ASME Conference Presenter Attendance Policy and Archival Proceedings

2015;():V010T00A001. doi:10.1115/DETC2015-NS10.

This online compilation of papers from the ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference (IDETC/CIE2015) represents the archival version of the Conference Proceedings. According to ASME’s conference presenter attendance policy, if a paper is not presented at the Conference, the paper will not be published in the official archival Proceedings, which are registered with the Library of Congress and are submitted for abstracting and indexing. The paper also will not be published in The ASME Digital Collection and may not be cited as a published paper.

Commentary by Dr. Valentin Fuster

ASME 2015 Power Transmission and Gearing Conference: Bearings, Clutches, Couplings, and Splines

2015;():V010T11A001. doi:10.1115/DETC2015-46302.

At present, the existing problems in gear volume optimization include: (1) the clearance volume caused by the bottom clearance and addendum modification is not considered in the volume models which causes the error of volume calculation. (2) Gears employ fixed structure and their structural changes caused by the dimension changes are not considered in the process of optimization. In view of the above mentioned problems, the paper firstly deduces the formula of clearance volume. An example is provided to verify that the clearance volume should be considered in the accurate calculation of gear volume. Secondly, volume formulas of different structure of spur gear including solid structure, web-type structure, spoke type structure with cross shape section and with H-shape section are deduced. The design variables, objective function and constrains are briefly introduced. Finally, a single stage spur gear train is as an example, the optimization is carried out. The result shows when the transmission ratio is changed from 3.2 to 2, the structure of gear changes from the web-type to the solid. It means gear with fixed structure is not reasonable in the process of optimization.

Topics: Design , Spur gears , Trains
Commentary by Dr. Valentin Fuster
2015;():V010T11A002. doi:10.1115/DETC2015-47336.

Due to the lack of knowledge in terms of their flexibility and deformation, spline joints are typically assumed to be rigid in dynamic models of gearboxes, transmissions and drive trains. As various dynamic phenomena are associated with the stiffness of a spline joint, any high-fidelity dynamic model of drivetrains must properly capture the stiffness of spline joints. In this study, a general analytical stiffness formulation for spline joints is proposed based on a semi-analytical spline load distribution model. This formulation defines a fully-populated stiffness matrix of a spline joint including radial, tilting and torsional stiffness values as well as off-diagonal coupling terms. A blockwise inversion method is proposed and implemented with this analytical formulation to reduce computational time required. At the end, a detailed parametric study is presented to demonstrate the sensitivity of the spline stiffness matrix to torque level, tooth modifications, misalignments, and tooth indexing errors.

Topics: Splines , Stiffness
Commentary by Dr. Valentin Fuster
2015;():V010T11A003. doi:10.1115/DETC2015-48086.

In this paper, topology optimization of gearbox to reduce the radiated noise is studied based on the analysis of modal acoustic contribution and panel acoustic contribution. Firstly, the bearing dynamic loads are obtained by solving the dynamic equations of gear system. Secondly, the vibration of gearbox is calculated using FEM and the radiated noise is simulated using BEM by taking these bearing dynamic loads as excitations. Thirdly, the panel having larger contribution to the sound pressure level (SPL) at a specific field point is found by panel acoustic contribution analysis (PACA), and this panel is taken as design domain. The mode order with larger contribution is determined by modal acoustic contribution analysis (MACA), and making corresponding natural frequency becomes far away from excited frequency is taken as a constraint. Finally, the topology optimization of gearbox is completed using SIMP method, and the ribs are arranged according to the optimization results. The results show that the equivalent sound pressure level at objective field point can be reduced obviously by using this method.

Commentary by Dr. Valentin Fuster

ASME 2015 Power Transmission and Gearing Conference: Gear Analysis, Materials, Fatigue

2015;():V010T11A004. doi:10.1115/DETC2015-46253.

This paper presents the main results of the performed experimental investigations and theoretical studies carried out to investigate the main parameters affecting facing edge tooth flank fracture damages of case carburized helical gears.

These facing edge tooth fractures were observed in different industrial gearbox applications as well as within several experimentally based research projects on the pitting load carrying capacity of case hardened gears. The crack origin of these unexpected tooth flank fractures was found to be in the area of the acute facing edge.

As a part of a special research project extensive experimental and test-accompanying investigations as well as theoretical studies were carried out to investigate the main parameters affecting facing edge tooth flank fractures.

The herein found failure mechanism is discussed in detail. Finally, recommendations to avoid gear facing edge tooth flank fractures are given in order to optimize the gear load carrying capacity.

Commentary by Dr. Valentin Fuster
2015;():V010T11A005. doi:10.1115/DETC2015-46274.

The space shuttle orbiter’s body flap actuator gearing was assessed as a case study of the stresses for very heavily loaded external-internal gear pairs (meshing pinion and ring gear). For many applications, using the high point of single tooth contact (HPSTC) to locate the position of the tooth force is adequate for assessing the maximum tooth root stress condition. But for aerospace gearing such an approach may be inadequate for assessing the stress condition while also simultaneously minimizing mass. In this work specialized contact analyses and finite element methods were used to study gear tooth stresses of body flap actuator gears. The analytical solutions considered the elastic deformations as an inherent part of the solutions. The ratio for the maximum tooth stresses using the HPSTC approach solutions relative to the contact analysis and finite element solutions were 1.40 for the ring gear and 1.28 for the pinion gear.

Commentary by Dr. Valentin Fuster
2015;():V010T11A006. doi:10.1115/DETC2015-46299.

The flank load carrying capacity of case-hardened gears is significantly influenced by the condition of the case properties. A negatively influenced case, e.g. due to grinding burn, may result in a significantly reduced load carrying capacity of the tooth flank. On the other hand, additional finishing methods such as shot peening and superfinishing allow a positive influence on the case properties, resulting in a further increase of the tooth flank load carrying capacity. The variation of the case properties is not adequately taken into account by the current standards DIN 3990 / ISO 6336.

This paper summarizes the results of the FVA research project 521 I. This project investigated the effects of shot peening and superfinishing on the tooth flank load carrying capacity. Based on the experimental results, an extension of the calculation method for the permissible contact stress σHP is proposed.

Commentary by Dr. Valentin Fuster
2015;():V010T11A007. doi:10.1115/DETC2015-46325.

This paper presents the main results of performed investigations and discusses the possible influences of different low temperature treatments on relevant material characteristics in correlation with the obtained tooth root bending strength of case-hardened gears made of materials 18CrNiMo7-6, 20MnCr5 and 15NiCr13. Most of the investigations were performed on gears that were exposed to low temperatures after heat treatment. Additionally, the effect of low temperatures within the heat treatment process was examined. For shot blasted gears, which were treated by low temperatures after heat treatment process, all examined materials showed no decrease of the tooth root bending strength. In contrast, for almost all gears which were cooled down to low temperatures within the heat treatment, a decrease in the tooth root bending strength was observed in unpeened as well as in shot blasted condition. Additional investigations show a correlation of tooth root bending strength and relevant material properties.

Commentary by Dr. Valentin Fuster
2015;():V010T11A008. doi:10.1115/DETC2015-46488.

Gear misalignments originate unwanted uneven load distributions that increase contact pressures and the bending stresses, reducing the service life of gear drives. Therefore, it is very important to take into account the misalignments in the determination of contact pressures when designing a gear transmission. Some of these misalignments are related to manufacturing and assembly errors, but others are produced by the deformation of the shafts when power is transmitted. These deformations cause misalignment of the gears, modifying the contact bearing and the pressure distribution, which modifies the deformation of the shafts, leading to a coupled problem not always easy to solve. In this work, a new approach to solve this problem is proposed, based on an iterative algorithm which uncouples the determination of the deformation of the shafts from the contact problem. The proposed approach has been tested through various configurations of spur gear drives. The obtained results are compared with those obtained using a finite element model, showing a good correlation between them, but with a significant reduction of the computational cost.

Commentary by Dr. Valentin Fuster
2015;():V010T11A009. doi:10.1115/DETC2015-46556.

The power-split gear mechanisms is widely applied in power transmission because of the advantages of compact design, lighter weight and high power density. The load sharing and the load distribution are the important performance issues while designing the power split mechanisms. The paper propose a computerized approach based on the influence coefficient method for loaded tooth contact analysis of such the gear transmission. Not only the load sharing of the multiple contact tooth pairs and the loaded transmission errors, but also the distributed contact stresses and the corresponding contact patterns on all the engaged tooth flanks can be calculated by using the proposed LTCA approach. Some analysis results are also discussed with a study case of the first planetary stage of a compound cycloid planetary gear drive.

Commentary by Dr. Valentin Fuster
2015;():V010T11A010. doi:10.1115/DETC2015-47283.

