Tooth Mesh Research Articles

Effect of change of contact ratio on contact fatigue stress of involute spur gears

This paper dealt on the effect of change of contact ratio on the contact fatigue stresses generated on meshing involute spur gear teeth during operation. In this study, different cases of six contact ratio gearing between and have been analyzed. For each contact ratio the rate of load sharing and angular and radial position of load were determined on the involute profile of meshing tooth of each gearing to determine contact fatigue stress at critical condition. To come up at the result CATIA and Solid Works software involute spur gear models have been developed for stress analysis on ANSYS Workbench (FEM). Because of the decrease in value and the change in location and direction of applied load, higher contact ratio gearing resulted higher generated tooth fatigue contact stress life. The results obtained from ANSYS Workbench are compared with results of the AGMA gear formula results.

Improved analytical models for mesh stiffness and load sharing ratio of spur gears considering structure coupling effect

Abstract Due to the lack of efficient formulas, fillet foundation stiffness under double tooth engagement has long been a challenging problem for mesh stiffness calculation of spur gears by analytical method. Direct summation of the mesh stiffness of each meshing tooth pair overestimates the total mesh stiffness, which may lead to a large calculation error. An improved fillet foundation stiffness calculation method is proposed considering the structure coupling effect, namely, one gear body is shared by two meshing teeth simultaneously. On the basis of the proposed method, a mesh stiffness model and a load sharing model are analytically established. In the mesh stiffness model, fillet foundation stiffness correction factor is introduced to improve the calculation accuracy. Based on the minimum potential energy principle (MPEP), the load sharing ratio is determined by the proposed load sharing model. The accuracy of the proposed models is validated by comparing with finite element method (FEM).

Zależna od czasu niezawodność układu przekładni zębatej jako funkcja procesu stopniowego zużycia

To study dynamic evolution law of mechanical reliability caused by wear, gear transmission system is taken as a research object. Considering the effect of clearance caused by wear on gear teeth load in double meshing area, the formula of dynamic distribution load which is undertaken by two adjacent teeth is deduced. And the distributed pressure and meshing speed, which should be taken into account while calculating gear wear, are obtained based on the Winkler surface model and principle of tooth mesh. Based on the Archard’s wear model, numerical simulation model for wear in spur gear is deduced, and the wear depth of each meshing points on teeth outline with different wear cycles are obtained. The calculation wear model is replaced with a surrogate model with Neural Network and Kriging method to overcome time-consuming defect. Random process model is integrated with the surrogate model, and dynamic reliability for nonlinear stochastic structure with unknown distribution characteristic is obtained with Neural Network-based Edgeworth series technique and four moment methods, which is compared with Kriging-based Monte Carlo simulation method. The computational efficiency and accuracy are also demonstrated.

A GENERALIZED METHOD FOR PREDICTING CONTACT STRENGTH, WEAR, AND THE LIFE OF INVOLUTE CONICAL SPUR AND HELICAL GEARS: PART 1. SPUR GEARS

The paper presents the results of research undertaken to determine maximum contact pressures, wear, and the life of involute conical spur gear, taking into account gear height correction, tooth engagement, and weargenerated changes in the curvature of their involute profile. Moreover, we have established the following: (a) the initial contact pressures are higher in the internal section with double-single-double tooth engagement; (b) the highest values can be observed at the entry of single tooth engagement; (c) the maximal tooth wear of the wheels in the frontal section will be less than half of that in the internal section; (d) profile shift coefficients have an optimum at which the highest gear life is possible; and (e) gear life in the internal section will be less than half of that the frontal section. The calculations were made for a reduced cylindrical gear using a method developed by the authors. The effect of applied conditions of tooth engagement in the frontal and internal sections of a cylindrical gear ring is shown graphically. In addition, optimal correction coefficients ensuring the longest possible gear life are determined.

A GENERALIZED METHOD FOR PREDICTING CONTACT STRENGTH, WEAR, AND THE LIFE OF INVOLUTE CONICAL SPUR AND HELICAL GEARS: PART 2. HELICAL GEARS

The paper presents the results of research undertaken to determine maximum contact pressures, wear, and the life of involute conical helical gear, taking account of gear height correction, tooth engagement, and weargenerated changes in the curvature of their involute profile. We have established the following: (a) initial maximal contact pressures will be almost the same at the engagement in external and internal segments; (b) their highest meanings occur in different points of engagement depending on the coefficients of displacement; (c) the maximal tooth wear of the rings in the internal section will be a little bit lower than in the external; (d) the coefficients of displacement have an optimum at which the highest gear life is possible; and, (e) the gear life in the frontal section will be 1.25 lower than in the internal section. The calculations were made for a reduced cylindrical gear using a method developed by the authors. The effect of applied conditions of tooth engagement in the frontal and internal sections of a cylindrical gear ring is shown graphically. In addition, optimal correction coefficients ensuring the longest possible gear life are determined.

