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There is a growing and prevalent trend in the power transmission field of high-performance polymers replacing metallic materials given the strict light-weight requirement. Polymer gears exhibit a low elasticity modulus, high-temperature sensitivity, and increased geometric design flexibility, presenting technical challenges to the straightforward application of metallic design methods to polymer gear systems. This study is centred on the development of a high-power-density polymer gear transmission system for the accessory unit of a gas turbine engine, utilising an adaptive NSGA-III algorithm and surrogate sub-models. A comprehensive assessment indicator for the operating performance of the transmission system is suggested, encompassing gear strength, bearing temperature, and shaft torsional stiffness. The model made it possible to simultaneously optimise forty-six structural parameters, including gear tooth module, web thickness, and bearing clearance. In contrast to the original steel design scheme, the optimised polymer gear transmission system indicated a 49% reduction in weight and a 1.96-fold increase in power density. This presents a method for substituting steel with polymers for effective power transmission.

With the increasing requirements of power density，load capacity and service life of gear transmission for aviation，wind power and other equipment，gear contact fatigue failure has become an important bottleneck limiting the service performance and reliability of modern gear equipment，and the material microstructure characteristics determine the fatigue performance of gear and other service parts. Through the surveys of the current related research situation both at home and abroad，the main microstructure features of gear materials such as retained austenite，carbide，grain size and their influence on the contact fatigue performance of gears are introduced. The reported numerical simulations of gear contact fatigue based on microstructure modeling and micromechanics constitutive model are summarized to describe the microscopic mechanical behavior of in gear contact fatigue，and to improve the understanding of the key characteristics and mechanism of gear fatigue. The various contact fatigue failure forms of gears occurred in the engineering practice are expounded in detail，and the main factors affecting the contact fatigue failure of gears，the induced microstructure evolution and degradation of mechanical properties，as well as the potential mechanisms of the gear contact fatigue failure，are analyzed. This review aims to provide the further understanding of the relationship between microstructure evolution characteristics and mechanical property degradation during the service process of gears，as well as the internal mechanism of contact fatigue failure，and providing the reference for anti-fatigue design and manufacturing method of high-performance gears.

With the development of wind turbine，high-speed railway，aero-engine and other large equipment towards the direction of high reliability，long life and intelligence，it has put forward higher requirements for the life of basic components such as gears and bearings. It is urgent to use more scientific and efficient fatigue life prediction method. The life prediction methods of mechanical components can be divided into physical failure model，data-driven model and fusion model（physical failure and data-driven model fusion） three types. With the development of components life prediction research towards high precision and high efficiency，physical model is difficult to meet modern needs due to its complexity，time-consuming and non-universal disadvantages. With the rapid development of machine learning，deep learning and other technologies，data-driven model has become a hot topic in the research of components fatigue life prediction of due to the advantages of no need to know detailed failure mechanism and accurate prediction results. In view of this，the fatigue life prediction method of components based on data-driven is described. The application of these methods in the life prediction of components is introduced，including neural network，support vector machine，random forest and deep learning，and the characteristics of each method are summarized，and the developing trend of the life prediction method of components based on data-driven is discussed. And a case study of gear contact fatigue life prediction based on GA-BP neural network is presented.

Abstract A compound oscillatory roller reducer (CORR) with a first-stage gear transmission and a second-stage oscillatory roller transmission is presented. The transmission principle of oscillatory roller transmission is introduced, and the tooth profile equation of the inner gear is derived. The analytical model of mesh force considering the installation errors and manufacturing errors is proposed. Then, parametric studies considering different errors on the mesh force are conducted. Results show that the design parameters are significant factors for mesh force. The mesh force is reduced by 17% as the eccentricity of disk cam increases from 2.5 mm to 4 mm. When the radius of the movable roller increases from 7 mm to 20 mm, the mesh force decreases by 8%. As the radius of disk cam increases from 125 mm to 170 mm, the mesh force is decreased by 26.5%. For the impacts of errors, the mesh force has a noticeable fluctuation when these errors exist including the manufacturing error of disk cam, the installation error of disk cam and the manufacturing error of movable roller change. The prototype of the reducer is manufactured and preliminary run-in test proved the feasibility of the transmission principle.