Mechanical (load-dependent) power losses of a planetary gear set occurs primarily along its lubricated rolling-sliding interfaces at the external and internal gear meshes, and planet bearings. The gear mesh originated portion of these losses are influenced by all key gear parameter, tooth profile correction and other parameters dictating the fluid film formation. In this study, a systematic planetary gear design search algorithm is combined with an efficiency formulation to (i) quantify the sensitivity of gear mesh mechanical losses of planetary gear sets to the basic gear design parameters and (ii) investigate the compromise that must take place between the mechanical efficiency and other functional attributes associated with durability and noise performance of the gear set. An example design study is presented at the end to demonstrate both of these points.

Commentary by Dr. Valentin Fuster
2015;():V010T11A011. doi:10.1115/DETC2015-47393.

Axle hypoid gear design needs axle system deformation data at mesh point under load to evaluate the contact pattern, contact pressure and bending stress of the gear pair. The system deformation data or gear deflection (GD), can be obtained through a standard test procedure defined several decades ago. The testing method has not been improved for data acquisition efficiency and reliability since then. Fundamentally it contains trade-offs that make contact pattern correlation difficult. It also cannot meet urgent axle development timing pressures and cost reduction requirements. Analysis methods have been developed in recent years to replace the testing method of GD calculation. However, published modeling methods have their own limitations, and still do not correlate well loaded contact pattern between testing and analysis. In this paper, existing approaches of GD calculation are first reviewed and compared. Then the development of a new method is outlined, which combines a general finite element software and a special gear bearing contact analysis tool in one process. The validation of the method is illustrated by comparing axle loaded contact pattern. Finally, two case studies are demonstrated. The first one shows the capability of the new method to investigate the compliance contribution of main axle components. The second one shows that during one gear rotation, GD experiences a significant variation which needs to be considered during gear design.

Commentary by Dr. Valentin Fuster
2015;():V010T11A012. doi:10.1115/DETC2015-47517.

Spur gear tooth root strains are calculated using a finite element/contact mechanics formulation for varying gear speeds and applied torques. Extensive comparisons with experiments, including those from the literature and new ones, confirm that the finite element/contact mechanics formulation accurately predicts the quasi-static and dynamic tooth root strains. The finite element/contact mechanics model is used to investigate the features of the tooth root strain curves as the gears rotate kinematically and the tooth contact conditions change. Tooth profile modifications are shown to strongly affect the shape of the strain curve. At non-resonant speeds the dynamic tooth root strain curves have similar shapes as the quasi-static strain curves. At resonant speeds, however, the dynamic tooth root strain curves are drastically different because large amplitude vibration causes tooth contact loss.

Topics: Spur gears
Commentary by Dr. Valentin Fuster

ASME 2015 Power Transmission and Gearing Conference: Gear Dynamics and Noise

2015;():V010T11A013. doi:10.1115/DETC2015-46040.

In this paper, a new nonlinear time-varying dynamic model for compound planetary gear sets, which incorporates the time-varying meshing stiffness, transmission errors and gear backlash, has been presented. The harmonic balance method (HBM), which is an analytical approach widely used for nonlinear oscillators, is employed to investigate the dynamic characteristics of the gear sets. The matrix form iteration algebraic equations has been established and solved by HBM and single rank inverse Broyden method to reveal the effect of transmission error and gear backlash on the frequency response characteristic of the system. Sub-harmonic resonant, super-harmonic resonant and jump phenomenon have been illustrated by several examples.

Commentary by Dr. Valentin Fuster
2015;():V010T11A014. doi:10.1115/DETC2015-46061.

Approximate formulae are presented which give the time-varying mesh stiffness function for ideal solid narrow-faced spur and helical gears. The corresponding results compare very well with those obtained by using 2D finite element models and specific benchmark software codes thus validating the proposed analytical approach. More deviations are reported on average mesh stiffness which, to a large extent, are due to the modelling of gear body deflections.

Commentary by Dr. Valentin Fuster
2015;():V010T11A015. doi:10.1115/DETC2015-46062.

This paper deals with the optimization of tooth profile modifications in planetary gears. A dynamic model is proposed based on 3D two-node gear elements connected to a deformable ring-gear discretized into beam elements. Symmetric tip relief on external and internal gear meshes are introduced as normal deviations along the lines of contact superimposed on a stiffness distribution aimed at simulating position- and time-varying mesh stiffness functions. The equations of motion are solved by the combination of a Newmark’s time-step integration scheme and a contact algorithm to account for possible partial or total contact losses. Symmetric linear profile modifications are then optimized by using a genetic algorithm with the objective of minimizing dynamic tooth loads over a speed range. Finally, the interest of the corresponding optimum profile modifications with regard to speed and torque variations is analyzed.

Commentary by Dr. Valentin Fuster
2015;():V010T11A016. doi:10.1115/DETC2015-46063.

A three-dimensional dynamic model is presented to simulate the dynamic behavior of single stage gears by using a combination of classic shaft, lumped parameter and specific 2-node gear elements. The mesh excitation formulation is based on transmission errors whose mathematical grounding is briefly described. The validity of the proposed methodology is assessed by comparison with experimental evidence from a test rig. The model is then employed to analyze the relationship between dynamic transmission errors and dynamic tooth loads or root stresses. It is shown that a linear dependency can be observed between the time variations of dynamic transmission error and tooth loading as long as the system can be assimilated to a torsional system but that this linear relationship tends to disappear when the influence of bending cannot be neglected.

Topics: Stress , Gears , Errors
Commentary by Dr. Valentin Fuster
2015;():V010T11A017. doi:10.1115/DETC2015-46105.

This paper proposes a new non-linear transverse-torsional coupled model for double stage planetary gear train, and gear’s geometric eccentricity error, synthetical transmission error, time-varying meshing stiffness, sun-planet and planet-ring gear pair’s backlashes and sun gear’s bearing clearance are taken into account. The differential governing equations of motion are derived and solved by applying variable step-size Runge-Kutta numerical integration method. The system motion state is investigated systematically and qualitatively, and exhibits diverse bifurcation and chaos characteristics under different bifurcation parameters including meshing frequency, sun-planet backlash and planet-ring backlash. Analysis results showed that the increasing damping could suppress the region of chaotic motion and improve the system’s stability significantly; the route of period-doubling to chaotic motion was observed for both first and second stage’s motion state under the bifurcation parameter of meshing frequency; The routes of period doubling and crisis to chaos were identified under the bifurcation parameter of sun-planet backlash; Besides, the increasing damping ratio could split the bifurcation diagram window into different sections and strong coupling effects are generated to second stage’s motion. Several different types of routes to chaos were observed under the bifurcation parameter of planet-ring backlash including period doubling and 3T-periodic channel; Besides, it concluded that planet-ring backlash could generate a strong coupling effect to both stage’s nonlinear behavior.

Commentary by Dr. Valentin Fuster
2015;():V010T11A018. doi:10.1115/DETC2015-46338.

The present paper addresses the development of a lumped parameters model used to analyze the dynamic behavior of a so-called tandem gear pump. The pump is composed of two coaxial stages, both with external gears: a high pressure stage with spur gears and a low pressure one with helical gears. In particular, the paper deals with the modelling and the analysis of the phenomena bound to the pressure distribution around the gears, since they have the most important effect in the dynamic behavior of the pump. The pressure variation in the inlet and outlet chambers, the variable pressure in the trapped volume as well as the pressure evolution from the low to the high pressure chamber is estimated based on the Euler’s approach. The model is developed in Matlab environment. Attention is particularly focused on the description of the methodology adopted for modelling the low-pressure stage, constituted by helical gears, and its influence on the calculation of the pump geometrical parameters. The results provided by the numerical model are compared with experimental measurements in terms of outlet pressure ripple and volumetric efficiency under different working conditions. The results of the validation can be considered satisfactory. Predicted pressure ripple is shown and the effects of interconnections between stages are analyzed studying the outlet pressure ripple in the frequency domain as well.

Topics: Pressure , Gear pumps
Commentary by Dr. Valentin Fuster
2015;():V010T11A019. doi:10.1115/DETC2015-46751.

So far, researches of the meshing performance of vehicles cylindrical gears are quite rare. Testers that can be used to test the gear pair’s performance for vehicles cylindrical gears do not exist. A tester that can be used to test vehicles cylindrical gears paring performance was developed, which fills the gaps of vehicles cylindrical gears meshing performance tester. The maximum diameter of gears measured is 500mm, the maximum spindle speed is 3000r/min and the maximum load torque is 200N.m. The tester can inspect and measure the following items simultaneously, such as the transmission errors, the vibration and noise, the contact pattern, the eccentricity errors and so on. There is gear error analysis function in this tester. In addition, it can meet the quality inspection requirements for the vehicles cylindrical gears with the accuracy of grade 5.

Topics: Gears , Vehicles
Commentary by Dr. Valentin Fuster
2015;():V010T11A020. doi:10.1115/DETC2015-46821.

