Gear Pair Research Articles

Research on the varying-displacement-coefficient modification method for automobile steering noncircular sector gears

The local drum shape tooth profile is adopted for automobile steering noncircular sector gears, which can be obtained according to a piecewise linear function modification on CNC gear shaper. In the practical process, the actual amount of drum shape is always smaller than the theoretical amount, and we conclude that overcut of the tooth profile occurred. Because the modification coefficient is variable, we call it varying-displacement-coefficient modification(VDCM). Currently, researches on tooth profile of noncircular sector gears are primarily concerned with constant modification coefficient to improve gear transmission performance, while modification functions, overcut, and methods of reducing or eliminating the overcut are rarely touched upon.This paper focus on the VDCM method of automobile steering noncircular sector gears. On the basis of noncircular sector gear and rack pair meshing theory, the modifying motion mathematical model is first established, including kinematic relations, pith curves, track of relative instantaneous centre point, calculation formula for the modified tooth profile. And then, the reasons for the overcut are analyzed, and the local overlap and separation of the tooth profile are found. To reduce the overcut amount, a cosine function modification method is proposed. Furthermore, an inverse calculation method for the rack tool tooth profile is proposed to eliminate the overcut entirely. The VDCM modification methods are verified by simulation, trial cutting and parts measurement.

Vibration signal modeling of planetary gearbox based on dynamics and finite element method for tooth crack diagnosis

Planetary gear set contains many kinds of nonlinear factors, such as time-varying meshing stiffness, bearing support, backlash, and comprehensive transmission error, which will deeply affect the gearbox response behaviors and vibration characteristics. During the operation of planetary gear set, there are several gear pairs meshing simultaneously, which will lead to multiple vibration sources and complicate vibration transmission. The revolution of the planet gears makes the meshing force of the gear pairs vary periodically, and the continuous motion of the meshing point also changes the length of vibration transmission path. This study aims to establish a hybrid model that can simulate the vibration signals of gearbox measuring points through fusing the dynamic model of planetary gear set and the transmission path model. Through the simulation analysis, the vibration characteristics of the measuring point signal of the planetary gearbox are revealed, and the crack fault of the planet gear tooth is effectively isolated. Finally, the availability and validity of the presented model are experimentally verified, and the magnitude match is up to 78%. The model can not only provide a theoretical basis for data-driven fault diagnosis methods, but also solve the pain point of diagnostic samples scale and balance by simulation means.

Optimization design for dynamic characteristics of face gear drive with surface-active modification

The surface-active modification(SAM) method is proposed to decrease the vibration of the face gear drive. Firstly, the unloading performances such as the fourth-order transmission error(4-TE), the length of the contact ellipse, and the direction of the contact path are preset to modify the face gear pair. Secondly, a dynamic model is developed to attain the normal vibration acceleration(NVA) which is chosen as the optimization objective. The genetic algorithm(GA) is applied to solve the optimization model for searching for the optimal modification parameters. Thirdly, a numerical calculation is performed to investigate the influence of the modification parameters and the meshing stiffness on vibration. Besides, the bifurcation characteristics of the system are also explored. The results show that the amplitude of the loaded transmission error(ALTE) and the vibration are reduced after the optimization. Not only is vibration linked to mean meshing stiffness, but also the harmonic amplitude of meshing stiffness impacts it significantly. SAM lessens the range of chaotic motion, which helps to improve system stability. This study provides a theoretical basis for the vibration reduction of face gear pairs design.

Analyzing the Life Prediction of Spur Gear based on Vinyl Ester with Different Fibre Proportion

The gear is an essential part of every mechanical power transmission system, as well as most industrial rotating machinery. Gears may grow to dominate as the most effective mechanism for transmitting power in future machines due to their high degree of durability and compactness. The vinyl ester resin have high strength and low frictional of porous carbon material. The Vinyl ester resin is used as a reinforced material in plastic gear. In this work, Vinyl Ester and Glass fiber composite material with different proportions were equipped for strengthen cast plastic gear. The spur gear pair was used as the test gears, and the glass transition temperature and fatigue tests were used to determine the gear's life span. Finally, the composite gear has to be analyzed.

