Hypoid Gears Research Articles

GENERATION AND TOOTH CONTACT ANALYSIS (TCA) OF HYPOID GEAR DRIVE

The present work covers the Face-Hobbing method for generation and simulation of meshing of Face hobbed hypoid gear drive. In this work the generation process of hobbed hypoid gear has been achieved by determination of the generation function of blade cutter. The teeth surfaces have been drawn depending on the simulation of the cutting process and the head cutter motion. Tooth contact analysis (TCA) of such gear drive is presented to evaluate analytically the transmission error function for concave and convex tooth side due to misalignment errors. TCA results show that the gear is very sensitive to misalignment errors and the increasing of the gear teeth number decrease the transmission error for both concave and convex tooth sides and ensure smooth motion with low vibration.

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.

High-performance tooth flank collaborative optimization model for spiral bevel and hypoid gears

The tooth flank collaborative optimization considering both geometric and loaded contact performances is an increasingly significant target in design and manufacturing for spiral bevel and hypoid gears. Recently, numerical loaded tooth contact analysis (NLTCA) is always an important access of mapping of the required performance evaluations and design variables. In addition to the conventional solution to NLTCA, an innovative discrete convolution and fast Fourier transformation (DC-FFT) method focusing on the micro-scale tooth flank topography is developed for high-performance spiral bevel and hypoid gears. Then, combining with accuracy and efficiency, a new top-rem tool modification is proposed to establish a new collaborative optimization model. Where, while the target flank can be prescribed by considering the user needs in the actual manufacturing, a small number of tool parameters are selected as the unknown design variables. It can significantly deal with the strong nonlinearity and coupling effect from the traditional modification and improve the optimization efficiency. Moreover, a top-rem tool modification is used as the optimization strategy to get a high optimization accuracy. The spiral bevel gear set from aerospace industrial applications is exercised to demonstrate the impact of the proposed collaborative optimization model on the tooth flank geometric and loaded contact performances.

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.
 

A Bootstrap-Based Tooth Surface Errors Statistics Methodology for Batch Hypoid Gears after Heat Treatment

In the manufacturing and production of hypoid gears, it is a necessary key problem to improve the tooth surface heat treatment precision and production efficiency of the hypoid gears. How to use advanced statistical theory and methods to evaluate the whole batch machining quality of the tooth surface after heat treatment is particularly urgent. In this connection, for the same batch of hypoid gears with the same gear material, numerical control gear milling method, and heat treatment specifications, a bootstrap-based statistics scheme of tooth surface errors after heat treatment is proposed in this paper. The bootstrap statistics model of the tooth surface errors for the batch hypoid gears is established. The bootstrap probability eigenvalues and confidence intervals of the measurement sequence points on the tooth surface errors are solved, and the optimizing selection of the single sampling numbers and the repeated sampling times is completed. On this basis, by applying the cubic NURBS surface fitting method, the mean value difference surface of the batch tooth surface errors data is constructed, the statistics laws of the whole batch tooth surface errors after heat treatment is determined, and the effective evaluation of the whole batch tooth surface accuracy is realized. Finally, the feasibility and correctness of the bootstrap-based statistics scheme are verified by the tooth surface errors bootstrap statistics application experiment of one kind of hypoid gear. The results show that with the help of the bootstrap statistics method proposed in this paper, it is not necessary to accurately measure the tooth surface errors of the whole batch of hypoid gears one by one. Only by randomly selecting 10 tooth surface samples and repeatedly sampling 2000 times, the original sample characteristic values of the whole batch tooth surface errors can be accurately estimated, and the heat treatment deformation statistics laws of the whole patch tooth surfaces can be also counted.

