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.

Design of Pinion Machine Tool-settings for Spiral Bevel Gears by Controlling Contact Path and Transmission Errors

This paper proposes a new approach to design pinion machine tool-settings for spiral bevel gears by controlling contact path and transmission errors. It is based on the satisfaction of contact condition of three given control points on the tooth surface. The three meshing points are controlled to be on a predesigned straight contact path that meets the pre-designed parabolic function of transmission errors. Designed separately, the magnitude of transmission errors and the orientation of the contact path are subjected to precise control. In addition, in order to meet the manufacturing requirements, we suggest to modify the values of blank offset, one of the pinion machine tool-settings, and redesign pinion ma- chine tool-settings to ensure that the magnitude and the geometry of transmission errors should not be influenced apart from minor effects on the predesigned straight contact path. The proposed approach together with its ideas has been proven by a numerical example and the manufacturing practice of a pair of spiral bevel gears.

GEOMETRIC MODELING OF GENERATING-MANUFACTURED SPIRAL BEVEL GEARS BASED ON CUTTING SIMULATION

A geometric modeling method for generating-manufactured spiral bevel gears（SBGs） is proposed. It consists of two steps： （1） creating a reference model by simulating the process of cutting spiral bevel gear,（2） reconstructing the final solid model by collecting data points from the reference model and fitting these points into NURBS surfaces. In this method,cutting simulation avoids abstruse mathematical theories and complex methods,thus making it convenient to obtain data points on the complex tooth surface before the gear is manufactured and efficient to increase the accuracy of the solid model. Also,the representations of tooth surfaces of the final model is unified as a NURBS surface function. The NURBS surface is continuous and smooth,thus it is available for wide applications in CAD/CAE. The experiment proves that the method can be used to establish an accurate pair of SBG models,thus providing a feasible and effective way for CAD/CAE modeling.

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 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 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.

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.

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.

Time-Varying Mesh Stiffness Calculation and Dynamic Modeling of Spiral Bevel Gear with Spalling Defects

Time-varying mesh stiffness(TVMS)is a vital internal excitation source for the spiral bevel gear(SBG)transmission system.Spalling defect often causes decrease in gear mesh stiffness and changes the dynamic characteristics of the gear system,which further increases noise and vibration.This paper aims to calculate the TVMS and establish dynamic model of SBG with spalling defect.In this study,a novel analytical model based on slice method is proposed to calculate the TVMS of SBG considering spalling defect.Subsequently,the influence of spalling defect on the TVMS is studied through a numerical simulation,and the proposed analytical model is verified by a finite element model.Besides,an 8-degrees-of-freedom dynamic model is established for SBG transmission system.Incorporating the spalling defect into TVMS,the dynamic responses of spalled SBG are analyzed.The numerical results indicate that spalling defect would cause periodic impact in time domain.Finally,an experiment is designed to verify the proposed dynamic model.The experimental results show that the spalling defect makes the response characterized by periodic impact with the rotating frequency of spalled pinion.

Design of face-hobbed spiral bevel gears with reduced maximum tooth contact pressure and transmission errors

The aim of this study is to define optimal tooth modifications, introduced by appropriately chosen head-cutter geometry and machine tool setting, to simultaneously minimize tooth contact pressure and angular displacement error of the driven gear （transmission error） of face-hobbed spiral bevel gears. As a result of these modifications, the gear pair becomes mismatched, and a point contact replaces the theoretical line contact. In the applied loaded tooth contact analysis it is assumed that the point contact under load is spreading over a surface along the whole or part of the ‘‘potential’’ contact line. A computer program was developed to implement the formulation provided above. By using this program the influence of tooth modifications introduced by the variation in machine tool settings and in head cutter data on load and pressure distributions, transmission errors, and fillet stresses is investigated and discussed. The correlation between the ease-off obtained by pinion tooth modifications and the corresponding tooth contact pressure distribution is investigated and the obtained results are presented.

Dynamics of lubricated spiral bevel gears under different contact paths

To assess the meshing quality of spiral bevel gears,the static meshing characteristics are usually checked under different contact paths to simulate the deviation in the footprint from the design point to the heel or toe of the gear flank caused by the assembly error of two gear axes.However,the effect of the contact path on gear dynamics under lubricated conditions has not been reported.In addition,most studies regarding spiral bevel gears disregard the lubricated condition because of the complicated solutions of mixed elastohydrodynamic lubrication(EHL).Hence,an analytical friction model with a highly efficient solution,whose friction coefficient and film thickness predictions agree well with the results from a well-validated mixed EHL model for spiral bevel gears,is established in the present study to facilitate the study of the dynamics of lubricated spiral bevel gears.The obtained results reveal the significant effect of the contact path on the dynamic response and meshing efficiency of gear systems.Finally,a comparison of the numerical transmission efficiency under different contact paths with experimental measurements indicates good agreement.

