Experimental Research on the Surface Quality of Milling Contour Bevel Gears

Contour bevel gears have the advantages of high coincidence,low noise and large bearing capacity,which are widely used in automobile manufacturing,shipbuilding and construction machinery.However,when the surface quality is poor,the effective contact area between the gear mating surfaces decreases,affecting the stability of the fit and thus the transmission accuracy,so it is of great significance to optimize the surface quality of the contour bevel gear.This paper firstly analyzes the formation process of machined surface roughness of contour bevel gears on the basis of generating machining method,and dry milling experiments of contour bevel gears are conducted to analyze the effects of cutting speed and feed rate on the machined surface roughness and surface topography of the workpiece.Then,the surface defects on the machined surface of the workpiece are studied by SEM,and the causes of the surface defects are analyzed by EDS.After that,XRD is used to compare the microscopic grains of the machined surface and the substrate material for diffraction peak analysis,and the effect of cutting parameters on the microhardness of the workpiece machined surface is investigated by work hardening experiment.The research results are of great significance for improving the machining accuracy of contour bevel gears,reducing friction losses and improving transmission efficiency.

Filling Rules of Bevel Gears in the Closed-die Cold Forging

The closed-died cold forging technology of the bevel gears used in Jada car was investigated. With the analysis of the strain field and velocity field of the plastic deformation and the endured forces of the dies, the filling rules for the metal were analyzed by the elastic-plastic finite element method （FEM）. The results show that there is a great difference among closed-die cold forging, extrusion and forging, as far as the metal flowing is concerned. The outer addendum cannot be filled completely in the closed-die cold forging of the bevel gears, and the round angle will be formed. But it does not influence the application of the bevel gears. At the beginning, the rigid area is formed in the cavity of the lower die. And then it will move upwards to supply the metal for the gear filling. For the closed-die cold forging of the bevel gears, the force acting on the upper die and the lower die is significantly different.

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.

Influence of Alignment Errors on Contact Pressure during Straight Bevel Gear Meshing Process

Straight bevel gears are widely applied in automotive, aerospace, chemical and many other fields as one of the most common type of gears. Currently, the researches on straight bevel gears have focused on the fields of fatigue, wear, noise and vibration, while little attention is paid to the effect of multiple alignment errors on the gear tooth wear. To study the influence of alignment errors on the gear tooth wear, a simulated model of a straight bevel gear pair is established. Then, the contact pressure on the tooth surface is analyzed under the various alignment errors according to the Archard wear relationship. The main combinations of alignment errors played vital roles on the tooth wear are investigated. The result shows that under the single alignment error, the contact pressure moves to the tooth heel and increases greatly at here when ？P=0.1 or ？G=0.1; when ？E=–0.03, the contact pressure greatly increases at the tooth heel, but it obviously increases at the tooth toe when ？E=0.03; the alignment error ？γ=1 has little effect on the contact pressure on the tooth surface. Moreover, the combination of ？P, ？G, ？E〈0 and ？γ is the most dangerous type among the multiple alignment errors. This research provides valuable guidelines for predicting the tooth wear under various alignment errors.

Research on global form deviations for spiral bevel gear based on latticed measurement

In order to improve the machining ac cu racy of spiral bevel gear,difference surface was adopted to characterize its gl obal form deviations quantifiably and correct its deviations.The theoretical to oth surface model of spiral bevel gear was built,and the actual tooth surface o f spiral bevel gear had been got by using latticed measurement.The equation of difference surface which can characterize the actual tooth surface deviation s was built by means of mathematical method in combination with measurement prin ciple.The quantitative mathematical relationship between the actual tooth surfa ce deviations of spiral bevel gear and the corrected values of the machine-sett ing parameters had been referred,and the theoretical correction formula of the global form deviations had been got by the least square method.Finally,the pinion of spiral bevel gear in the automobile rear axle has been set for an exam ple to account for the effectiveness of the deviation correction by use of the d ifference surface method.

Design Analysis of Bevel Gear for Gearmotor Selection in Revolving Platform

The design of bevel gear for use in the development of revolving rostrum is presented. The pinion gear is designed to rotate at 1400 rpm for the output gear of 23 rpm. A suitable gearmotor was selected for the design based on the bevel gear design analysis. The motion is transmitted to the rostrum via a shaft keyed to it with a gib-head key and assembled on the rostrum with a spline connector. The analysis of the bevel mesh shows that maximum deformation of about 26.552 mm occurs in the pinion due to the loading the pinion tooth. The deformation of the tooth is observed to affect considerable the performance of the system. The transmission efficiency of the mechanism was obtained as 86% though effective for the operation of the system but could be improved by a more careful material selection for the bevel gear mesh.

