Hypoid Gear Set Research Articles

Forecasting model for hypoid gear elastohydrodynamic lubrication considering entrainment effect

In full consideration of time-varying meshing performance and oil film characteristics, entrainment effect on elastohydrodynamic lubrication (EHL) is developed for establishing accurate forecasting model of the complex hypoid gears. Firstly, dynamic loaded tooth contact analysis (DLTCA) is employed to determine the meshing interface kinematics, load distribution and entrainment speed under dynamic load condition. Then, entrainment speed is introduced into the EHL governing equation and accurate forecasting model is established. With accurate discretization of EHL governing equation, discrete convolution and fast Fourier transformation (DC-FFT) method is employed to compute the flank elastic deformation. Finally, a hypoid gear set in automotive industrial application is exercised to verify entrainment effect on EHL assessment in the proposed model.

Failure Analysis and Product Improvement for Hypoid Gearset of Rear Axle

The current market trend shows that LCV vehicle sales are in increasing phase and more demands are expected by customers in which the Vehicle manufacturers should meet their requirements and applicate the right product accordingly. This paper will briefly explain about the investigation results of Ring gear premature failure in LCV Rear axles. The rear axle is a Structural member which should meet both Fatigue and impact strength requirements; thereby axle can meet Customer requirements which are used to experiencing different duty cycles and load patterns. The scope of this paper explains about detailed Investigation which has been taken like Field Study, Failure Part’s Strip down analysis and Fracture analysis. In addition to that Failure simulation analysis was also performed through CAE verification and Vehicle level Validation for correlation study. Based on the Investigation results, Gear design modification proposals have been taken and underwent the CAE analysis to finalize opt design for development. Post development of new gear set, Vehicle level validation has been carried out and found no issues in Field operating condition. Keywords: LCV vehicles, CAE Analysis, Hypoid Gearset, Ring Gear, Failure analysis, Fracture Analysis, Strip down analysis, Failure, simulation analysis

Holistic Optimal Design of Face-Milled Hypoid Gearsets

Abstract The aim of this paper is to present a holistic framework to design optimized spiral bevel and hypoid gearsets with accurate finite element simulations in the loop. Starting from the basic transmission data, we first size gear and pinion blanks, and then we synthesize the basic machine-tool settings required to generate the two toothed members. This first step represents the macro-geometry design phase and its outcome is a conjugate spiral bevel or hypoid gearset. The second design phase is represented by the definition of the optimal pinion micro-geometry. This is formulated as a multi-objective optimization problem (MOOP) where the obtained optimal ease-off is guaranteed to be manufacturable. To this end, an original strategy is proposed where the search for the pinion optimal tooth surface happens in the space of the coefficients of a polynomial representation of its micro-topography. However, thanks to a fast identification algorithm that can handle all the higher-order motions, the ideal ease-off is projected onto set of machine-tool settings, thus ensuring manufacturability from the outset. It is worth remarking that the objective functions in the MOOP are evaluated by calling as a back-end solver one of the most accurate loaded tooth contact analysis software available on the market. A dedicated parallel implementation of such MOOP allows to maintain computation times within very reasonable limits. A fully worked out numerical test case clearly demonstrates that the whole procedure far surpasses the current state of the art.