A bending-torsional coupled nonlinear dynamic model which contains the modification parameters of herringbone planetary gear train is presented. A formula of modification incentive is analyzed and deduced. The impact of the straight line and parabolic modification parameters on the amplitude of system transmission error is researched. The optimum modification parameters are acquired according to the minimum amplitude of system transmission error. Different amplitudes of the system transmission error, before and after modification, are compared at different rotational speed. The results indicate that the straight line modification parameters on the amplitude of system transmission error are more sensitive. Modification parameters on the amplitude of system transmission error are researched. When the length of the modification is specified, the amplitude of system transmission error is reduced sharply at first, then increased rapidly with the maximum magnitude of the modification increasing; When the maximum magnitude of the modification is specified, the amplitude of system transmission error is increased weakly at first, then decreased sharply, and increased rapidly in the end, with the length of the modification increasing. The modification parameters could form a crescent-shaped zone which can reduce the system transmission error amplitude significantly. The amplitudes of the system transmission error with modification are all reduced at different rotational speed, especially when there is a sympathetic vibration.

Commentary by Dr. Valentin Fuster
2015;():V010T11A021. doi:10.1115/DETC2015-47048.

Transmission error is typically understood to act as the primary source of gearbox noise and vibration. This paper investigates the effect of sliding friction on the transmission error and tooth load of spur gears. To do so, the kinematic relation for the sliding mechanism of spur gears and mesh stiffness was calculated. The relationship between tooth load, tooth errors and mesh compliance as well as the moment balance equation in consideration of the teeth friction force are derived. Transmission error, tooth load, and the teeth friction force of gears with/without modification were investigated. As the results, friction caused an increase in tooth load and transmission error in gear approach and a decrease in tooth load and transmission error in gear recess.

Commentary by Dr. Valentin Fuster
2015;():V010T11A022. doi:10.1115/DETC2015-47093.

Modern wind turbines are designed to cope with their increased size and capacity. One of the most expensive components of these machines is the gearbox. Its design is more complex than a mere upscaling exercise from predecessors. The stress levels experienced by the different gear stages, the dynamic effects induced by their size and the unparalleled loads transmitted are some of the challenges that design engineers face. Moreover, unexpected events that load the wind turbines such as voltage dips, wind gusts or emergency breaking are expected to be major contributors to the premature failure of these gearboxes. The lack of engineering experience at this scale calls for accurate and efficient simulation tools thereby enabling reliable gearbox design.

Standard lumped-parameters models or rigid multibody approaches do not provide a sufficient level of details to study the dynamic effects induced by e.g. gear design modifications (micro-geometry) or to analyze local stress concentrations.

More advanced numerical tools are available such as flexible multibody or non-linear FE and allow to model complex contact interactions including all the relevant dynamic effects. Unfortunately the level of mesh refinement needed for an accurate analysis causes these simulations to be computationally expensive with time scales of several weeks to perform a single full rotation of a gear pair.

This work introduces a novel efficient simulation tool for dynamic analysis of transmissions. This tool adopts a flexible multibody paradigm but incorporates several advanced features that allows to run simulations up to two orders of magnitudes faster as compared to non-linear FE with the same level of accuracy. A unique non-linear parametric model order reduction technique is used to develop a simulation strategy that is quasi mesh-independent allowing the usage of very fine FE meshes.

Finally, in order to limit the memory consumption, a technique is developed to be able to finely mesh only a few of the gears teeth while the remaining gears are coarsely meshed. The main novelty of this approach lies in the possibility to perform full gear rotations without losing spatial resolution as compared to a finely meshed gear.

After an accuracy check performed with a sample pair of helical gears, the framework is used to simulate the high speed stage of a three-stage wind turbine gearbox. The combined efficiency and accuracy of the approach is demonstrated by performing a dynamic stress analysis of the high-speed stage with and without a tip-relief modification. Accuracy of the results, simulation time, and memory usage are assessed.

Commentary by Dr. Valentin Fuster
2015;():V010T11A023. doi:10.1115/DETC2015-47136.

A gear tooth profile optimization study is performed with the target being defined as the maximization of tooth bending fatigue life for a selected operational range, where the operating torque and speed ranges are defined along with their corresponding durations. For this purpose, a nonlinear lumped gear dynamics model is combined with the S/N curve of the gear material in order to estimate tooth bending fatigue life of the spur gear pair. The differences between the predicted lives of the optimally modified and non-modified gear pairs are presented based on example spur gear pairs. The proposed tooth bending fatigue life estimation is compared with the standard AGMA procedure.

Commentary by Dr. Valentin Fuster
2015;():V010T11A024. doi:10.1115/DETC2015-47263.

Although tremendous effort has been applied to develop reliable strategies for detecting tooth cracks of gearboxes, these methods have generally fallen short of the required performance. Cracks are usually initiated at the root of a tooth and are very difficult to be identified from time-domain measurement. The vibration signal transformed by wavelet is sensitive to energy change. In this study, the transient vibration variations induced by different sizes of cracks at the tooth root are captured using wavelet. Firstly, as the main parametric excitation, the time-varying gear meshing stiffness caused by the alternating of engaged gear teeth is accurately calculated based on energy method, in which comprehensive deformations including Hertz contact, axial compression, bending, shearing and fillet-foundation deflection are taken into consideration. Moreover, a sophisticated dynamic theoretical model is used to simulate a practical gear system. Unique vibration signatures are captured through the comparison of cracked and perfect gear system.

Commentary by Dr. Valentin Fuster
2015;():V010T11A025. doi:10.1115/DETC2015-47324.

The dynamics of an automotive differential hypoid gear pair is investigated. The gear pair model is a 4 degree-of-freedom torsional model, including the torsional deflections of the supporting shafts of the pinion and the gear. It also includes the dynamic transmission error of the mating teeth pairs. The variations in teeth contact stiffness/contact, principal radii of contact and static transmission error are determined during the meshing cycle, using the CALYX software. The equations of motion are solved using a numerical integration scheme. A preliminary parametric study is presented, enabling identification of different periodic responses as the vehicle cruising speed alters.

Commentary by Dr. Valentin Fuster
2015;():V010T11A026. doi:10.1115/DETC2015-47426.

In this study, a two-dimensional, steady-state, discrete dynamic model of a double-planet planetary gearset is proposed. The dynamic model is generalized such that it can consist of number of planet branches and can operate under any operating conditions (load and speed). The contact between each external to external and external to internal gear pair is modeled to obtain stiffnesses and mesh displacement excitations using a generalized load distribution model. The natural modes are computed by solving the corresponding eigenvalue problem. The forced vibration response to gear mesh excitations is obtained by applying the modal summation technique. The model is capable of predicting gear mesh dynamic load and dynamic transmission error spectra for each gear mesh, dynamic bearing load spectra for each bearing as well as gear body dynamic displacements. Forced vibration response of an example system that consists of three double-planet branches is studied to demonstrate the influence of some of the key design parameters.

Topics: Dynamic models
Commentary by Dr. Valentin Fuster
2015;():V010T11A027. doi:10.1115/DETC2015-47646.

This paper describes the effect of gear blank topology on the gear meshing stiffness and consequently on the dynamic loads in gear transmissions. The characteristics of these forces, especially their frequency content, will determine the NVH and durability properties of the entire transmission. To assess the level of induced vibrations and the acoustic radiation from the transmission housing, it is important to properly model the excitation mechanism originating from the meshing gears. Several authors have proposed semi-empirical formulas [1–3] to compute the meshing stiffness, however most of them assume a solid gear blank and provide some correction factors in case of thin rims and webs [4]. Nevertheless current trends in transmission design also include extreme measures to reduce the gear weight that have an influence of the meshing stiffness that cannot be fully captured with the abovementioned methodologies. This papers proposes a methodology to model this phenomenon and shows by means of a numerical example that lightweight flexible gear blanks have a non-negligible effect on meshing forces.

Commentary by Dr. Valentin Fuster
2015;():V010T11A028. doi:10.1115/DETC2015-48022.

A new nonlinear dynamics model of the double helical planetary gear train with 44 degrees of freedom is developed, and the coupling effects of the sliding friction, time-varying meshing stiffness, gear backlashes, axial stagger as well as gear mesh errors, are taken into consideration. The solution of the differential governing equation of motion is solved by variable step-size Runge-Kutta numerical integration method. The influence of tooth friction on the periodic vibration and nonlinear vibration are investigated. The results show that tooth friction makes the system motion become stable by the effects of the periodic attractor under the specific meshing frequency and leads to the frequency delay for the bifurcation behavior and jump phenomenon in the system.

Commentary by Dr. Valentin Fuster

ASME 2015 Power Transmission and Gearing Conference: Gear Geometry

2015;():V010T11A029. doi:10.1115/DETC2015-46256.