Measurement and analysis of cutting force and product surface quality during end-milling of thin-wall components

Improving product quality during machining of thin-wall components has always been a challenging problem due to the low rigidity of work parts. Therefore careful selection of process parameters to obtain the desired performance is of utmost importance. Accordingly, this study aims to contribute to the existing literature by providing the latest experimental results based on a systematic measurement of process response parameters viz. cutting force and surface roughness. Full factorial 34 experiments were carried out on end-milling of aluminum alloy AL 2024-T351 using a set of judiciously chosen cutting parameters. Furthermore, analysis of variance (ANOVA) and regression analysis were carried out on the experimental datasets to study the influence of process parameters in achieving low cutting force and surface roughness. One of the important findings was that cutting tool of 8 mm diameter produces superior surface quality at moderate cutting power consumption when employed with lower values of feed per tooth, axial depth of cut and radial depth of cut. Three dimensional (3-D) surface topography of machined surfaces revealed that chatters are more prominent at the free end of the wall. Intermittent cutting teeth engagement with the workpiece also affects the quality of the surface. Experimental investigations provided robust mathematical models to accurately predict the cutting force and surface roughness for chosen process conditions. The prediction error (absolute) of these models varies from 3.72% to 8.70%.

Intermediate layer as measure against rolling bearing creep

AbstractRolling bearings are a part of every wind‐turbine transmission. In terms of bearing design, the bearing rings are of particular interest. The current trend for increasing power and dynamic stress, together with the associated increases in specific loads, have brought creep―an irreversible relative motion between bearing rings and shafts or housings―to the forefront. Creep leads to wear and can cause shaft displacements with serious consequences for the meshing of teeth in gearboxes, for example. In fact, many insurance companies cite the creep of bearing rings as one of the main causes of wind‐turbine gearbox failures.This article presents a complex kinematic 3D FE multi‐body simulation of a rolling bearing. This simulation makes a detailed analysis of the relative motion or creep of bearing rings possible for the first time.It also presents options, based on materials technology and design, for reducing or eliminating creep in existing systems or at the product‐development phase. The 2 key solutions, both based on an additional layer between bearing and housing, that show best results are presented within this article. This gives the user specific information for optimizing the bearing structure with respect to the choice of bearing and bearing ring design to ensure that future damage is prevented.

Geometry Modification of Helical Gear for Reduction of Static Transmission Error

Gear systems are extensively employed in mechanical systems since they allow the transfer of power with a variety of gear ratios. So gears cause the inherent deflections and deformations due to the high pressure which occurs between the meshing teeth when transmit power and results in the transmission error. It is usually assumed that the transmission error and variation of the gear mesh stiffness are the dominant excitation mechanisms. Predicting the static transmission error is a necessary condition to reduce noise radiated from the gear systems. This paper aims to investigate the effect of tooth profile modifications on the transmission error of helical gear. The contact stress analysis was implemented for different roll positions to find out the most critical roll angle in view point of root flank stress. The PPTE (peak-to-peak of transmission error) is estimated at the roll angles by different loading conditions with two dimensional FEM. The optimal profile modification from the root to the tip is proposed.

Tooth surface deviation and mesh analysis of beveloid gears with parallel axis considering machine tool adjustment errors

Tooth surface deviation and mesh analysis of beveloid gears with parallel axis considering machine tool adjustment errors

Dynamic characteristics of a planetary gear system based on contact status of the tooth surface