Effect of boundary slip on elastohydrodynamic lubrication with arbitrary entrainment angle in elliptical contacts

PurposeThe purpose of this study is to describe and observe the influence of boundary slip associated with an arbitrary entrainment angle on the contact lubrication properties of ellipses.Design/methodology/approachBased on the modified Reynolds equation, the boundary slip of any angle is considered in the elliptic contact, and numerical simulation is carried out. In the above calculation, the progressive mesh densification method is used, which greatly reduces the computation time.FindingsThe results indicate that the variation of film thickness corresponding to different entrainment angles is distinct from those without considering boundary slip. In addition, boundary slip reduces the central film thickness and minimum film thickness, which makes the hydrodynamic pressure distribution smoother.Originality/valueThe present study focuses on the specific condition with the arbitrary direction of rolling and sliding velocity found in hypoid gears and worm, and some other components. The influence of boundary slip associated with arbitrary entrainment angle on the lubrication film thickness in elliptical contacts is first revealed, which improves a good understanding of elastohydrodynamic lubrication characteristics.

The mathematical model of non-circular crossed-axis gear

Non-circular crossed gear can be regarded as the general form of the single stage gear, which can be converted into hypoid gearing, non-circular bevel gearing, non-circular external gearing, and non-circular internal gearing with specific parameters. This paper established its mathematical model, deduced equation of its axode, and put forward a new method of tooth profile generation with introduction of relative velocity. In term of the theory above, the 3D model of a pair of conjugated gears was built, and its output angular velocity was obtained in analysis of ADAMS. Finally, the physical prototype of the gearing was developed and output angular velocity was measured as well. Both the simulation and measurement results show the motion is in good condition, which confirms the correctness of the theory and algorithm.

Dynamic Processes of Self-Organization in Nonstationary Conditions of Friction

Self-organization mechanisms of metastable dissipative structures during friction depending on base and oil functional additives for hypoid gears are considered. Research was conducted on a software-hardware complex with simulation of gears’ operation in rolling with slipping conditions in start-stop mode. Indicators of formation of wear-resistant dissipative structures include the following: improvement of antifriction characteristics, lubricant boundary layers’ formation, contact surfaces’ strengthening, and formation of heterogeneous deformation microrelief with a fine-grained structure. The formation of chemically modified boundary layers on 90% of the contact area of tribo-coupling elements ensures an increase in the wear resistance of leading and lagging surfaces by 2 and 1.4 times, respectively. The sclerometry method was used to establish that the formation of dissipative structures when lubricating tribo-coupling elements with various transmission oils can reduce deformation processes in metal near-surface layers by 23%. Highly viscous flavored lubricant with distillate oil and additive composition ensures wear-resistant dissipative structures with active components, including oxygen, sulfur, and phosphorus.

On micro flank geometric topography design for spiral bevel and hypoid gears

Focusing on comprehensive effect of both macro and micro geometries, accurate flank geometric topography design in a micro scale is developed for spiral bevel and hypoid gears showing a complex flexural behaviors. Firstly, macro flank modeling is performed for determining sparse tooth surface by using the discrete point interpolation. For micro-scale and smooth flank points, the vector between the current point and the adjacent tooth surface point are used as the tangent vector, and the vector in normal direction is obtained by calculating vector product of tangent vector. Then, fast Fourier transform (FFT) method is employed for the micro flank geometric topography reconstruction considering comprehensive effect. While determining the height distribution parameters from the actual measurement, autocorrelation function (ACF) is established to obtain the reconstructed roughness height matrix, and these microscopic height data are added to the corresponding macroscopic smooth tooth surface points in the normal direction for accurate micro flank geometric topography generation. The proposed method is exercised with an example double helical grinding spiral bevel gear from an aerospace application to demonstrate the impact of reconstruction design on flank performance.

