DESIGN OF NONCIRCULAR GEARS WITH DISCONTINUOUS PITCH CURVE

When the noncircular gear pair is applied to the continuously variable transmission (CVT) with gear, the transmission ratio function is discontinuous. In accordance with this unique characteristic, a new approach to design and analyze noncircular gears with discontinuous pitch curve is proposed. The design courses of various noncircular gear pairs with discontinuous pitch curve are unified based on the numerical algorithm of spline fitting and "fairing boundary condition". According to the particularity of discontinuous pitch curve, the rules and procedures for teeth distribution are recommended. It is explained in detail why the undercut is formed and how to manage the undercut based on meshing principle. In addition, the calculation formulas for each tooth profile segment are also derived. If the tooth profile data are calculated, the measurement and the incision process for noncircular gear can be conducted and the CAD simulation can be achieved easily. To ensure the continuity of the transmission, the transmission interference of the tooth which is located at the pitch curve joint point is managed by utilizing Bezier curve with CAD software. And the contact ratio of gear pair is obtained. The case study shows that this approach is successful and opens up a new way for the design of noncircular gear.     

Properties and Applications of the Eccentric-gear Drive

The eccentric-gear can be used for variable speed transmission.But,due to the vibrations caused by variation of backlash in working process,the eccentric-gear is seldom applied in engineering project.There is just a little study about the eccentric-gear.And it is necessary to take a further research on eccentric-gear transmission for the applications in the transplanting mechanism of high-speed rice transplanter.The key of this paper is to extend understanding of three following characteristics of this drive:(1) The rotation-center-distance and the geometrical-center-distance of the two meshing eccentric gears are respectively the hypotenuse and the straight edge of a right triangle in a cycle.(2) The geometrical center line of two meshing gears divides the linking-line of the two rotational centers equally.(3) When two times the eccentricity of gear,the rotation-center-distance and the geometrical-center-distance form a right triangle,the optimal value of rotation-center-distance can be determined.In addition,the kinematic analysis,such as the relationship between contact point and midpoint of the linking-line of two gears’ rotational centers,transmission ratio between the driving-gear and the driven-gear,contact angle and coordinate of contact point are be made,further the formula for calculation of contact force,flow chart for writing optimization program and curve for analysis of data are also be developed.The relationship between the rotation-center-distance and the geometrical-center-distance,which is determined by three characteristics mentioned above, is a key for the rational design and application of eccentric-gear transmission.Particularly,the presented right triangle property of eccentric gear drive is an important reference for effective analysis of dynamic characteristic of eccentric-gear mechanism and its reliable design.     

TOOTH CONTACT ANALYSIS OF CONICAL INVOLUTE GEARS

The mathematical model of conical involute gears is developed based on the theory of gearing and the generating mechanism. Tooth contact analysis (TCA) is performed to examine the meshing and bearing contact of the conical involute gear pairs with intersected and crossed axes. In addition, the principal directions and curvatures of the gear surfaces are investigated and the contact ellipses of the mating tooth surfaces are also studied. Finally, the numerical illustrative examples are provided to demonstrate the computational results, test gears are made for tooth-bearing tests, and the conclusion is verified that the theory has the applicability.     

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.     

Reverse engineering of machine-tool settings with modified roll for spiral bevel pinions

Although a great deal of research has been dedicated to the synthesis of spiral bevel gears, little related to reverse engineering can be found. An approach is proposed to reverse the machine-tool settings of the pinion of a spiral bevel gear drive on the basis of the blank and tooth surface data obtained by a coordinate measuring machine(CMM). Real tooth contact analysis(RTCA) is performed to preliminary ascertain the contact pattern, the motion curve, as well as the position of the mean contact point. And then the tangent to the contact path and the motion curve are interpolated in the sense of the least square method to extract the initial values of the bias angle and the higher order coefficients(HOC) in modified roll motion. A trial tooth surface is generated by machine-tool settings derived from the local synthesis relating to the initial meshing performances and modified roll motion. An optimization objective is formed which equals the tooth surface deviation between the real tooth surface and the trial tooth surface. The design variables are the parameters describing the meshing performances at the mean contact point in addition to the HOC. When the objective is optimized within an arbitrarily given convergence tolerance, the machine-tool settings together with the HOC are obtained. The proposed approach is verified by a spiral bevel pinion used in the accessory gear box of an aviation engine. The trial tooth surfaces approach to the real tooth surface on the whole in the example. The results show that the convergent tooth surface deviation for the concave side on the average is less than 0.5 μm, and is less than 1.3 μm for the convex side. The biggest tooth surface deviation is 6.7 μm which is located at the corner of the grid on the convex side. Those nodes with relative bigger tooth surface deviations are all located at the boundary of the grid. An approach is proposed to figure out the machine-tool settings of a spiral bevel pinion by way of reverse engineering without having known the theoretical     

