EFFECT OF GEAR WIDTH AND HELIX ANGLE ON FACTOR OF DYNAMIC LOAD OF DOUBLE CIRCULAR ARC HELICAL GEARING

Based on theory of mechanical dynamics, meshing characteristic as well as thedynamic model of double circular arc helical gearing, an analysis approach and a computer programhave been developed for studying the state of dynamic load and factor of dynamic load of thegearing, the changing situation of dynamic load and dynamic load factor vs some affecting factorssuch as gear width, helix angle and accuracy grade etc are investigated. A series of conclusions areobtained: ①With the increasing in the values of gear width, the dynamic load factor appears slowdecreasing tendency in most region of gear width. ②When the accuracy grades of the gearing areimproved, the values of dynamic load factor decrease. ③The value of dynamic load factor appears adecreasing tendency with the increasing of value of helix angle at the same ratio of criticalrotational speed.

Research on Cavitation Characteristics and Influencing Factors of Herringbone Gear Pump

Cavitation is a common issue in pumps,causing a decrease in pump head,a fall in volumetric efficiency,and an intensification of outlet flow pulsation.It is one of the main hazards that affect the regular operation of the pump.Research on pump cavitation mainly focuses on mixed flow pumps,jet pumps,external spur gear pumps,etc.However,there are few cavitation studies on external herringbone gear pumps.In addition,pumps with different working principles significantly differ in the flow and complexity of the internal flow field.Therefore,it is urgent to study the cavitation characteristics of external herringbone gear pumps.Compared with experimentalmethods,visual research and cavitation area identification are achieved through computation fluid dynamic(CFD),and changing the boundary conditions and shape of the gear rotor is easier.The simulation yields a head error of only 0.003%under different grid numbers,and the deviation between experimental and simulation results is less than 5%.The study revealed that cavitation causes flow pulsation at the outlet,and the cavitation serious area is mainly distributed in the meshing gap and meshing area.Cavitation can be inhibited by reducing the speed,increasing the inlet pressure,and changing the helix angle can be achieved.For example,when the inlet pressure is 5 bar,the maximumgas volume fraction in themeshing area is less than 50%.These results provide a reference for optimizing the design and finding the optimal design parameters to reduce or eliminate cavitation.

Helix Angle Effect on the Helical Gear Load Carrying Capacity

The aim of this study is to investigate the helix angle effect on the helical gear load carrying capacity, including the bending and contact load carrying capacity. During the simulation, the transverse contact ratio is calculated with respect to the constant pressure angle. By changing the helix angle, both the overlap contact ratio and total contact ratio are calculated and simulated. The bending stress and contact stress of a helical gear are calculated and simulated with respect to the helix angle. Solid (CAD) modelling of a pinion gear was obtained using SOLIDWORKS software. The analytically obtained results and finite elements method results are compared. It is observed that increasing the helix angle causes an increase of the contact ratio of the helical gear. Furthermore, increasing the contact ratio reduces the bending stress and contact stress of the helical gear. However, with a constant transverse contact ratio, it is possible to improve the total contact ratio depending on the helix angle. It is concluded that a higher helix angle increases the helical gear bending and contact load carrying capacity.

Research of the Pressure Angle for Whole Cycloidal Gears

The working profile of whole cycloidal gear is made up of epicycloid and hypocycloid entirely, according to the theory of meshing of gears and the properties of the cycloid, deals with the derivation of the pressure angle formula for the whole cycloidal gear in theory, and reveals changes of the pressure angle of whole cycloidal gear through examples, finds the application relationships between the pressure angle and other design parameters of the whole cycloidal gear, proves the possibility that the whole cycloidal gear can be used in internal parallel move gear mechanism, also provides theoretic fundament for designing internal parallel move whole cycloidal gear correctly.

Research on Design Method of Non-Circular Gear Pair with Double Generating Angles

In order to enhance the bearing capacity of non-circular gear pair, the non-circular gear pair with double generating angles is proposed based on the design idea of unsymmetrical gear with double pressure angles. The tooth profile is designed by generating cutting theory, the pure rolling mathematic model that the center line of unsymmetrical rack roll along non-circular pitch curve is built, the digital model of non-circular gear with double generating angles is created through the second development method of CAD software, and then the drive characteristic and tooth strength are analyzed. The results show that the design method for double generating angles non-circular gear proposed in this paper is feasible, which is significant to improve the bearing capacity of non-circular gear pair.