Modelling method, simulation and experimental verification of hypoid gear involved tooth surface deviation under manufacturing process

Tooth surface errors are inevitable in manufacturing process, and directly affect the meshing performance and NVH properties. In this paper, the tooth profile deviation and midpoint tooth pitch error were considered. Firstly, the theoretical tooth surface model was established by simulating the manufacturing process of face-hobbed hypoid gear. Then, a novel modelling method of tooth surface errors was proposed based on the relationship between discrete tooth surface points and measured error points. A solid model and finite element model by using CAD and CAE technologies were developed to study the effects of tooth surface errors and meshing phase on the contact pattern and transmission error. Results show that the gear tooth surface error was the primary factor while the tooth meshing process contributes the least of total transmission error. The peak-to-peak of the transmission error values of pinion and gear with error was 24.786 times higher than standard. The meshing phase of gear had greater impact on the contact pattern. The range of transmission error fluctuation was 210 μrad within different meshing phases. The tooth surface points measurement and rolling experiment were performed and the fluctuation range was around 233.86 μrad with a 10.2% difference.

Investigation of the effect of multi-segment cutter section on meshing characteristics for face-hobbed hypoid gears

Investigation of the effect of multi-segment cutter section on meshing characteristics for face-hobbed hypoid gears

Life cycle assessment-driven collaborative optimization model of power dry cutting for face-hobbing hypoid gear production

Efficient, high-precision, energy-saving, green manufacturing and low-cost design is an increasingly important target to life cycle assessment (LCA) for high-performance hypoid gear production. With development of numerical controlled (NC) technology of hypoid generator, power dry cutting is enabling ever-higher levels of production efficiency and sustainability. It also has the potential to dramatically influence sustainable development of hypoid gear product. Sufficient guidance, in this respect, is lacking in the scholarly or practitioner literature. In this work, focusing on LCA for hypoid gear production, we further examine power dry cutting in terms of application and sustainability implications. We introduce collaborative optimization considering geometric accuracy and loaded contact performances into the power dry cutting. Here, LCA-driven power dry cutting collaborative optimization model is proposed for face-hobbing hypoid gear production. At first, complex machine kinematics between cutting tool and work blank are developed for power dry cutting simulation. Then, tooth flank mathematical modeling is performed to output discretization points in a closed-form of the whole tooth flank including concave flank and convex flank. Moreover, in order to improve LCA, an accurate model of material removal collaborative optimization considering both geometric accuracy and loaded contact pattern is established for face-hobbing hypoid gears. Where, time-varying material removal path planning is developed. Then, sensitivity analysis strategy and genetic algorithm (GA) are proposed for the proposed model solution, respectively. Finally, numerical instances can demonstrate that the proposed model can get a very important access to power dry cutting having high LCA for face-hobbing hypoid gear production.

A Study on the Influence of Plasma Nitriding Technology Parameters on the Working Surface Deformation of Hypoid Gears

This paper presents the results of the research on the influence of plasma nitriding technology parameters on the working surface deformation of hypoid gears. Blue light technology with non-contact measuring devices is used to determine the working surface deformation of hypoid gears after plasma nitriding. The study has determined a regression equation showing the influence of plasma nitriding technology parameters on the deformation of the working surface of the hypoid gear. The minimum deformation optimization value at the planning area is 0.0071746 at permeation temperature TL=4.89oC, permeation time h=510h, and gas flow 1 G1=6.02L/h.

Investigation and optimization of hypoid gear micro-geometry parameters and axle deflections to improve the contact stress distribution and fatigue life of hypoid gears

The automotive industry always demands more torque per kilogramme of weight. On the other hand, there is always a growing demand for increased warranty kilometres for customers. This puts increased pressure on the life of the drive axle, which is the major load and torque-carrying member in commercial vehicles. Drive head unit is a crucial contributor to this aim. This paper focuses on the work done towards the above targets wherein advanced tools helped to achieve them in the minimum time. Due attention is given to the hypoid gear system to sustain higher stress because of the heavy torque demanded by the application. It is accomplished by the optimum design of the gear tooth profile and system design. Gear durability is a major concern in heavily loaded axles. To have an optimum design with higher performance torque is a key challenge. The paper talks about the challenges overcome during the design, development, and validation of a single-reduction large-size gear axle to replace the hub reduction rear axle. It demands a better understanding of gear tooth and system behavior, which was analyzed by advanced software tools and measurement machines. The same is validated on the test bench, and the results are discussed.