The computing formulae, in different forms, for the normal vector of the instantaneous contact line are summarized systematically. For some of them, the distinct and sententious proof techniques are put forward. Based on the normal vector of the transient contact line, the computing formulae for the induced normal curvature and the induced geodesic torsion are deduced laconically and strictly. Owing to making use of the normal vector of the transient contact line, the style of the obtained formulae is more elegant. Particularly, a novel developing approach for the computing formula of the induced geodesic torsion is proposed. On the basis of the induced geodesic torsion, the computing formulae for the induced principal directions are derived. From this, the calculating formulae for the induced principal curvatures are obtained rigorously and conveniently. All these work reveal the pivotal position of the normal vector of the momentary contact line in the meshing theory for the line conjugate gearing. By right of the meshing theory established, the meshing analysis for the modified TA worm drive is performed. A number of basic and important formulae are attained and the numerical outcome of the induced principal curvature is given out.

Commentary by Dr. Valentin Fuster
2015;():V010T11A030. doi:10.1115/DETC2015-46675.

In this paper, the planar double-enveloping method is presented for the generation of tooth profiles of the internal gear pair for various applications, such as gerotors and gear reducers. The main characteristic of this method is the existence of double contact between one tooth pair such that the sealing property, the load capacity and the transmission precision can be significantly improved as compared to the conventional configuration by the single-enveloping theory. Firstly, the generation principle of the planar double-enveloping method is introduced. Based on the coordinate transformation and the envelope theory, the general mathematical model of the double-enveloping internal gear pair is presented. By using this model, users can directly design different geometrical shape profiles to obtain a double-enveloping internal gear pair with better meshing characteristics. Secondly, to validate the effectiveness of the proposed model, specific mathematical formulations of three double-enveloping internal gear pairs which apply circular, parabolic and elliptical curves as the generating curves are given. The equations of tooth profiles and meshing are derived and the composition of tooth profiles is analyzed. Finally, numerical examples are provided for an illustration.

Topics: Gears
Commentary by Dr. Valentin Fuster
2015;():V010T11A031. doi:10.1115/DETC2015-47182.

Two methods for the design of the pinion apposite to an existing spiral bevel gear are proposed. In both methods, the gear is given by a discrete or smooth parameterization, and the pinion is described in the same way, i.e. it can be produced on a CNC machining center without any further efforts. The first method gives full control on the position, direction, and the extent of the contact area of the pinion. The second method starts by choosing a quite arbitrary transmission function of the gear drive to be designed, and then gives full control on the position, direction, and the width of the contact area. Therefore, both methods provide much freedom in the design process.

Commentary by Dr. Valentin Fuster
2015;():V010T11A032. doi:10.1115/DETC2015-47327.

The teeth of ordinary spur and helical gears are generated by a (virtual) rack provided with planar generating surfaces. The resulting tooth surface shapes are a circle-involute cylinder in the case of spur gears, and a circle-involute helicoid for helical gears. Advantages associated with involute geometry are well known: in particular, the motion transmission function is insensitive to center distance variations, and contact lines (or points, when a corrective surface mismatch is applied) evolve along a fixed plane of action, thereby reducing vibrations and noise emission. As a result, involute gears are easier to manufacture and assemble than non-involute gears, and silent to operate. A peculiarity of their generation process is that the motion of the generating planar surface, seen from the fixed space, is a rectilinear translation (while the gear blank is rotated about a fixed axis): the component of such translation that is orthogonal to the generating plane is the one that ultimately dictates the shape of the generated, envelope surface. Starting from this basic fact, we set out to investigate this type of generation-by-envelope process and to profitably use it to explore new potential design layouts. In particular, with some similarity to the basic principles underlying conical involute (or Beveloid) gears, but within a broader scope, we propose a generalization of these concepts to the case of involute surfaces for motion transmission between skew axes (and intersecting axes as a special case). Analytical derivations demonstrate the theoretical possibility of involute profiles transmitting motion between skew axes through line contact and, perihaps more importantly, they lead to apparently novel geometric designs featuring insensitivity of transmission ratio to all misalignments within relatively large limits. The theoretical developments are confirmed by various numerical examples.

Topics: Design , Gear teeth
Commentary by Dr. Valentin Fuster

ASME 2015 Power Transmission and Gearing Conference: Gear Manufacturing

2015;():V010T11A033. doi:10.1115/DETC2015-46402.

As the emerging economies expand, demand for low cost production of internal gears has been increasing. And skiving is in focus as a potential method than can meet this demand.

Skiving was invented in 1910, since then, mechanical machine has been developed to NC machine and cutter design technologies have developed dramatically. As a result, several machine and tool manufacturer started to release their skiving machine and skiving cutter as well.

Furthermore, many studies on the kinematics have been conducted both in research institutions and private companies. However, most of these studies are subject to understanding the cutting mechanisms as a basic research and establishing cutter design methods.

For further improvement and boost widespread application of the process, optimization of the manufacturing process is an issue. Particularly, the effects of cutter accuracy and cutter set up deviations on the skived gear are important to ensure reliability of the process. Unfortunately, few studies on those effects can be found.

In this paper, geometrical model that can predict the effect of pitch deviation and of run out of a cutter on a skived gear is proposed. Experiments were also carried out to verify the validity of the model, and the results were in good agreement with the simulated ones.

Topics: Gears
Commentary by Dr. Valentin Fuster
2015;():V010T11A034. doi:10.1115/DETC2015-46682.

As gears that have been honed offer excellent wear characteristics and are extremely quiet, gear honing has become an essential part in the production of high-speed transmissions. In this paper, a novel gear honing technology based on toothskipped gearing theory is proposed. So far, this theory has been used only in the gear dynamic integrated error measuring machine, which was invented by a Chinese engineer. It is the first time that the theory has been introduced into gear manufacturing. Firstly, the whole tooth-skipped honing process is analyzed by taking the rack and pinion as an example. Secondly, the kinematics model of relationship between the rack and the gear is established, which takes the rack addendum meshing process, the gear addendum meshing process and the involute meshing process into consideration. Finally, the boundary points of each process are analyzed. The velocity curve of the gear to be manufactured is obtained. Tooth-skipped gear honing as a gear fine finishing approach has high processing efficiency and can increase the gear quality.

Topics: Kinematics , Gears
Commentary by Dr. Valentin Fuster
2015;():V010T11A035. doi:10.1115/DETC2015-46744.

A new design of rapid inspection machine for automotive gears based on Gear Integrated Error (GIE) technology is introduced in this paper. The novel equipment can be used in production workshops to get analytical results such as profile deviations and pitch deviations of spur and helical cylindrical gears.

The distinguishing features of GIE are summarized by analyzing the principle of GIE method, the specific measuring master, and the curves of GIE measuring results. Then the design approach, system structure, procedure of inspection, key parameters, and specifications of the newly designed rapid inspection machine are introduced.

It is difficult and critical in the GIE technology to distinguish the involute meshing phase and to determine the exact coordinates of the starting and end points in a GIE curve. An innovative algorithm is also proposed to solve this problem.

The performance of the rapid inspection machine has been verified by experiments in two aspects, the accuracy and the efficiency. It can be seen that the accuracy of the rapid inspection machine for automotive gears is good enough to meet the design requirements and the efficiency is much higher than Gear Measuring Centers (GMCs).

Commentary by Dr. Valentin Fuster
2015;():V010T11A036. doi:10.1115/DETC2015-47421.

The design of spiral bevel gears is still very complex because tooth geometry and thus kinematics performance depend on the manufacturing process of this type of gear. The cutting process is dominated by two major manufacturers: Gleason and Klingelnberg. The shape of the teeth surfaces are governed by a large number of programmed machine settings, so they cannot be optimized intuitively. Due to the progress made during the last decade by CNC machines and CAM (Computer Aided Manufacturing) softwares, it is now possible to manufacture spiral bevel gears with quite good quality on a 5-axis milling machine.

In a previous study, the authors presented a numerical model for calculating the quasi-static load sharing of spiral bevel gears. Two kinds of geometries were developed: a simplified Gleason type, and a geometry based on classical spherical involutes combined with a logarithmic spiral. After being generated using a CAD (Computer-Aided Design) software, these two geometries were manufactured with a 5-axis milling machine controlled by CAM software. A metrological study showed that manufacturing by a 5-axis milling machine can be an alternative to conventional cutting methods.

The aim of the present paper is to validate the numerical model. To reach this goal, a test bench was designed to measure the loaded transmission error and visualize the contact patterns. The test bench is integrated inside a numerical 3-axis milling machine: the pinion is mounted on the spindle, while the base of the bench is clamped on its plate. Thus assembly errors can be imposed easily and accurately. Measured and simulated transmission errors are then compared for different axis misalignments cases.

Commentary by Dr. Valentin Fuster
2015;():V010T11A037. doi:10.1115/DETC2015-47424.

One key component of powertrains is gears which are used in a continuously increasing quantity with improving quality. A productive process for finishing gears is the generating gear grinding process. The process is used mainly for large-batch production of small or mid-size gears after case hardening, especially in the automotive sector.