Design System of the Two-step Gear Reducer on Case-based Reasoning

The design of the two-step gear reducer is a tedious and time-consuming process. For the purpose of improving the efficiency and intelligence of design process, case-based reasoning（CBR） technology was applied to the design of the two-step gear reducer. Firstly, the current design method for the two-step gear reducer was analyzed and the principle of CBR was described. Secondly, according to the characteristics of the reducer, three key technologies of CBR were studied and the corresponding methods were provided, which are as follows： （a） an object-oriented knowledge representation method, （b） a retrieval method combining the nearest neighbor with the induction indexing, and （c） a case adaptation algorithm combining the revision based on rule with artificial revision. Also, for the purpose of improving the credibility of case retrieval, a new method for determining the weights of characteristics and a similarity formula were presented, which is a combinatorial weighting method with the analytic hierarchy process（AHP） and roughness set theory. Lastly, according to the above analytic results, a design system of the two-step gear reducer on CBR was developed by VC＋＋, UG and Access 2003. A new method for the design of the two-step gear reducer is provided in this study. If the foregoing developed system is applied to design the two-step gear reducer, design efficiency is improved, which enables the designer to release from the tedious design process of the gear reducer so as to put more efforts on innovative design. The study result fully reflects the feasibility and validity of CBR technology in the process of the design of the mechanical parts.

Load Sharing Behavior of Star Gearing Reducer for Geared Turbofan Engine

Load sharing behavior is very important for power-split gearing system, star gearing reducer as a new type and special transmission system can be used in many industry fields. However, there is few literature regarding the key multiple-split load sharing issue in main gearbox used in new type geared turbofan engine. Further mechanism anal- ysis are made on load sharing behavior among star gears of star gearing reducer for geared turbofan engine. Compre- hensive meshing error analysis are conducted on eccentricity error, gear thickness error, base pitch error, assembly error, and bearing error of star gearing reducer respectively. Floating meshing error resulting from meshing clearance variation caused by the simultaneous floating of sun gear and annular gear are taken into account. A refined mathematical model for load sharing coefficient calculation is established in consideration of different meshing stiffness and support- ing stiffness for components. The regular curves of load sharing coefficient under the influence of interactions, single action and single variation of various component errors are obtained. The accurate sensitivity of load sharing coefficienttoward different errors is mastered. The load sharing coef- ficient of star gearing reducer is 1.033 and the maximum meshing force in gear tooth is about 3010 N. This paper provides scientific theory evidences for optimal parameter design and proper tolerance distribution in advanced devel- opment and manufacturing process, so as to achieve optimal effects in economy and technology.

Design and Dynamics Simulation of a Novel Double-Ring-Plate Gear Reducer

A patented double-ring-plate gear reducer was designed and its dynamic performance was simulated. One unique characteristic of this novel drive is that the phase angle difference between two parallelogram mechanisms is a little less than 180 degree and four counterweights on two crankshafts are designed to balance inertia forces and inertia moments of the mechanisms. Its operating principle, advantages, and design issues were discussed. An elasto-dynamics model was presented to acquire its dynamic response by considering the elastic deformations of ring-plates, gears, bearings, etc. The simulation results reveal that compared with housing bearings, planetary bearings work in more severe conditions. The fluctuation of loads on gears and bearings indicates that the main reason for reducer vibration is elastic deformations of the system rather than inertia forces and inertia moments of the mechanisms.

Cycloidal Magnetic Gear Speed Reducer

A cycloidal speed reducer employing gears with permanent magnets acting as teeth is described. The magnets, which have their axes radially oriented in both the orbiting gear and the fixed internal gear, are inserted in holes drilled in nonmagnetic rims without protruding from the cylindrical exposed surfaces. Because the orbiting gear is not restrained radially, it contacts the fixed gear and rolls on its inner surface. A normal force is developed at the contact point between the gears to balance the magnetic attraction and the centrifugal force of the orbiting gear. The friction available due to this normal force increases the transmission’s torque capacity, which is further increased by elimination of the gap between the gears. Also, the radial load on the supporting orbiting gear bearing is eliminated. A prototype with a reduction ratio of 26 is being tested.

