Pinion Tooth Surface Research Articles

Research on noise reduction of drive axle hypoid gear based on tooth surface mismatch modification

In order to reduce the transmission noise of drive axle hypoid gear, a method of tooth surface mismatch modification was proposed. Firstly, on the basis of establishing the grinding mathematical model of hypoid gear with cutter tilt, the theoretical tooth surface equation was derived, and the numerical tooth surface was calculated by dividing the grid points on tooth surface. Secondly, the pinion tooth surface which was full conjugated with gear tooth surface was constructed, and the tooth surface mismatch topography was established and decomposed into the first order and second order mismatch coefficients. According to the modification requirements, the pinion target surface was constructed by modifying the tooth surface mismatch coefficients, and the pinion modified machine setting parameters were acquired by establishing the pinion processing parameters corrected mathematical model. Finally, the loaded tooth contact analysis with finite element simulation and drive axle NVH (Noise, Vibration, Harshness) simulation were carried out for a pair of hypoid gear, therefore the loaded tooth contact areas, transmission errors curves, and noise simulation curves were obtained, and the simulation results show that after modification the tooth contact stress, loaded transmission errors amplitude, and NVH simulation curves value are all reduced. The road test results indicate that the drive axle hypoid gear howling phenomenon under the high speed operation can be eliminated, so the effectiveness of tooth surface modification method and NVH simulation method were verified.

Investigating tooth surface reconstruction principle of a gear rack and pinion system with variable transmission ratio pinion

Rack-and-pinion gear sets with variable transmission ratios have gradually become a standard core component in steering systems, as the harmony between portability and sensitivity in vehicle steering can be achieved with such applications. When the conventional meshing theory is adopted to calculate point clouds of variable-ratio tooth surfaces, drawbacks will occur with respect to unevenness in point cloud density, inaccessible tooth surface boundaries, and point cloud fusion at the interface between the working tooth surface and fillet. Thus, the generated point cloud of variable ratio tooth surfaces is inapplicable for computer-aided engineering (CAE) and plastic forming. In this study, the point cloud reconstruction of pinion tooth surfaces with variable transmission ratio was investigated. Meanwhile, based on the analysis of transient length in contact lines that occur during gear meshing, various criteria were proposed to determine the validity of the variable-ratio rack-and-pinion design in terms of whether continuous and reverse driving can be achieved. By adopting the proposed methods, the designed variable-ratio pinion tooth surfaces demonstrate point clouds with equidistant distributions and clear boundaries. CAE analysis results also indicate a good quality in gear meshing. The real-time gear meshing status of variable-ratio rack-and-pinion sets is characterized by the transient length of contact lines. The measured variation curves for the transmission ratios of a prototype demonstrate significant consistency with the theoretical curves, indicated by attaining transmission ratio errors within a reasonable range. The validity of the design methods proposed in this study has been verified by the aforementioned results.

A method to remanufacture large-size spiral bevel gear with ease-off topology modification by face-milled generator

Spiral bevel gears are manufactured and used in pairs. When one part usually pinion fatigued, the pair will be replaced. It inevitably leads to a waste of resources and time. To solve this phenomenon, a method to remanufacture pinion with ease-off topology modification is proposed. First, the wheel and pinion were measured to fitting tooth surface, and then a conjugate surface of wheel fitting tooth surface was derived. Secondly, an ease-off topology surface was superimposed to the conjugate surface to improve mesh performance, and then a design tooth surface was obtained. Thirdly, a mathematical model to process pinion was established and original machine-tool settings parameters of pinion were calculated. The deviations between design and original tooth surface of pinion were count, and an error correction model of tooth surface was established to adjust machine-tool settings parameters. Finally, an experimental verification was conducted. The pinion was remanufactured by a face-milled generator and the mesh performance was consistent with design. The result demonstrates the method proposed is effectiveness and feasible. It provides reference for the remanufacture of large-size spiral bevel gears and has good value for engineering application.