Currently, the knowledge regarding the generating grinding process is limited and research is based mostly on empirical studies. The reasons for this are complex contacting conditions as well as the undetermined interactions between various process parameters.

This paper focusses on current questions about generating gear grinding such as new approaches for a simulation based process design in consideration of cutting forces as well as the changing contact conditions.

Topics: Grinding , Gears , Cutting
Commentary by Dr. Valentin Fuster

ASME 2015 Power Transmission and Gearing Conference: Gearbox Design, Reliability, and Diagnostics

2015;():V010T11A038. doi:10.1115/DETC2015-46245.

Wolfrom planetary gear (WPG), James Ferguson planetary gear (JFPG) and plus-planetary gear (PPG), feature high speed ratios and a low number of gears, but their efficiency is low and their performance is sensitive to manufacturing errors. In this paper, low-loss gears are used to improve the efficiency of these high-speed-ratio planetary gear transmissions. The methods to achieve the low-loss gears are optimizing modification coefficients and addendum coefficients simultaneously in order to equalize approach-contact ratio and recess-contact ratio. Besides, the sensitivity of the load sharing performance to manufacturing errors is analyzed in the view of load sharing characteristics. A load sharing model, which includes position errors of planet bearings and tooth profile errors of planets, is built up to obtain the load sharing characteristics of WPG, JFPG and PPG. Load sharing performance of WPG, JFPG and PPG with manufacturing errors are analyzed. And effects of load sharing measures are compared.

Commentary by Dr. Valentin Fuster
2015;():V010T11A039. doi:10.1115/DETC2015-46586.

This paper proposes a CAE-based method to predict the maximum load at which bolts start to loosen. The qualitative validity of this method was confirmed using the fastening bolts between the differential case and ring gear.

In general, the differential case and ring gear are fastened with bolts. Therefore, it is essential to estimate the maximum load of bolt loosening when designing these bolts. Moreover, prototypes found that tightening bolts are more likely to loosen as the thickness of the differential case or ring gear decreases and becomes easier to deform. This indicates that the deformation of the differential case and ring gear must be considered in bolt design. However, predicting the maximum load is relatively difficult because the behavior of both the screw and the contact surface between the differential case and ring gear is complicated.

In contrast, recent transmissions require further weight reduction without sacrificing reliability. Consequently, a method of predicting the maximum load of bolt loosening is required.

First, this paper describes a CAE model for estimating the pressure and friction generated at the contact surface between the differential case and ring gear, as well as at the screw surface and bolt seating surface. Furthermore, a method for determining bolt loosening is described that incorporates the pressure and friction on the bolt seating surface into friction circle theory. This method was used to derive the maximum load of bolt loosening. In addition, it was also confirmed that the results qualitatively agree with actual cases of bolt loosening.

Second, this paper identifies the relative sliding of the screw surface and contact surface when the load increases. In this case, it was verified that the sliding on the contact surface between the differential case and ring gear induces relative sliding of the screw, followed by sliding of the bolt bearing surface and loosening of the bolt.

Finally, this paper refers to design guidelines for reducing the weight of the differential case using an experimental design method. Certain ribs cause non-uniform bolt bearing surface pressure distribution, which likely affects bolt loosening.

Through this research, the validity of the method was confirmed and the bolt behavior was clarified when a differential case and ring gear are loaded in one direction. Based on these results, it should be possible to apply this method to more complicated load cases in the future.

Commentary by Dr. Valentin Fuster
2015;():V010T11A040. doi:10.1115/DETC2015-46599.

Vibration monitoring is used to detect a failure in gear systems. An approach in this paper uses Mahalanobis-Taguchi System (MTS) along with vibration monitoring to improve a sensitivity of failure detection. Running tests were conducted by using a power-circulating-type gear test machine. Gear and bearing failures were examined. The Mahalanobis distance was calculated by using measured vibration acceleration data during the running tests. Relations between the Mahalanobis distance and the initiation and propagation of the gear failures or the bearing failures were discussed. The results show that the Mahalanobis distance is an effective indicator of the gear and bearing failures.

Commentary by Dr. Valentin Fuster
2015;():V010T11A041. doi:10.1115/DETC2015-46704.

In order to enrich the synthesis theory of planetary gearbox and meet the needs of multiple gearshifts this paper proposes a comprehensive method for the planetary gear transmission. Based on the topological graph atlas, the kinematic chains of 9-link and 2 degrees of freedom are synthesized. By the topological graph selection principle and gear function diagram transformation principle, 6-speed transmission mechanisms are obtained.

Commentary by Dr. Valentin Fuster
2015;():V010T11A042. doi:10.1115/DETC2015-47175.

The ring gear boundary conditions can have a great influence on the ring-planet mesh stiffness. Two different boundary conditions have been compared in this study using the finite element analysis (FEA) method, namely the full constraint condition and the pin-supported condition. Cracks can cause changes in the gear mesh stiffness and the effect of ring gear crack locations has been analysed under both boundary conditions. Multiple crack locations were chosen and especially in the pin-supported model, where the crack locations were between two pin supports. The same ring-planet mesh stiffness change between the healthy model and the cracked model was observed wherever the crack locations were in the full constraint model. However, different ring-planet mesh stiffness changes were observed when the cracks were implanted to different teeth in the pin-supported model. The highest value was observed when the crack was close to the pin support and the lowest value was observed when the crack was in the middle of two pin supports. These observed changes can provide additional information to help identify the locations of the ring gear cracks in the planetary gear when the mounting method makes use of pin-supports.

Commentary by Dr. Valentin Fuster
2015;():V010T11A043. doi:10.1115/DETC2015-47252.

We developed a method which can diagnose damage on a gear tooth surface by using laser beam without a rotary encoder. This method is as follows: 1) The tooth bottom, the tooth tip and their two medians are detected by the differentials of the laser reflection data. 2) The gear rotation speed is calculated with these four positions, and interpolated according to the rotation fluctuation. 3) By using the calculated gear rotation speed, the measured data can be converted corresponding to the gear rotation angle. Thus we diagnose gear tooth surface damage without being influenced by rotational fluctuation. We did diagnosis experiments and we made contour maps show diagnosis accuracy. From these maps, we got the following conclusions: 1) The accuracy of damage diagnosis is the same level regardless of the presence or absence of a rotary encoder. 2) The cycle of rotational fluctuation hardly affects the accuracy. 3) Bigger fluctuation amplitude makes the range accuracy worse, however the position accuracy improves.

Topics: Laser beams , Gears
Commentary by Dr. Valentin Fuster
2015;():V010T11A044. doi:10.1115/DETC2015-47275.

An experimental study on the overall loaded motion transmission error of planetary gear sets is presented in this study. A test rig is designed and procured for the purpose of measuring the input-to-output transmission error of planetary gear sets within a range of input torque. The test matrix includes three distinct phasing conditions (in phase, sequentially phased and counter-phased) of a four-planet gear set as well as two planet tooth profile modifications. Two different power flow conditions with a fixed planet carrier and a fixed ring gear are considered. The transmission error results indicate that the phasing condition of the gear set is the most critical factor resulting in varying levels and numbers of modulation sidebands around the gear mesh orders. Planetary gear sets having in-phase planet meshes exhibit dominant gear mesh harmonic orders with little sideband activity, while sequentially-phased and counter-phased gear sets show an increase in planetary sideband orders associated with the sun, ring and planet gears. In addition, the power flow condition with fixed carrier is shown to have higher root-mean-square amplitudes of transmission error than configuration with a fixed ring gear.

Commentary by Dr. Valentin Fuster
2015;():V010T11A045. doi:10.1115/DETC2015-47318.

The strong market trend toward lower fuel consumption for heavy road transports requires more frequent gear shifting and increased gear shift performance, i.e. shorter shift time. Increased shift performance means higher loads for the synchronizer which brings component and shifting process optimization more into focus.

Traditionally, synchronizer development has relied on physical testing of complete synchronizers in general gearbox test rigs or in specialized synchronization test rigs leaving much of the causes of the observed effects unclear. This paper presents a generalized FE-based thermomechanical simulation model to be used for model-based synchronizer analysis and design. The model is targeted for studies of how different external loads and the values of different synchronizer design parameters affect the temperature transient in the friction lining. Recommendations of how major modeling complications should be treated are presented. The developed simulation model is verified and validated with a combination of analytical means and transient temperature measurements of bulk and surface temperatures. The applicability of the presented model, as well as its limitations, are discussed and exemplified with different design cases.

Topics: Simulation , Design , Trucks
Commentary by Dr. Valentin Fuster
2015;():V010T11A046. doi:10.1115/DETC2015-47470.

