Gear Tooth Contact Research Articles

Method of spiral bevel gear tooth contact analysis performed in CAD environment

Purpose – The purpose of this paper is to present the use of a CAD system for the analysis of meshing of spiral bevel gears. Design/methodology/approach – The TCA computer programs are based on a purely mathematical model and require to get the numerical solution of a set of nonlinear equations. There are situations that the programs fail to obtain the proper solution. In such cases, geometrical gear models defined in CAD environment prove to be a good choice. This paper describes a tool for analyzing tooth contact and transmission errors of spiral bevel gear sets with tooth flanks represented as CAD free-form surfaces. Findings – A new method has been proposed to keep those surfaces in continuous contact in the whole range of meshing of a mating tooth pair. During meshing, the points of contact as well as the corresponding angles of rotation of both the pinion and the ring gear are recorded. Thus, the tooth contact path as well as the motion transmission error graph is determined. Then, the contact pattern that is formed by a set of instantaneous contact ellipses is designated. Practical implications – The TCA results are essential for the assessment of the gear set quality in the early stages of the process of its development. Originality/value – All the results presented in graphical form are very illustrative and easy to interpret.

Tooth contact analysis for helical gear pairs generated by a modified hob with variable tooth thickness

Conventionally, the longitudinal crowning of helical gears can be accomplished by varying the center distance between the hob and work gear in gear hobbing process. Without a crossed angle compensation, however, this center distance variation produces twisted tooth flanks on the work gear. A methodology is thus proposed herein to reduce the tooth flank twisting of a longitudinal crowning gear by applying a modified variable tooth thickness hob and having a diagonal feed without varying the center distance. This study also investigates the gear tooth surface topologies, contact ellipses and transmission errors of the work gear pairs, generated by a conventional hob and the proposed modified hob with variable tooth thickness, respectively. Three numeral examples are presented to illustrate and verify the merits of the proposed gear hobbing method with longitudinal crowning.

The Stress Analysis on Spur Gear Meshing Simulation

The gear meshing is a very complicated process due to the nonlinear behaviors during the teeth contact. It is necessary to build a reliable model to simulate gear meshing process which can consider geometry and boundary conditions nonlinear behavior in gear tooth contact analysis. This paper propose a 3D finite element model to simulate the meshing process of a pair of spur gears, and then carry out the gear tooth contact analysis with the consideration of nonlinear behaviors. The results and relevant discussions will indicate and explain some significant phenomena of the gear tooth contact characteristics in gear meshing process.

Neural network model for condition monitoring of wear and film thickness in a gearbox

Mechanical gears are used to transmit power and motion in mechanical, electrical and chemical process industries. Influenced by vibration, torque, temperature, lubrication and specific film thickness, the gear teeth contacts may experience change leading to unexpected failures such as wear, scuffing, pitting and micro-pitting on teeth surface. In order to avoid these damages, continuous monitoring is essential using knowledge-based systems. Generic capability of artificial neural network is exploited to formulate prediction and classification based on heuristic models of condition of lubricating oil in spur gears. Based on the loading conditions such as vibration, temperature and torque, the algorithm predicts film thickness to classify oil conditions as elasto-hydrodynamic, mixed wear and severe wear that helps in finding faults during operation of gears.

Application of discrete wavelet transform and Zhao-Atlas-Marks transforms in non stationary gear fault diagnosis

Gears are one of the most common mechanisms for transmitting power and motion.Studies on gear teeth contacts have been considered as one of the most complicated applications. Depending on the application, the speed and load conditions of teeth may cause several types of failures on teeth surface which leads to non stationary operating conditions. This paper is attempt to analyze the effectiveness of the new time-frequency distributions called the Zhao-Atlas-Marks (ZAM) distribution to enhance non stationary signal analysis for fault diagnosis in spur gears. Also the performance of ZAM with other methods like short term fourier transform (STFT) and discrete wavelet transform (DWT) is discussed in this paper.