Optimisation of Effective Design Parameters for an Automotive Transmission Gearbox to Reduce Tooth Bending Stress

Optimisation of effective design parameters to reduce tooth bending stress for an automotive transmission gearbox is presented. A systematic investigation of effective design parameters for optimum design of a five-speed gearbox is studied. For this aim contact ratio effect on tooth bending stress by the changing of contact ratio with respect to pressure angle is analysed. Additionally, profile modification effects on tooth bending stress are presented. During the optimisation, the tooth bending stress is considered as the objective function, and all the geometric design parameters such as module, teeth number etc. are optimised under two different constraints, including tooth contact stress and constant gear centre distance. It can be concluded that higher the contact ratio results in a reduced tooth bending stress, while higher the pressure angle caused an increase in tooth bending stress and contact stress, since decreases in the contact ratio. In addition, application of positive profile modification on tooth reduces tooth bending stress. All of the obtained optimum solutions satisfy all constraints.

Theoretical calculation and experimental study on the load distribution coefficient (LDC) of three-ring gear reducer

In this paper, primary manufacturing and assembling errors of three-ring gear reducer （TRGR） are analyzed. TRGR is a new transmission type whose eccentric phase difference between middle ring plate and side ring plates is 120°, Its mass of middle ring plate is equal to that of side ring plate or 180°, and its inass of middle ring plate is twice of that of side ring plate, which affects load distribution between ring plates. The primary manufacturing and assembling errors include eccentric error of eccentric sheath E111, internal gear plate E1 and output external gear E11. A new theoretical method is presented in this paper, which converts load on ring plates into the dedendum bending stress of ring plate to calculate load distribution coefficient （ LDC ）, by means of gap element method （GEM）, one of finite element method （FEM）. The theoretical calculation and experimental study, which measures ring plate dedendum bending stress by means of sticking strain gauges on the dedendum of middle ring plate internal gear and side ring plate internal gears, are presented. The theoretical calculation and comparison with experiment result of LDC are implemented an two kinds of three-ring gear reducers whose eccentric phase difference between eccentric sheaths is 120° and 180°respectively. The research indicates that the result of theoretical calculation is consistent with that of experimental study. That is to say, the theoretical calculation method is feasible.

Experimental Study on Load Equilibration and Vibration Reduction in 3-Ring-Gear Reducer

Following the principle of elastic floating compensation, this paper presents a new metal elastic ring for load equilibration and vibration reduction in 3-ring-gear reducer, and design and fabrivcation of a metal elastic ring for SCH 3-ring-gear reducer. Comparison tests run with 3-ring-gear reducers without or with the metal elastic ring show satisfactory load equilibration and vibration reduction can be achieved with the metal elastic ring, and the metal elastic ring is a good solution for the problem of unequilibrated load and excessive vibration from which 3-ring-gear reducers suffered long.- This will further the improvement of design and application of 3-ring-gear reducers in both theory and practice.

Research on Torque-Angle Characteristic of Large Gap Magnetic Drive System

The principle and design method of the large gap magnetic drive system is studied in this work. The calculation model of the torque-angle characteristic in the large gap magnetic drive system driven by traveling wave magnetic field is established. The calculation model is computed by using MATLAB software, and the pattern of the system’s torque-angle characteristic is obtained by analyzing study results. These results indicate that: torque-angle characteristic and the driving torque of the system can be adjusted by changing the electric current of coil, the magnetization of permanent magnetic gear, the inner diameter of permanent magnetic gear, the coupling distance between electromagnet and permanent magnetic gear, the outer diameter of permanent magnetic gear, and the axial length of permanent magnetic gear.

无传动间隙的3K行星齿轮减速器设计

3K行星齿轮减速器的啮合齿轮副存在齿侧间隙,使得传动链中引入了传动间隙,导致传动精度降低以及换向冲击。为消除3K行星齿轮减速器的传动间隙,利用3K行星齿轮传动中行星架不参与力矩传递的特性,提出了一种柔性行星架以消除传动间隙,并通过仿真分析验证了所提消隙机构的有效性。通过配齿及效率优化实现了高效的正向和反向传动。研制样机并进行了传动精度、滞回特性、正弦响应误差、正向传动效率、反向传动效率以及反向启动扭矩测试,结果验证了所提柔性行星架对消除3K行星齿轮减速器传动间隙、提高传动精度和传动效率以及提高反向传动性能的有效性。

基于ProE的联合收割机二级齿轮减速器仿真分析

针对联合收割机二级齿轮减速器总体结构进行了设计,基于Pro/E建立了二级齿轮减速器模型并完成了产品的装配,最后利用Pro/E Mechanism仿真模块对所设计产品进行了运动仿真。结果表明:模型满足设计需求,具有较好的稳定性,对二级齿轮减速器进一步的优化设计具有一定参考作用。