Optimization Method of Design Parameters of Hypoid Gears With Low Sliding Ratio

Abstract To reduce the wear, an optimization method of hypoid gears with the objective of minimizing the pinion sliding ratio is proposed. First, the sliding ratio model of the hypoid gear is established on the basis of the spatial gear meshing theory. Furthermore, the influence of design parameters on the sliding ratio and the relative sliding velocity is discussed, and the analysis results show that the parameters, especially the spiral angle and the pressure angle, have the most significant influence on the sliding ratio of the pinion. Additionally, the optimization model of hypoid gears is established, and the optimization objective is to minimize the sum of the absolute sliding ratios of 34 meshing points on the pinion tooth surfaces. Through comparison before and after optimization, it is found that the maximum drops of the sliding ratios for the pinion drive and coast side are 68.6% and 29.58%, respectively. Finally, the results of the running temperature tests demonstrate that the temperature of the optimized gear pair is significantly reduced and that the proposed method is effective.

Grinding of hypoid gears by applying generating and Waguri motions

In this paper, a new method for grinding hypoid gears by applying generating and Waguri (1964) motions is presented. Two motions that contribute to the roughness of the tooth surface are considered: (i) the rotation of the grinding wheel and (ii) the generating motion of the grinding wheel to the pinion and the Waguri motion for finishing the gear tooth surface. It is supposed that the grains are spheres with a random diameter and random location on the surface of the grinding wheel. The cutting edges of the grinding wheel are generated by the dressing tool. The grinding wheel-pinion/-gear interaction is described. The 3D topography of the grinding wheel is mapped to the tooth surfaces of the pinion and the gear by using the motion of pinion tooth surface generation and by using the Waguri motion for gear tooth finishing. The influence of the grain size and the relation of motions in the grinding process on the obtained roughness of the ground tooth surface is investigated.

A Novel Asymmetric Face Gear Cut by Duplex Face-Milling With Multiple Auxiliary Flank Modification Motions

Abstract Face gear sets, comprising a face gear and a cylindrical pinion, are used in the crossed axes transmission with the advantages of easy assembly and a large gear ratio. Based on the geometry of a pinion tooth flank, the tooth surface of the face gear is derived and manufactured by gear hobbing or shaping processes. However, the hobbing and shaping processes to make a face gear require special machine attachments to achieve the spatial relationship between the gear cutter and the workpiece of the face gear. These special machine attachments are not always available in a typical gear-machining factory, so this study develops a manufacturing process that uses a standard spiral bevel gear generator and standard face-milling cutting tools to produce a face gear. The productivity and the gear quality of a face gear that is made using the proposed cutting method are similar to that for a spiral bevel gear that is produced by indexed duplex cutting. The machine settings for the spiral bevel gear generator are derived using the tooth surface of a face gear, which is conjugated to the tooth surface of specific pinion. This study uses a duplex face-milling method with multiple auxiliary flank modification motions to minimize the flank normal deviation between the conjugate and the generated face gear. A numerical example and a cutting experiment are performed to verify the feasibility of the proposed methodology.

Investigation of the effect of contact pattern design on the mechanical and thermal behaviors of plastic‐steel helical gear drives

This article describes an investigation that has been conducted to assess the effects of the contact pattern design on the mechanical and thermal behaviors of plastic-steel helical gear drives. The maximum contact pressure, frictional power loss, transmission error function and operating temperature are determined for different designs of the pinion tooth surfaces. Several numerical examples based on loaded tooth contact analyses and steady-state heat transfer analyses are carried out considering different types of micro-geometry modifications of the involute tooth surfaces. The obtained results show that an appropriate design of the pinion tooth surfaces can help reducing the maximum contact pressure and the maximum operating temperature, increasing the durability of the transmission. The frictional power loss and the peak-to-peak transmission error can be diminished, improving the performance of the transmission and increasing its efficiency. Also, it has been shown that the design of the pinion tooth surfaces can provide some capability to the transmission to absorb angular misalignments.

Nonlinear Optimization Method for Transmission Error of Hypoid Gear Machined by the Duplex Helical Method

In this study, synchronous cutting of concave and convex surfaces for hypoid gear was achieved using a duplex helical method. Precise, nonlinear optimization of the transmission error driven by machine tool parameters was performed to reduce the vibration noise of the gear pair. First, the transmission error curve and contact path of the tooth surface of the initial pinion were solved using tooth contact analysis. Second, according to the preset parabolic transmission error curve, the initial gear was used to generate the target pinion, which coincided with the contact path of the initial pinion. Finally, a deviation correction model of the discrete points, corresponding to the contact paths on the concave and convex surfaces of the target and initial pinions, was established. This model was solved using the Levenberg–Marquard algorithm with the trust region strategy, to obtain optimized machine tool parameters. Synchronous optimization of the transmission errors of concave and convex surfaces of the pinion was achieved by correcting the deviations of the contact points. The effectiveness of the proposed method was verified by a numerical example and by performing a contact area rolling test.