Studies on the planetary gear have attracted considerable attention because of its advantages, such as compactness, large torque-to-weight ratio, vibrations, and high efficiency, which have resulted in its wide applications in industry, wind turbine, national defense, and aerospace fields. We have established a novel dynamic model of the planetary gear transmission by using Newton’s theory, in which some key factors such as time-variant meshing stiffness, phase relationships, and tooth contact characteristics are considered. The influences of gear axial tipping, operating conditions, and the meshing phase on the contact characteristics and the dynamic characteristics were researched systematically. It was found that the contact area of the tooth surface was moved due to the axial gear tipping, which obviously affected the meshing stiffness. With the increase in the inclination angle of the sun gear, the meshing stiffness decreases, which produces an evident influence on the high natural frequency in the planetary transmission system. In terms of the dynamic characteristics of the system, the component of rotating frequency appeared in the dynamic meshing force of the sun gear and the planetary gear. Moreover, the floating track of the center wheel varied significantly and exhibited an oval distribution as the inclination angle of the sun gear changed. When the inclination angle of the sun gear increased, the rotating frequency component increased significantly, but the other meshing frequency components remained unchanged; meanwhile, the deformation of the floating track also increased. If the inclination angle of the sun gear changes, the vibration state of the system and the collision impact could become more serious, and the lifetime of the planetary transmission system will reduce. Furthermore, when the load was increased, we found that the gear-tooth contact zone transformed from line contact to surface contact, the meshing stiffness increased, the effect of high natural frequency on the planetary transmission system became more evident, but its low-order natural frequency remained stable. With regard to the dynamic characteristics of the system, the components of the major frequency at the external gearing remained unchanged, but the rotation frequency of the sun gear and the meshing frequency amplitude increased linearly with the increase in load. In conclusion, the variation in the meshing stiffness of the planetary gear system had minor impact on the low-order natural frequency, but had a significant impact on the high natural frequency of the planetary transmission system due to the phase variation of the gear.

Power loss analysis in altered tooth-sum spur gearing

The main cause of power loss or dissipation of heat in case of meshed gears is due to friction existing between gear tooth mesh and is a major concern in low rotational speed gears, whereas in case of high operating speed the power loss taking place due to compression of air-lubricant mixture (churning losses) and windage losses due to aerodynamic trial of air lubricant mixture which controls the total efficiency needs to be considered. Therefore, in order to improve mechanical efficiency it is necessary for gear designer during gear tooth optimization to consider these energy losses. In this research paper the power loss analysis for a tooth-sum of 100 altered by ±4% operating between a specified center distance is considered. The results show that negative altered tooth-sum gearing performs better as compared to standard and positive altered tooth-sum gearing.

Power loss analysis in altered tooth-sum spur gearing

The main cause of power loss or dissipation of heat in case of meshed gears is due to friction existing between gear tooth mesh and is a major concern in low rotational speed gears, whereas in case of high operating speed the power loss taking place due to compression of air-lubricant mixture (churning losses) and windage losses due to aerodynamic trial of air lubricant mixture which controls the total efficiency needs to be considered. Therefore, in order to improve mechanical efficiency it is necessary for gear designer during gear tooth optimization to consider these energy losses. In this research paper the power loss analysis for a tooth-sum of 100 altered by ±4% operating between a specified center distance is considered. The results show that negative altered tooth-sum gearing performs better as compared to standard and positive altered tooth-sum gearing.

Vibrations of Flat‐End Cutter Entering Workpiece Process: Modeling, Simulations, and Experiments

During all the machining process, the milling cutter has to enter the workpiece either from the boundary or from the machined/unmachined surface, due to the change of machining sequence/cutter or the variation of cutting depth. Unlike the stable cutting process, the contact between cutter and machined workpiece changes significantly in the entering process, resulting in vibration and leaving marks on the machined surface. Aiming at in‐depth understanding the mechanism of this phenomenon, this paper presents a novel time‐domain simulation model to predict the dynamic response of the cutter during the entering process. Two typical entering conditions, including entering from the workpiece boundary and from the machined surface along the cycle path, are modeled based on the dynamic cutting force calculation by considering dynamic undeformed chip thickness created by consequential teeth engagement. Then, it is synthesized with the time‐varying immersion angle and exit angle of cutter teeth in the entering process to simulate the dynamic cutting forces and cutter vibrations. To validate the developed model, eight conditions in boundary entering and six conditions in cycle path entering are carried out by comparing the collected data and the predicted results. Results show that the developed model could precisely predict the dynamic cutting forces and cutter vibration, especially the forces and displacements under the varied cutter‐workpiece contact.

An efficient model of load distribution for helical gears with modification and misalignment

An efficient model is introduced for evaluating the load distribution of helical gears, considering tooth modifications and misalignment errors. Instant contact points are obtained by unloaded meshing simulation. Combined with the full numerical method for elliptical Hertzian contact, the contact line under load is determined. Then the load distribution is derived from the minimization of potential energy. The proposed model is numerically implemented by a fixed-point iteration method based computational scheme, assuring high efficiency and superior versatility for tackling modifications and misalignments. And it is verified by finite element analysis. The effects of profile crowning, lead modification, misalignment and input torque on load distribution are investigated. Results indicate that contact pattern shrinks with increasing magnitude of profile crowning and decreasing input torque, resulting in abrupt load transitions between two and three meshing tooth pairs. While lead modification can transfer load from the edge of tooth surface to the center by inclining contact pattern to longitudinal direction, providing desirable load distribution. In addition, misalignment deviates contact pattern and sharing load respectively towards the ends of tooth profile and meshing cycle.