Planet-to-planet load sharing is a major design and manufacturing tolerancing issue in planetary gear sets. Planetary gear sets are advantageous over their countershaft alternatives in many aspects, provided that each planet branch carries a reasonable, preferably equal, share of the torque transmitted. In practice, the load shared among the planets is typically not equal due to the presence of various manufacturing errors. This study aims at enhancing the models for planet load sharing through a three-dimensional formulation of N-planet helical planetary gear sets. Apart from previous models, the proposed model employs a gear mesh load distribution model to capture load and time dependency of the gear meshes iteratively. It includes all three types of manufacturing errors, namely constant errors such as planet pinhole position errors and pinhole diameter errors, constant but assembly dependent errors such as nominal planet tooth thickness errors, planet bore diameter errors, and rotation and assembly dependent errors such as gear eccentricities and run-outs. At the end, the model is used to show combined influence of these errors on planet load sharing to aid designers on how to account for manufacturing tolerances in the design of the gears of a planetary gear set.

Commentary by Dr. Valentin Fuster

ASME 2015 Power Transmission and Gearing Conference: Lubrication and Efficiency

2015;():V010T11A047. doi:10.1115/DETC2015-46034.

This study proposes a formulation for the description of the gear mesh mechanical power loss under the thermal tribodynamic condition. A six degree-of-freedom motion equation set that models the vibratory motions of a general spur gear pair is coupled with the governing equations for the description of the gear thermal mixed elastohydrodynamic lubrication to include the interactions between the gear dynamics and gear tribology disciplines in the modeling of the gear mesh mechanical power loss. The important role of the gear thermal tribo-dynamics in power loss is demonstrated by comparing the predictions of the proposed model to those under the thermal quasi-static condition, and the iso-thermal tribo-dynamic condition, respectively.

Topics: Spur gears
Commentary by Dr. Valentin Fuster
2015;():V010T11A048. doi:10.1115/DETC2015-46549.

In a previous study, we analyzed the mechanical loss factors of a small-sized geared motor comprising an induction motor and a parallel gear reducer. The load dependent loss is mainly caused by gear mesh friction, which is related to grease characteristics.

This study investigates how the grease characteristics influence the friction loss of the gear mesh. The important grease characteristics are the cone penetration, kinematic viscosity, type of base oil, and type of thickener.

The loss of gear mesh friction was evaluated in terms of the average friction coefficient between the gear teeth and was found to be unrelated to the cone penetration and kinematic viscosity of the base oil. The average friction coefficient of grease combined with lithium soap/poly urea and mineral base oil was 0.09–0.11; when combined with aluminum complex soap and synthetic base oil, the friction coefficient reduced to 0.07–0.08.

Topics: Friction , Gears
Commentary by Dr. Valentin Fuster
2015;():V010T11A049. doi:10.1115/DETC2015-46730.

The lubrication performances of cycloid drives affect the dynamic characteristics, the mechanical efficiency and the contact fatigue behavior of the system. To maintain tranmission precision it is required to minimum the times of disassebly, hence grease lubrication is often applied where starvation might occur in service. Starved lubrication performance of a cycloid gear drive is studied using a numerical finte line starved-elastohydrodynamic lubrication model. The parameter of the inlet oil film thickness is chosen to represent the starved status. Effects of the inlet film thickness on the centralfilm thickness, the friction coefficient and the frictional power loss are investigated. In addition, effects of different shape of inlet oil-supply layer in the same starved degree on lubrication performance are studied. Under the same inlet oil supply volume, the convex type profile would present a better oil film within the nominal contact zone compared with other four different shapes of the inlet film supply.

Topics: Lubrication , Shapes
Commentary by Dr. Valentin Fuster
2015;():V010T11A050. doi:10.1115/DETC2015-47257.

Reducing windage loss can be achieved by vacuuming the gear box. This study examines the possibility of implementing a gear pump characteristic with a working helical gear pair inside the gear box itself. An air-tight gear box is constructed and its vacuuming ability, windage loss, and temperature rise in speed range up to 60 m/s are investigated. The vacuuming ability is satisfactory, as it can reduce the pressure to less than 0.02 MPa (absolute), but large heat is generated by adiabatic compression associated with the temperature elevation of about 200°C. This presents excess loss and is due to the pressure difference before and after mesh engagement. Since this loss is proportional to the speed, further higher-speed condition will make total loss smaller than the expected windage loss which is proportional to the third power of the speed. In addition, this self-vacuuming ability can be improved with the assistance of a small vacuum pump to maintain the interior pressure at the beginning of engagement as small as possible. Finally, the feasibility of lubricant feeding is also examined.

Commentary by Dr. Valentin Fuster
2015;():V010T11A051. doi:10.1115/DETC2015-47344.

A computational methodology is proposed for prediction of power losses due to pocketing (pumping or squeezing) of oil at the mesh interface of spiral bevel gears. The model employs an existing cutting simulation procedure to define surface geometries of the gears through face-milling and face-hobbing processes. A novel hypoidal discretization method is proposed to define pocket volumes between meshing gear teeth along circumferential and face width directions. An existing fluid mechanics formulation, utilizing principles of conservation of mass, momentum and energy, is used to compute the load-independent (spin) power losses due to pocketing of the medium in the gear mesh interface. A simulation of aerospace applications is presented to highlight the effects of lubrication conditions, on pocketing power losses.

Commentary by Dr. Valentin Fuster

ASME 2015 Power Transmission and Gearing Conference: Transmission Systems Including Novel Concepts

2015;():V010T11A052. doi:10.1115/DETC2015-46414.

The requirements for general aero-engines are becoming increasingly severe to achieve higher efficiency and lower emission. The Open Rotor Engine is one of the next-generation aero-engine concepts expected to satisfy these requirements. The Open Rotor Engine has a set of counter-rotating unducted fans to increase the propulsion efficiency. A 20,000 hp class differential planetary gear system is suitable for driving these counter-rotating fans. To realize a 20,000 hp class differential planetary gear system, there are some design challenges to be accomplished 1) large power (20,000 hp class), 2) sufficiently small and light to fit an engine (envelope), 3) high transmission efficiency over 99.5%, 4) precise misalignment control for gears and bearings, 5) high reliability (50,000 hour MTBF). At Kawasaki Heavy Industries, Ltd., development of the Open Rotor Power Gearbox started in 2007. The purpose of this development is to establish a design practice for the 20,000 hp class gear system and to demonstrate that its readiness level (TRL) is appropriate for whole-engine development. In this development, various state-of-the-art simulation technologies such as lube oil flow CFD, FEA, and tooth contact analysis were fully utilized to optimize the design. Details of the design, fabrication, and validation tests of a full-scale prototype up to 2012 were presented at the IDTC/CIE in 2013. This paper presents a summary of the previous activity and subsequent works and achievements as a final report.

Commentary by Dr. Valentin Fuster
2015;():V010T11A053. doi:10.1115/DETC2015-46739.

Current research suggests that the performance of electric vehicle with a single-speed transmission can still be widely improved. The novel two-speed uninterrupted transmission consists of a single-row planetary, a centrifugal clutch, a brake, and two motor controlling clutch and brake. Changing the switch of clutch and brake can achieve two-speed uninterrupted gearshifts. Different from the traditional centrifugal clutch, a novel adjustable device is specifically designed to control the switch of clutch. Torque characteristics of clutch prototype are displayed. Some differences of the gearshift methodology are specifically designed to compensate for the characteristics of the electric traction motor and the adjustable centrifugal clutch. The specific simulation model is established according to the novel uninterrupted transmission prototype. The dynamic characteristics of the two-speed uninterrupted transmission system are analyzed. The higher utilization ratio of the traction motor power increases the efficiency of the traction motor with the novel two-speed uninterrupted transmission.

Commentary by Dr. Valentin Fuster
2015;():V010T11A054. doi:10.1115/DETC2015-46773.

Manual transmissions for passenger cars and trucks are equipped with synchronizer mechanisms. A synchronizer mechanism as a key component of a transmission system must be able to prevent transmission gears from shocking, reduce the noise and it has a great impact on driving comfort and transmission efficiency. Gear shifting improvement with respect to smooth, quick and energy efficient synchronizer’s performance is still an important issue for automotive industry.

A synchronization process comprises several phases within which presynchronization, main synchronization, pre-engagement and engagement phases can be recognized. Aiming an understanding of internal dynamics and existing possibilities for optimization of synchronization processes in transmission systems during the main synchronization phase an engineering model of a generic synchronizer mechanism is proposed. The synchronizer mechanism is modeled by a contacting triple-body system consisting of the selector sleeve, the blocker ring and the gearwheel. The algorithm has developed to solve the direct dynamics synchronization problem for the generic synchronizer mechanism. By using the developed algorithm the rotational motion of the contacting triple-body system and the synchronizing torques between contacting interfaces are determined for given vehicle resistance torque, the drag torque, and the control torque applied to the selector sleeve that all together satisfy the equations of motion and guarantee synchronization of the rotational speeds of the sleeve, the blocker ring and the gearwheel for the final time. It is shown that the solution to the direct dynamics synchronization problem for the generic synchronizer mechanism is not unique and it allows formulation different optimization problems.

