Spiral Bevel Gear Pair Research Articles

Mesh characteristic changes of spiral bevel gear pair with assembly errors during tooth crack propagation

Spiral bevel gears (SBGs) are often used because of their strong carrying capacity and lower vibration. However, this heightened load capacity can sometimes result in the development of tooth surface cracks. This study aims to simulate the three-dimensional propagation of cracks in SBGs under various assembly conditions and explore how the presence of cracks affects mesh characteristics. This paper investigates crack propagation in SBGs by applying principles of fracture mechanics. Employing a combination of finite element software ABAQUS and fracture mechanics software FRANC3D, the study conducts a three-dimensional analysis of crack propagation in SBGs. The study analyzes the impact of crack propagation on the lifespan and mesh characteristics of SBGs, including crack propagation morphology, transmission error, time-varying meshing stiffness (TVMS), gear life, and tooth surface force, under various assembly errors.

Loaded tooth contact analysis and meshing stiffness calculation for cracked spiral bevel gears

Tooth cracks may occur in spiral bevel gear transmission system of the aerospace equipment. In this study, an accurate and efficient loaded tooth contact analysis (LTCA) model is developed to predict the contact behavior and time-varying meshing stiffness (TVMS) of spiral bevel gear pair with cracked tooth. The tooth is sliced, and the contact points on slices are computed using roll angle surfaces. Considering the geometric complexity of crack surface, a set of procedures is formulated to generate spatial crack and determine crack parameters for contact points. According to the positional relationship between contact point and crack path, each sliced tooth is modeled as a non-uniform cantilever beam with varying reduced effective load-bearing tooth thickness. Then the compliance model of the cracked tooth is established to perform contact analysis, along with TVMS calculations utilizing three different models. By employing spiral bevel gear pairs with distinct types of cracks as examples, the accuracy and efficiency of the developed approach are validated via comparative analyses with finite element analysis (FEA) outcomes. Furthermore, the investigation on effects of cracks shows that tooth cracks can induce alterations in meshing performance of both entire gear pair and individual tooth pairs, including not only cracked tooth pair but also adjacent non-cracked tooth pairs. Hence, the proposed model can serve as a useful tool for analyzing the variations in contact behavior and meshing stiffness of spiral bevel gears due to different cracks.

Time-varying mesh stiffness calculation of spiral bevel gear with spalling defect

Spiral bevel gears often operate at high speeds and under heavy loads, which can easily lead to the occurrence of spalling faults on the tooth surfaces, particularly in cases of inadequate lubrication. In this study, we introduce an efficient and accurate numerical calculation method to determine the time-varying meshing stiffness (TVMS) of a spiral bevel gear pair with actual spalling faults, taking into consideration the effects of multi-tooth meshing and the flexibility of the gear flank. In parallel, a finite element model is established to verify the accuracy of the proposed method across various spalling parameters. We delve into the impact of spalling length, width, location, and shape. The results demonstrate that the TVMS values obtained from our proposed method align closely with those obtained using the finite element method. The range of TVMS reduction caused by the spalling fault is primarily determined by the spalling location and width. Moreover, the magnitude of TVMS decline is strongly associated with the spalling length. Furthermore, the clearances between two conjugated tooth surfaces change due to the presence of the spalling fault, resulting in a redistribution of contact forces on the same contact surface and other meshing tooth surfaces.

Numerical study on the churning power loss of spiral bevel gears at splash lubrication system

AbstractIn order to predict the spiral bevel gear churning power loss, based on the Computational Fluid Dynamics (CFD) method, the computational model for the splash lubrication of the spiral bevel gear pair is established and validated by experiments. The churning power loss of spiral bevel gears is obtained and the corresponding flow field distribution in the gearbox with a pair of spiral bevel gears is analysed under a standard operating condition. For the churning power loss of spiral bevel gears, the loss of teeth surface is mainly caused by pressure while the loss of gear side is mainly generated by the viscous force. The effects of the gear rotational speed, oil level, oil temperature and oil shroud on the churning loss are also investigated and analysed. Ultimately, an optimisation method is proposed for the original spiral bevel geared transmission.