Frictional Effects on Gear Tooth Contact Analysis

The present paper concentrates on the investigations regarding the situations of frictional shear stress of gear teeth and the relevant frictional effects on bending stresses and transmission error in gear meshing. Sliding friction is one of the major reasons causing gear failure and vibration; the adequate consideration of frictional effects is essential for understanding gear contact behavior accurately. An analysis of tooth frictional effect on gear performance in spur gear is presented using finite element method. Nonlinear finite element model for gear tooth contact with rolling/sliding is then developed. The contact zones for multiple tooth pairs are identified and the associated integration situation is derived. The illustrated bending stress and transmission error results with static and dynamic boundary conditions indicate the significant effects due to the sliding friction between the surfaces of contacted gear teeth, and the friction effect can not be ignored. To understand the particular static and dynamic frictional effects on gear tooth contact analysis, some significant phenomena of gained results will also be discussed. The potentially significant contribution of tooth frictional shear stress is presented, particularly in the case of gear tooth contact analysis with both static and dynamic boundary conditions.

Prediction of wind turbine gear micropitting under variable load and speed conditions using ISO/TR 15144-1: 2010

Wind turbine gearbox operates under a wide array of highly fluctuating and dynamic load conditions caused by the stochastic nature of wind and operational wind turbine controls. Micropitting damage is one of failure modes commonly observed in wind turbine gearboxes. This article investigates gear micropitting of high-speed stage gears of a wind turbine gearbox operating under nominal and varying load and speed conditions. Based on the ISO standard of gear micropitting (ISO/TR 15144-1:2010) and considering the operating load and speed conditions, a theoretical study is carried out to assess the risk of gear micropitting by determining the contact stress, sliding parameter, local contact temperature and lubricant film thickness along the line of action of gear tooth contact. The non-uniform distributions of temperature and lubricant film thickness over the tooth flank are observed due to the conditions of torque and rotational speed variations and sliding contact along the gear tooth flanks. The lubricant film thickness varies along the tooth flank and is at the lowest when the tip of the driving gear engages with the root of the driven gear. The lubricant film thickness increases with the increase of rotational speed and decreases as torque and sliding increase. It can be concluded that micropitting is most likely to initiate at the addendum of driving gear and the dedendum of driven gear. The lowest film thickness occurs when the torque is high and the rotational speed is at the lowest which may cause direct tooth surface contact. At the low-torque condition, the varying rotational speed condition may cause a considerable variation of lubricant film thickness thus interrupting the lubrication which may result in micropitting.

Analysis of Micro-Elastohydrodynamic Lubrication and Prediction of Surface Fatigue Damage in Micropitting Tests on Helical Gears

The paper describes results obtained from the micro-elastohydrodynamic lubrication (micro-EHL) modeling of the gear tooth contacts used in micropitting tests together with a contact fatigue and damage accumulation analysis of the surfaces involved. Tooth surface profiles were acquired from pairs of helical test gears and micro-EHL simulations were performed corresponding to surfaces that actually came into contact during the meshing cycle. Plane strain fatigue and damage accumulation analysis shows that the predicted damage is concentrated close to the tooth surfaces and this supports the view that micropitting arises from fatigue at the asperity contact level. A comparison of the micropitting performance of gears finish-ground by two alternative processes (generation-grinding and form-grinding) suggests that 3D “waviness” may be an important factor in explaining their different micropitting behavior.

Time domain-based gear contact fatigue analysis of a wind turbine drivetrain under dynamic conditions

This paper presents a general approach to predict the contact fatigue life of the gears in the drive-train system of a wind turbine under dynamic conditions. A simplified predictive pitting model that estimates service lives is presented and validated by comparisons with published experimental evidence. Finally, the predictive model is used to estimate the contact fatigue lives of the sun gear and planetary gears in the drive-train system of the National Renewable Energy Laboratory’s 750kW land-based wind turbine based on time domain simulations. The occurrence frequencies of different wind speeds are described by the generalized gamma distribution. The time series of the torques in the main shaft are obtained from a global dynamic response analysis of the wind turbine. The time series of the gear contact forces is obtained from a dynamic analysis of the gearbox using multi-body simulation. The two-parameter Weibull distribution, the three-parameter Weibull distribution, and the generalized-gamma distribution are used to fit the long-term probabilistic distribution of the gear tooth contact pressures. The case study shows the validity of the approach presented in this paper.