Mathematical statement of multi-objective Pareto optimal control problem for synchronizer mechanism is given. Within the proposed model of the generic synchronizer mechanism the time-comfort Pareto optimal control problem is considered. Assuming that the resistance torque on the synchronizer owing to the vehicle inertia, the drag torque, and the synchronizing torques at the contacting interfaces are substantially constant during the main phase of a synchronization process, the solution to the time-comfort Pareto optimal control problem has been obtained.

It was shown that there exist the external control torque (or shift force) applied to the selector sleeve such that the synchronization of rotational speeds of the sleeve, the blocker ring and the gearwheel is guaranteed and the synchronization process is optimal both with respect to minimal possible synchronization time as well as lowest possible inertial load acting on the synchronizer mechanism. Analysis of the obtained Pareto solution is presented.

Commentary by Dr. Valentin Fuster
2015;():V010T11A055. doi:10.1115/DETC2015-46782.

Race cars are known for their brilliant acceleration as well as cornering performance. This requires optimization of each and every component of the car to shed every ounce of extra weight while maximizing the performance. This paper focuses on optimization of the powertrain of a Formula Student electric vehicle. The electric vehicle in question is a Formula style rear-wheel driven electric single person race car. The rear wheel drive is achieved with separate motors for each wheel controlled by electronic differential. Extensive research has been done in the area of gear design and several standards have been set. This paper follows the AGMA 2001-D04 standard as given in Shigley’s Mechanical Engineering Design [4]. A planetary gearbox was developed for a Formula Student vehicle with permanent magnet DC motor by Bakshi[2] et al. This paper tries to optimize the planetary gearbox and considers other suitable designs.

Commentary by Dr. Valentin Fuster
2015;():V010T11A056. doi:10.1115/DETC2015-46812.

There exists the potential for major simplifications to current hybrid transmission architectures, which can lead to advances in powertrain performance. This paper assesses the technical merits of various hybrid powertrains in the context of high-performance vehicles and introduces a new transmission concept targeted at high performance hybrid applications. While many hybrid transmission configurations have been developed and implemented in mainstream and even luxury vehicles, ultra high performance sports cars have only recently begun to hybridize. The unique performance requirements of such vehicles place novel constraints on their transmissions designs. The goals become less about improved efficiency and smoothness and more centered on weight reduction, complexity reduction, and performance improvement. To identify the most critical aspects of a high performance transmission, a wide range of existing technologies is studied in concert with basic physical performance analysis of electrical motors and an internal combustion engine. The new transmission concepts presented here emphasize a reduction in inertial, frictional, and mechanical losses. A series of conceptual powertrain designs are evaluated against the goals of reducing mechanical complexity and maintaining functionality. The major innovation in these concepts is the elimination of a friction clutch to engage and disengage gears. Instead, the design proposes that the inclusion of a large electric motor enables the gears to be speed-matched and torque-zeroed without the inherent losses associated with a friction clutch. Additionally, these transmission concepts explore the merits of multiple electric motors and their placement as well as the reduction in synchronization interfaces. Ultimately, two strategies for speed-matched gear sets are considered, and a speed-matching prototype of the chosen methodology is presented to validate the feasibility of the proposed concept. The power flow and operational modes of both transmission architectures are studied to ensure required functionality and identify further areas of optimization. While there are still many unanswered questions about this concept, this paper introduces the base analysis and proof of concept for a technology that has great potential to advance hybrid vehicles at all levels.

Topics: Design , Vehicles
Commentary by Dr. Valentin Fuster
2015;():V010T11A057. doi:10.1115/DETC2015-47096.

The paper describes the results of design and production of new generation valve drives for oil and gas machinery. The drives are based on the use of pan precess gear. The gear has a high performance coefficient (88…90%), smooth operation, low starting torque and ability to remain functioning even under severe conditions of operation. Basic dependencies for geometric calculation of the gear are showed. The problem of synthesizing geometric parameters of the gear as well as calculating parameters and settings of tools (circular cutting heads) and gear-cutting machines has been solved. The results of synthesizing the gear geometric parameters according to the size and shape of the contact pattern are showed. Methods of calculating pan precess gear loading have been developed considering multiple contact of teeth in meshing. The manufactured drives for valves and reduction valves used in progressive cavity pumps for heavy oil production are presented.

Topics: Machinery , Design , Gears
Commentary by Dr. Valentin Fuster

23rd Reliability, Stress Analysis, and Failure Prevention Conference: Design Methods and Analyses

2015;():V010T12A001. doi:10.1115/DETC2015-46568.

To solve the problem that there are many factors influencing the reliability allocation of feed mixers, and some of which are difficult to analyze quantitatively, a comprehensive reliability allocation method is researched using triangular fuzzy number, fuzzy synthetic assessment and analytic hierarchy process. In this paper, a reliability allocation model is proposed for feed mixers, which considered several influence factors, and used triangular fuzzy number instead of real number to express uncertain information. It could make use of the reliability test information and experts’ experience comprehensively. Finally, the application of this method is illustrated with an example, and the result showed that the allocation method is feasible and effective for the reliability allocation of feed mixers.

Topics: Reliability
Commentary by Dr. Valentin Fuster
2015;():V010T12A002. doi:10.1115/DETC2015-46664.

In Reliability based Multidisciplinary Design and Optimization (RBMDO), saddlepoint approximation has been utilized to improve reliability evaluation accuracy while sustaining high efficiency. However, it requires that not only involved random variables should be tractable; but also a saddlepoint can be obtained easily by solving the so-called saddlepoint equation. In practical engineering, a random variable may be intractable; or it is difficult to solve a highly nonlinear saddlepoint equation with complicated Cumulant Generating Function (CGF). To deal with these challenges, an efficient RBMDO method using Third-Moment Saddlepoint Approximation (TMSA) is proposed in this study. TMSA can construct a concise CGF using the first three statistical moments of a limit state function easily, and then express the probability density function and cumulative distribution function of the limit state function approximately using this concise CGF. To further improve the efficiency of RBMDO, a sequential optimization and reliability analysis strategy is also utilized and a formula of RBMDO using TMSA within the framework of SORA is proposed. Two examples are given to show the effectiveness of the proposed method.

Commentary by Dr. Valentin Fuster
2015;():V010T12A003. doi:10.1115/DETC2015-46689.

In order to increase the accuracy of surrogate models in structural reliability analysis, we put forward a kind of surrogate model based on local radial point interpolation method (LRPIM). Three kinds of radial basis function (RBF) are employed for the shape function construction to form different kinds of LRPIM model.

In order to illustrate the approximating ability of each surrogate model, we build up a nonlinear function model and carry out a numerical experiment on gas turbine disk’s estimated life-span. Compared with polynomial model, Chebyshev orthogonal polynomial model, Kriging model and RBF neural network model, LRPIM model has a demonstrable difference in terms of accuracy. For different polynomial basis order with constant sampling nodes amount, we conclude that fluctuant accuracy can be described by the balance between the describing improvement brought by polynomial basis order increase and the local impairment brought by support domain expansion. For sampling nodes amount with constant polynomial basis order, we conclude that accuracy of LRPIM model improves when sampling nodes amount increases.

In order to illustrate the potential in reliability analysis, we apply the best performing LRPIM model to a set of widely used test problems, which certifies the accuracy and robustness of this kind of surrogate model.

In a word, LRPIM model is one of the most promising surrogate models compared with other models on nonlinear approximating problems and reliability analysis.

Topics: Interpolation
Commentary by Dr. Valentin Fuster
2015;():V010T12A004. doi:10.1115/DETC2015-47113.

Service-life is a widely used reliability index in reliability engineering. For a complex dynamic system for which whole system tests are limited, and there is insufficient information to determine the distribution function of reliability models. Fortunately, the boundaries of lifetime variable can be obtained, which can be incorporated through the theory of interval uncertainty. In this study, a service-life assessment method for complex dynamic systems under interval uncertainty is introduced based on Bayesian networks (BN). Firstly, a dynamic fault tree (DFT) model is built for a system. Based on the comprehensive integration of test data, field data, design data and engineering experience, the lifetime of system units are expressed as interval numbers. Then, a coefficient of variation (COV) method is employed to determine the parameters of life distributions. Finally, the BN method is used to estimate the mean life of the example system, and the service-life of this system is assessed as well. The presented method can be easily used in engineering practice for service-life evaluation of complex dynamic systems under interval uncertainty, where lifetime data is limited.

Commentary by Dr. Valentin Fuster
2015;():V010T12A005. doi:10.1115/DETC2015-47183.