Multi-Point Control for Face-Milled Spiral Bevel Gears with a Predesigned Fourth-Order Motion Curve

This paper presents an ultimate motion methodology of a face-milling spiral bevel gear pair to synthesize the mating tooth surfaces with a predesigned fourth-order motion curve. The methodology is to control some contact points along the contact path in the process of tooth contact analysis via application of an extended local synthesis which permits some transmission errors rather than zero at the concerned contact point. The modified offset motion correction is selected to demonstrate the proposed methodology. Applied torque corresponding to an elastic approach of 0.00635 mm at the mean contact point is calculated and the loaded tooth contact analysis is performed. Numerical results show that the extended local synthesis can effectively control the transmission errors on the predesigned fourth-order motion curve at arbitrarily predesigned contact points along the contact path of the spiral bevel gear pair. The tooth contact pattern for the actual tooth pair is scattered into three segments since the rotational motion of the driven gear at any instant angular position is dependent on the tooth pair with the least transmission error among the three adjacent tooth pairs. The actual tooth contact patterns of the spiral bevel gear pair become continuous when meshing tooth surfaces are elastically deformed.

Spiral Bevel Gears: nonlinear dynamic model based on accurate static stiffness evaluation

In the present paper non-linear dynamics of a spiral bevel gear pair with backlash are investigated in order to clarify the internal excitations of major importance from the vibration point of view: manufacturing errors in the teeth profile, teeth spacing errors, and elastic deformation of the teeth. In some conditions, like in the case of backside contact, the destructive effect of internal excitations can be intensified leading to complex dynamics; for such reasons here backside contacts and reverse rotation are investigated in detail using a nonlinear time-varying model. The effect of damping is investigated as well. A one-DOF model is developed in order to study the dynamic behavior; the resulting a nonlinear differential equation with time-varying mesh stiffness is solved via numerical integration based on an adaptive step-size implicit Runge-Kutta scheme. The dynamic response of the system is analyzed through time histories, phase portraits, bifurcation diagrams, and Poincaré maps. Results show that for small backlash values, the possibility of backside contact increases. Meanwhile, by increasing the backlash value, the amplitude vibration of the gear rotation rises as well. By comparing the dynamic response of the system with different damping ratios, the results show that higher damping effectively reduces gear vibration resonance, although the probability of unsteady response still exists.

Dynamic Simulation of Cracked Spiral Bevel Gear Pair Considering Assembly Errors

The tooth root crack fault is a common fault type of the spiral bevel gear pair (SBGP). Affected by the strong bearing capacity, the early crack fault of the SBGP cannot be found in time. In this study, a finite element (FE) model of the SBGP is established and assembled through the tooth contact analysis. The maximum tooth root stress is analyzed considering the variation of assembly errors. Meanwhile, this study simulates the tooth root crack fault of the bevel pinion with different crack degrees. The initial position of the crack is located where the maximum tooth root stress appears. The time-varying mesh stiffness (TVMS) of the SBGP considering different degrees of the pinion tooth root crack fault is obtained. The TVMS and the non-load transmission error are brought into a hybrid FE dynamic model, and steady responses are solved. Based on this, the sensitivities of various statistical indicators for identifying the tooth root crack fault of SBGP under the influence of assembly errors are verified. This paper can provide the necessary theoretical basis for the analysis and diagnosis of tooth root crack faults in the SBGP transmission system.

Geometry design, meshing analysis and error influences of face-hobbed cycloidal bevel gears with double circular-arc profile for a nutation drive

As the core components of nutation drive, the internal meshing pair of bevel gear must be delicately designed to achieve desirable operational performances for the transmission device. For this purpose, this paper designs a face-hobbed internal meshing pair of cycloidal bevel gears with double circular-arc profile (DCAP). First, a cutter head with DCAP cutting edges is designed to generate the tooth surface of internal gear pair. Then, the tooth geometry of the external and internal bevel gears are derived according to the meshing theory. Finally, a finite element model is developed to simulate the meshing characteristics of the gear pair. The simulation results reveal that the proposed face-hobbed cycloidal bevel gear pair with DCAP has higher contact/bending strength, better load sharing and smaller transmission error compared with the logarithmic spiral bevel gear pair with DCAP. The effects of four typical manufacturing errors on meshing characteristics of the proposed bevel gear pair are investigated to provide fundamental references for the tolerance design of cycloidal bevel gears.

