Gear Load Distribution Research Articles

The influence of gear load distribution based on coupled systems on gearbox meshing noise

Introduction: With the rapid development of the gearbox manufacturing industry, the internal gear response has received attention, and the control of meshing noise during gear operation has been studied. Conventional noise reduction methods are usually based on gear order, and with the improvement of gearbox manufacturing technology, this method gradually becomes difficult to cope with a wide range of data.Methods: To expand the search domain of noise control systems, this study combines gear response and gear order, and adds the condition of gear uniform load. For common noise reduction problems in composite systems, this study improves the time-varying stiffness excitation mechanism and generates a coupled system.Results: Finally, this study conducts experiments on the Gmnoi dataset and compares it with three systems including quantum genetics to verify the superiority of the proposed system. The suppression effects of the four systems on gear meshing noise were 98.4%, 95.8%, 93.5%, and 92.7%, respectively. Their highest performance for different gear groups was 623, 514, 406, and 423, respectively.Discussion: The experimental results showed that the proposed coupling system has strong robustness and high accuracy in controlling gearbox meshing noise, and is of great significance in reducing noise pollution and improving the working environment of the gearbox.

Numerical modeling and experimental validation of power loss and efficiency in an electric-drive axle system

Power loss and efficiency are pivotal performance metrics significantly impacting the quality of electric-drive axles. This study outlines a numerical method for determining the electric-drive axle system power loss, which includes gear meshing, gear churning, and bearing power losses. Power loss from gear meshing was calculated by analyzing load distribution and friction coefficient. The frictional loaded tooth contact analysis method was employed to ascertain the load distribution during gear meshing. A formula based on a weighting function was utilized to compute the friction coefficient. The finite element method was used to verify the gear load distribution and meshing power loss. Subsequently, empirical formulas were used to calculate the gear churning and bearing power losses. To substantiate the proposed numerical method, an experimental apparatus was employed to measure the power loss and efficiency of an electric-drive axle under various operating conditions. The experimental study demonstrated a strong correlation between the numerical and calculated results. These findings suggest that the proposed method can be an effective tool in predicting the power loss and efficiency of electric-drive axles.

A dynamic gear load distribution model for epicyclic gear sets with a structurally compliant planet carrier

Structural deformations in a planet carrier under operating conditions results in misalignment of planet gears, which can significantly effect the gear mesh load distribution and load sharing of a planetary gear set. Therefore, to capture the influence of structural compliance associated with planet carrier, planet pin, and input/output shaft, a hybrid planetary dynamic load distribution model is developed in this paper. Finite element sub-structuring techniques are employed to ensure that the model is computational efficiency. The proposed model employs a simplex algorithm to iteratively solve for the elastic gear mesh contacts in conjunction with a numerical integration scheme, which enables it to inherently capture the influence of several component and system level design variations without the need for an empirical mesh stiffness formulation or transmission error excitation of the system. The developed formulation is used to study the effects of planet carrier flexibility on both the quasi-static and dynamic response of planetary gearsets. The discussed results not only illustrate the influence of carrier flexibility on the system response but also highlight the need for such computationally efficient models which could be used as design tools.

A Transient Mixed Elastohydrodynamic Lubrication Model for Helical Gear Contacts

Abstract In this study, a non-Newtonian, transient, isothermal, mixed elastohydrodynamic lubrication (EHL) model is proposed for helical gear contacts. The model accounts for nonelliptical contacts subject to spatially varying sliding and rolling velocity fields that are not aligned with any principal axis of the contact region, which is the case for helical gear contacts. The time-varying changes pertaining to key contact parameters and relative motion of roughness profiles on mating tooth surfaces are captured simultaneously to follow the contact from the root to the tip of a tooth while accounting for the transient effect due to relative motions of the roughness profiles. Actual tooth load distributions, contact kinematics, and compliances of helical gear contacts are provided to this model by an existing helical gear load distribution model. Measured three-dimensional roughness profiles covering the entire meshing zone are incorporated in the analyses to investigate its impact on the EHL conditions as well as mechanical power loss. Results of a parametric sensitivity study are presented to demonstrate the influence of operating conditions and surface roughness on the EHL behavior and the resultant gear mesh mechanical power loss of an example helical gear pair. The accuracy of the proposed mixed-EHL model is assessed by comparing the mechanical power loss predictions to available experimental results.

Study on wear in spur gears based on an improved load distribution model considering the effects of corner contact

Gear surface wear is an unavoidable tooth profile deviation and can influence gear load distribution and transmission error. Because of that, it is necessary to study the interaction between them and wear. For that purpose, a modified wear prediction model has been established by combining the potential energy method, and an improved load distribution model considering the effect of corner contact. The load share ratio (LSR) obtained from the improved model is verified by the finite element method (FEM). And relative to the FEM, the proposed model is much more efficient. Besides, the influences of wear accumulation process and corner contact on loaded static transmission error (LSTE) and load distribution are discussed. The results show that considering the effect of corner contact is necessary and can improve the accuracy of the wear prediction. And, it can be observed that there is a significant time-varying characteristic on LSTE, LSR of worn gear, as well as a correlation between them. Furthermore, the influence of gear modulus and gear ratio is discussed as well and it is found that both can effectively reduce the wear depth and significantly influence the condition of corner contact.