Pinion tooth surface generation strategy of spiral bevel gears

Aviation spiral bevel gears are often generated by spiral generated modified(SGM) roll method.In this style,pinion tooth surface modified generation strategy has an important influence on the meshing and contact performances.For the optimal contact pattern and transmission error function,local synthesis is applied to obtain the machine-tool settings of pinion.For digitized machine,four tooth surface generation styles of pinion are proposed.For every style,tooth contact analysis(TCA) is applied to obtain contact pattern and transmission error function.For the difference between TCA transmission error function and design objective curve,the degree of symmetry and agreement are defined and the corresponding sub-objective functions are established.Linear weighted combination method is applied to get an equivalent objective function to evaluate the shape of transmission error function.The computer programs for the process above are developed to analyze the meshing performances of the four pinion tooth surface generation styles for a pair of aviation spiral bevel gears with 38/43 teeth numbers.The four analytical results are compared with each other and show that the incomplete modified roll is optimal for this gear pair.This study is an expansion to generation strategy of spiral bevel gears,and offers new alternatives to computer numerical control(CNC) manufacture of spiral bevel gears.     

Modeling and Calculation of Impact Friction Caused by Corner Contact in Gear Transmission

Corner contact in gear pair causes vibration and noise,which has attracted many attentions.However,teeth errors and deformation make it difficulty to determine the point situated at corner contact and study the mechanism of teeth impact friction in the current researches.Based on the mechanism of corner contact,the process of corner contact is divided into two stages of impact and scratch,and the calculation model including gear equivalent error-combined deformation is established along the line of action.According to the distributive law,gear equivalent error is synthesized by base pitch error,normal backlash and tooth profile modification on the line of action.The combined tooth compliance of the first point lying in corner contact before the normal path is inversed along the line of action,on basis of the theory of engagement and the curve of tooth synthetic complianceload-history.Combined secondarily the equivalent error with the combined deflection,the position standard of the point situated at corner contact is probed.Then the impact positions and forces,from the beginning to the end during corner contact before the normal path,are calculated accurately.Due to the above results,the lash model during corner contact is founded,and the impact force and frictional coefficient are quantified.A numerical example is performed and the averaged impact friction coefficient based on the presented calculation method is validated.This research obtains the results which could be referenced to understand the complex mechanism of teeth impact friction and quantitative calculation of the friction force and coefficient,and to gear exact design for tribology.     

NEW TYPE OF LIMITED-SLIP DIFFERENTIAL WITH THREE-PITCH FLUCTUATING SPEED RATIO

A type of three-pitch fluctuating speed ratio limited-slip differential （TPLSD） is presented for the first time, analyzed its working principle, introduced the tooth profile design method of using non-involute tooth profile and separated tooth profile design along the pitch line. Performance comparison between vehicles equipped with three-pitch fluctuating speed ratio limited-slip differential and common open differefitial is finished. The data from experiments prove that three-pitch fluctuating speed ratio limited-slip differential can increase the traction of a vehicle, improve its acceleration performance, decrease braking distance and limit sideslip. The basic structure of new differential is the same of open differential, the only difference is that they have different tooth profile, so the new differential has a high performance price.     

PROPER CONDITIONS OF MESHING FOR Hy-Vo SILENT CHAIN AND SPROCKET

Proper meshing of Hy-Vo silent chain and sprocket is important for realizing the transmis- sion of the silent chain with more efficiency and less noise.Based on the study of the meshing theory of the Hy-Vo silent chain with the sprocket and the roll cutting machining principle of the sprocket with the hob,the proper conditions of the meshing for the Hy-Vo silent chain and the sprocket are put forward with the variable pitch characteristic of the Hy-Vo silent chain taken into consideration,and the proper meshing design method on the condition that the value of the link tooth pressure angle is unequal to the value of the sprocket tooth pressure angle is studied.Experiments show that this new design method is feasible.In addition,the design of the pitch,the sprocket tooth pressure angle and the fillet radius of the sprocket addendum circle are studied.It is crucial for guiding the design of the hob which cuts the Hy-Vo silent chain sprocket.     

EFFECT OF INVOLUTE CONTACT RATIO ON THE DYNAMIC PERFORMANCE OF SPUR GEAR WITH NOTOOTH PROFILE MODIFICATION

The effect of involute contact ratio on the torsional vibration behavior of spur gear-pair isstudied analytically through a mass-spring model. The tooth stiffness in model not only has a relationwith time, as many prior studies presented, but, more important, with involute contact ratio (ICR) aswell. The ICR embodies its impact on the spur gear's dynamic performance through changing theproportion of tooth stiffness when there are n+1 teeth in contact to tooth stiffness when there are n     

齿轮副端面重合度统一定义及其计算式

针对各种齿轮传动提出端面重合度的统一定义，并且推导其计算表达式，进一步讨论了渐开线齿轮副、微线段齿轮副和正弦齿廓齿轮副的端面重合度的计算问题。齿轮副的端面重合度定义为齿轮作用角（即一对轮齿从进入啮合到脱离啮合过程中齿轮所转过的角度）与齿轮的齿距转角的比值。根据齿轮啮合原理，由基本齿条的轮廓曲线能够获得其啮合线方程。根据所获得的啮合线方程，以及给定的齿轮副齿顶线方程，就能够根据本文的计算式得到齿轮副的重舍度。对于渐开线齿轮副，该定义与众所周知的“啮合线长度与基节之比”的结果相同。该定义同样适用于非渐开线齿轮副，例如微线段齿轮副、正弦齿廓齿轮副等，而且计算结果更可靠。     

变齿厚渐开线齿轮副啮合效率研究

由于变齿厚渐开线啮合副变位系数沿轴向变化的特点,其啮合角、锥角、重合度、不同端截面齿顶圆上的压力角、滑动率等参数与普通渐开线啮合副不同,其啮合效率计算也与普通渐开线啮合副有所区别.分析了变齿厚齿轮啮合副效率的计算特点和影响因素,如变位系数对变齿厚齿轮副重合度和啮合效率的影响;在此基础上,提出了一种新型效率计算方法;通过...     