Effect of Forging Grain Flow on Performance of Hypoid Gear Set - Case Study

Gear sets are one of the prime components in rear axle assembly that drives the wheel by taking the power from gear box. Typically forged gears are used for automotive applications in order to perform to its maximum level while in their service. In this case study heavy truck axle hypoid gear sets with deeper gear ratio (> 6) are considered. The batch-A & batch-B samples are produced through two separate forging routes. Batch A sample is processed through press forge route & Batch B samples are through ring rolling route. Both the batches (4 samples of each) are tested for gear set fatigue bench test validation with particular torque. Test suspended upon failure of the parts. The failure mode of both the batch A & batch B are fatigue in nature & fractured at the tooth root due to root bending phenomenon. But the life of batch A is 58892 ring rear cycles where that of Batch B are is 46496 ring gear cycles. There is drop of 21% in life of gearset performance. Fracture analysis conducted & complete metallurgical results tabulated shows no significant difference in raw material, heat treatment, dimensional & any other parameters. Ishikawa diagram plotted to understand the root cause. The only difference is forging process. Both the samples are analyzed for the grain flow pattern. The batch A gears being made through press forging route are having the well defined grain flow pattern runs in part in radial direction. The batch B gears being made through ring rolling route are having the grain flow in the circumferential direction. In gear tooth cutting method, the cutter moves from outer diameter to inner diameter in both the batches. While doing so the batch A gears having radial grain flow, the cutting action will be along the grain flow. The grain flow in the tooth is not cut & they will have good bonding with the gear tooth root. This grain flow bonding enhances the resistances to tooth root bending fatigue characteristics. But in case of batch B gears having the circumferential grain flow, the cutter cuts the tooth in transverse direction of grain flow. This makes the individual tooth will not have grain flow bonding at the tooth root. Such grain flow pattern hinders the resistance to gear tooth root bending fatigue characteristic. This leads to the early failure of batch B gear than batch A gears. This case study shows that grain flow has great effect on fatigue performance. The gear tooth of press forge can take more deflection or bending fatigue loading condition than the ring rolling route, resulting in higher part performance.
 

Extended calculation method for determining the pitting load carrying capacity of bevel and hypoid gears

The flank load carrying capacity of bevel and hypoid gears is mainly limited by the failure modes pitting, scuffing, tooth flank fracture and the phenomenon micropitting. By application of a standardized calculation method, e.g. according to the international standard ISO 10300:2014, a first estimation of the flank load carrying capacity can be made based on the macro geometry of the bevel or hypoid gear set. According to method B of ISO 10300:2014 the complexity of the real geometry of bevel and hypoid gears is reduced to a virtual cylindrical gear geometry.The load carrying capacity regarding scuffing, micropitting and tooth flank fracture can be determined by using the virtual cylindrical gear geometry along the path of contact. However, the determination of the pitting load carrying capacity is carried out on a single representative point on the path of contact of the virtual cylindrical gear.This paper shows an extended calculation method for the determination of the pitting load carrying capacity of bevel and hypoid gears along the path of contact of the virtual cylindrical gear geometry. Due to the calculation along the path of contact the extended method allows a more precise estimation of the pitting load carrying capacity than the current standard calculation method ISO 10300-2:2014 using the same input data. Within this paper all relevant factors of the extended calculation method are explained in detail. Furthermore, the verification of the extended calculation method with calculation results of an intense validated loaded tooth contact analysis, corresponding to method A of ISO 10300-2:2014, is presented.

Friction-Induced Efficiency Losses and Wear Evolution in Hypoid Gears

A correct methodology to evaluate the friction coefficient in lubricated gear pairs is paramount for both the estimation of energy losses and the prediction of wear. In the first part of the paper, a methodology for estimating the coefficient of friction with a semi-empirical formulation is presented, and its results are also employed to analyze mechanical efficiency losses in a hypoid gearset. Hypoid gears have complex tooth surface geometries, and the entraining kinematics of the lubricant is quite involved. The second part of the paper showcases a simulated wear investigation based on the Archard model. The main focus is on the impact of the frequency adopted for updating the worn geometry of the gear and pinion teeth on the fidelity and consistency of the tribological outcomes. These are measured in terms of overall quantity of material removed and characteristics of the loaded contact pattern. More in detail, a sensitivity analysis is presented that compares the total wear of a hypoid gearset after 30 million cycles estimated using different geometry update steps. Contact pressures, which are necessary to perform the aforementioned analyses, are calculated through an accurate, state-of-the-art loaded tooth contact analysis solver.