Planetary roller screw mechanism (PRSM) is a novel high-performance linear transmission device. The non-uniformity of load distribution over PRSM threads is a vital problem severely affecting its load-carrying capacity and service performance. This work aims to develop a PRSM load distribution improvement approach with good manufacturability and general applicability. A roller taper modification method for load distribution optimization is proposed based on the deformation compatibility and force equilibrium, then the roller grinding experiment is carried out. Finally, the effects of external load and thread number on load sharing optimization are analyzed to examine the applicability. The results show that the maximum reduction in load sharing coefficient reaches 31.4% after roller taper modification under the case studied. The taper modification of roller threads could be rapidly implemented by only adjusting the roller grinding angle. The roller grinding experiment results agree well with the theoretical values, and the maximum error is no more than 2 μm. As the external load and thread number change, the improvement approach still works well. The proposed method has been verified by comparisons with finite element simulations and available references. This work can provide theoretical guidance for the optimal design of PRSM and has good engineering application prospects.

As a new type of transportation for future urban air transportation，flying cars are intelligent，efficient and convenient. As a key component of the power transmission of a flying car，the safety and reliability of gear transmission has become a difficult problem restricting the development of flying cars. However，the current reliability analysis method for the gear transmission system of flying cars is lacking. The existing design method fails to consider the influence of the strength degradation and failure correlation on the reliability of the transmission system which has a potential failure risk. Therefore，a dynamic reliability analysis model of a flying car gear transmission system considering the correlation between strength degradation and failure is established based on the theory of stress-strength interference. According to the flight mission profile，the load spectrum is established and the gear contact and bending stress are obtained. The complex stress history is equivalent to symmetric cyclic stress by Goodman criterion，which matched the fatigue damage calculation based on S-N curve. A gear strength degradation model is established based on the theory of non-linear fatigue cumulative damage，and the Copula function is used to describe the failure coupling correlation in the transmission system. Combined with the stress-strength interference theory，the reliability evolution law of the flying car gear transmission system is expounded，which lays a foundation for the dynamic design and reliability optimization of the gear transmission system of flying car.

The meshing temperature of plastic gear affects the mechanical behaviors such as fatigue， wear and noise， which should not be ignored in the mechanical response and performance prediction of plastic gear. In order to predict the meshing temperature of plastic gears， a finite element numerical model of plastic gear temperature field is established considering the temperature-modulus effect of POM material and the multi-heat sources effect of frictional heat and hysteresis heat flux. Based on POM thermo-viscoelastic contact analysis， frictional heat flow and hysteresis loss heat flow are obtained as heat sources. Through the iterative calculation of the interaction between the steady meshing temperature and elastic modulus of plastic gear， the steady meshing temperature and tooth surface flash temperature are obtained. The steady meshing temperature results are in good agreement with the test results， and the flash temperature is in good agreement with the Blok theory. It is found that the temperature rise of hysteresis loss heat has little effect on the steady meshing temperature under dry condition， while the temperature rise caused by friction is the main component of the steady running temperature of plastic gear.

Non-metallic inclusions in the gear have significant influence on the contact fatigue strength of gear. To improve the fatigue performance of the gear， it is essential to understand the mechanism of the influence of the non-metallic inclusions on the fatigue life of the gear. A finite element model of gear pair with inclusions is established， and the Brown-Miller multiaxial fatigue criterion is applied to predict the contact fatigue life. The influence of inclusion size， elasticity modulus， depth and arrangement of inclusions on contact fatigue performance of the gear is investigated. The results show that the size of inclusions increases the stress concentration area， with the increase of elastic modulus difference between inclusion and matrix， the harm of inclusion increases. The damage reaches its maximum when the inclusion located in the depth of about 0.49bH（contact half width depth）. The arrangement angle and spacing of two adjacent inclusions also affect the fatigue relief strength， with the decrease of the distance of the two adjacent inclusions， the stress concentration effect is more obvious， the harm will be greater.

Abstract This study presents the results of detailed wear process examination on polyformaldehyde gears under both dry and lubricated conditions. A multi-purpose durability test rig was employed to study the wear performance of polyformaldehyde gear pairs. The wear behaviors of polyformaldehyde gears under dry and oil-lubricated operating conditions were characterized via measurements of gear tooth surface micro-topography and tooth profile deviation. Under the dry running condition, a hump and a gully appear on the tooth surface in the pitch line area of the driving gear and the driven wheel, respectively. The largest amount of wear was observed around the tooth root of the driving gear. However, the gear tooth wear pattern with lubrication is different from that under the dry running condition.