Enhanced model of load distribution along the line of contact for non-standard involute external gears

The presence of undercut at the tooth root, non-equal addendum on pinion and wheel, non-standard tooth height or non-standard center distance may have decisive influence on the load distribution along the line of contact of spur and helical gear teeth. The curve of variation of the meshing stiffness along the path of contact, quite symmetric respect the midpoint of the interval of contact, loses its symmetry for non-standard geometries and operating conditions. As a consequence, the critical contact points for bending and wear calculations may be shifted from their locations for standard gears. In this paper, a non-uniform model of load distribution along the line of contact of standard spur and helical gears, obtained from the minimum elastic potential criterion, has been enhanced to fit with the meshing conditions of the above mentioned non-standard cylindrical gear pairs. The same analytical formulation of the initial model may be used for the non-standard gears by considering appropriate values of a virtual contact ratio, which are also presented in the paper.

Modelling of elastohydrodynamic lubrication and fatigue of rough surfaces: The effect of lambda ratio

The article describes a numerical model for the analysis of elastohydrodynamic lubrication under conditions in which the nominal lubricant film thickness is small compared to the roughness present on the surfaces (lambda ratio less than unity). These conditions occur in most types of gear tooth contacts and in many other heavily loaded machine elements. In these situations, lubrication occurs at the roughness asperity level (micro-elastohydrodynamic lubrication), and in extreme cases ‘mixed’ lubrication behaviour occurs in which momentary solid contacts between the surfaces take place. In both micro-elastohydrodynamic lubrication and mixed lubrication regimes high, localised pressures are applied cyclically to asperity features as they move through the nominal contact leading to fatigue at the asperity level, which culminates in micropitting wear. Results of the modelling show the effect of lambda ratio in lubricated gear tooth contacts, and demonstrate the transition from full-film to micro-elastohydrodynamic lubrication and mixed lubrication, and the consequences in terms of predicted fatigue damage.

An investigation of tooth mesh nonlinearity and partial contact loss in gear pairs using a lumped-parameter model

A three-dimensional lumped-parameter model for a pair of helical gears is developed and shown to be equivalent to an arbitrary tooth contact force distribution. The nonlinearity of the gear mesh is due to portions of gear teeth contact lines losing contact (partial contact loss). The lumped-parameter model accounts for the net force and moment arising from an arbitrary load distribution including partial contact loss. This model is shown to be equivalent to a four-parameter model defined by a translational stiffness acting at the center of stiffness and a twist stiffness. The twist stiffness generates a moment, which is solely due to the spread of contact across the tooth face. The movement of the translational stiffness across the tooth face generates an additional moment. The four parameters in the model are useful post-processing output quantities to track and interpret the gear mechanics and the mesh forces and moments that develop under static or dynamic conditions.The translational and twist stiffnesses and the center of stiffness depend strongly on the relative translation and twist at the gear mesh, introducing nonlinearity. Tooth surface modifications smoothen the translational stiffness profile and decrease the twist stiffness. The twist stiffness fluctuates periodically with gear rotation generating fluctuating moments (shuttling) that can potentially excite vibrations.

The Dynamics Analysis of a Multi-Stage Hybrid Planetary Gearing

This paper introduces a complex multi-body dynamics model which is established to simulate the dynamic behaviors of a multi-stage hybrid planetary gearing based on the finite element method and the software ADAMS. The finite element method is used to introduce deformable ring-gears and sun-gears by using 3D brick units. A whole multi-body dynamics model is established in the software ADAMS. Mesh stiffness variation excitation and gear tooth contact loss are intrinsically considered. A rich spectrum of dynamic phenomena is shown in the multi-stage hybrid planetary gearing. The results show that the static strength of main parts of the gearing is strong enough and the main vibration and noises are excited by the dynamic mesh forces acting on the tooth of planet-gears and ring-gears.