Effect of Material Change from 20MnCr5 to EN 353 on Fatigue Performance of Crown Wheel Pinion ( Hypoid Gear Sets) of Full Float Axles - Case study

Crown wheel pinion is a prime member in transferring the power from transmission to wheel ends in automotive truck axles. Gear material is one of the deciding factors to estimate the fatigue life of the part. Higher the fatigue characteristics of the material better the fatigue performance of the part. In this case study, heavy truck axle with particular size having deep gear ratio is considered for material change from DIN 20MnCr5 to BS-EN 353, because its challenging to meet the life requirement in deeper gear ratios typically above 6. The basic material comparison conducted for metallurgical properties, jominy values, heat treatment properties, fatigue endurance limits, impact strength & fracture toughness. The analysis shows the EN 353 has 50% better impact strength, 35% better fracture toughness & 6.5% better endurance limit than that of 20MnCr5. The impact strength of EN 353 is 50J where as 20 MnCr5 is 25J, the fracture toughness of EN353 is 99.5 MPa√m & that of 20MnCr5 is 64.3MPa√m. The fracture toughness is calculated using Roberts-Newton formula. The endurance limit for EN 353 is 1000MPa & that of 20MnCr5 is 935MPa. The case carburized results show EN 353 has better case structure than 20MNCr5. The total 12 Numbers of gear sets, 6 each for 20 MnCr5 & EN 353, are validated for gear set fatigue on bench for particular torque. The performance of EN 353 is 24% better than 20MnCr5. The fatigue life of EN 353 is 39983 Cycles & that of 20MnCr5 is 30212 Cycles. The fracture mode is same in both the grades & typical fracture is on the Pinion. This study shows us the material change over is contributed significantly by improving the fatigue life of crown wheel pinion particularly for deeper gear ratios in heavy truck axles.

Case Study: Controlling The Distortion of a Crown Wheel (Hypoid Gear)

Abstract This study looks at whether adding an annealing step to the heat treating process has an effect on residual stress and distortion on hypoid gear sets. Test results indicate that the annealing heat treatment introduced between gear set soft cutting and case carburizing helped to minimize distortion.

On evolutoids and spatial involutoids to define hypoid flank geometry

Introduced are special evolutoid curves and spatial involutoid curves based on the special evolutoid curves. The special evolutoid is the striction curve to the family of constant pressure angle contact normals defined by a single transverse curve. Each axial position between the toe and heel of mating hyperboloidal pitch surfaces defines a unique transverse curve, and consequently, a special evolutoid and its spatial involutoid. The active tooth flank is comprised of a family of involutoid segments. This family of involutoid segments is used to define conjugate tooth flanks for hypoid gear sets. For hypoid gear sets, the pressure angle varies axially with each transverse curve. The generation of spatial involutoid curves is similar to the classical and well understood case of planar involute curves; the involutoid curve is obtained by the unwrapping of a taut chord from a planar and circular evolutoid. The line of action between the two conjugate flanks is simultaneously coincident with the input and output gear evolutoids. This process differs from the generation of planar involute curves in that the spatial involutoid curves are non-planar and there exists slip as the taut chord is unwrapped. Three gear sets are presented to showcase the process.

A methodology for simulation-based, multiobjective gear design optimization

Design optimization of geared transmissions has become more of a necessity than ever before. Typically, conflicting design goals must be concurrently achieved. The difficulty of such a multiobjective design optimization problem is exacerbated by the fact that modern design practices rely on increasingly sophisticated, computationally-expensive simulation tools for tooth contact analysis. Their intrinsic nonlinearities add complexity to the problem, hampering gear designers’ efforts to obtain globally optimal solutions. Practical optimization problems of this class have often been solved by evolutionary algorithms, but their computational burden may well be inappropriate for CPU-intensive simulation models. The present work details an algorithmic framework inspired by deterministic multiobjective optimization methods, specially combined with a direct-search global optimization algorithm to obtain globally Pareto-optimal solutions. Nonlinear constraints are enforced through an exact penalty formulation. A comprehensive description of all theoretical and algorithmic details is provided, with the intention of enabling gear designers to implement or adapt the proposed methodology to their design optimization purposes. Two tests on a challenging gear design problem, namely ease-off topography optimization of a hypoid gear set for maximum efficiency and minimum contact stress, demonstrate that the proposed method can efficiently obtain solutions belonging to the global Pareto front.Declarations of interest: none.

