弧齿锥齿轮建模方法。首先使用成形法得到大轮；然后采用变异的铣刀盘成形加工得到变异大轮，再依据共轭原理，利用变异大轮展成小轮毛坯实体得到小轮齿面。按照此方法基于UG软件实现了一对21—35齿的弧齿锥齿轮副的建模。该方法基于传统的格里森弧齿锥齿轮加工方法，有创新之处，是格里森弧齿锥齿轮建模和加工的一种实用的新方法。     

准双曲面齿轮的修正节锥设计方法及切齿试验

为了提高准双曲面齿轮的强度和耐磨性,提高准双曲面齿轮的使用寿命,提出准双曲面齿轮的修正节锥设计方法。在不改变大轮外径和中点工作齿高的的情况下,令大轮的齿顶高系数fa≤ ,从而可以导出新的节锥参数,此时新的节锥与面锥重合或在准双曲面齿轮实体之外。利用齿面接触分析(TCA)、齿面承载接触分析(LTCA)和有限元法(FEM),分析齿轮副的啮合性态、齿面接触应力、齿根最大拉伸应力和齿根最大压缩应力。计算机模拟显示,采用修正节锥设计方法设计的准双曲面齿轮的齿面接触应力、齿根最大拉伸应力和齿根最大压缩应力显著减少,采用修正节锥设计方法设计的准双曲面齿轮在加工过程中可用一般的刀具,不需要特殊的工具。     

新型高阶非圆锥齿轮的设计及其节面修形方法研究

将帕斯卡曲线和阿基米德螺线应用到非圆锥齿轮的设计中,推导了该新型非圆锥齿轮节面的数学模型。针对非圆锥齿轮设计过程中可能存在的节面尖点问题,将产形刀具的部分节面作为非圆锥齿轮节面尖点处的节面,依据产形刀具节面与高阶非圆锥齿轮节面之间的运动关系,建立了新型非圆锥齿轮的节面修形模型,开发了非圆锥齿轮的齿廓产形算法。并采用该方法对实例中的高阶阿基米德螺线锥齿轮和二次曲线锥齿轮的节面尖点进行了修正。     

内齿轮滚刀的几何特征

研究内齿轮滚刀、媒介齿轮的共轭啮合及其坐标变换关系，推导出内齿轮滚刀螺旋面方程式，根切曲线方程式，零前角直槽内齿轮滚刀切削刃方程式，通过电算分析，证明内齿轮滚刀切削刃具有关于基准轴的对称性，沿媒介齿轮节圆的分布均匀性，对渐开线的可拟合性等几何特征。     

Head-cutter for optimal tooth modifications in spiral bevel gears

A method for the determination of optimal tooth modifications in spiral bevel gears based on improved load distribution and reduced maximum tooth contact pressure and transmission errors is presented. The modifications are introduced into the pinion tooth-surface by using a head-cutter with bicircular profile and with optimal diameter. In the optimization of tool parameters the influence of relative position errors of the mating gears is included.By using the computer program developed for load distribution calculation, the influence of head-cutter parameters and relative position errors of the mating gears on tooth contact and transmission errors is investigated. Based on the results obtained, the radii and the position of the circular tool profile arcs and the cutter diameter for pinion teeth finishing were optimized. By applying the optimal tool parameters, the maximum tooth contact pressure is reduced by 45% and the maximum angular position error of the driven gear by 60%, in regard to the spiral bevel gear pair with a pinion manufactured by a cutter of straight-sided profile and of diameter determined by the commonly used methods.     

Effects of shaft angle on cutting tool parameters in internal gear skiving

Gear skiving has received considerable attention because of its high productivity, particularly in internal gear cutting, and skiving cutter design methods have been widely investigated. At the beginning of a cutter design process, a shaft angle, a center distance, and the number of teeth are examined as basic parameters for cutting gears. In current gear skiving, a shaft angle is generally set to be approximately 20°; however, the reason for selecting this value has not been clarified. In the present study, the validity of the value of shaft angle is discussed by calculating the cutting tool parameters, such as instantaneous rake angles, clearance angles, cut depths, and cutting speeds at continuously moving cutting points against various shaft angles. Therefore, the widely used value of shaft angle would result in moderate cutting tool parameters. In addition, the cutting force and cutter wear would be low when a cutter axis inclines opposite to the gear helix to be cut.     