相交轴渐开线变厚齿轮几何设计与啮合特性分析

根据空间齿轮啮合原理,建立相交轴渐开线变厚齿轮传动工作节圆锥模型,确定工作节锥角、齿线倾斜角及两齿轮安装距。提出空间点接触到线接触的转变控制条件,实现相交轴齿轮副的近似线接触;推导齿轮变位系数对节圆锥左右两侧有效齿宽的影响;基于相交轴变厚齿轮副参数关系,分析设计参数对啮合主方向角(FPD角)和齿轮副重合度的影响;根据线接触控制条件完成齿轮副参数设计并采用有限元法进行啮合特性分析,结果表明,考虑线接触条件的节圆锥设计得到的相交轴齿轮副在加载情况下,啮合状态呈现明显的线接触且啮合区域达到整个区域的50%左右,试验验证了理论分析的正确性。     

谐波齿轮传动重合度的计算方法研究

针对谐波齿轮传动的特殊性提出谐波齿轮重合度的定义,即柔轮和刚轮轮齿的啮合区间角与刚轮单个齿距圆心角的比值。基于瞬心线运动几何学,推导出柔轮和刚轮轮齿的相对瞬心线方程,然后根据Willis定理的结论,计算出柔轮和刚轮之间的啮合区间角,最后由重合度定义计算出重合度。此计算方法适用于各种不同齿形的谐波齿轮传动重合度的计算,对于衡量新齿形谐波齿轮传动的啮合性能,具有重要的参考意义,因此该方法具有通用性。     

基于ANSYS的渐开线斜齿轮副参数化建模

在ANSYS中利用APDL语言，通过求解斜齿轮端面齿廓渐开线和过渡曲线的交点，形成端面齿廓，再沿螺旋线拖拉，直接生成了一对斜齿轮的参数化模型，模型端面上啮合点与节点重合，便于进一步分析齿轮的齿面接触应力和齿根应力以及斜齿轮的啮合过程。     

齿轮弯曲强度有限元精确分析方法研究

通过计算轮齿弹性共轭接触迹,确定齿轮在啮合过程中各个位置的压力角、齿廓接触长度以及接触位置等参数。并对ANSYS进行二次开发,制作了一个精确计算齿轮弯曲强度有限元分析的软件。运用此软件对相同参数的渐开线齿轮与点线啮合齿轮进行弯曲强度的有限元精确计算,得出点线啮合齿轮比渐开线齿轮弯曲强度提高11.7%的结论。     

偏心渐开线齿轮传动的不等分模型及其数值解法

针对等分模型下配对齿工作齿廓出现实际啮合不会发生的齿廓交叉或者分离现象,根据渐开线齿廓啮合几何关系,提出一种不存在假设误差的偏心渐开线齿轮传动不等分模型,以奇数齿偏心齿轮传动为例,给出不等分模型数值求解的完整算法。根据内公切线与两轮配对齿工作齿廓的交点数不同,啮合点搜索算法能处理任意转角关系下连续转动的4种情形,能正确产生7种不同的配对结果。计算结果表明,几何中心连线与内公切线段的交点不相互等分两线段,啮合点不总是在内公切线上,和轴心距大小无关。当基准齿工作齿廓坐标点数为5 000点时,啮合点搜索的坐标控制精度可达到0.001 mm,转角误差精度可达到0.001°,计算方法可以得到非常精确的转角关系,可以为偏心齿轮传动的准确分析和优化设计提供依据。     

双圆弧弧齿锥齿轮传动的切齿啮合分析

基于双圆弧齿轮的齿形特点 ,结合弧齿锥齿轮的加工原理 ,进行双圆弧弧齿锥齿轮的切齿啮合分析 ,得到了切齿啮合过程中的啮合方程、产形轮齿面方程以及双圆弧弧齿锥齿轮的通用齿面方程表达式     

基于差齿面拓扑的轮齿承载拟赫兹接触分析

基于齿条曲面多项式与齿轮公切共轭产形原理,建立了数值齿面、差齿面ease-off模型;通过ease-off曲面映射,解析了齿面接触路径、传动误差、接触线等轮齿啮合特性信息。利用势能法、变形协调方程与拟赫兹接触分析解决了齿面载荷计算、边缘接触应力求解问题,获得了轮齿啮合刚度、传动误差、齿间载荷分担、载荷分布、接触应力等齿面啮合的时变历程特性。计算结果与第三方软件的计算结果具有较好的一致性。