A REGRESSION METHOD FOR THE COMPUTATION OF LOCAL SPIRAL BEVEL AND HYPOID DEFLECTIONS FROM FINITE ELEMENT MODELS

The process of designing and analyzing the performance of spiral-bevel and hypoid gear sets requires a compact description of the gear set deflections under load. Three translational deflections E, P, G, and one angular deflection α are traditionally used to uniquely specify the relative orientation of a single spiral-bevel or hypoid pair.The movement of the contact pattern correlates strongly with these deflections, but only if the deflections E, P, G, α represent local deformations in the vicinity of the contacting teeth, rather than global deflections.It is possible to compute E, P, G, α that better represent the local deformations. This paper provides the mathematical basis for extracting the E, P, G and α numbers from a dispersed Finite Element nodal field.The assumptions and mathematics of the regression process, and its limitations are presented. An examples of its application to a flexible hypoid gear pair is shown.

New methodology for determining basic machine settings of spiral bevel and hypoid gears manufactured by duplex helical method

The duplex helical method is an advanced and primary manufacturing method of face milled spiral bevel and hypoid gears for its characteristics of higher efficiency, lower cost, higher strength and power dry cutting. A new methodology for calculating the basic machine-tool settings of spiral bevel and hypoid gears manufactured by the duplex helical method is proposed in this work. Firstly, the blank design theory of spiral bevel and hypoid gears with the duplex depth taper is described in detail. In order to obtain the optimal machine settings, three reference points are defined. The basic machine settings for spiral bevel and hypoid gears manufactured by the duplex helical method in accordance with the five steps are determined. Finally, a hypoid gear set generated by the duplex helical method is used as an example to validate the developed methodology. The results reveal that the tooth bearings and the transmission error functions on the drive and coast sides are favorable, and the results of the simulation and experiment are consistent.

An active tooth surface design methodology for face-hobbed hypoid gears based on measuring coordinates

An active tooth surface design methodology is proposed for face-hobbed hypoid gears based on fitting the measuring coordinates of real tooth surface that includes the flank deviations caused by machine errors and the deformation of heat treatment. Firstly, non-uniform rational B-spline (NURBS) is used as a tool to fit the discrete measuring coordinates of gear and pinion, then real tooth surface equations are obtained. Secondly, the pinion auxiliary tooth surface that is in line contact with the gear real tooth surface and has a parabolic transmission error (TE) is obtained by using the gear as a virtual cutter to generate the pinion under a predesigned motion function, then the pinion target tooth surface is obtained by modifying the pinion auxiliary tooth surface along the contact line with a predesigned contact pattern (CP). Thirdly, an optimization model is proposed to solve the adjustments of pinion machining parameters, this model is solved by using sequence quadratic program (SQP). The feasibility of this methodology is demonstrated by using a numerical example of a Klingelnberg–Oerlikon's Spirac hypoid gear set; the results are in line with the preconditions. This proposed methodology provides a new approach for meshing performances control of face-hobbed hypoid gears in the phase of trial-manufacture.