齿轮传动性能检测系统设计与试验

齿轮传动中的啮合角和重合度受制造精度、载荷、齿廓磨损、变形等因素影响会发生改变,导致传动的平稳性和连续性下降。为检测齿轮传动啮合参数,基于机器视觉技术设计了齿轮传动性能检测系统。该系统由轮系、传动装置、测量装置和图像分析系统等组成。使用工业摄像机拍摄齿轮啮合运动图像,基于最小二乘法进行数据分析,检测齿轮节圆、啮合角、重合度等啮合参数。检测结果表明,实际啮合角和重合度值检测结果与设计值相对误差低于5%。该检测系统具有高效、实时、非接触等优点,为齿轮智能制造及检测提供技术支持。

改进KnEA的二级斜齿圆柱齿轮减速器优化设计

在实际工程中,复杂的多目标问题是导致优化结果收敛性和多样性损失的重要因素。为了提高优化算法在复杂问题中维持解多样性和收敛性平衡的能力,提出了基于KnEA(A Knee Point Driven Evolutionary Algorithm)的辅助点进化算法。首先,该算法借助进化过程中有明显趋势的拐点作为邻域空间的中心;其次,通过分析邻域空间中的拐点与上一代拐点之间的关系,从侧面来定量分析了邻域空间的潜力;再次,为了解决对复杂问题优化过程中收敛性不足的缺陷,提出了根据邻域空间的进化潜力来增加辅助点的策略,进一步地提高了进化过程中的空间搜索能力。在种群的环境选择中,优先选择拐点和辅助点进化下一代,以此平衡种群的收敛性和多样性。将该算法在多目标测试问题上与流行的算法进行了比较,实验结果表明提出的算法在多目标问题优化中有明显优势。最后,将该算法应用到二级斜齿圆柱齿轮减速器优化设计当中。

平行轴变齿厚齿轮接触应力解析计算

变齿厚齿轮作为一种新型齿轮,目前尚无成熟的接触应力理论和计算方法。为了从理论上计算变齿厚齿轮齿面上的最大接触应力,了解变齿厚齿轮在不同参数下接触应力的变化情况。文中在赫兹公式的基础上,考虑变齿厚齿轮的几何结构,确定了变齿厚齿轮重合度、曲率半径、法向载荷、接触线长、重合度系数和齿形角系数的计算方法。研究了不同节锥角、齿数、模数和压力角对变齿厚齿轮接触应力的影响,通过有限元分析验证了变齿厚齿轮接触应力理论计算公式的正确性。研究结果表明:推导出的变齿厚齿轮接触应力计算公式具有较高的精度,能够准确地反映齿面的真实接触应力值,为变齿厚齿轮的结构设计、强度校核等提供了一定的依据。

基于差分进化算法的减速器齿轮参数优化设计

根据上海道路循环工况,利用载荷的随机连续性和20CrMnMo材料的低载强化特性进行减速器齿轮有限寿命的轻量化设计。基于线性损伤理论,分别计算编制载荷谱和连续载荷谱在低载强化效应下的疲劳损伤,将疲劳损伤约束在一定范围内为选取条件,以齿轮体积最小为优化目标,建立了齿轮有限寿命的轻量化优化模型,通过差分进化算法求解得到优化后的齿轮参数。实验结果表明,设计的模型可快速准确优化齿轮参数,在采用连续载荷谱和考虑低载强化效应时,优化的齿轮参数最小。优化的模型可移植性好,可直接迁移到其他变速系统零件的轻量化设计。

基于压力角的摆线针轮齿廓曲线优化方法

根据摆线针轮传动理论,提出一种基于压力角的齿廓优化方法。将摆线针轮齿廓分为工作段与非工作段,区分影响工作段压力角的因素为修形参数与设计参数,讨论两类参数对压力角的影响,以此两类参数为设计变量,以工作段平均压力角为目标函数,以运动与润滑要求确定边界条件,对RV⁃550E型减速器摆线轮进行优化设计。结果表明,此方法使算例的工作段平均压力角降低了4.14%,使单齿啮合过程的压力角最大值降低了1.35%,优化前后接触齿对最大Mises应力下降了20.77%,发生位置由摆线轮转移至针轮,模型质量减小了9.38%,在确保无根切现象的同时能获得良好的组合修形效果。