Research on Multiobjective Optimization Design of Meshing Performance and Dynamic Characteristics of Herringbone Gear Pair Under 3D Modification

Abstract Herringbone gear transmission system is widely used in high-speed overloaded fields such as ships. Tooth deformation and installation error, which can cause meshing impact, load mutation, and load uneven, will seriously affect dynamic performance of the whole transmission system. Modification technology is the most effective way to achieve damping and noise reduction. In this article, we propose a three-dimensional (3D) modified tooth surface by grinding wheel along axial to the spiral rise and along radial to the parabolic movement based on the grinding principle and a multiobjective ant lion optimizer model for optimizing meshing performance and dynamic characteristics of herringbone gear transmission system and analyze the impact of optimized modifications of tooth profile, axial, and three dimension on meshing performance, loaded transmission error, load distribution coefficient and meshing impact, meshing stiffness, and vibration acceleration by the example. The results show that the 3D modification of optimization can not only eliminate the contact between the tooth side edge and tooth top edge but also eliminate the influence of installation error on contact performance. The root mean square values of the relative comprehensive vibration acceleration of tooth profile modification, axial modification, and 3D modification are reduced by 30.11%, 49.24%, and 61.41% compared with the standard, respectively. The 3D modification can greatly reduce tooth vibration, reduce resonance peak, and achieve the goal of noise reduction.

Dynamic modeling and analysis of elastic isolation damping gears

Transmission error is the main excitation source of gear vibration and noise, how to reduce the transmission error has always been the focus of the research on gear dynamics. In this study, a new type of cylindrical spur gear with elastic isolation is developed for the reduction of transmission error. The elastic isolation damping gear includes three parts: the gear body, the elastic isolation layer, and the involute profile body. Dynamic models are established with the elastic isolation damping gear using lumped parameter method. Dynamic characteristics are simulated via spur gear pair examples by the Runge-Kutta algorithm. By comparing the simulation results of three gear models, the dynamic response of the elastic isolation damping gear with sliding friction is illustrated. The influence of different parameters of the elastic isolation layer on the dynamic response for the elastic isolation damping gear model is carried out. The results indicate that the proposed elastic isolation damping gear model is effective in reducing dynamic transmission error, especially for torque fluctuation, high-speed and heavy-duty conditions. Parameter influence analysis guides the design of elastic isolation damping gears with low transmission error.

Wear prediction and meshing characteristics for the planetary gear set considering angular misalignment and rotating carrier

This paper focuses on the effect of angular misalignment on wear prediction of the planetary gear set with the rotating carrier, which is more complex than that of the parallel-axis gear due to the position changing of the planet gears. The wear depth is calculated based on the Archard’s wear theory, the load distribution is obtained by the three dimensional loaded tooth contact analysis (3D-LTCA) method, and the effect of angular misalignment is considered by introducing the change in meshing clearance between the two engaged tooth flanks. The load distribution, the time-varying mesh stiffness (TVMS) and the backlash of gear pairs are presented under different wear levels. The results show that, with the combined effect of angular misalignment and rotating carrier, the wear depth on both sides of the face width is larger than that in the middle, and the difference is the greatest at the root. Moreover, TVMS is affected not only by the tooth wear, but also by the rotating carrier, and the cycle of TVMS and the backlash is half of that of the carrier rotation.

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.

Failure Modes and Effect Analysis of Gear Pair

In the present study, the failure mode and effect analysis (FMEA) process has been used to determine the probable failure mechanisms of gear pairs and their implications on the performance, availability, and cost. The risk priority number (RPN) is calculated to rank the failure modes and identify high-risk failures. The methods are proposed to minimize high-risk failure modes.