Contact stiffness and damping of spiral bevel gears under transient mixed lubrication conditions

Existing studies primarily focus on stiffness and damping under full-film lubrication or dry contact conditions.However,most lubricated transmission components operate in the mixed lubrication region,indicating that both the asperity contact and film lubrication exist on the rubbing surfaces.Herein,a novel method is proposed to evaluate the time-varying contact stiffness and damping of spiral bevel gears under transient mixed lubrication conditions.This method is sufficiently robust for addressing any mixed lubrication state regardless of the severity of the asperity contact.Based on this method,the transient mixed contact stiffness and damping of spiral bevel gears are investigated systematically.The results show a significant difference between the transient mixed contact stiffness and damping and the results from Hertz(dry)contact.In addition,the roughness significantly changes the contact stiffness and damping,indicating the importance of film lubrication and asperity contact.The transient mixed contact stiffness and damping change significantly along the meshing path from an engaging-in to an engaging-out point,and both of them are affected by the applied torque and rotational speed.In addition,the middle contact path is recommended because of its comprehensive high stiffness and damping,which maintained the stability of spiral bevel gear transmission.

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.

Microstructures and Mechanical Properties of Helical Bevel Gears Made by Mn-Cu Alloyed Austempered Ductile Iron

Austempered ductile iron （ADI） has several advantages of replacing cast steel and forged steel in many engineering fields. A new Mn-Cu alloyed ADI with excellent mechanical properties has been developed in order to cut the cost and enlarge the application of ADI. The helical bevel gears were made of the new-developed Mn-Cu alloyed ADI. The microstructure and mechanical properties of the standard sample were investigated by optical microscope （OM）, scanning electron microscope （SEM） and performance measurement. The results showed that after a series of treatments, the mechanical properties （Rm 1007. 4 to 1200 MPa, A 5.2% to 8. 8%, HRC 32 to HRC 35, O^K 70 to 120 J/cmz ） of the Mn-Cu alloyed ADI standard sample could reach European standard EN1564-97/ EN-CJS-1000-5. The surface hardness after helical bevel gears meshing was significantly increased due to the formation of martensite. The bench test and traffic running testing results suggested that the new Mn-Cu alloyed ADI with ultimate life and median life respectively exceeding 30×104 and 50 × 10^4 times could replace 20CrMnTi forged steel for manufacturing the EQ140 helical bevel gears.

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.

Virtual System Solution of CNC Machine for Spiral Bevel and Hypoid Gears

A virtual computerized numerical control C CNC） processing system is built for spiral bevel and hypoid gears. The pre-designed process of the solution to locate the way of realization is investigated. A kind of combined programming method and principle of solid modeling are chosen. Multienvironmental programming thought and the inter-connected mechanisms between different environments are applied in the proposed system. The problems of data exchange and compatibility of modules are settled. Environment of the system is founded with object oriented programming thought. AutoCAD is located as the graphic environment. Matlab is used for editing the computation module. Virtual C ＋＋6.0 is the realization environment of the main module. Windows is the platform for realizing the multi-environmental method. Through establishing the virtual system based windows message handling mechanism and the component object model, the application of multienvironmental programming is realized in the manufacture system simulation. The virtual gear product can be achieved in the accomplished software.

Microstress cycle and contact fatigue of spiral bevel gears by rolling-sliding of asperity contact

The rolling contact fatigue(RCF)model is commonly used to predict the contact fatigue life when the sliding is insignificant in contact surfaces.However,many studies reveal that the sliding,compared to the rolling state,can lead to a considerable reduction of the fatigue life and an excessive increase of the pitting area,which result from the microscopic stress cycle growth caused by the sliding of the asperity contact.This suggests that fatigue life in the rolling-sliding condition can be overestimated based only on the RCF model.The rubbing surfaces of spiral bevel gears are subject to typical rolling-sliding motion.This paper aims to study the mechanism of the micro stress cycle along the meshing path and provide a reasonable method for predicting the fatigue life in spiral bevel gears.The microscopic stress cycle equation is derived with the consideration of gear meshing parameters.The combination of the RCF model and asperity stress cycle is developed to calculate the fatigue life in spiral bevel gears.We find that the contact fatigue life decreases significantly compared with that obtained from the RCF model.There is strong evidence that the microscopic stress cycle is remarkably increased by the rolling-sliding motion of the asperity contact,which is consistent with the experimental data in previous literature.In addition,the fatigue life under different assembling misalignments are investigated and the results demonstrate the important role of misalignments on fatigue life.

TOOTH CONTACT FINITE ELEMENT ANALYSIS OF SPIRAL BEVEL AND HYPOID GEARS

A very useful new method of tooth contact finite element analysis(TCFEA) for spiralbevel and hypoid gears is presented, combines 3-d finite element contact stress analysis withLTCA (Loaded Tooth Contact Analysis). The TCFEA uses mixed finite element method to ana-lyze the 3-d contact stress. The related formulas are derived and an efficient analyzing method asseveral pairs of teeth in contact occurs is presented, which greatly reduce the computationalamount. It is of great significance that the tooth stress. geometry. contact condition and load areall considered in the same model. Finally the related experimental results are used to verify thesolution of TCFEA .

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 tooth surfaces and the corresponding machine-tool settings.