METHOD FOR PRECISE CALCULATION OF ROOT STRESS OF SPIRAL BEVEL GEARS

A method for precise calculation of tooth root stress of spiral bevel gears is presentedand developed. On the basis of the machine settings analysis, tooth geometry anaysis and loadedtooth contact analysis, by using the tooth surface distribution load from tooth load analysis, thecalculation model is established and the root stress is calculated by means of finite element meth-od. The method mentioned is verified by a tested gears example.

ANALYSIS AND PREDICTION OF INTERFERENCE IN ASSEMBLING CURVED BEVEL GEARS

The phenomena of interference in the course of assembling curved bevel gears are ana. lysed and the corresponding prediction program of interference is established taking KlingInberg bevel gear as an exmple. The factors influencing interferenee are discussed and the coneept ofcritical cutter radius is proposed. Finally, a simplified approximate function between the critical cutter ra- dius and the other factors is derived,and the designing method of avoiding interferenee is provided. The analysis and caiculation are proved to consistent with a case of actual product.

ANALYSIS OF TOOTH FORM ERROR OF EQUAL BASE CIRCLE BEVEL GEAR

The basic principle of equal base circle bevel gear (EBCBG) is illustrated simply Thetooth surface equation of EBCBG manufactured by end milling cutter with involute profile is de-rived. The tooth form error is analyzed on the basis of spherical involute

Finite element analysis of contact fatigue and bending fatigue of a theoretical assembling straight bevel gear pair

The aim of this work is to propose a 3D FE model of a theoretical assembling straight bevel gear pair to analyze the contact fatigue on the tooth surface and the bending fatigue in the tooth root. Based on the cumulative fatigue criterion and the stress-life equation, the key meshing states of the gear pair were investigated for the contact fatigue and the bending fatigue. Then, the reliability of the proposed model was proved by comparing the calculation result with the simulation result. Further study was performed to analyze the variation of the contact fatigue stress and the bending fatigue stress under different loads. Furthermore, the roles of the driving pinion and the driven gear pair were evaluated in the fatigue life of the straight bevel gear pair and the main fatigue failure mode was determined for the significant gear. The results show that the fatigue failure of the driving pinion is the main fatigue failure for the straight bevel gear pair and the bending fatigue failure is the main fatigue failure for the driving pinion.

STUDY ON DOUBLE CIRCULAR ARC PROFILE SPIRAL BEVEL GEAR TRANSMISSION

A stepped double arc spiral bevel gear tooth profile is examined. The development ofconjugate tooth surfaee of double are profile spiral bevel gears is described. The design and man-ufacture of the cutter is also discussed. Experimental results show that these gears have high loadcarrying capacity and that they are suitable for heavily loaded transmission. It is asserted thatsuch gears have higher power-to-weight ratios, are longer-lived, and provide more reliable per-formance than ordinary spiral bevel gears.

Effect of static transmission error on dynamic responses of spiral bevel gears

The effect of static transmission error on nonlinear dynamic response of the spiral bevel gear system combining with time-varying stiffness and backlash was investigated.Firstly,two different control equations of the spiral bevel gear model were adopted,where the static transmission error was expressed in two patterns as predesigned parabolic function and sine function of transmission errors.The dynamic response,bifurcation map,time domain response,phase curve and Poincare map were obtained by applying the explicit Runge-Kutta integration routine with variable-step.A comparative study was carried out and some profound phenomena were detected.The results show that there are many different kinds of tooth rattling phenomena at low speed.With the increase of speed,the system enters into stable motion without any rattling in the region(0.72,1.64),which indicates that the system with predesigned parabolic function of transmission error has preferable capability at high speed.

Analysis and modeling of error of spiral bevel gear grinder based on multi-body system theory

Six-axis numerical control spiral bevel gear grinder was taken as the object, multi-body system theory and Denavit-Hartenberg homogeneous transformed matrix (HTM) were utilized to establish the grinder synthesis error model, and the validity of model was confirmed by the experiment. Additionally, in grinding wheel tool point coordinate system, the errors of six degrees of freedom were simulated when the grinding wheel revolving around C-axis, moving along X-axis and Y-axis. The influence of these six errors on teeth space, helix angle, pitch, teeth profile was discussed. The simulation results show that the angle error is in the range from -0.148 4 rad to -0.241 9 rad when grinding wheel moving along X, Y-axis; the translation error is in the range from 0.866 0 μm to 3.605 3 μm when grinding wheel moving along X-axis. These angle and translation errors have a great influence on the helix angle, pitch, teeth thickness and tooth socket.

Numerical Simulation of Deforming Manufacture Process for Automobile Bevel Gear Blank

Aiming at solving the difficulties of deforming manufacture of the automobile rear axle bevel gear blank,the paper presented to adopt the numerical simulation method to study the rolling process of the bevel gear blank instead of the traditional expensive trail-and-error method. A three-dimensional simulation model of the Φ500 bevel gear blank radial ring rolling machine was firstly created based on the general dynamic explicit finite element code ANSYS/LS-DYNA,and then realized the virtual simulation of the entire rolling process of the bevel gear blank within a producing cycle. The simulation results displayed the real-time blank enlarging and fleck generating as well as the stress,strain and displacement contours,which are in good agreements with the real ring rolling process. It is concluded that this numerical simulation method is feasible and can be used to guide the practical rolling process of the bevel gear blank as well as other profile-shaped annular blanks.