Bayesian approaches have been demonstrated as effective methods for reliability analysis of complex systems with small-amount data, which integrate prior information and sample data using Bayes’ theorem. However, there is an assumption that precise prior probability distributions are available for unknown parameters, yet these prior distributions are sometimes unavailable in practical engineering. A possible way to avoiding this assumption is to generalize Bayesian reliability analysis approach by using imprecise probability theory. In this paper, we adopt a set of imprecise Dirichlet distributions as priors to quantify uncertainty of unknown parameters and extend traditional Bayesian reliability analysis approach by introducing an imprecise Dirichlet model (IDM). When the prior information is rare, the result of imprecise Bayesian analysis method is too rough to support engineering decision-making, so we proposed an optimization model to reduce the imprecision of the new method. Spindles are crucial for machine tools and reliability data related to spindles of new-developed machine tools are often rare. We can then use the imprecise Bayesian reliability analysis method to assess its reliability. In this paper, we mainly investigate the reliability assessment of a motorized spindle to illustrate the effectiveness of the proposed method.

Commentary by Dr. Valentin Fuster

23rd Reliability, Stress Analysis, and Failure Prevention Conference: Fatigue and Failure Prevention and Analyses

2015;():V010T12A006. doi:10.1115/DETC2015-46953.

In the case of variable amplitude loading, fatigue damage accumulation theory is closely related to loading histories, such as load sequences, load interactions, and so on. Due to the lack of load histories, there may be a large deviation with the reality for linear damage rule (Miner rule). Although many non-linear fatigue damage accumulation models can deal with the effect of load sequences, load interaction effect cannot be ignored and it plays an important role in damage accumulation behavior. This paper describes the damage evolution behavior based on nonlinear damage rule under variable amplitude loading. A new method to describe the load interaction effects is proposed, it is assumed that the load ratio between adjacent stress levels is used to present this phenomenon. Thereafter, the method is introduced to a non-linear damage model, and a modified model is developed to predict the residual lifetime. Four categories of experimental data sets from literatures are employed to investigate the validity of the proposed model. The results indicate that the modified model shows a good agreement between experimental data and theoretical results. It is also found that the modified model demonstrates an improvement in prediction accuracy over the primary model and Miner rule. Furthermore, the modified model can be easily implemented with the use of Wöhler curve only.

Commentary by Dr. Valentin Fuster
2015;():V010T12A007. doi:10.1115/DETC2015-47915.

In this paper, fatigue life assessment of a tensioner is studied through dynamic load analysis, stress analysis, and stress-life fatigue analysis approach. Tensioner is a critical part of an automotive front end accessory drive system, providing pre-tension to the belt. The front end accessory drive systems are responsible for transmitting power from the crankshaft to the accessory components. Due to the engine pulsation, components of the accessory drive including the tensioner are subjected to dynamic loads leading to fatigue failure. The fatigue life assessment of a mechanical component highly depends on loading, geometry, and material properties. In addition, the dynamic behavior of the front end accessory drive is complicated due to coupling between several modes of vibrations in belt, pulleys, and the tensioner arm. Duo to the complexity of the parameters involved and complicated dynamics, the fatigue life analysis of FEAD components is a challenging task. This paper includes three main parts, namely stress analysis, fatigue properties prediction, and life estimation. The dynamic analysis of a generic front end accessory drive system is performed in order to obtain effective loads on the tensioner. Stress state for the tensioner in case of different applied loading conditions is performed via a series of Finite Element (FE) analyses, and the critical region of the part is determined. Finally, fatigue life is estimated through strain-life approach. Modest work has been found in this area providing a comprehensive solution to the fatigue life investigation of power train components. The present study offers a comprehensive modeling approach which predicts the automative tensioner lifetime. The lifetime of any FEAD system components can be determined using the developed fatigue life prediction approach.

Topics: Fatigue life
Commentary by Dr. Valentin Fuster
2015;():V010T12A008. doi:10.1115/DETC2015-47961.

Welded joints are usually the weakest link for welded structures due to the existence of stress concentration caused from welding. Fracture mechanics-based approach is a main method used to predict fatigue life for welded joints structures. In engineering, there are two main problems in fatigue life prediction, one is whether crack initiation life can be ignored or not, and the other one is to determine the crack size starting to propagate. Based on this research, a practical procedure is proposed to predict fatigue life of welded joints structures using an initial crack life model and Paris law. Emphasis is put on the discussion about crack initiation life and how to choose an appropriate method to determine the initial crack size. Noted that the proposed method in this paper does not need any tests to determine crack initiation life when crack size reaches a specified value, which depends on experience and is considered as crack size starting to propagate, thus human factors and uncertainty can be minished. Through comparison analysis, fatigue life predictions based on the proposed method are in a good agreement with experimental data.

Commentary by Dr. Valentin Fuster
2015;():V010T12A009. doi:10.1115/DETC2015-48076.

The fatigue and fracture of gears in Power Split Device (PSD) can be sensitive to stochastic load which is often difficult to be measured and predicted. Due to the load randomness associated with the mode-switch in a hybrid car, non-parametric extrapolation (NPE) method can be applied in the load spectrum compiling of PSD. In this paper, a kernel selection method based on the multiple-criteria decision making method (MCDM) was presented to improve the accuracy of the kernel density estimation. According to the dynamic and contact analysis of gears, a short-term bending stress spectrum was calculated to provide the reference for the fatigue design. Based on the NPE method considering the kernel selection, a whole-life load spectrum was compiled to supply the input data for the fatigue life test of PSD.

Topics: Stress , Gears
Commentary by Dr. Valentin Fuster

23rd Reliability, Stress Analysis, and Failure Prevention Conference: Material Considerations for Design and Failure Prevention

2015;():V010T12A010. doi:10.1115/DETC2015-46042.

By identifying well-known failures in pistons, uniquely on skirt area where overlapping with cylinder mainly occurs and causing pistons to fail are investigated. Hence, aim of this paper is to compare two different pistons by analyzing their temperature and stress/strain distributions on specific areas, specifically crown and skirt. By considering the unique properties of carbon, mainly the low coefficient of thermal expansion, density and toughness; expectations in carbon/carbon pistons seemed highly promising compared to conventionally used aluminum pistons. Furthermore, necessary analyses are made by a finite element software package, AbaQus. It is observed that the usage of carbon/carbon composite as a material for pistons shows a high thermal durability which is crucial for necessary cooling stage than aluminum due to its low thermal conductivity property. It is also shown that compared to aluminum, carbon/carbon pistons are 30% lighter in weight, more resistible to mechanical loadings such being pressure, inertial loadings, side forces, and thermal effects. Carbon/carbon composite piston’s tolerance to higher Von Mises stresses around 489 MPa and temperatures up to 664 °C shows a clear superiority when compared to aluminum. Carbon/carbon composite pistons are also much more relevant to be used in an engine for weight reduction and increasing clearance tolerance down to 0.01 mm between the piston and cylinder liner which indirectly reduces the mass of components and directly reduces side forces by a longer connecting rod usage allowance.

Commentary by Dr. Valentin Fuster
2015;():V010T12A011. doi:10.1115/DETC2015-46248.

To maintain the integrity of corroded oil and gas pipelines, the reliability at times of exposure over the lifecycle duration need to be understood. This paper describes the procedures for predicting the performance of internally corroded oil and gas pipelines using a probabilistic-based Markovian process. The Pipeline Corrosivity Index (PCI), which is expressed as a function of the retained pipe-wall thickness was used to describe the condition of the corroded pipelines at exposure durations for low, moderate, high and severe corrosion rates. The time variation of the predicted Pipeline Corrosivity Index (PCI) was compared with field measured Pipeline Corrosivity Indexes (PCIs) of corroded API X52 grade pipelines and the results indicate that the model developed in this research is viable for integrated management of aged corroded pipelines and remaining useful life predictions.

Commentary by Dr. Valentin Fuster
2015;():V010T12A012. doi:10.1115/DETC2015-48059.

In this study, composites of polypropylene (PP), as well as linear low density polyethylene (LLDPE) thermoplastics filled with wood flour have been investigated to study the effect of size and amount of wood flour on their mechanical, thermal and aging properties. PP and LLDPE were mixed with five different types of wood flour, i.e., cedar, maple, oak, poplar, and select pine, by adding different percentages of wood flour at 30, 40 and 50 weight percentages. Mixing was done using a mini compounder at 180–210°C and dog-bone shape samples were produced by using a mini-injection molding machine. Two different sizes of wood flour labeled as thin (425–500 μm) and thick (600–710 μm) were compared for PP-wood and LLDPE-wood composites. Mechanical properties of blends were investigated by tensile testing and thermal behaviors of blends were characterized by using DSC analyses. Poplar and maple show better tensile results among other wood types with 543.7 MPa and 600.5 MPa Young’s modulus and 21.05 MPa and 24.53 MPa tensile strength for LLDPE when comparing thick and thin wood flour blends, respectively. In the case of PP; poplar and select pine gave higher Young’s modulus and tensile strength results. Samples were also aged in acid and water solution for 3 days, and their weight and dimensional changes were recorded and compared with neat polymer samples to show physical stability.

Commentary by Dr. Valentin Fuster

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