High-Speed Spiral Bevel GEAR Dynamic Rules Considering the Impact of Web Thicknesses and Angles

Gear transmission system dynamic responses under high-speed and heavy-duty working conditions were obviously affected by support structures, especially in lightweight design. However, web thicknesses and angles were usually ignored in dynamic modeling process. Therefore, a full mesh model with web structure was built and its dynamic characteristics were analyzed by a modified vector form intrinsic finite element (VFIFE), which is proposed to solve high-speed dynamic problems with good efficiency. For spiral bevel gear pair dynamic characteristics, the impacts of web thicknesses and angles were simulated and discussed. Simulation results showed that web support angles will affect gear meshing performance and dynamic characteristics more remarkable than web thickness did. In addition, the good performance of the proposed modified VFIFE method was proved, which showed good computing efficiency.

Optimal Design of Computational Fluid Dynamics: Numerical Calculation and Simulation Analysis of Windage Power Losses in the Aviation

Based on the theory of computational fluid dynamics (CFD), with the help of the Fluent software and the powerful parallel computing capability of the super cloud computer, the single-phase flow transient simulation calculation of the windage power loss of the engagement spiral bevel gear pair (SBGP) was performed. The two-equation SST k-ω turbulence model based on the assumption of eddy viscosity was adopted, which was improved from the standard k-ε model combined with the Wilcox k-ω model. The SST k-ω turbulence model inherited the respective advantages of the Wilcox k-ω model in the near-wall region and the k-ε model in the free shear layer and could more accurately describe the resistance and separation effect of the gear tooth surface on the airflow. The simulation analyzed the airflow characteristics around SBGP and the mechanism of the windshield to reduce the windage loss of the gear. It also studied the influence of the windshield clearance and opening size on the windage power loss. Then the orthogonal experimental analysis method was adopted to perform numerical simulation analysis. The windage torque was studied under different clearance values between the windshield and the gear tooth surface, as well as the large end and the small end. The variance analysis was performed on the numerical simulation data. The results showed that when the windshield clearance value was 1 mm and the engagement opening was 30°, the windage torque was the smallest, and the effect of reducing the windage power loss was the best. According to the changes in the pressure, velocity, and turbulent kinetic energy cloud diagram of the flow field in the reducer during multi-group simulation tests, the local optimal windshield configuration was obtained, which provided a method for further research on the multi-objective optimization of the windshield and the windage loss of the gear pair under the oil–gas two-phase flow and also provided a reference for the practical engineering application of the windshield.

Spiral Bevel Gears Nonlinear Vibration Having Radial and Axial Misalignments Effects

In gear transmissions, vibration causes noise and malfunction. In actual applications, misalignments contribute to intensifying the destructive effect of vibrations. In this paper, the nonlinear dynamics of a spiral bevel gear pair, with small helix angle, considering different misalignments, are deeply investigated. Axial misalignment, radial misalignment, and the combination of these two types are considered in this study. The governing equation is numerically solved through an implicit Runge–Kutta scheme. Since the main goal of this study is the analysis of the dynamic scenario, the mesh stiffness of the gear pair is obtained from the literature. The dynamical system is nonlinear and time-varying; it is analyzed through time responses, phase portraits, Poincaré maps, and bifurcation diagrams. Results show that, among the considered three cases with different types of misalignments, the spiral bevel gear with axial misalignment is the worst destructive case; aperiodic, subharmonic, and multiperiod responses are observable for this case. It is interesting that the chaotic responses for the case, having both types of misalignments, are less likely for the case with axial misalignment, only.

