Planetary Gear Profile Modification Design Based on Load Sharing Modelling

In order to satisfy the increasing demand on high performance planetary transmissions, an important line of research is focused on the understanding of some of the underlying phenomena involved in this mechanical system. Through the development of models capable of reproduce the system behavior, research in this area contributes to improve gear transmission insight, helping developing better maintenance practices and more efficient design processes. A planetary gear model used for the design of profile modifications ratio based on the levelling of the load sharing ratio is presented. The gear profile geometry definition, following a vectorial approach that mimics the real cutting process of gears, is thoroughly described. Teeth undercutting and hypotrochoid definition are implicitly considered, and a procedure for the incorporation of a rounding arc at the tooth tip in order to deal with corner contacts is described. A procedure for the modeling of profile deviations is presented, which can be used for the introduction of both manufacturing errors and designed profile modifications. An easy and flexible implementation of the profile deviation within the planetary model is accomplished based on the geometric overlapping. The contact force calculation and dynamic implementation used in the model are also introduced, and parameters from a real transmission for agricultural applications are presented for the application example. A set of reliefs is designed based on the levelling of the load sharing ratio for the example transmission, and finally some other important dynamic factors of the transmission are analyzed to assess the changes in the dynamic behavior with respect to the non-modified case. Thus, the main innovative aspect of the proposed planetary transmission model is the capacity of providing a simulated load sharing ratio which serves as design variable for the calculation of the tooth profile modifications.

Effect of Tooth Profile Modification on Vibration of Power Split Gear Transmission System

Based on Newton ' s second law,the bend-torsion-shaft coupling nonlinear dynamic model and equations of power split gear transmission system are established.According to the principle of tooth profile modification,the tooth profile modification is considered as time-varying gear backlash function acting along the line of action.Then the dynamic functions are solved by using Runge-Kutta numerical method.After analyzing the effect of tooth profile modification quantity( TPMQ) and relative tooth profile modification length( TPML) to the nonlinear dynamic characteristics of power split gear transmission,the following conclusions are drawn:1 The TPMQ of a certain stage transmission affects the vibration of its own stage more significantly than the other stage,and the coupling effect between two stages can be ignored usually in the modification design;2 If the first stage TPMLs are less than 0.3,the influence of the first stage TPMLs to the first stage transmission vibration is much more greatly than the influence of the second stage TPMLs to the first stage transmission vibration,or else both the first and second stage TPMLs affect the first stage transmission vibration largely.The same is true for the second stage TPMLs,and the cutoff value is 0.2;3 The TPMQ affects the vibration of power split gear transmission system more principally than the TPML,and should be top-priority in the modification design.

Effects of Shear Fracture on In-depth Profile Modification of Weak Gels

Two sand packs were filled with fine glass beads and quartz sand respectively. The characteristics of crosslinked polymer flowing through the sand packs as well as the influence of shear fracture of porous media on the indepth profile modification of the weak gel generated from the crosslinked polymer were investigated. The results indicated that under the dynamic condition crosslinking reaction happened in both sand packs, and the weak gels in these two cases became small gel particles after water flooding. The differences were： the dynamic gelation time in the quartz sand pack was longer than that in the glass bead pack. Residual resistance factor （FRR） caused by the weak gel in the quartz sand pack was smaller than that in the glass bead pack. The weak gel became gel particles after being scoured by subsequent flood water. A weak gel with uniform apparent viscosity and sealing characteristics was generated in every part of the glass bead pack, which could not only move deeply into the sand pack but also seal the high capacity channels again when it reached the deep part. The weak gel performed in-depth profile modification in the glass bead pack, while in the quartz sand pack, the weak gel was concentrated with 100 cm from the entrance of the sand pack. When propelled by the subsequent flood water, the weak gel could move towards the deep part of the sand pack but then became tiny gel particles and could not effectively seal the high capacity channels there. The in-depth profile modification of the weak gel was very weak in the quartz sand pack. It was the shear fracture of porous media that mainly affected the properties and weakened the in-depth profile modification of the weak gel.