Correlation of Planetary Bearing Outer Ring Creep and Gear Load Distribution in a Full-Size Wind Turbine

In this work, bearing outer ring creep in the planetary gear of a gear wind turbine gearbox is investigated. So far, gear creep has only been investigated experimentally on very small bearings under simplified load conditions. This paper presents experimental measurement results from a full-size 2.75 MW wind turbine. The test were performed on a system test bench capable of applying loads in all six degrees of freedom at the rotor hub. The objectives of this investigation are to provoke and measure bearing outer ring creep and to identify correlations to the gear load distributions acting on the planetary gear. After a motivation, a literature overview on bearing ring creep is given. Influences on and occurrences of ring creep are described and the two mechanisms roller-induced creep and gear creep explained. Then, the test setup and the evaluated experiments are presented. The influence of torque, rotational speed and additional non-torque loads on gear load distribution and bearing outer ring creep is shown, discussed and put in relation to findings from literature. Key findings are that outer ring creep speed increases with global rotational speed and torque. Also, gear creep – acting in the opposite direction of roller-induced creep – was found at the generator-sided bearing ring for loads below 40% nominal torque. The planet gear load distributions with sun and ring gear were highly uneven and opposed to each other at low torques while leveling out at high torques due to the load-dependent deformations of sun gear, planet carrier and ring gear. The average gear load distribution over all ring gear positions showed to be influenced only by torque and to be independent of non-torque loads. In accordance, even extreme non-torque loads were found to not influence the creep behavior of the two planetary bearing outer rings.

Research of Deformability of Satellite Unit of Planetary Transmission

Многопоточные планетарные передачи нашли широкое распространение в технике благодаря хорошим технико-экономическим показателям: высокой нагрузочной способности при небольших габаритах и массе, малым потерям мощности на трение, большому передаточному отношению в одной ступени. Существенным недостатком этих передач является неравномерность распределения нагрузки в зацеплениях колес, что вызвано неизбежными погрешностями изготовления и деформациями их звеньев. Однако податливость отдельных элементов передачи (осей и подшипников сателлитов, щек водила) способствует выравниванию нагрузки по сателлитам и их рядам при многорядном исполнении механизма. В связи с этим важно установить степень влияния деформации элементов планетарной передачи на распределение нагрузки в зацеплениях колес и на такой важный технико-экономический показатель, как отношение массы к моменту на выходном валу. Коэффициент неравномерности распределения нагрузки по сателлитам определялся из решения системы уравнений совместности перемещений с учетом деформации щек водила, подшипников и осей сателлитов. Причем ось сателлита в местах ее сопряжения со щеками водила и кольцом подшипника качения рассматривалась как балка на упругом основании, а щеки водила выполнены с пазами для снижения их жесткости. Таким образом, было установлено, что выполнение щек водила податливыми позволяет снизить коэффициент неравномерности распределения нагрузки по сателлитам на 8-11 %, что благоприятно сказывается на несущей способности привода и его массогабаритных показателях. При ограниченном радиальном размере передачи ее целесообразно выполнить многорядной. Однако в этом случае деформация кручения солнечной шестерни ведет к неравномерному распределению нагрузки по рядам сателлитов. Для предотвращения этого негативного явления предлагается водило выполнить с разными по ширине перемычками, размеры которых подобрать так, чтобы их деформация соответствовала деформации кручения шестерни. Таким образом, использование предложенных конструкций многопоточных планетарных передач при рациональном выборе их параметров позволяет существенно снизить неравномерность распределения нагрузки в зацеплениях колес и улучшить технико-экономические показатели привода.

Impact of Tooth Indexing Errors on Dynamic Factors of Spur Gears: Experiments and Model Simulations

This paper investigates the influences of tooth indexing errors on dynamic factors of spur gears. An experimental study is performed using root strain measurements to (i) establish baseline dynamic behavior of gears having negligible indexing errors and (ii) characterize changes caused by tightly controlled intentional indexing errors to this baseline dynamic behavior. For this, test gears having different forms of indexing errors are paired with an instrumented gear having negligible indexing error. Dynamic root strains of teeth in the neighborhood of teeth with indexing error are measured. A dynamic gear load distribution model is employed to simulate these experiments. Both measurements and predictions indicate clearly that the baseline dynamic response, dominated by well-defined resonance peaks, is altered significantly by transient vibrations induced by indexing errors, in the process increasing dynamic factors significantly in comparison to the case of negligible indexing error.