An exact system of generation for face-hobbed hypoid gears: Application to high reduction hypoid gear drives

The determination of the pitch cones for hypoid gears is already well defined either through numerical methods as those shown in the Standard ANSI/AGMA ISO 23509-B17 or through algorithms available in the specialized literature. However, a procedure to determine the gear tooth surfaces for hypoid gears directly from their pitch cones is still missing. An analytical approach to determine the basic machine-tool settings for the pinion and the wheel of hypoid gear drives is proposed here. It is based on the condition of exact generation, which means that the gears will operate under conjugate condition. It can be applied for generation of face-hobbed hypoid gears, produced either by the CycloCut or the CycloPalloid generation methods. A numerical example proves the goodness of the proposed methodology in a high reduction hypoid gear drive. The results of tooth contact and stress analyses prove that the bearing contact is localized and stable against misalignments, requiring just a small adjustment through the application of an optimum tip relief to the gear tooth surfaces to minimize the maximum contact pressure.

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.

Effect of Steel Inclusion on Heat Treatment Quench Crack - Case Study

Hypoid pinion is a major member in the heavy truck axle as it transmits the power from propeller shaft to hypoid ring gear. This is the first member in axle assembly to receive the power from transmission. Metallurgical quality is inevitable parameter in this part. In this case, a fracture analysis of hypoid pinion carried out, root cause is found & corrections are addressed. The quench crack is generated during the case carburizing treatment. The fractography shows that this crack is initiated from the gross non-metallic inclusion present at the sub surface of the drive pinion. SEM EDS analysis conducted & identified inclusion as Aluminium Oxide predominantly with a dimension 7 mm in length & 1mm in width caused the longitudinal crack on the pinion. The ishikawa diagram plotted for steel mill process to understand the cause. Since the type of inclusion is Al2O3, focused more on ladle refining station, VD process & continuous casting parameters in steel mill process where entrapment could occur. The appropriate corrective action taken in steel mill on VD process, post VD soft rinse, multiple sampling for inclusion from first & last billet, NDT method UT phased array system is introduced by developing the master sample having size same as inclusion. The Inclusion went undetected whole the process starting from steel mill to pinion case carburizing heat treatment & is opened up after quenching due to volumetric difference in crystal, happens during heating & cooling. The mechanism of crack generation is discussed which involves crystallographic changes takes place during carburizing cycles.

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.

EXPANDING THE TECHNOLOGICAL CAPABILITIES OF MACHINES FOR CUTTING BEVERED WHEELS WITH CIRCULAR TOOTH WITH INCREASED OUTER TONE DISTANCE

Considered in the article. expansion of technological capabilities of machine tools mod. 528С for cutting bevel gears with a circular tooth with an increased outer taper distance of the gears with a crossing angle of 300. Optimizing programs are analyzed to determine the geometric parameters with obtaining the localization of the contact zone in height, for the tooth shape III, even on a machine tool without tilting the tool, and in the presence of a machine with the inclination of the tool spindle, widely apply the double-double-sided cutting method for a wide range of bevel and hypoid gears, and not only for gears of small modules, but also for wheels of medium modules, which was previously considered impossible without the use of special machines with helical movement. The machine settings with an increased external taper distance on a machine with insufficient adjustment offsets are analytically determined. As a result, it was found that with certain axial displacements of the headstock of the product, it is possible to place a wheel blank with an increased size of the outer conical distance. In this case, the processing is carried out by a reduced flat producing wheel. Partial displacement of the lateral surface of the wheel teeth is compensated by the optimization of the setting parameters when processing a paired gear, while the calculated displacements, due to the possible intersection of the wheel with the base parts, can be corrected upwards. The new displacement values are again entered into the optimization program as initial ones.