Calculation and Analysis of TVMS Considering Profile Shifts and Surface Wear Evolution Process of Spur Gear

Profile shift is a highly effective technique for optimizing the performance of spur gear transmission systems.However,tooth surface wear is inevitable during gear meshing due to inadequate lubrication and long-term operation.Both profile shift and tooth surface wear(TSW)can impact the meshing characteristics by altering the involute tooth profile.In this study,a tooth stiffness model of spur gears that incorporates profile shift,TSW,tooth deformation,tooth contact deformation,fillet-foundation deformation,and gear body structure coupling is established.This model efficiently and accurately determines the time-varying mesh stiffness(TVMS).Additionally,an improved wear depth prediction method for spur gears is developed,which takes into consideration the mutually prime teeth numbers and more accurately reflects actual gear meshing conditions.Results show that consideration of the mutual prime of teeth numbers will have a certain impact on the TSW process.Furthermore,the finite element method(FEM)is employed to accurately verify the values of TVMS and load sharing ratio(LSR)of profile-shifted gears and worn gears.This study quantitatively analyzes the effect of profile shift on the surface wear process,which suggests that gear profile shift can partially alleviate the negative effects of TSW.The contribution of this study provides valuable insights into the design and maintenance of spur gear systems.

CNC FLEXIBLE GENERATING SPECIFIC GEAR TOOTH PROFILE BASED ON STANDARD INVOLUTE GEAR HOB

A new method named orthogonal two-way link-shift here has been proposed.Based on the method and a standard involute gear hob, a specific gear tooth profile (including anarbitrary gear tooth profile and a modified involute gear tooth profile) can be generated on aCNC(computer numerical control) bobbing machine. Computer simulation has been carried out, and theresults prove that the method is right and practicable. So, the fabrication costs can be greatlydecreased than before. The new method has momentous significance to realize gear's optimizedmodification under different work conditions.

A distributed dynamic mesh model of a helical gear pair with tooth profile errors

A dynamic model of a helical gear rotor system is proposed.Firstly,a generally distributed dynamic model of a helical gear pair with tooth profile errors is developed.The gear mesh is represented by a pair of cylinders connected by a series of springs and the stiffness of each spring is equal to the effective mesh stiffness.Combining the gear dynamic model with the rotor-bearing system model,the gear-rotor-bearing dynamic model is developed.Then three cases are presented to analyze the dynamic responses of gear systems.The results reveal that the gear dynamic model is effective and advanced for general gear systems,narrow-faced gear,wide-faced gear and gear with tooth profile errors.Finally,the responses of an example helical gear system are also studied to demonstrate the influence of the lead crown reliefs and misalignments.The results show that both of the lead crown relief and misalignment soften the gear mesh stiffness and the responses of the gear system increase with the increasing lead crown reliefs and misalignments.

Influence of Setting Error of Tool on Tooth Profile and Contact Point of Face Gear Drive

In order to analyze the influence of setting error of tool on both tooth profile and contact characteristic of orthogonal face gear drive,the coordinate systems with and without setting error are established.Moreover,the equations of tooth profile and contact points of face gear drive are derived by envelope principle.According to the equations,the change of tooth profile and the contact points position on face gear are analyzed.The tooth surface and contact points are obtained by numerical simulation.Results show that the tooth profile and contact characteristic of face gear drive are not sensitive to the setting error of tool.

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.

Active Design Method of Tooth Profiles for Cycloid Drive Based on Meshing Efficiency

An active design method of tooth profiles for cycloid gears based on their meshing efficiency is proposed.This method takes the meshing efficiency as one of the design variables to determine the tooth profiles.The calculation method for the meshing efficiency of planetary transmission is analyzed and the equation of the meshing efficiency is deduced.Relationships between the meshing efficiency,the radius of the pin wheel and the eccentric distance are revealed.The design constraint quations and the strength constraint quations are deduced.On the basis of this,a design procedure is laid out.Some examples using different input parameters are conducted to demonstrate the feasibility of the approach.A dynamic simulation of the rigid flexible coupling of cycloid gears is also presented.The results show that the proposed design method is more flexible to control the tooth profiles by changing the input values of the transmission efficiency.