굴삭기용 선회감속기의 베어링 특성이 기어 하중 분포에 미치는 영향 분석

굴삭기용 선회감속기의 베어링 특성이 기어 하중 분포에 미치는 영향 분석

A Fatigue Model for Spur Gear Contacts Operating Under Mixed Elastohydrodynamic Lubrication Conditions

This paper presents a model to predict the crack formation fatigue lives of spur gear contacts operating under mixed lubrication conditions where surface roughnesses introduce intermittent metal-to-metal contacts and severe stress concentrations. The proposed model consists of several submodels, including (i) a gear load distribution model to determine the normal tooth force distribution along the tooth surface, incorporating any profile modifications and manufacturing deviations, (ii) a mixed elastohydrodynamic lubrication model customized to handle transient contact conditions of gears, (iii) a stress formulation that assumes the plane strain condition to compute the transient elastic stress fields on and below the tooth surface induced by the mixed lubrication surface pressure and shear stress distributions, and (iv) a multi-axial fatigue model to predict the crack nucleation life distribution. The proposed spur gear fatigue model is used to simulate the contacts of gear pairs having different surface roughness amplitudes. The predictions are compared to the measured gear fatigue stress-life data for each surface condition to assess the model accuracy in the prediction of the crack nucleation fatigue lives as well as the location of the critical failure sites.

A Transient Mixed Elastohydrodynamic Lubrication Model for Spur Gear Pairs

In this study, a transient, non-Newtonian, mixed elastohydrodynamic lubrication (EHL) model of involute spur gear tooth contacts is proposed. Unlike the contact between two cylindrical rollers, spur gear contacts experience a number of time-varying contact parameters including the normal load, radii of curvature, surface velocities, and slide-to-roll ratio. The proposed EHL model is designed to continuously follow the contact of a tooth pair from the root to the tip to capture the transient characteristics of lubricated spur gear contacts due to these parameter variations, instead of analyzing the contact at discrete positions assuming time-invariant parameters. The normal tooth force along the line of action is predicted by using a gear load distribution formulation and the contact radii and tangential surface velocities are computed from the kinematics and geometry of involute profiles. A unified numerical approach is adapted for handling asperity interaction in mixed EHL conditions. The differences between the transient and discrete EHL analyses are shown for a spur gear pair having smooth surfaces and different tooth profile modifications. The transient behavior predicted by the proposed model is found to be mainly due to the squeezing and pumping effects caused by sudden load changes. The lubrication behavior under rough conditions is also investigated at different operating conditions.

Prediction of Mechanical Efficiency of Parallel-Axis Gear Pairs

AbstractA computational model is proposed for the prediction of friction-related mechanical efficiency losses of parallel-axis gear pairs. The model incorporates a gear load distribution model, a friction model, and a mechanical efficiency formulation to predict the instantaneous mechanical efficiency of a gear pair under typical operating, surface, and lubrication conditions. The friction model uses a new friction coefficient formula obtained by using a validated non-Newtonian thermal elastohydrodynamic lubrication (EHL) model in conjunction with a multiple linear regression analysis. The load and friction coefficient distribution predictions are used to compute instantaneous torque/power losses and the mechanical efficiency of a gear pair at any given rotational position. Efficiency measurements from gear pairs having various gear designs and surface treatments are compared to model predictions. Mechanical efficiency predictions are shown to be within 0.1% of the measured values, indicating that the proposed efficiency model is accurate. Results of a parametric study are presented at the end to highlight the influence of key basic gear geometric parameters, tooth modifications, operating conditions, surface finish, and lubricant properties on mechanical efficiency losses.

Influence of Planetary Needle Bearings on the Performance of Single and Double Pinion Planetary Systems

Abstract Planetary gears are widely used in automotive and aerospace applications. Due to demands for greater power density, these gearsets often operate at extremely high stress levels. This has caused system level influences once considered secondary to become critical to the success of planetary gears. One such system level effect that has been largely overlooked is the influence of support structures like planetary needle bearings. There are interactions between the gear distributed loads and the resulting bearing loads and deflections that have implications for both gear and bearing designs. Also, double pinion planetary arrangements are increasingly becoming common. There are still greater interactions between the gear and bearing components in double pinion planetary arrangements. In this paper, we will examine the influence of the bearing deflections (tilt) on the gear load distribution and contact pattern. We will also show the influence of distributed gear loads on the bearing loads (moments) and deflections (tilts). Both, single and double pinion planetary arrangements will be considered. It will be shown that the tilting stiffnesses of the needle bearings have a major influence on gear contact pattern and consequently on contact and bending stresses. It will also be shown that the double pinion planetary arrangement is more likely to result in off-centered loading. Parametric studies will be performed to show the influence of a few design parameters. Theoretical derivations will be validated by numerical simulations. A system level gear analysis model will be used to illustrate the issues involved and quantify the results.