TRIGONOMETRIC CURVE MODIFICATION OF SCROLL PROFILE AND ITS EFFECT ON PERFORMANCES OF A SCROLL COMPRESSOR

A modification of central profile with trigonometric curve is proposed based on the theory of engagement of scroll compressor. General modification equations for central profile of a pair of scrolls are given and various modification patterns are discussed. The equidistant method is employed to calculate the volume of a sealed chamber and a set of general equations is represented. Modification parameters affecting geometric and dynamic property of a scroll compressor are analyzed systematically, and the relations between them are accurately determined. The condition for transforming a trigonometric curve modification into an arc-curve modification is explained. The conclusions can also be applied to other scroll fluid machines.

Investigation on Instantaneous Meshing Stiffness and Profile Modification of Involute Helical Gear

An efficient finite element model of involute helical gear is presented. A program based on compliance matrix method is developed for the calculation of instantaneous meshing stiffness, and the relationship between the rate of meshing stiffness and overlap ratio is given. On the basis of stiffness calculation, an optimization program for the optimal design of profile modification is developed according to the principle of internal point punishment function method.

Influence of Different Geomorphic Surfaces and Profile Modification on the Growth of <i>Maesopsis eminni</i>(Engl) at the Yongka Western Highlands Research Garden Park Nkwen-Bamenda, North West Cameroon

The growth of Maesopsis under the influence of various geomorphic surfaces was followed within a period of 70 months. Young plants of two months old were transplanted into 70 × 70 × 70 cm holes under natural conditions (no inputs such as manure and other amendments). A randomized complete block design was set up for the experiment, alongside a control, and growth parameters followed (height and collar circumference). Three blocks with different geomorphic surfaces were put in place for the experiment (upper slope or block 1, middle slope or block 2 and foot slope or block 3). Results of the experiment indicated that geomorphic surface had a significant effect on height but not on collar circumference. Plant height increased progressively from upper slope to foot slope;less tall trees were found at the upper slope, while the tallest trees were found at the foot slope. After 70 months, maximum average height attained by plants for the experiment was 1228.3 cm, observed in block 3 (foot slope), significant at 0.05 confidence level with respect to geomorphic surface. In blocks 1 and 2 (upper slope and middle slope), maximum average heights attained were 798.5 and 937.5 cm, respectively and were shown to be statistically equal at 0.05 confidence level. Geomorphic surface had no effect on collar circumference. Maximum average collar circumferences attained after 70 months were 62.8 cm (observed at the upper slope), 61.3 cm (observed at the middle slope) and 76.3 cm (observed at the foot slope) and the various collar circumferences were shown to be statistically the same at 0.05 confidence level. For the control, maximum height attained after 70 months was 1240 cm (observed at the foot slope). At the upper slope and middle slope, maximum average heights were respectively, 800 cm and 905 cm, and were statistically equal at the 0.05 confidence level but different from the foot slope value of 1240 cm. Maximum average collar circumference was observed at the foot slope (76.3 cm), while circumferences of 62.8 cm and 61.3 cm were respectively observed at the upper and middle slopes. In the control, collar circumference was shown to be statistically equal at the upper and middle slopes but different from that at the foot slope at 0.05 confidence level. Correlations between growth parameters were more explained for the control than for the experiment. Increasing plant height was associated with decreasing percent slope (at a p-value of 0.05) corresponding to increasing soil depth favoring root exploration and soil and water retention. Profile modification enhanced plant growth and enabled the cultivation of trees on all geomorphic surfaces.

Profile Modification for Increasing the Tooth Strength in Spur Gear Using CAD

This paper examines the tooth failure in spur gears. Corrective measures are taken to avoid tooth damage by introducing profile modification in root fillet. In general, spur gear with less than 17 numbers of teeth had the problem of undercutting during gear manufacturing process which minimizes the strength of gear at root. In this study, a novel design method, namely circular root fillet instead of the standard trochoidal root fillet is introduced in spur gear and analyzed using ANSYS version 11.0 software. The strength of these modified teeth is studied in comparison with the standard design. The analysis demonstrates that the novel design exhibit higher bending strength over the standard trochoidal root fillet gear. The result reveals that the circular root fillet design is particularly suitable for lesser number of teeth in pinion and where as the trochoidal root fillet gear is more opt for higher number of teeth.