Geometric Design, Meshing Simulation, and Stress Analysis of Pure Rolling Rack and Pinion Mechanisms

Abstract The geometric design, meshing simulation, and stress analysis of pure rolling rack and pinion mechanisms are presented. Both the pinion and the rack are based on the active design of the meshing line to provide pure rolling for the whole cycle of meshing. The parametric equations of the contact curves on the rack and pinion tooth surfaces are determined by coordinate transformation of the meshing line equations. Three types of meshing are derived according to the motion of the generatrices along the calculated contact curves: convex-to-concave meshing, convex-to-plane meshing, and convex-to-convex meshing. Then, the basic design parameters are analyzed and formulas for calculation of the geometric size are given. Four different cases of design are considered to compare the meshing performance and mechanical behavior of the proposed gear mechanisms. The results include contact patterns, the unloaded function of transmission errors, and the evaluation of stresses along two cycles of meshing. The analysis of the results shows that the proposed method of design of pure rolling meshing reduces the relative sliding between tooth surfaces, whereas it decreases the contact strength of the tooth surfaces. However, if the design parameters are properly evaluated as a result of simulation and applied as proposed here, the mechanical behavior of the proposed rack and pinion mechanisms can be more favorable than that of the standard geometry of involute rack and pinion sets.

An Active Ease-Off Topography Modification Approach for Hypoid Pinions Based on a Modified Error Sensitivity Analysis Method

A new active ease-off topography modification approach is proposed to improve the meshing performance of hypoid gears based on a fourth-order predesigned transmission error (PTE) model and a modified error sensitivity analysis method. Ease-off topography modifications that describe local deviations of pinion tooth surfaces can be conducted by converting the fourth-order PTE into equivalent deviations of pinion tooth surfaces. The modified error sensitivity analysis method is developed to investigate the effects of misalignments on the moving velocity of a contact point of a hypoid gear pair. The moving velocity of the contact point can describe transmission error (TE) curve shapes of ease-off tooth surfaces. The ease-off topography modification approach can achieve TE precontrol and modification curvature adjustment of the pinion for stable meshing performance of the hypoid gear pair. Moreover, pinion ease-off tooth surfaces are finished by a five-axis computer numerical control swarf-cutting machine tool. Swarf-cutting tests and TE measurement tests are conducted on hypoid gear pair specimens to demonstrate the feasibility and effectiveness of the proposed methodology.

Nonlinear dynamic model of a gear-rotor-bearing system considering the flash temperature

The instantaneous flash temperature is an important factor for gears in service. To investigate the effect of the flash temperature of a tooth surface on the dynamics of the spur gear system, a modified nonlinear dynamic model of a gear-rotor-bearing system is established. The factors such as the contact temperature of the tooth surface, time-varying stiffness, tooth surface friction, backlash, the comprehensive transmission error and so on are considered. The flash temperature of a tooth surface of pinion and gear is formulated according to Blok's flash temperature theory. The mathematical expression of the contact temperature of the tooth surface varied with time is derived and the tooth profile deformation caused by the change of the flash temperature of the tooth surface is calculated. The expression of the mesh stiffness varied with the flash temperature of the tooth surface is derived based on Hertz contact theory. The temperature stiffness is proposed and added to the nonlinear dynamic model of the system. The influence of load on the flash temperature of the tooth surface is analyzed in the parameters plane. The variation of the flash temperature of the tooth surface is studied. The numerical results indicate that the calculated method of the flash temperature of the gear tooth surface is effective and it can reflect the rules for the change of gear meshing temperature and sliding of the gear tooth surface. The effects of frequency, backlash, bearing clearance, comprehensive transmission error and time-varying stiffness on the nonlinear dynamics of the system are analyzed according to the bifurcation diagrams, Top Lyapunov Exponent (TLE) spectrums, phase portraits and Poincaré maps. Some nonlinear phenomena such as periodic bifurcation, grazing bifurcation, quasi-periodic bifurcation, chaos and its routes to chaos are investigated and the critical parameters are identified. The results provide an understanding of the system and serve as a useful reference in designing such systems.