Motor-gear linkage in a motor-transmission module

Recommendations are made regarding the design of the motor-gear link in an integrated motor-transmission system. Algorithms are presented for calculating a cylindrical involute gear transmission with a small number of pinion teeth, the glued joint of the pinion with the gear system’s input shaft, and the pinion body.     

连续变位的斜齿圆锥齿轮的切齿工艺

通过二次特殊的安装 ,用盘状齿轮成形铣刀在万能卧式升降台铣床上切削连续变位的斜齿圆锥齿轮的轮齿 ,保证了齿轮的接触精度和使用寿命     

Optimization of asymmetric spur gear drives to improve the bending load capacity

In a given size of symmetric involute gear designed through conventional approach, as the load carrying capacity is restricted at the higher pressure angle due to tipping formation, the use of the asymmetric toothed gear to improve the fillet capacity in bending is examined in this study. Non-standard asymmetric rack cutters with required pressure angles and module are developed to generate the required pinion and gear of a drive with asymmetric involute surfaces and trochoidal fillet profiles. The respective profiles thus generated are optimized for balanced fillet stresses that are equal and possibly the lowest also. For this study of optimization, several non-standard asymmetric rack cutters are designed to accommodate different combinations in the values of pressure angle, top land thickness ratio, profile shift, speed ratio and the asymmetric factors. However for any drive with a given center distance and a speed ratio, only two non-standard asymmetric rack cutters, one for the pinion and other for the gear are used to generate a required numbers of pinion and gear with different cutter shift values for the purpose of optimization. The influence of these parameters on the maximum fillet stress has been analyzed to suggest the optimum values of these parameters that improve the fillet capacity in bending. The optimization of the asymmetric spur gear drive is carried out using an iterative procedure on the calculated maximum fillet stresses through FEM for different rack cutter shifts and finally the optimum values of rack cutter shifts are suggested for the given center distance and the speed ratio of an asymmetric gear drive. Comparisons have also been made successfully with the results of the AGMA and the ISO codes for symmetric gears to justify the results of the finite element method pertaining to this study.     

单齿飞刀连续分度加工平面齿蜗轮方法的研究

针对单角度盘铣刀加工平面蜗轮效率低等缺点，提出了一种用单齿飞刀连续分度加工平面齿蜗轮的方法。单齿飞刀制造方便，加工过程简单，连续分度的加工效率比单齿分度高。建立了飞刀直刃运动数学模型，分析了飞刀切得的齿面与理论齿面之间的关系，提出了飞刀安装倾角的求解方法。对于高精度平面蜗轮制造，该方法具有很高的应用价值。     

锥基波形前刀面硬齿面插齿刀切削刃几何角度分析

在提出一种硬齿面插齿刀的新构形方法 (锥基波形前刀面硬齿面插齿刀 )的基础上 ,对新构形方法插齿刀的前角、后角及刃倾角进行了分析 ,建立了切削刃几何角度的数学模型 ,并与原构形法插齿刀进行了对比研究。     

Dynamic analysis and load-sharing characteristic of multiple pinion drives in tunnel boring machine

A dynamic model of multi-gear drive in a tunnel boring machine is demonstrated in this study in which the effects of inertia on the driving mechanism and cutter head are considered. With the nonlinear coupling factors between the ring gear and multiple pinions considered, a dynamic analysis of multiple pinion drives is conducted, and their load-sharing characteristic is proposed. The load-sharing coefficients at different rotating cutter head speeds and input torques are determined and are found to reach up to 1.2–1.3. A simulated experimental platform of multiple pinion drives is performed, and subsequent torque distributions are measured under step load in the driving shaft of pinions. An imbalance in torque distribution of pinions is verified, and the load-sharing coefficients in each pinion can reach 1.262. Torque load fluctuation is regarded as system noise that can directly be coupled into the control system in the control strategy.     

刻线加工的新刀具——刻线插齿刀

介绍了一种在插齿机上加工度数环用的刻线插齿刀。这种刻线插齿刀解决了在普通铣床上用分度头加工时劳动强度大、生产效率低以及分齿精度达不到技术要求的问题,具有一定实用性。     

椭圆齿轮插齿加工的数学模型及图形仿真

分析了用范成法加工椭圆外啮合齿轮及内啮合齿轮时刀具与椭圆齿轮节曲线间的位置关系,提出了加工内,外啮合椭圆齿轮时的数学模型,并根据该模型对加工外啮合椭圆齿轮,内啮合椭圆齿轮的范成过程用计算机C语言进行了仿真,该模型为非圆齿轮的加工和啮合特性的理论研究提供了基础。