Tooth surface geometry optimization of spiral bevel and hypoid gears generated by duplex helical method with circular profile blade

In order to effectively improve meshing performance of spiral bevel and hypoid gears generated by the duplex helical method, the effects of straight lined and circular cutting edges profile on meshing and contact of spiral bevel and hypoid gears were investigated analytically. Firstly, a mathematical model of spiral bevel and hypoid gears with circular blade profile was established according to the cutting characteristics of the duplex helical method. Based on a hypoid gear drive, the tooth bearings and the functions of transmission errors of four design cases were analyzed respectively by the use of the tooth contact analysis(TCA), and the contact stresses of the four design cases were analyzed and compared using simulation software. Finally, the curvature radius of the circular profile blade was optimized. The results show that the contact stresses are availably reduced, and the areas of edge contact and severe contact stresses can be avoided by selecting appropriate circular blade profile. In addition, the convex and concave sides are separately modified by the use of different curvature radii of inside and outside blades, which can increase the flexibility of the duplex helical method.

Study of Water Treatment Residue Used as a Profile Control Agent

A large amount of residue from the water treatment process has gradually accumulated and thus caused serious environmental pollution in waterflood oilfields. The water treatment residue is a grey suspension, with a density of 1.08 g/cm^3, and mainly contains over 65% of light CaCO3, MgCO3, CaSO4, Fe2S3 and Ca（OH）2. This paper ascertains the effect of water treatment residue on core permeability and its application in oilfields. Coreflooding tests in laboratory were conducted in two artificial cores and one natural core. Core changes were evaluated by cast model image analysis, mercury injection method and scanning electron microscopy （SEM）. Fresh water was injected into another natural core, which was plugged with water treatment residue, to determine the effective life. The results indicate that the water treatment residue has a strongly plugging capability, a resistance to erosion and a long effective life, and thus it can be used as a cheap raw material for profile control. In the past 8 years, a total of 60,164 m^3 of water treatment residue has been used for profile control of 151 well treatments, with a success ratio of 98% and an effective ratio of 83.2%. In the field tests, the profile control agent increased both starting pressure and injection pressure of injectors, and decreased the apparent water injectivity coefficient, significantly improving intake profiles and lengthening average service life of injectors. 28,381 tons of additional oil were recovered from these corresponding oil wells, with economic benefits of ￥3,069.55×10^4 （RMB） and a remarkable input-output ratio of 8.6：1.

Compensation modification of plastic gear tooth profile considering meshing deformation

The plastic gear is widely used in agricultural equipment,electronic products,aircraft,and other fields because of its light weight,corrosion resistance,and self-lubrication ability.However,it has a limited range of working conditions due to the low modulus and thermal deformation of the material,especially in high-speed and heavy-duty situations.A compensation modification method(CMM)is proposed in this paper to restrain the heat production of the plastic gear tooth surface by considering the meshing deformation,and the corresponding modification formulas are derived.Improving the position of the maximum contact pressure(CP)and the relative sliding velocity(RSV)of the tooth surface resulted in a 30%lower steady-state temperature rise of the modified plastic gear tooth surface than that of the unmodified plastic gear.Meanwhile,the temperature rise of plastic gear with CMM is reduced by 19%compared with the traditional modification of removal material.Then,the influences of modification index and the segment number of modification on the meshing characteristics of plastic gear with CMM are discussed,such as maximum CP and steadystate temperature rise,RSV,transmission error,meshing angle,and contact ratio.A smaller segment number and modification index are beneficial to reduce the temperature rise of plastic gear with CMM.Finally,an experiment is carried out to verify the theoretical analysis model.