Influence of cutter diameter on meshing performance in spiral bevel gears

Playing a critical role in transmitting movement and power, the meshing performance of spiral bevel gears has a significant effect on products' operational performance. To evaluate the meshing performance, the accurate three-dimensional(3D) spiral bevel gear models are established through the Pro/E and MATLAB softwares, and the finite element analysis(FEA) methods are applied to the theoretical investigation of the influence of cutter diameter on meshing performance in spiral bevel gears. The results obtained show that the cutter diameter has a significant influence on spiral bevel gears' meshing performance, such as the contact area, contact pressure, bending stress, torsional stiffness and transmission error.

Effect of key factors on cold orbital forging of a spur bevel gear

Cold orbital forging is an advanced spur bevel gear forming technology. Generally, the spur bevel gear in the cold orbital forging process is formed by two steps: the preforming step and the final step. Due to the great importance of the final step to gear forming and its complication with interactive factors, this work aims at examining the influence of key factors on the final step in cold orbital forging of a spur bevel gear. Using the finite element(FE) method and control variate method, the influence rules of four key factors, rotation velocity of the upper tool, n, feeding velocity of the lower tool, v, tilted angle of the upper tool, γ, friction factor between the tools and the billet, m, on the geometry and the deformation inhomogeneity of the cold orbital forged gear are thoroughly clarified. The research results show that the flash becomes more homogeneous with increasing v, increasing m, decreasing n or decreasing γ. And the deformation of the gear becomes more homogeneous with increasing v, decreasing n or decreasing γ. Finally, a corresponding experiment is conducted, which verifies the accuracy of FE simulation conclusions.

NC Machining of Spiral Bevel Gear and Hypoid Gear Based on Unity Transformation Model

A unity transformation model (UTM) was presented for flexible NC machining of spiral bevel gears and hypoid gears. The model can support various machining methods for Gleason spiral bevel gears and hypoid gears, including generation machining and formation machining for wheel or pinion on a universal five-axis machining center, and then directly produce NC codes for the selected machining method. Wheel machining and pinion machining under UTM were simulated in Vericut 6.0 and tested on a five-axis machining center TDNC-W2000 with NC unit TDNC-H8. The results from simulation and real-cut verify the feasibility of gear machining under UTM as well as the correctness of NC codes.

Research on theory of gearing for epicycloidal bevel gear

The engaged feature of a pair of gears was determined by the geometrical characteristics of their tooth surfaces. Through an analysis of gearing theory on epi-cycloidal bevel gears, the method to examine if there exists undercut during manufacturing of epicycloidal bevel gears, the approximate formulae to calculate the gap between the convex and concave tooth surfaces in meshing so as to guarantee against the occurrence of point-contact for tooth surfaces even in maximum angle of inclination are derived in this paper. Those formula derived are simple, compact and have practical value to the design and production of epicycloidal bevel gears.

Approximation Solution for TEHL of Bevel Gears in PSD

To study the lubrication of the contact zone between half-shaft gears and planet gears in the power-split device (PSD), TEHL line contact of bevel gears in PSD is approximately computed based on a theory in which a bevel gear is equalized to an equivalent spur gear. In the calculation, the housing is taken as the reference system and the influence of the housing’s rotating on the lubrication is ignored. Film pressure, film thickness and temperature rise are analyzed under maximum load condition. This research provides some approximate reference data for the design of lubrication and cooling system of PSD.

Design and analysis of spiral bevel gears with seventh-order function of transmission error

This paper proposes a new approach to mial function of transmission error （TE） for spiral design and implement a seventh-order polyno- bevel gears with an aim to reduce the running vibration and noise of gear drive and improve the loaded distribution of the tooth. Based on the constraint conditions of predesigned seventh-order polynomial function curve and the theory of linear algebra, the polynomial coefficients of the seventh-order polynomial function of transmission error can be obtained. By applying a method named reverse tooth contact analysis, the modified roll coefficients as well as parts of machine-tool settings for the face-milling of spiral bevel gears can be individually determined. Therefore, a predesigned seventh-order polynomial function of transmission error for spiral bevel gears can be obtained by the modified roll with high-order coef- ficients, and comparisons of the seventh-order polynomial and parabolic functions of transmission error are also performed. The achievement of spiral bevel gears with the seventh-order function of transmission error can be accomplished on a universal Cartesian-type hypoid gear generator or a numerically controlled cradle-style hypoid gear generator due to its simple generating motion of axes of the cradle and the work piece. The results of a numerical example show that the bending stresses of the tooth of seventh-order are less than those of a parabolic one, while the contact stresses remain almost eouivalent.