A simple and robust method for spiral bevel gear generation and tooth contact analysis

A simple and robust method to simulate spiral bevel gears generating and meshing processes is proposed. In a first part, a mathematical model of universal hypoid tooth surfaces generator is formulated. It is based on Fong’s approach. The model takes into account all the kinematic motions of common CNC machine tools dedicated to hypoid gears machining. It is general enough to enable the simulation of various hypoid gears cutting methods such as face-hobbing, face-milling, plunge cutting and bevel-worm-shaped-hobbing processes. In this paper, only developments related to face-milled spiral bevel gear generation are presented. We show that the results obtained are in good agreement with those of certified software. In a second part, a simple and numerically stable algorithm is proposed for unloaded tooth contact analysis. The simulation method is based on a discretization of one of the two tooth flank surfaces in contact and a specific projection of the points on the opposite flank. It gives a good approximation of the contact pattern location. The accuracy of the contact point locations and computing time is directly dependent on the mesh density. However, this approach enables obtaining in a very short time sufficiently accurate results to meet the needs of designers, particularly in the preliminary stages of design. The relative displacements of the gears can be taken into consideration. The robustness of the proposed computing process and the adjustable accuracy of the results are the two main advantages of the presented approaches.

Three-dimensional nonlinear vibration of gear pairs

This work investigates the three-dimensional nonlinear vibration of gear pairs where the nonlinearity is due to portions of gear teeth contact lines losing contact (partial contact loss). The gear contact model tracks partial contact loss using a discretized stiffness network. The nonlinear dynamic response is obtained using the discretized stiffness network, but it is interpreted and discussed with reference to a lumped-parameter gear mesh model named the equivalent stiffness representation. It consists of a translational stiffness acting at a changing center of stiffness location (two parameters) and a twist stiffness. These four parameters, calculated from the dynamic response, change as the gears vibrate, and tracking their behavior as a post-processing tool illuminates the nonlinear gear response. There is a gear mesh twist mode where the twist stiffness is active in addition to the well-known mesh deflection mode where the translational stiffness is active. The twist mode is excited by periodic back and forth axial movement of the center of stiffness in helical gears. The same effect can occur in wide facewidth spur gears if tooth lead modifications or other factors such as shaft and bearing deflections disrupt symmetry about the axial centers of the mating teeth. Resonances of both modes are shown to be nonlinear due to partial and total contact loss. Comparing the numerical results with gear vibration experiments from the literature verifies the model and confirms partial contact loss nonlinearity in experiments.

풍력발전기 증속기에 전달되는 풍하중 변동특성 연구

본 논문은 정상풍속과 돌발풍속을 수학적으로 모델링하고 풍향에 따라 전달되는 메인축에서의 전달모멘트를 조사하여 기어박스에 전달되는 풍하중의 특성을 파악하였다. 정상풍속은 지상에서 고도가 높아짐에 따라 속도가 증가하게 설정을 하였다. 풍하중에 의해서 메인축으로 전달되는 모멘트의 평균값과 하모닉값을 풍향 입사각을 -45° ~ 45°로 변화를 주며 특성을 파악하였다. 또한 기어 트레인의 미스얼라인먼트를 유발시키는 굽힘 모멘트의 특성을 파악하였다. 정상풍속모델에서는 블레이드의 3배수 주파수(3X)로 하는 토크의 가진이 생기며, 바람의 방향이 +22.5° 일 때 수평방향의 굽힘 모멘트가 주축으로 들어가는 토크의 50%수준으로 발생하는데 이는 수평방향으로의 탄성 축 휘임을 유발하여 치가 모서리에서 물림이 발생하게 하는 원인을 제공함을 알 수 있었다. 돌발풍속의 경우, 3X, 6X, 9X를 가진주파수로 하는 토크의 가진이 바람의 방향이 +방향으로 커질수록 하모닉항의 상대 비율이 증가하였다.