Coefficient of friction behavior of gear oils and significance for the meshing process of spur gears

The mechanical properties of oils are determined using test methods. There are standardized test methods for determining viscosity and density. The characterization of transmission oil based on its dynamic viscosity alone is not sufficient for the physical explanation of different levels of noise emissions in vehicle transmissions. For this reason, the test procedure for determining the coefficient of friction is used in the following to enable a further differentiation between the oils according to mechanical properties.In gear transmissions with involute gear teeth, rolling friction occurs in the gear pair meshing along the line of action due to the variation in the equivalent curvature radii throughout the meshing cycle. This is rolling friction on which a sliding friction component, so-called slip, is superimposed. Pure rolling friction only occurs in the pitch point. From the pitch point to the start and end of the meshing, there is a superimposed sliding friction component that increases with increasing distance from the pitch point. Slip values occur in the range of 5–50% depending on tooth geometry.These friction conditions during tooth flank lubrication can be assessed using the Stribeck curve. The Stribeck curve represents the coefficient of friction as a function of the speed. A mini traction machine from PCS Instruments with a ball/plate measurement setup was used to determine the coefficient of friction behavior of gear oils. This allows the coefficient of friction of an oil to be assessed at low speeds in the range from boundary and mixed friction to elastohydrodynamic fluid friction at high speeds.The investigations show that the coefficient of friction behavior of a gear oil depends on the oil viscosity and above all on the chemical composition. The lower the coefficient of friction, the less energy is required to shear the lubricating film and the lower the power transmission through the fluid. The coefficient of friction is a property that is dominated by the type of base oil and the type of VI improver in the area of mixed and fluid friction, especially with additional sliding in contact.It will be shown in the paper that the use of a gear oil that has been optimized with regard to the coefficient of friction curve can reduce the entry impacts of meshing gear pairs under vibration excitation and the gear transmission thus generates lower noise emissions.

Novel kinematic and geometric views for improving tooth contact analysis of spatial gears

AbstractTooth contact analysis (TCA) has been widely applied to evaluate the working performance of gear pairs. TCA is often formulated with five unknowns and five independent scalar equations. The solution process involves a global optimization problem with strong nonlinearity and numerical instability, especially for spatial gears with complicated tooth geometries. This study proposes novel kinematic and geometric views of gearing that reveal insights into the meshing process of spatial gears. One unknown can be removed from the position and normal equations of the TCA formulation. To solve the remaining four unknowns, a simplified optimization model with two unknowns is proposed, and the other two unknowns are obtained by using geometric iterative methods or directly from explicit expressions in some cases. A general algorithm was developed to solve the simplified TCA. The test results of both the spiral bevel and face gear drives validate the effectiveness of the proposed method.

Modulation sidebands analysis of coupled bevel gear pair and planetary gear train system

This paper proposed a dynamic model based on the lumped parameter method and the Timoshenko beam theory to explore the sideband distribution law of the coupled bevel gear pair (BGP) and planetary gear train (PGT) system. The pass-effect of the PGT is simulated without adding extra window functions. A finite element method is proposed to solve the time-varying mesh stiffness (TVMS) of the BGP. The vibration signal of the system triggered by the TVMS of all gear pairs is obtained and validated by the experiment. It is observed that the carrier rotation frequency can modulate both the meshing frequency of the PGT and that of the BGP and their harmonics. Furthermore, the influence of the supporting state of the intermediate shaft on the sideband energy is studied. It is revealed that the farther the support positions of the intermediate shaft are from both ends, and the smaller the radial support stiffness of the bearing near the sun gear, the better it is to obtain smaller sideband energy near the meshing frequency of the BGP.