Modification Design Method for an Enveloping Hourglass Worm Gear with Consideration of Machining and Misalignment Errors

The influences of machining and misalignment errors play a very critical role in the performance of the anti-backlash double-roller enveloping hourglass worm gear(ADEHWG).However,a corresponding efficient method for eliminating or reducing these errors on the tooth profile of the ADEHWG is seldom reported.The gear engagement equation and tooth profile equation for considering six different errors that could arise from the machining and gear misalignment are derived from the theories of differential geometry and gear meshing.Also,the tooth contact analysis(TCA) is used to systematically investigate the influence of the machining and misalignment errors on the contact curves and the tooth profile by means of numerical analysis and three-dimensional solid modeling.The research results show that vertical angular misalignment of the worm wheel(Δβ) has the strongest influences while the tooth angle error(Δα) has the weakest influences on the contact curves and the tooth profile.A novel efficient approach is proposed and used to minimize the effect of the errors in manufacturing by changing the radius of the grinding wheel and the approaching point of contact.The results from the TCA and the experiment demonstrate that this tooth profile design modification method can indeed reduce the machining and misalignment errors.This modification design method is helpful in understanding the manufacturing technology of the ADEHWG.

Investigation of a Design Modification for Double Helical Gears Reducing Vibration and Noise

To reduce vibration and noise and increase transmission efficiency, a three segment method for modifying the pinion profile was proposed. Cutter surface equations were deduced by changing the shape of the cutter-edge, substituting three segment parabolas for the line. The influence of longitudinal tooth modifications on tooth surface load distributions was discussed. Transmission error minimization and uniformity of tooth surface load distribution were chosen as optimization goals and the modified parameters were obtained by applying the complex method. Finally, an experiment comparing the loaded transmission error, vibration, and noise both before and after modifications was carried out. The results indicate that the modified design is reliable.

杯形谐波减速器齿廓修形方法及寿命预测分析

杯形谐波减速器柔轮与波发生器装配时产生的径向变形量理论与实际不符,柔轮与刚轮轮齿出现啮合干涉,基于柔轮装配的变形情况提出了柔轮齿廓修形方法。通过有限元法装配仿真确定了合适的修形量,修形后柔轮经过装配和运转有限元分析,最后基于Miner线性疲劳理论采用Fe-safe软件对柔轮寿命进行了预测。结果表明,修形后柔轮装配时最大应力从962.2 MPa降低至532.7 MPa,负载运转时应力为609.9 MPa,轮齿应力有较大改善且啮合干涉情况得到解决,柔轮寿命循环次数为4.28×10^(6)。

双摆线针齿传动齿廓特性与啮合特性分析

将双摆线齿廓运用到NN型少齿差行星齿轮传动领域,通过分析内外摆线轮齿廓的凹凸性、曲率和曲率半径,获得了内、外摆线齿廓的特性;通过图解法推导双摆线针齿传动中内、外摆线轮的压力角计算公式,获得了啮合过程压力角变化规律,以及双摆线针齿主要参数对于内、外摆线轮压力角的影响;通过对等距修形和移距修形进行研究,表明齿廓修形对齿形有明显影响。

修形斜齿轮成形磨削中齿廓精度补偿方法

建立了斜齿轮齿廓修形的坐标方程与成形磨削砂轮修整的几何算法,优化出齿廓修形后的砂轮截面廓形;通过数值模拟分析,得到了机床位置误差与齿廓偏差之间的耦合关系;编制了成形磨削齿廓精度调整软件,计算出斜齿轮修形与之对应的成形砂轮廓形和齿廓精度调整参数。通过修形斜齿轮的成形磨削试验,验证了砂轮廓形修整的正确性和齿廓精度调整的有效性。