To investigate the influence of the manufacturing parameters on mesh behaviors for harmonic gear drive, the mathematical model of slotting the circular spline was established using kinematic method based on the tooth profile of the circular spline. Considering the circular runout errors from the machine tool and slotting cutter, the influences of two kinds of circular runout errors on the transmission error for harmonic gear drive were analyzed. Then, the influences of the slotting cutter teeth number and the slotting cycles of the circular spline on the transmission error were discussed. Two circular splines were machined by two types of slotting cutters with different teeth number to verify the theoretical analysis. Results show that the influence of the machine tool's circular runout error on the transmission error is more significant than that of the slotting cutter's circular runout error. For the slotting of the circular spline with one circle, the transmission error is the smallest when the tooth number of the slotting cutter is one third of that of the circular spline. For the slotting of the circular spline with two or three circles, the transmission error is the smallest when the tooth number of the slotting cutter is two thirds of that of the circular spline. However, the transmission error of harmonic gear is the largest when the tooth number of the slotting cutter is half of that of the circular spline.

Abstract Carburized gears are widely used in geared machines such as wind turbines. Contact fatigue problems occur in engineering practice, reducing reliabilities of machines. Contact fatigue failures are related to many factors, such as gradients of mechanical properties of the hardening layer. In this work, an elastic-plastic contact model of a carburized gear is developed based on the finite element method to evaluate contact fatigue failure risk, considering variations in hardness and strength. The Dang Van multiaxial equivalent stress is calculated via Python coding within the Abaqus framework. The gradient of yield strength along the depth from case to core is considered. The concept of local material fatigue failure risk is defined to evaluate the probability of pitting failure. The effects of design factors, such as the case hardening depth (CHD), surface hardness, and contact pressure on fatigue failure risk, are studied. As the CHD increases or the surface hardness decreases, the risk of deep spalling failure reduces. The increase in surface hardness leads to a decreased risk of pitting failure, while the variation in CHD hardly affects the pitting failure risk.

Abstract The structure of an improved wind turbine gearbox is presented for meeting the operation of the optimized wind turbine power‐wind speed curve (P‐v curve). When the wind speed is lower than the cut‐in wind speed, the operation mode of the wind turbine is changed by the extra power, which is supplied by the motor excited source to keep the wind turbine running. Moreover, the transmission principle of the improved wind turbine gearbox is discussed. Various motor power impacts on the transmission characteristic for the improved transmission structure are investigated and results are compared with the professional software. Results indicate that as the motor power increases, the transverse vibration of sun gears and meshing forces of the low‐speed and medium‐speed planetary stages decreases. The transverse vibration for the pinion gear of the high‐speed stage enhances with the increase of the motor power. Load‐sharing coefficients of the planetary gear stages are augmented with the enlargement of the motor power. It is found that meshing forces of the torque‐implement parallel stage are increased with augmentation of the motor power.

Abstract The current research of wind turbine drivetrain is mainly concentrated in dynamic characteristics of gearbox with a specific suspension of main shaft, such as one-point and two-point suspension. However, little attention is paid to the effects of these suspension configurations on the dynamic responses of wind turbine gearbox. This paper investigates the influences of suspension configurations of main shaft on the dynamic characteristics of drivetrain. For evaluating the dynamic behaviors of drivetrain with multi-stage transmission system more realistically, a dynamic modeling approach of drivetrain is proposed based on Timoshenko beam theory and Lagrange’s equation. Considering the flexibility and different suspension configurations of main shaft, time-varying mesh stiffness excitation, time-varying transmission error excitation and gravity excitation, etc., a three-dimensional dynamic model of drivetrain is developed, and the dynamic responses of drivetrain are investigated. Results show that with the one-point suspension of main shaft, the resonance frequencies in gearbox, especially at the low-speed stage, obviously shift to the higher frequency range compared to the gearbox without main shaft, but this trend could be inversed by increasing main shaft length. Meanwhile, the loads in main shaft, main shaft bearing and carrier bearing are greatly sensitive to the main shaft length. Hence, the load sharing is further disrupted by main shaft, but this effect could be alleviated by larger load torque. Comparing to the one-point suspension of main shaft, there occurs the obvious load reduction at the low-speed stage with two-point suspension of main shaft. However, those advantages greatly depend on the distance between two main bearings, and come at the expense of increased load in upwind main shaft unit and the corresponding main bearing. Finally, a wind field test is conducted to verify the proposed drivetrain model. This study develops a numerical model of drivetrain which is able to evaluate the effects of different suspension configurations of main shaft on gearbox.