Estimation of Bending Fatigue Life of Hypoid Gears Using a Multiaxial Fatigue Criterion

In this study, a crack initiation life prediction methodology for the tooth bending fatigue of hypoid gears is proposed. This methodology employs a previously developed finite-element based hypoid gear root stress model (Hotait et al. 2011, “An Investigation of Root Stresses of Hypoid Gears with Misalignments,” ASME J. Mech. Des., 133, p. 071006) of face-milled and face-hobbed hypoid gears to establish the multiaxial stress time histories within the root fillet regions. These stress time histories are combined with a multiaxial crack initiation fatigue criterion to predict life distributions along roots of the pinion and the gear. The predictions of the multiaxial fatigue model are compared to those from a conventional uniaxial fatigue model to establish the necessity for a multiaxial approach. The model is exercised with an example face-milled hypoid gear set from an automotive application to demonstrate the impact of various misalignments well as the key cutting tool parameters on the resultant tooth bending lives.

F111003 デフハイポイドギヤセット流しによる歯車品質向上(【F11100】省資源・環境保全に貢献する機械要素技術,機素潤滑設計部門企画,先端技術フォーラム)

In the process of hypoid gear manufacturing, we normally check the tooth bearing ,patterns in order to confirm their final qualities. But sometimes insufficient bearing patterms worry us by various reasons. This paper tells that we could reduce such defects considerably by manufacuturing the hypoid gear sets in complete pairs through all processes.

Ease-off based compensation of tooth surface deviations for spiral bevel and hypoid gears: Only the pinion needs corrections

This paper presents a novel methodology to restore the designed functional properties of hypoid gear sets whose teeth deviate from their theoretical models due to inevitable imperfections in the machining process. Corrective actions are applied to one member only: the pinion. The concept of ease-off is profitably employed as the true means to evaluate the contact properties of a gear set as a whole. It is indeed the sameness of the designed and the real ease-off that ultimately renders two gear sets equivalent in terms of contact pattern, transmission error and vibrational properties. On this basis, gear deviations can be mapped into equivalent pinion deviations, added to those of the pinion itself, and cumulatively compensated for by applying corrective machine-tool settings to the pinion. The gear member is perfect “as is”. The ensuing advantages are highlighted in the paper. The method is illustrated with a real-life numerical example. It demonstrates that, applying corrective (i) machine-tool settings and (ii) machine settings only to the pinion grinding process, the originally designed transmission properties can be restored with a high level of accuracy.

Effects of Bearing Preload, Oil Volume, and Operating Temperature on Axle Power Losses

In order to boost the fuel economy of their vehicles, automotive Original Equipment Manufacturers (OEMs) and suppliers have been investigating a range of options from alternate vehicle propulsion systems down to optimized component level technologies. The hypoid gear set in a rear axle is one of the least efficient drive train components, and as such, provides unique opportunities for improvements. It has therefore attracted significant attention from researchers to reduce the power losses. Both loaded and unloaded power losses have been studied before and found to vary significantly with load and speed conditions. This paper will focus on the effects of the axle pinion bearing preload, axle gear oil levels, and operating temperatures on axle power losses during the fuel economy driving cycles where both axle load and speed vary significantly. In this paper, power loss measurements from experiments conducted on an automotive rear drive axle on a dedicated dynamometer will be presented. Tests were conducted under a range of speed and load conditions that were developed from Environmental Protection Agency (EPA) fuel economy driving cycles. Both urban and highway cycles were included in the tests. Separate tests were conducted for unloaded spin losses and loaded power losses. The tests were conducted at a few different controlled levels of gear oil operating temperatures, gear oil volumes, and pinion bearing preloads, and their influence on power losses was quantified. The measured power losses at a matrix of load and speed conditions provide a series of power loss maps as a function of gear oil operating temperature, oil volume, and bearing preload. Using these power loss maps, the overall axle efficiency or power loss during any driving cycle can be quantified by integrating the instantaneous power losses as the axle goes through the driving cycles. Similar maps can be created for other influences and the proposed procedure can be utilized to quantify their influences on a given driving cycle. Results from this study indicate that with the combination of appropriate preloads, gear oil volume, and temperature control, axle efficiency can potentially be improved by roughly 3% in the tested axle.