Geometry design and tooth contact analysis of crossed beveloid gears for marine transmissions

Beveloid gears, also known as conical gears, gain more and more importance in industry practice due to their abilities for power transmission between parallel, intersected and crossed axis. However, this type of gearing with crossed axes has no common plane of action which results in a point contact and low tooth durability. Therefore, a geometry design approach assuming line contact is developed to analyze the tooth engagement process of crossed beveloid gears with small shaft angle for marine transmission applications. The loaded gear tooth contact behavior is simulated by applying a quasi-static analysis to study the effects of gearing parameters on mesh characteristics. Using the proposed method, a series of sensitivity analyses to examine the effects of critical gearing parameters such as shaft angle, cone angle, helix angle and profile-shift coefficient on the theoretical gear mesh is performed. The parametric analysis of pitch cone design shows that the dominant design parameters represented by the angle between the first principle directions (FPD) and normal angular factor are more sensitive to the shaft and cone angles than they are to the helix angle. The theoretical contact path is highly sensitive to the profile-shift coefficient, which is determined from the theoretical tooth contact analysis. The FPD angle is found to change the distribution of contact pattern, contact pressure and root stress as well as the translational transmission error and the variation of the mesh stiffness significantly. The contact pattern is clearly different between the drive and coast sides due to different designed FPD angles. Finally, a practical experimental setup for marine transmission is performed and tooth bearing test is conducted to demonstrate the proposed design procedure. The experimental result compared well with the simulation. Results of this study yield a better understanding of the geometry design and loaded gear mesh characteristics for crossed beveloid gears used in marine transmission.

Modal and stress analysis of gear train design in portal axle using finite element modeling and simulation

The portal axle is a gearbox that is specially designed for off-road driving conditions. It is installed between the wheel and the axle shaft to give higher ground clearance to the vehicle. The modeling and simulation of spur gears in portal axle is important to predict the actual motion behavior. However, gear train design in portal axle is difficult to study comprehensively due to their relatively low cost and short product life cycle. In this study, modal analysis of portal axle is simulated using finite element method (FEM). Modal analysis is simulated on three different combinations of gear train system commonly designed for portal axle. The three gear trains being analyzed are gear train without idler gear, one idler gear and two idler gears. FEM static stress analysis is also simulated on three different gear trains to study the gear teeth bending stress and contact stress behavior of the gear trains in different angular positions from 0° to 18°. The single and double pair gear teeth contact are also considered. This methodology serves as a novel approach for gear train design evaluation, and the study of gear stress behavior in gear train which is needed in the small workshop scale industries.

Dynamic Response of Marine Gear under External Impact Load

In order to determine the anti-shock performance of marine gear, dynamic model of gear-rotor-bearing system under external load is established. On the base of Hertz contact theory, the mathematical model of maximum stress response of the gear tooth contact area is developed and the typical shock spectrum was transferred to double peaks and triangle wave to simulate the process of base excitation. By simulating different impact pulse width and acceleration peak value, the programming result is in good agreement with Finite-Element simulation. The study considers that the bearing oil film can absorb impacting load and Information on stress response of gear contact area under external load could offer references for the design of marine gearbox to enhance the resistance to underwater shock damage.

Study of Transient Elastohydrodynamic Lubrication of Spur Gears under Impact Load

Spur gear contacts experience a number of time-varying contact parameters including the load, surface velocities, radii of curvature, and slide-to-roll ratio. It is very hard to obtain transient elastohydrodynamic lubrication (EHL) solution of spur gears. In this study, a transient EHL model of involute spur gear tooth contacts is proposed. A full transient EHL solution of involute spur gear under impact load is obtained by utilizing the multigrid technique. The influences of impact load on the EHL of spur gear are analyzed in the paper. The numerical results show that the approach impact load has strong transient influence on the oil film thickness and pressure distribution between contact zones. The impact load may lead to instantaneous lubrication film deterioration between contact teeth of involute spur gears.