The mathematical model of teeth distribution optimization for the promote gearbox is presented considering the objective functions such as the volume, efficiency, strength difference for the adjacent stages, and the design variables such as module, sun gear teeth, face width and transmission ratio of all stages. The improved genetic algorithm is used to solve the model and an analysis model of the promote gearbox is established using Masta to verify the proposed model. Results show that, after optimization, the attribute value of the synthesized objective function increases by 82.73%, the volume decreases by 17.61%, and the efficiency increases by 0.02%. The objective function value of equal contact and bending strength decreases by 55.93% and 51.10%, respectively. The difference for the safety coefficients for the adjacent stages decreases obviously. The constraint conditions of single-stage and adjacent stages satisfy the requirements. Through the strength verification calculation by the analysis model, the variation trend of the strength before and after optimization is consistent with the proposed optimization model, which indicates that the multi-objective optimization model established in this paper and the improved genetic algorithm selected are correct and effective.

Considering the system deformation, a procedure to predict the mesh behaviors for face-hobbed hypoid gear pair in car rear axle was proposed based on the tooth surface model and the finite element analysis (FEA) tooth contact model. The mathematical model of face-hobbed hypoid gear was derived based on the manufacturing process. The systematic model of the whole rear axle was developed in Masta, and the misalignments caused by system deformation of the hypoid gear pair was calculated. The impacts of the comprehensive misalignments and independent misalignments on mesh behaviors of hypoid gear were studied, respectively. Results show that the comprehensive misalignments under the rated load level have less influence on the contact characteristics. However, for the parametric studies of independent misalignment, the offset misalignment, and the gear axial misalignment have obvious influences on the contact pattern and transmission error. The peak-to-peak value for angular transmission error with the offset misalignment decreases significantly, when misalignment change from negative to positive. While that with the gear axial misalignment increases progressively. For shaft angle misalignment has an obvious impact on the location of the contact area and it causes a little increase of the peak-to-peak value for transmission error. Relatively, the pinion axial misalignment has diminutive impacts on the contact pattern and transmission error.

Taking the NW planetary gear transmission of an electric wheel hub as the research object, the mesh model was developed to calculate the mesh parameters using Masta. Then the lump parameter method was used to establish the dynamic model of the NW planetary transmission system considering the time-varying mesh stiffness, transmission error and bearing stiffness. The impacts of the torque load on the dynamic characteristics including the dynamic mesh force, center trajectory, offsets and load sharing coefficients were investigated. Results show that the dynamic mesh force waveform and spectral characteristics of each planetary gear at high and low speeds under the rated and maximum torque load are almost identical. Compared to the peak response at speed 485 rpm and 1770 rpm, both the magnitude and location of the third response at relative high speed about 4300 rpm are increased due to the load increasing. The mean and fluctuation range of the offsets in the radial direction are both larger than the tangential direction. As the load increases, the mean value of the radial offset increases and the magnitude decreases significantly. The mean value of the tangential offset decreases significantly, but the magnitude increases first and then decreases. The load sharing characteristics of the low-speed stage of the NW planetary gear is better than the first stage. With the increase of the load, the load sharing performance of a two-stage planetary transmission gets better and the difference in load sharing between the high-speed and low-speed stages also decreases.

Abstract Coating is an effective way to reduce friction and wear and to improve the contact-fatigue lives of gear components, which further guarantees a longer service life and better reliability of industrial machinery. The fact that the influence coefficient linking the tractions and stress components could not be expressed explicitly increases the difficulty of coated solids contact analysis. The complicated tribological behavior between tooth surfaces influenced by lubrication and surface roughness further adds difficulty to the coated gear pair contact problems. A numerical elastohydrodynamic lubricated (EHL) contact model of a coated gear pair is proposed by considering the coupled effects of gear kinematics, coating properties, lubrication, and surface roughness. The frequency response function and the discrete convolute, fast Fourier transformation (DC-FFT) method are combined to calculate the surface deformation and the subsurface stress fields at each meshing position along the line of action (LOA). The Ree-Eyring fluid is assumed to incorporate the non-Newtonian effect, which is represented in the generalized Reynolds equation. Influences of the ratio between the Young’s modulus of the coating and the substrate on the contact performance, such as pressure, film thickness, tooth friction coefficient, and subsurface stress field, are studied. The effect of the root mean square (RMS) value of the tooth surface roughness is studied by introducing the roughness data, deterministically measured by an optical profiler.