A method for the global optimization of the tooth contact pattern and transmission error of spiral bevel and hypoid gears

In this paper, we present a method for the global optimization of the tooth contact pattern and transmission error of spiral bevel and hypoid gears, which includes three optimization objectives, three control parameters, and a complex-constrain genetic algorithm solving method. A new set of fundamental equations for pitch cone parameters of hypoid gear drives are established, as well as the relationships between pitch cone and curvature parameters. Based on this theory, three control parameters are selected to determine the pinion tooth surface. A hypoid gear drive is chosen for case studies. The results verify that the optimization methodology can achieve the expected optimization objectives and has good convergence. Correlations between optimization objectives and control parameters are discussed. Furthermore, a finite element model of a simplified hypoid gear drive system is established and its quasi-static meshing characteristics analyzed. The results again confirm the correctness of the optimization method. The effects of torque load on the contact pattern and transmission error are discussed. The results provide a theoretical reference for geometric calculations, quasi-static analysis, and optimal design of spiral bevel and hypoid gears.

Numerical approach for determination of rough-cutting machine-tool settings for fixed-setting face-milled spiral bevel gears

Spiral bevel gear drives manufactured by the so-called five-cut method are designed to achieve the best conditions of meshing and contact since convex and concave pinion tooth surfaces are generated independently, allowing the achievement of optimized contact patterns and favorable functions of transmission errors for both flanks of gear tooth surfaces, and reducing with it noise and vibration and increasing the endurance of the gear drive. As part of the process of manufacturing, roughing of both flanks of the pinion tooth surfaces is needed. In this paper, a novel numerical approach for determination of machine-tool settings for roughing of the pinion by using a spread-blade face-milling cutter is proposed. The main purpose of the proposed procedure is the reduction of the manufacturing cycle time and maximizing the material cut during the rough-cutting operation, without damaging the to-be-finished surfaces. The procedure is based on the resolution of a constrained optimization problem. A numerical example shows the applicability of the developed numerical approach. The obtained numerical results disclose that acceptable rough-cut geometries are possible to be managed during the first iterations as trade-off solutions.

Fault Index Statistical Study for Gear Fault Detection Using Stator Current Space Vector Analysis

This paper presents a statistical analysis on a fault index computed based on the stator current space vector instantaneous frequency on a real-time platform for online noninvasive gear tooth surface damage fault detection in a single-stage gearbox. This analysis is crucial for defining a threshold beyond which the condition of gear teeth can be considered defective with a significance level less than the critical value. Besides, the efficiency of the fault detection algorithm realized on a real-time platform will be evaluated for both pinion and wheel tooth surface damage faults by using a setup based on a 250-W three-phase squirrel-cage induction machine shaft-connected to a single-stage spur or helical gearboxes.

Determination of Geometrical Parameters for Semi-Rolling Bevel Precessional Gears With Straight Teeth

The aim of this paper is to analyse the semi-rolling bevel precessional gear with straight teeth. The given method of cutting pinion and gear teeth significantly simplifies its manufacture technology. Authors have given a system of equations to study the analysis of generating pinion tooth surfaces and geometry of meshing for semi-rolling bevel precessional gear with straight teeth. A computer program was developed to enable implement formulas provided in the paper. By using this program authors obtained contact lines on the pinion tooth surface and number of tooth pairs in gears mesh.

LONGITUDINAL CROWNING OF THE GEAR TOOTH SURFACE OF STRAIGHT BEVEL GEARS WITH A SMALL SHAFT ANGLE WITHNON-GENERATED GEAR AND GENERATED PINION

The aim of this thesis is to develop computer program shows generating process of the longitudinal-crowned gear for straight bevel gears with a small shaft angle with non-generated gear and generated pinion. The purpose of computer program is the simulation of meshing and contact of the gear tooth surface with longitudinal crowning and straight pinion tooth surface with localized bearing contact.