Performance of a New Aeronautic Oil-Guiding Splash Lubrication System

Among ever-increasing demands for low power consumption, low weight, and compact reducer systems, an oil-guiding splash lubrication method integrating the oil-guiding cylinder and pipes is suggested to be more suitable for light helicopters, instead of conventional splash or oil jet lubrication. Aiming at improving the lubrication and cooling performance of this special lubrication method, this paper introduces an oil-guiding channel to increase oil quantity reaching the driving gear, bearings, and spline. Firstly, the lubrication and cooling effect of the oil-guiding channel in the main gearbox is investigated at various speeds and oil depths by leveraging with a computational fluid dynamics (CFD) technique. Then, a specialized test bench is set up and utilized for experiments to verify the CFD study. These results show that the numerical results are very satisfactory with the data of experimentation, and the maximum value of relative errors is no more than 15%. What is more, the oil flow rate passing through the monitoring plane with the oil-guiding channel is much greater than that without the channel by about three orders of magnitude. It also suggests that the oil-guiding channel could dramatically increase the lubricating oil in the meshing gear pair, and significantly improve the lubrication and cooling effect.

Estimation of the damping model of a spur gear pair system including a time-varying loading

The integral method was used in a previous research to identify the damping model but this technique has some limitations in estimating the damping model in a gear system including time-varying loading conditions. To overcome these limitations, the integral method is reformulated in this research to identify the damping model on spur gear pair system including variable loading. The motion equations presented in terms of integrals, including time-varying loading conditions, are solved by linear least squares method to characterise the constant piecewise model. Continuous wavelet transform method is used to validate the constant damping model. The new methodology is tested with a signal obtained from numerical simulation.

Nonlinear Dynamics Analysis of a Multistage Planetary Gear Transmission System

A nonlinear dynamic model for a multistage planetary gear transmission system, which consists of two-stage planetary gear plus one-stage parallel shaft gear, is proposed. The time-varying meshing stiffness, comprehensive meshing errors and backlash between gear pairs are taken into account in the model, and the connections between the gear stages are characterized by coupling stiffness. The dimensionless vibration differential equations of the system are derived and solved numerically. By means of global bifurcation diagram, largest Lyapunov exponent (LLE), phase diagram and Poincaré map, the stability of the system is studied with the bifurcation parameters variation including excitation frequency and comprehensive meshing errors. The results demonstrate that the system presents strange attractors with rich forms under different parameter combinations. With the increase of the excitation frequency, the meshing state of the system changes, showing a complex motion and indicating the sensitivity of the system to external excitation. Under the variation of the bifurcation parameter of comprehensive meshing error, the complex dynamic behavior of the system is observed, it is found that the increase of comprehensive meshing error has a negative impact on the stability of the system.

Simulation of Meshing of Herringbone Double Circular-Arc Helical Gears using Multibody Dynamic Analysis Software

This paper aims to complete the simulation of meshing of a pair of herringbone double circular-arc helical gears by using the multibody dynamic analysis software, SolidWorks motion. Three types of edge modifications, including no edge modification, chamfered edge modification, and rounded edge modification, are applied respectively to the pair of gears. The output angular velocities and contact regions corresponding with the three types of edge modifications are analyzed. Moreover, whether the center distance assembly error affects the output angular velocity and contact regions are analyzed. The results obtained by the simulation of meshing show that rounded edge modification is better than chamfered edge modification, and chamfered edge modification is better than no edge modification. The center distance assembly error has no effect on the output angular velocity and has little effect on the contact regions. Therefore, double circular-arc helical gears are not sensitive to center distance assembly errors.

Cutterhead approximation machining method of line contact spiral bevel gear pairs based on controlling topological deviations

To improve the meshing performance and increase the bearing capacity and service life of spiral gear pairs, a cutterhead approximation machining method based on controlling geometric topological deviations was proposed to solve the problem where line contact spiral bevel gears with tapered teeth depth cannot be machined by cutterheads. First, a mathematical model of the line contact conjugate flank was established, and the geometric topological deviations model of the comparison between the machining tooth flank and the theoretical tooth flank was obtained. Second, the deviation of each tooth flank point was calculated by the topological differential calculus analysis. Finally, with the machining tooth flank approaching the theoretical tooth flank as the modification objective, the additional cutting motions and machining compensation parameters of cutterheads were obtained to control the machining tooth flank deviations and reduce them to the allowable deviations of the theoretical tooth flank, and the cutterhead approximation machining of line contact spiral bevel gear pairs with tapered teeth depth was realized. The contact simulation analysis and rolling test verified the correctness of the line contact conjugate flank model and the feasibility of the cutterhead approximation machining method.