Gear contact fatigue has becoming a bottleneck restricting the safety and reliability of wind turbine transmission systems. Tooth interior fatigue fracture (TIFF) failure is commonly observed in case-hardened wind turbine gears. In this work, a contact fatigue model is developed to investigate the effect of design parameters and material properties on TIFF of wind turbine gears. The sub-surface stress field is obtained by superposing the load-introduced stress and initial residual stress. The hardness gradient of the hardened layer is measured by Vickers hardness tests. Based upon the stress field and material properties, a fatigue parameter analysis is presented to characterize the risk of TIFF by using the Dang Van multiaxial fatigue criterion. Results show that the risk of TIFF increases with increasing external load. Increasing pressure angle and residual compressive stress could reduce TIFF risk. The combination of high surface hardness, low core hardness, and large effective case depth could inhibit the crack initiation.

The wind turbine drivetrain suffers significant impact loads that severely affect the reliability and safety of wind turbines. Bearings and gears within the drivetrain are critical components with high repair costs and lengthy downtime. To realistically assess the system reliability, we propose to establish an electromechanical coupling dynamic model of the wind turbine considering the control strategy and environmental parameters and evaluate the system’s reliability of wind turbine drivetrain based on loads of gears and bearings. This paper focuses on the dynamic reliability analysis of the wind turbine under the control strategy and environmental conditions. SIMPACK (v9.7, Dassault Systèmes, Gilching, Germany) is used to develop the aero-hydro-servo-elastic coupling dynamic model with the full drivetrain that considers the flexibility of the tower and blade, the stochastic loads of wind and waves, gear meshing features, as well as the control strategy. The system reliability level of wind turbine drivetrain at different wind conditions is assessed using survival signature and fault tree analysis (FTA), and the influences of strength degradation of the transmission components on the system reliability are explored. Following this, the bending fatigue reliability and contact fatigue reliability concerning different wind conditions are compared in this paper. A case study is performed to demonstrate the effectiveness and feasibility of the proposed methodology.

Due to the high cost of failures of wind turbines, redundancy designs are commonly applied in wind turbines for improving the reliability and availability of systems. For this reason, replacing failed components with other working components of the same type in redundant systems is becoming an attractive option of maintenance strategies towards more resilient systems. To quantitatively evaluate system’s reliability, this paper focuses on the reliability analysis of redundant systems of offshore wind turbines based on swapping existing components. The survival signature-based component swapping method is introduced to describe the new structure-function of the system upon swapping. Furthermore, the reliability model of redundant systems is established using the fault tree and survival signature. Following this, the influences of component swapping on component reliability importance measure (marginal reliability importance and joint reliability importance) without and with considerations of the imprecision of failure rates are explored. Finally, a 5MW offshore wind turbine is presented to show the applicability of the proposed approach for redundant systems, and the results show that the proposed approach can obtain realistic reliability assessment of redundant systems and considering component swapping can significantly improve system reliability.

In this paper, a potential energy based slice grouping method was proposed to calculate the mesh stiffness for straight beveloid gears with parallel axes. The mathematical mesh stiffness model was derived. The finite element tooth contact model was developed and the loaded tooth contact analysis was conducted to calculate the mesh stiffness. The verification for the mesh stiffness was conducted with the error 3 %, which proves the feasibility and accuracy. Then, the effects of parameters such as pressure angle, pitch cone angle, and profile shift coefficient on the mesh stiffness were investigated. Results show that the normal pressure angle and the tooth width have obvious effects both on the single tooth and synthesized mesh stiffness. When pressure angle is less than 20°, mesh stiffness will be increased with the increase of pressure angle. However, it decreases rapidly when the pressure angle exceeds 20°. Both the single tooth and synthesized mesh stiffness increase obviously as the tooth width increases. The increase of the cone angle and addendum coefficient have a little effect on the single tooth mesh stiffness, but have the obvious incremental effects on the synthesized mesh stiffness. The contact ratio increases obviously with the increase of the addendum coefficient. The profile shift coefficient and the clearance coefficient have unsubstantial effects both on the single and synthesized mesh stiffness.