Computerised Design and Simulation of Meshing and Contact of Formate Hypoid Gears Generated with a Duplex Helical Method

The duplex helical method has higher machining efficiency for face-milling spiral bevel and hypoid gears. An accurate and practical approach for calculating the basic machine-tool settings of spiral bevel and hypoid gears manufactured with the duplex helical method is proposed in the present work. The gear tooth surface vector functions and curvature parameters based on basic machine, and head-cutter settings are calculated. Two types of curvature parameters for pinion tooth surfaces are obtained by utilizing the conjugation of gear and pinion tooth surfaces, and the conjugation of pinion tooth surfaces and pinion head-cutter surfaces at the reference point. Next, the basic machine settings for generating pinions in accordance with the two types of curvature parameters for pinion tooth surfaces are determined. Finally, a numerical examples using the duplex helical method are performed and validated by comparing with experimental results. New hypoid gear software has been developed using the new approach.

Design and analysis of modified cylindrical gears with a higher-order transmission error

A design of tooth surface modifications for cylindrical gears that are provided with a controllable higher order polynomial function of transmission error (H-TE) are proposed to reduce vibration and noise, and the procedures for creating mathematical models of the tooth surfaces are described. Firstly, the polynomial coefficients of H-TE curve as well as processing parameters for rack generating pinion tooth surface can be individually determined based on TCA and LTCA by optimizing the aim of minimum amplitude of loaded transmission error (ALTE) of drive gears by using the particle swarm optimization (PSO). Secondly, the deviations of pinion tooth surface with H-TE from the theoretical one are derived according to the rack movement parameters. Thirdly, a numerical simulation of example based on spur gears and helical gears with different order transmission error are performed, which prove that the actual contact ratio and the effective contact ratios are the valid indices and the gear drive with H-TE has the lowest ALTE. The proposed gear drives are proved numerically to be able to reproduce the H-TE function and the effective contact ratios are the valid indices of LTE.

An approach of calculation on sliding friction power losses in involute helical gears with modification

Sliding friction between the teeth is recognized as one of the main reasons of power losses in transmission as well as a potential reason of vibration and noise. A new approach is proposed to accurately calculate the sliding friction power losses in involute helical gears considered modification and geometric deviations resulting from the manufacturing processes, assembly errors, and deflections of support structures based on the simulation of gear mesh under light and significant load. Firstly, the paths of contact points on the pinion tooth surface are obtained from tooth contact analysis. Tooth surface load distributions and loaded transmission errors in one mesh period are obtained from loaded tooth contact analysis. Secondly, tooth surface load distributions are converted into the normal forces of tooth surface points of contact, loaded transmission errors are brought to the calculation formulas of sliding velocity, and the sliding friction coefficients of tooth surface points of contact are calculated by a non-Newtonian thermal elastohydrodynamic lubrication model. Substituting the sliding velocities, the normal forces, and the sliding friction coefficients into the power calculation formulas gives the sliding friction power losses of tooth surface points of contact. By the soft MATLAB, the values of the sliding friction power losses are integrated and the sliding friction power loss in helical gears from engagement to disengagement is obtained. Finally, an example of this approach is shown in the end. The results indicate that it is very necessary to consider the influence of loaded transmission errors for calculation of sliding friction power losses.

Modified geometry of spur gear drives for compensation of shaft deflections

One of the main problems when standard spur gears are in mesh is the appearance of edge contact on the gear tooth surfaces caused by misalignments. Those misalignments are caused partially by deflections of gear supporting shafts. As a result of an edge contact, a non-favorable condition of the bearing contact occurs, yielding high level of contact stresses. An intensive research and many practical solutions have been directed to modify the gear tooth surfaces in order to avoid edge contact. An innovative procedure is proposed here for: (1) determination of errors of alignment caused by shaft deflections, (2) compensation of predicted shaft deflections during generation of spur gears, and (3), obtaining a favorable function of transmission errors for the design load. A finite element model of a spur gear drive that comprises pinion and gear supporting shafts is used for the determination of errors of alignment along a cycle of meshing. Compensation of misalignments caused by shaft deflections in gear generation is then accomplished by modification of pinion tooth surfaces whereas the gear tooth surfaces are kept unmodified. Additional modifications of pinion tooth surfaces may be required for obtaining a favorable function of transmission errors. The effect of several misalignment compensations in the reduction of contact stresses has been investigated. Postprocessing of load intensity functions and loaded transmission errors is included. The developed approach is illustrated with numerical examples.