糠醇浸渍速生人工林木材的干燥特性研究

木材浸渍改性商业应用的主要技术难点之一是二次干燥速度慢、易开裂、易变形。本文以杨木和杉木为研究对象,使用浓度为30%和50%的糠醇水溶液对其进行浸渍改性,再以百度干燥法分析糠醇浸渍材的干燥特性,辅以干缩试验和剖面密度(VDP)试验探究干燥缺陷成因。结果表明:50%浓度浸渍材的干燥缺陷等级均大于30%浓度浸渍材,杨木浸渍材的等级均高于杉木浸渍材;杉木30%和50%浓度浸渍材百度干燥平均时间分别为24 h和29 h,而杨木30%和50%浓度浸渍材分别为20 h和30 h。浸渍材不同位置的干缩系数存在显著差异,浸渍后密度分布更加不均匀。杉木和杨木糠醇浸渍材二次干燥困难的主要原因为固化的糠醇堵塞了水分内部迁移通道,从而使干燥速度降低;糠醇分布不均匀导致干缩系数差异进一步加大,处理材易开裂、易变形。

齿廓修形在降低齿轮箱啮合噪声中的应用

本研究旨在解决齿轮箱在啮合过程中由负载齿轮产生的啸叫问题。为解决这个问题,利用牛顿运动定律,建立一个齿轮副啮合的一维振动模型。在不改变齿轮基本参数的前提下,分别对齿轮齿顶和齿根进行修形。通过对比多种不同齿廓修形量的方案,计算齿廓修形量对齿轮强度及性能参数的影响,并根据齿廓修形量、修形长度和齿形公差绘制齿轮齿形检测的“K”形图。通过齿轮箱台架试验评估所提出的解决方案的有效性,证明齿轮啮合噪声的显著降低,从根源上改善齿轮啸叫现象。研究结果表明,齿廓修形是降低齿轮箱中齿轮啮合噪声的有效方法。

基于形函数的非一致网格接触修形新方法

针对接触压力分布不均导致机械零部件过早失效的问题,提出了一种非一致网格接触修形新方法。基于单元形函数和“虚拟节点”建立了非一致网格接触节点之间的力学关系,推导得到了节点修形量与接触压力之间的数学方程,提出了一种通过最小化最大接触压力求解修形量的极小极大模型,并根据其数学特点将该模型转换为线性规划模型,提高了修形量计算的效率和全局收敛性。通过三个弹性接触修形实例,验证了该方法对一般弹性接触修形问题的适用性和有效性。

RV减速器摆线针轮传动机构轮齿承载接触分析

RV减速器摆线针轮传动机构的轮齿承载接触分析是进行该机构润滑分析的基础。为明确摆线轮齿与针齿、曲拐轴承滚针与内外圈之间的动态接触特性,基于摆线针轮传动机构啮合原理,分析了6种不同齿廓修形方式下的轮齿间隙及啮合点的运动学特性;结合静力平衡方程及变形协调条件,引入非线性赫兹接触刚度,建立了摆线针轮传动机构的三维动态承载接触分析模型,确定了含有初始间隙的轮齿受载变形,利用迭代法完成模型求解,明确了传动过程中轮齿及曲拐轴承滚针内外圈啮合处的时变受力特性。

基于时变啮合刚度的修形齿轮承载接触分析

为了解决传统齿轮承载接触分析力学解析方法难以考虑齿廓修形的问题,以齿廓修形渐开线直齿轮为研究对象,基于时变啮合刚度,提出了一种齿轮承载情况下齿间载荷分配系数与齿面接触应力解析算法。通过对比齿轮承载接触时接触点在啮合线方向的变形量与修形量,提出修形齿轮单双齿啮合状态判定方法,并计算不同状态下的啮合刚度;推导修形齿轮的啮合力、刚度与变形的力学关系,建立各啮合齿对的齿间载荷分配系数计算模型,应用赫兹接触理论求解齿面接触应力;分别在不同修形高度、修形曲线与配对齿数情况下,计算分析多种齿廓修形算例的齿间载荷分配系数与齿面接触应力。结果表明,解析算法求解的齿间载荷分布系数、齿面接触应力及相应单双齿啮合区间与有限元结果相一致,相对误差较小,证明了该算法有较高的精度与稳定性,为齿廓修形齿轮承载接触分析提供一种高效便捷的新方法。