The mathematical beveloid gear tooth surface model considering machine tool adjustment errors was derived. The definition and calculation process of tooth surface deviations along the tooth trace and profile directions for beveloid gear were proposed. Also, the solid model and the finite element mesh model of a paralleled beveloid gear pair were developed. Then, the effects of the machine tool adjustment errors including independent helix angle error, independent cone angle error and combined helix and cone angle errors on tooth surface deviation and contact characteristics were investigated. Results show that all the machine tool adjustment errors cause an incremental trend for the tooth profile and tooth trace deviations. And positive errors have the opposite impact on the surface deviation compared with the negative errors. The independent helix angle error has a stronger impact on the tooth surface deviations than the independent cone angle error and combined angle errors. Also, the tooth surface deviations caused by the independent helix angle error, independent cone angle error and combined angle errors have the similar magnitude level as the tooth surface modifications. All the independent helix angle error, independent cone angle error and combined angle errors tend to have deteriorative effects on the mesh characteristics, making edge contact worse, decreasing the contact area, increasing the contact pressure and the transmission error. The independent helix angle error has the strongest impact both on the contact pattern and transmission error, which is similar to the impact on the tooth surface deviations. However, the independent cone angle error shows less effects on the mesh characteristics. Thus the machine tool adjustment errors should be strictly controlled especially for the helix angle error during manufacturing.

A working pitch cone based geometry design approach for the intersected beveloid and cylindrical involute gear pair with small shaft angle was proposed. The cutter and geometry design parameters can be determined by the proposed method. Also, a quasi-static loaded mesh model was developed to calculate the contact characteristics. Then the influences of torque load, helix angle and misalignments on the mesh behaviors were investigated. Results show that the contact type is point contact both for light and heavy load situations. The increase of load tends to increase the root stress, transmission error and mesh stiffness obviously. However, the variations of the peak-peak value of transmission error and mean value of the mesh stiffness are greater under light load level compared with heavier load level. The increase of the helix angle obviously tends to increase the contact area, which is desirable. It also decreases the peak-peak value of transmission error and increases the mean mesh stiffness due to more area coming into contact. The shaft angle error tends to shift the position of the contact pattern and the peak value of the root stress along the tooth width direction slightly. Overall, the contact characteristics are not sensitive to the shaft angle error and gear axial position error.

A micro-TEHL finite line contact model for a helical gear pair is developed by considering sinusoidal waviness on tooth surfaces. Effects of working conditions, the amplitude, and the wavelength of the waviness roughness on the lubrication performance are studied. Results show that surface roughness has a significant influence on the pressure, the temperature, and so forth. The pressure within the nominal contact zone for a rough-surface case fluctuates around the smooth-surface solution. For the working conditions studied, at local area within the contact zone, the maximum pressure may be 50% higher than the smooth-surface result. The film contraction at the outlet zone becomes more remarkable. The film temperature also fluctuates regularly. As the amplitude of the roughness increases, the local pressure within the nominal contact zone increases while the minimum film thickness decreases. As the wavelength of the roughness decreases, the local pressure and the temperature within the nominal contact zone increase while the film thickness decreases. Effect of wavelength on the lubrication performance is more evident along the rolling speed direction than along the contact line direction.

Based on the spatial position relationship of spiral bevel gear, mathematical model and mesh model applied with finite element analysis (FEA) approach has been established. The influence of axial position errors of pinion and wheel, offset error, and shaft angle error on the meshing characteristics has been investigated. A method has been proposed to compensate the gear assembly errors by the axial displacement of the pinion and wheel, and the correctness of this method verified by numerical examples. The performed results indicate that the existence of assembly errors can cause contact pattern on the tooth surface to deviate from its design position, resulting in poor meshing quality and having a certain impact on transmission error (TE) and peak-to-peak transmission error (PPTE). The pinion and wheel's axial positioning errors can be offset by each other, whereas the offset error and shaft angle error can be mitigated by the interplay between the axial positioning of the pinion and wheel. By compensating for assembly errors with axial displacement, the position of the contact pattern can be precisely controlled, and TE will not significant changes. [ABSTRACT FROM AUTHOR]