Experimental Investigation of the Deformation of Helical Gears with Double－Circular－Arc Tooth Profile Using Linear Variable Differential Transformer

A small hole of 0.9mm in diameter is drilled at the theoretical contact point of the convex tooth flank of the measured gear, and the hole leads throughout to the non-working flank. A stylus glued to the core of transformer is put into the hole, and the stylus can freely contact with the meshed concave tooth flank. The transformer is installed on the body of gear to be measured. Rotate the positioning worm slowly after loading, and locate the contact point at the hole of convex tooth flank, the displacement value measured is considered as the deformation of convex tooth. The deformations at the middle and the two ends of tooth breadth for the helical gears with double-circular-cra tooth profile whose modules are 3mm and 4mm respectively are measured in the paper.

Generation Principle of Helix Tooth Profile in Hypocycloid Pinw heel Transmission and Its Contact Characteristics

The transmission characteristics of gear drive can be improved with the use of novel tooth profiles.A theoretical study on tooth profile of the hypocycloid pinwheel transmission and contact analysis of gear pair based on finite element method(FEM) are carried out,respectively.The line contact between mated tooth surfaces becomes point contact according to a plus movement.Through loaded tooth contact analysis(LTCA),the contact stress and load distributions for the proposed hypocycloid pinwheel transmission and the traditional one are discussed.The analysis results show that the developed tooth surfaces have anticipatory point contact characteristics under loads and contact fatigue dangerous area locates around the ultimate contact position.

Geometric design and simulation of tooth profile using elliptical segments as its line of action

A mathematical model of gear tooth profiles using the ellipse curve, whose curvature is convenient to control by changing the mathematical parameters as its line of action, was built based on the meshing theory. The equation of undercutting condition was derived from the model. A special epicycloidal tooth profile was also presented. An example gear drive with variation of the ellipse parameters was taken to illustrate the proposed method. The contact ratio of the gear drive designed by the proposed method was analyzed. A comparison of the property of the gear drive designed with the involute gear drive was also carried out. The results confirm that the proposed gear drive has higher contact ratio in comparison with the involute gear drive.

Accurate Modeling of the Spiral Bevel and Hypoid Gear with a New Tooth Profile

Distinguishing with traditional tooth profile of spiral bevel and hypoid gear, it proposed a new tooth profile namely the spherical involute. Firstly, a new theory of forming the spherical involute tooth profile was proposed. Then, this theory was applied to complete parametric derivation of each part of its tooth profile. For enhancing the precision, the SWEEP method used for formation of each part of tooth surface and G1 stitching schema for obtaining a unified tooth surface are put forward and made the application in the accurate modeling. Lastly, owing to the higher accuracy of tooth surface of outputted model, it gave some optimization approaches. Given numerical example about the model can show that this designed gear with spherical involute tooth profile can achieve fast and accurate parametric modeling and provide a foundation for tooth contact analysis （TCA） in digitized design and manufacture.

THEORETICAL TOOTH PROFILE AND ITS SUBSTITUTE CURVE OF THE PINION CUTTER FOR PINHOLES

The formula for the engaging curve of the pinion cutter with pitholes and the formula forthe theoretical tooth profile of the tinion cutter for the generating gearing of pinhoes are developedbased on the engaging theory. The substitute curve of the theoretical tooth profile of the pinion cut-ter is determined by the least square method.

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.

Y-Chromosomal Profile and Mitochondrial DNA of the Chevalier Bayard (1476?-1524)

Objective: We report the results of Y-chromosomal profile and mtDNA (mitochondrial DNA) of the Chevalier Bayard (1476?-1524). Methods: His genomic DNA was extracted from a tooth of his mandible. His Y-STRs profile was obtained using the AmFirst identifier PCR amplification kit. The mtDNA genomic sequence intervals for HVR1 and HVR2 were amplified by PCR, with specific primers. Results: We obtained the complete STR (Short Tandem Repeats) profile, based on fourteen STRs (DYS19, DYS385.a, DYS389.I and .b, DYS390, DYS391, DYS392, DYS393, DYS438, DYS439, DYS448, DYS456 and DYS458 and Y-GATA-H4). The deduced Y-STRs profile corresponds to the sub-clade S21 of the major European haplogroup R1b-M269 (the “Germanic” haplotype). There are six mutations (16093C, 16211T and 16519C in the HVR1 sequence, 263G, 309.1C and 315.1C in the HVR2 sequence) in the mtDNA of Bayard. The 263G mutation determines the H mtDNA haplogroup and the 16211T suggests the H5 sub-clade of the H haplogroup (a sub-clade found at >8% frequency in France, at the periphery of the Alpine arch region). This sub-clade H5 (subsequently assimilated to the H10e haplotype) is that (with a perfect match) of a modern living male related (to 32 generations) to the Bayard maternal ascendance. The Bayard mtDNA haplotype was found once only in a database of 100 South-German mtDNA control sequences. Conclusions: The resulting R1b-M269 Y haplogroup established confirms the Germanic origin of the Bayard ancestors, suggested by genealogic studies concerning his paternal ascendance. The result concerning the mtDNA H10e haplotype found in the modern living male related to Bayard by matrilinear ascendance establishes that the DNA tooth is well of him, with a 99% of chance.