Nonlinear vibration of the spiral bevel gear under periodic torque considering multiple elastic deformation evaluations due to different bearing supports

This paper investigates two parameters effect on vibrational responses of the spiral bevel gear. Changing the gear system overall stiffness (GSOS) considering elastic deformation and periodic torques are the two parameters which are represented as the main goals of this study. In order to investigate the effects of shaft stiffness and elastic deformation, two different cases with different support locations are considered. The first case is presented by locating the support close to the gear, and in the latter one, the distance between gear and support is increased. Besides, to study the effect of torque, two main types are considered: constant and periodic excitation torque. To illustrate the dynamic behavior, the governing differential equations are solved numerically according to the Runge–Kutta method. The equations are nonlinear due to backlash and time-varying coefficients as the results of GSOS variation. Vibrational phenomena are illustrated by means of bifurcation diagrams, RMS, and Poincaré maps. Particular vibrational behaviors such as “chaos” and “period-doubling” phenomena are illustrated with details. By investigating the effect of shaft stiffness, results show that when the support is far away from gear, the vibration response increased by 67.5%. Moreover, while the input torque is constant, the support movement does not cause undesirable responses such as chaotic or period-doubling responses. The periodic torque causes undesirable responses such as chaos and bifurcation and period-doubling responses.Article HighlightsWhat is done in the present paper can be mentioned in three main parts:The nonlinear dynamics of the spiral bevel gear pair under two different support situations is investigated in this paper.To scrutinize the dynamic behavior of the spiral bevel gear-pair in a nearly real situation, the input driver torque is periodically variable.The results show that the spiral bevel gear pair may comprise chaotic response with periodic torque excitation if the bearing supports locate far enough from the gears.

Natural characteristics analysis and experimental test of spiral bevel gear pair in the tractor transmission system

Spiral bevel gear is widely used in various mechanical transmission systems, such as tractor transmission system. Because it is mainly used in the heavy-load conditions, it would most likely resonate within the rated speed, resulting in tooth fatigue damage. In this paper, based on the principle of meshing and gear tooth machining, the spherically involute tooth profile equation of spiral bevel gear is deduced and the precise modeling method based on the CATIA is studied. The natural frequency and modal shape under free vibration are obtained by the finite element method (FEM), the influence of web thickness and web hole on the natural frequency of driven gear plate is analyzed as well. In addition, the experimental modal of bevel gear pair is carried out based on a multiple-reference impact test, Modal Assurance Criterion (MAC) is calculated, the three-dimensional modeling accuracy and the finite element analysis reliability are verified. The results show that the error between the measured frequency of bevel gear pair and the calculated frequency of the finite element simulation are both within 5%, and the MAC is above 0.8. The fourth-order natural frequency is the most sensitive to the web thickness, the second-order natural frequency is the most sensitive to the web hole.

A modified damping model of vector form intrinsic finite element method for high-speed spiral bevel gear dynamic characteristics analysis

The vector form intrinsic finite element (VFIFE) method is springing up as a new numerical method in strong non-linear structural analysis for its good convergence, but has been constricted in static or transient analysis. To overwhelm its disadvantages, a new damping model was proposed: the value of damping force is proportional to relative velocity instead of absolute velocity, which could avoid inaccuracy in high-speed dynamic analysis. The accuracy and efficiency of the proposed method proved under low speed; dynamic characteristics and vibration rules have been verified under high speed. Simulation results showed that the modified VFIFE method could obtain numerical solutions with good efficiency and accuracy. Based on this modified method, high-speed vibration rules of spiral bevel gear pair under different loads have been concluded. The proposed method also provides a new way to solve high-speed rotor system dynamic problems.

Influence of dynamic attitudes on oil supply for bearings and churning power losses in a splash lubricated spiral bevel gearbox

To study the influence of dynamic flight attitudes on the splash lubrication performance and churning power losses of the intermediate spiral bevel gearbox in a helicopter, a three-dimensional (3D) simulation model consisting of a spiral bevel gear pair, two bearing caps with oil guide holes and the housing is established, and CFD (Computational Fluid Dynamics) simulations with main flight attitudes are performed. The influences of turning directions, rotational speeds, circling attitude and accelerations on the distribution of lubricating oil, the flow rate of oil guide holes and churning power losses are discussed. A test rig for studying the splash lubrication performance of a gearbox under different dynamic attitudes is developed, and the feasibility of the present simulation method is validated by experiments.