Geometric contact characteristics and sensitivity analysis of variable hyperbolic circular-arc-tooth-trace cylindrical gear with error theory considered

Gear transmission characteristics are the most important research contents in gear transmission, and contact characteristics are important factors that affect gear transmission performance. The establishment of tooth surface contact analysis (TCA) model of a gear pair plays a guiding role in analyzing its contact characteristics. The rotary surface equation of the variable hyperbolic circular-arc-tooth-trace (VH-CATT) cylindrical gear cutter is obtained with the large cutter forming principle, and the mathematical model of the gear tooth surface is established based on the gear meshing conditions. With the influence of installation error on gear contact performance considered, a TCA model with installation error was established. The influence of different installation errors and different design parameters on the geometric contact characteristics and sensitivity of the gear pair is analyzed. The analysis results show that the central distance error may affect the contact ratio of the VH-CATT cylindrical gear pair and that the shaft parallelism error has a great influence on its transmission characteristics, greatly changing the size and position of the gear pair contact area. The design parameters also affect the size and location of the contact area to various degrees.

Analytical algorithm for time-varying meshing stiffness of modified herringbone gear pair

This paper jointly uses the slicing method and the potential energy method to propose an analytical algorithm that considers the meshing stiffness of the modified herringbone gear pair and its axial force. The calculation results are compared with the finite element and ISO calculation results to verify the accuracy of the analytical algorithm. The algorithm is used to analyze the influence of modification on meshing stiffness of the herringbone gear pair. The calculation results show that the modification length, axial modification and the meshing stiffness of the single pair of herringbone gears and the time-varying meshing stiffness of the herringbone gear pair decrease with the increase of tooth profile modification. The mean value of time-varying meshing stiffness decreases with the increase of tooth profile modification. It decreases first and then tends to be stable with the increase of tooth profile modification length and axial modification. The variance of time-varying meshing stiffness increases first and then decreases with the increase of tooth profile modification of the pinion. It decreases with the increase of tooth profile modification of the herringbone gear, increases first and then decreases and then tends to be stable with the increase of tooth profile modification length. The variance decreases with the increase of axial modification of the pinion. It decreases first and then increases and tends to be stable with the increase of axial modification of the herringbone gear.

Practical Example of Modification of a Gearbox Lubrication System

This paper presents the optimization of the lubrication method of a helical bevel gearbox, which is part of a pickling line. The first gear stage of this gearbox showed frequent failures. The bevel gearing and bearings were damaged. Damage analysis was performed, based on which a change in bevel gearing and bearing lubrication was proposed. In this case, the original transmission was lubricated by dip lubrication. The bevel gear wheel was insufficiently submerged below the lubricating oil level. Due to insufficient lubrication of the bevel gearing, both gear wheels, the bevel pinion, and the bevel wheel were damaged. Central circulating lubrication has been proposed for the bevel gear pair and first gearbox shaft bearings. This paper deals with the design of circulating lubrication components. Changes and modifications to an existing lubrication system are proposed. The layout of the gearbox in question was not originally designed and adapted for the circulating lubrication required. To improve the original lubrication system, it was decided that it should be redesigned with central circulating lubrication, which meant implementing the necessary gearbox casing modifications. Our novel contribution is the proposition of an innovative transmission lubrication system aimed at increasing the service life parameters of the transmission. After the implementation of the proposed modifications to the lubrication method, a period of monitoring the operating characteristics of the gearbox followed. With the modification of the lubrication system of the bevel gear pair, the temperature on the gearing surface was lowered by 39%. The service life of the gearbox increased from the original 1.9 years to at least 5 years. On the basis of the long-term monitoring of changes caused by the adjustment of the lubrication method, we can state that the requirement was met, and the frequent failures of this gearbox were eliminated.