Investigation of the Effects of Profile Shift in Helical Gear Mechanisms with Analytical and Numerical Methods

In this paper, the effects of profile shift in cylindrical helical gear mechanisms have been investigated with numerical and analytical calculations. The mathematical model for computer simulation of gears has been designed and the numerical calculations have been carried out. Analytical calculations have been made with an excel program which was designed at different profile shift coefficients for a selected mechanism. Analytical calculations of the same mechanism have been verified by using ANSYS 14.5. The results of analytical and numerical solutions have been compared to profile shift coefficients.

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)。

非圆齿轮电火花线切割加工工艺参数对齿廓误差的影响

线切割加工非圆齿轮时电参数是影响齿廓误差的关键因素之一.设计正交试验,分别采用非圆齿轮齿根、齿廓中部和齿顶的最大齿廓误差对线切割加工非圆齿轮进行分析.通过方差分析方法和主效应分析法,研究线切割加工电参数峰值电流、脉冲宽度、脉冲间隔和跟踪对非圆齿轮齿根、齿廓中部和齿顶的齿廓误差影响规律.同时,对齿廓误差、加工时长和工艺参数进行回归分析,并建立回归模型,基于灰狼优化算法对回归模型进行多目标优化求解.通过研究结果可以得出线切割加工非圆齿轮齿廓不同部位的最优参数组合,可为实际加工提供参考.

双圆弧齿廓椭圆齿轮建模与运动学仿真

为了满足齿轮变传动比运动、提高轮齿承载能力,结合齿轮啮合理论和双圆弧齿廓曲线结构参数特征,提出了一种新型双圆弧齿廓椭圆齿轮。阐述了其节曲线的设计方法,利用SolidWorks软件建立了双圆弧齿廓椭圆齿轮三维模型;使用Adams软件对双圆弧齿廓椭圆齿轮副模型进行了运动学仿真,分析了不同偏心率对双圆弧椭圆齿轮副传动比变化规律的影响,并对比理论传动比曲线,分析了仿真传动比曲线存在波动误差的影响因素;为了减小齿轮副振动脉冲,给出了偏心率适当的取值范围。本文的设计方法和分析结果对双圆弧齿廓非圆齿轮的参数化设计有理论参考价值,可为双圆弧齿廓椭圆齿轮副数控加工制造及应用提供依据。

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。

考虑齿形误差影响的摆线针轮承载特性分析

针对缺乏考虑齿形误差的承载分析软件,导致分析结果不符合实际工程状况的问题,提出了1种包含摆线轮齿形误差的摆线针轮副承载特性分析方法。利用三次非均匀B样条准确描述出包含齿形误差的摆线轮实际齿廓,构建并分析了摆线针轮误差齿廓接触分析模型(error tooth contact analysis,E-TCA),得到了初始啮合位置参数及啮合间隙。在此基础上,建立了齿形误差影响下的摆线针轮副负载接触分析模型,确定了零部件多体接触之间的力矩平衡和变形协调关系,利用能量最低原理获取了真实承载特性。通过有限元模型验证了RV-40E型号减速器的摆线针轮承载特性。结果表明:由于齿形误差的影响,啮合齿数减少了1对,啮合应力和传动误差增大了5.3%和5.7%。

摆线轮工作齿廓的二次分段修形方法

针对常规修形方法存在计算复杂、齿廓曲线形状控制不够灵活等问题,提出了一种摆线轮工作齿廓的二次分段修形方法。通过摆线轮齿廓压力角变化规律的分析,将工作齿廓最小压力角的位置作为二次分段修形的基准点,建立二次分段修形模型。利用直线法简单函数,推导出二次分段修形方法下各齿段修形量的计算公式及齿廓方程。采用轮齿接触分析的方法,研究了二次分段修形齿廓的传动误差和回差,并进行对比实验验证摆线轮工作齿廓二次分段修形方法的正确性和可行性。结果表明:二次分段修形的摆线轮工作齿廓与理论齿廓曲线更加吻合,传动误差和回程误差分别减少约14%和19%。