The efficiency of a hypoid axle—a thermally coupled lubrication model

The final drive unit in road vehicles, such as medium and heavy trucks, and four-wheel-drive and rear-wheel-drive passenger cars, usually consists of a hypoid or spiral bevel geared transmission and differential, housed in a self-contained, dip-lubricated axle. Such units are subjected to very variable duty—including extreme combinations of speed, gradient, applied torque and external temperature—and are typically cooled by natural and forced convection on the exterior surface. On the other hand, there are appreciable internal power losses due to gear friction and churning and to bearing and seal losses. These losses are highly dependent upon the lubrication regime of the internal components and hence to the thermal behaviour of the entire axle.In the present paper, we describe a thermally coupled model of axle lubrication. The torque and speed demand is first found from a specified duty (“drive cycle”) which includes terrain as well as speed-versus-time and external temperature data. The evolution of sump oil and component temperatures is followed, and increments of energy loss evaluated in each time-step. Elastohydrodynamic film thickness is determined for the hypoid gear set, using a development of Buckingham's method, and friction losses calculated using a simple oil rheological model based on tribometer (MTM) testing. Churning, seal and bearing (speed-dependent) losses are found using empirical algorithms. Energy losses over complete drive cycles for different lubricants are derived, enabling the relative fuel economy for different oils to be evaluated.Results show that (i) the bulk temperature rise of the axle is highly dependent on the specified vehicle duty and (ii) the efficiency can be strongly influenced by choices available to the lubricant formulator. Taken together, these findings suggest that specialist axle lubricant formulations for particular vehicle types and applications will be attractive as a route to optimum fuel economy.

Multi-Objective Ease-Off Optimization of Hypoid Gears for Their Efficiency, Noise, and Durability Performances

Microgeometry optimization has become an important phase of gear design that can remarkably enhance gear performance. For spiral bevel and hypoid gears, microgeometry is typically represented by ease-off topography. The optimal ease-off shape can be defined as the outcome of a process where generally conflicting objective functions are simultaneously minimized (or maximized), in the presence of constraints. This matter naturally lends itself to be framed as a multi-objective optimization problem. This paper proposes a general algorithmic framework for ease-off multi-objective optimization, with special attention given to computational efficiency. Its implementation is fully detailed. A simulation model for loaded tooth contact analysis is assumed to be available. The proposed method is demonstrated on a face-hobbed hypoid gear set. Three objectives are defined: maximization of gear mesh mechanical efficiency, minimization of loaded transmission error, minimization of maximum contact pressure. Bound constraints on the design variables are imposed, as well as a nonlinear constraint aimed at keeping the loaded contact pattern inside a predefined allowable contact region. The results show that the proposed method can obtain optimal ease-off topographies that significantly improve the basic design performances. It is also evident that the method is general enough to handle geometry optimization of any gear type.

An Investigation of Root Stresses of Hypoid Gears with Misalignments

In this study, the impact of misalignments on root stresses of hypoid gear sets is investigated experimentally and theoretically. An experimental set-up designed to allow operation of a hypoid gear pair under loaded quasi-static conditions with various types of tightly controlled misalignments is introduced. These misalignments include the position errors (V and H) of the pinion along the vertical and horizontal directions, the position error (G) of the gear along its axis, and the angle error (γ) between the two gear axes. For example, face-hobbed hypoid gear pair from an automotive axle application is instrumented via a set of strain gauges positioned at the roots along the faces of multiple teeth to measure root strains within a range of input torque. These root strain measurements at different V, H, G, and γ values are presented. A computational model is also proposed to predict the root stresses of face-milled and face-hobbed hypoid gear pairs under various loading and misalignment conditions. The model employs an automated finite elements mesh generator based on a predefined template for a general and computationally efficient treatment of the problem. Model predictions are compared to measurements at the end to assess the accuracy of the model and describe the measured sensitivities.