Theoretical and Experimental Study on Contact Characteristics of Spiral Bevel Gears under Quasi-Static and Large Loading Conditions

The precise mathematical model for the tooth surface and transition surface of spiral bevel gears is derived. Taking a pair of spiral bevel gears of a heavy vehicle as an example of calculation and analysis, a finite element model of spiral bevel gears transmission system is established. Through the finite element tooth contact analysis under quasi-static loading and high loading condition, the influences of torque on the root stress distribution, contact stress, and transmission error are discussed, and the results are compared with the empirical formula results. Finally, a contact performance test bench of spiral bevel gear pair is developed, then the root bending stress, contact pattern, and transmission error tests are carried out. These experiment results are compared with analyzed ones, which showed a good agreement.

Mathematical modeling and numerical simulation for determining an optimized oil jet layout for spiral bevel gear lubrication

In aeroengine industry, the oil jet layout significantly influences lubrication of high-speed and heavy-load transmission gears, as there is only extremely limited meshing clearance for the oil stream jetting into and an inevitable blocking effect of rotating gears. A novel mathematical model for calculating the exact impingement depth of the lubrication oil jet on the spiral bevel gear surface has been established, and it contains comprehensive and detailed design parameters for the jet nozzle layout and meshing gears. Furthermore, under different jet layout parameters conditions, computational fluid dynamic numerical simulations for oil jet lubrication of an aeronautical spiral bevel gear pair were conducted and, then, the simulation results are compared with the impingement depths based on the mathematical model. The simulation results reveal that the oil volume fraction and oil pressure on the meshing area increase with the impingement depth, validating the effectiveness and reliability of the method using the impingement depth mathematical model for evaluating oil jet lubrication. Optimized oil jet layout parameters including the jet nozzle position, jet elevation angle, and jet azimuth angle have been determined and recommended, and they provide valuable theoretical design methods and technical guidance for oil jet lubrication optimization for various practical high-speed and heavy-load spiral bevel gears.

EHL Analysis of Spiral Bevel Gear Pairs considering the Contact Point Migration due to Deformation under Load

The actual contact point of a spiral bevel gear pair deviates from the theoretical contact point due to the gear deformation caused by the load. However, changes in meshing characteristics due to the migration of contact points are often ignored in previous studies on the elastohydrodynamic lubrication (EHL) analysis of spiral bevel gears. The purpose of this article is to analyze the impact of contact point migration on the results of EHL analysis. Loaded tooth contact analysis (LTCA) based on the finite element method is applied to determine the loaded contact point of the meshing tooth pair. Then, the osculating paraboloids at this point are extracted from the gear tooth surface geometry. The geometric and kinematic parameters for EHL simulation are determined according to the differential geometry theory. Numerical solutions to the Newtonian isothermal EHL of a spiral bevel gear pair at the migrated and theoretical contact points are compared to quantify the error involved in neglecting the contact point adjustment. The results show that under heavy-loaded conditions, the actual contact point of the deformed gear pair at a given pinion (gear) roll angle is different from the theoretical contact point considerably, and so do the meshing parameters. EHL analysis of spiral bevel gears under significant load using theoretical meshing parameters will result in obvious errors, especially in the prediction of film thickness.

Mathematical model and tooth contact analysis of convexo-concave helical bevel Novikov gear mesh

This paper presents a mathematical model of convexo-concave helical bevel Novikov gear mesh. The usefulness of the designed mathematical model for tooth contact analysis was demonstrated. Moreover, a number of simulations were carried out aiming at evaluation of the influence of gear position errors as well as gear parameters on contact pattern and transmission error. Obtained results were compared with a conventional spiral bevel gear pair generated by duplex helical method. For the example provided, the Novikov one was shown to have greater instantaneous contact area and therefore reduced contact stress value.

螺旋锥齿轮副有限元分析及优化

螺旋锥齿轮副有限元分析及优化