Prediction of micropitting damage in gear teeth contacts considering the concurrent effects of surface fatigue and mild wear

The present paper studies the occurrence of micropitting damage in gear teeth contacts. An existing general micropitting model, which accounts for mixed lubrication conditions, stress history, and fatigue damage accumulation, is adapted here to deal with transient contact conditions that exist during meshing of gear teeth. The model considers the concurrent effects of surface fatigue and mild wear on the evolution of tooth surface roughness and therefore captures the complexities of damage accumulation on tooth flanks in a more realistic manner than hitherto possible. Applicability of the model to gear contact conditions is first confirmed by comparing its predictions to relevant experiments carried out on a triple-disc contact fatigue rig. Application of the model to a pair of meshing spur gears shows that under low specific oil film thickness conditions, the continuous competition between surface fatigue and mild wear determines the overall level as well as the distribution of micropitting damage along the tooth flanks. The outcome of this competition in terms of the final damage level is dependent on contact sliding speed, pressure and specific film thickness. In general, with no surface wear, micropitting damage increases with decreasing film thickness as may be expected, but when some wear is present micropitting damage may reduce as film thickness is lowered to the point where wear takes over and removes the asperity peaks and hence reduces asperity interactions. Similarly, when wear is negligible, increased sliding can increase the level of micropitting by increasing the number of asperity stress cycles, but when wear is present, an increase in sliding may lead to a reduction in micropitting due to faster removal of asperity peaks. The results suggest that an ideal situation in terms of surface damage prevention is that in which some mild wear at the start of gear pair operation adequately wears-in the tooth surfaces, thus reducing subsequent micropitting, followed by zero or negligible wear for the rest of the gear pair life. The complexities of the interaction between the contact conditions, wear and surface fatigue, as evident in the present results, mean that a full treatment of gear micropitting requires a numerical model along the lines of that applied here, and that use of overly simplified criteria may lead to misleading predictions.

Experimental study of dynamic strain for gear tooth using fiber Bragg gratings and piezoelectric strain sensors

It has always been a critical task to understand gear dynamics for gear design and condition monitoring. Many gear models have been proposed to simulate gear meshing dynamics. However, most of the theoretical models are based on simplified gear structure and may contain approximation errors. Direct measuring of gear strain is important for gear design validation, load analysis, reliability assessment, gear condition monitoring, etc. Most of the existing studies of tooth strain measurements are performed under static load condition. In this paper, we investigate new measuring techniques using fiber Bragg grating sensor and piezoelectric strain for gear dynamic strain measurement. We conduct gear dynamic strain measurement under both normal and pitted conditions to evaluate the strain transition process and pitting effect. The experiments are performed on an industrial gearbox with relatively small module gears. Multiple combinations of speed and load conditions are tested and the results are discussed and analyzed. We analyze multiple factors that affect the tooth root stress, including speed, load, extended tooth meshing, etc. It is found that under low operation speed range, the tooth root strain is mainly determined by the torque, while in the medium to high speed range, the tooth root strain is jointly affected by speed and torque. Extended tooth contact is shown in the measurement results with strong evidence. It conforms to earlier founding that the transmission error and dynamic load factor are overestimated for spur gear under heavy load. We also evaluate the change in dynamic strain caused by pitted tooth surface. It is shown that pitting faults lead to decreased bending strain on the tooth, especially in single-tooth contact zone, which represents a loss in torque and possibly reduced mesh stiffness. Numerical simulations are also provided to make comparisons and help to interpret the experimental results.

Analysis of Gear Wheel Body Influence on Gearing Stiffness

The development of modern machinery and production facilities is characterized by constantly increasing performance parameters at the decreasing weight of the machine. It is also a characteristic of the design of the body shape of larger wheel gears. The lowering the weight of the body of wheel gears affects to the deformation and mesh stiffness of the gearing. This work is dealing with the design of large gears, which is assessed based on tooth deformation and mesh stiffness of gearing. The task of this work is decide the design of a body of big gear wheels made as monolithic unit, relative on tooth deformation in meshing, accordingly on the mesh stiffness of gearing. Tooth deformation is calculated by finite element method.

Design and analysis of high contact ratio spiral bevel gears by modified curvature motion method

This paper presents a new method to design a seventh-order transmission error for high contact ratio spiral bevel gears by the modified curvature motion method to reach the purpose of reducing or eliminating gear vibration and noise. In this paper, firstly, based on the predesigned seventh-order transmission error, the polynomial coefficients of transmission error curve can be obtained. Secondly, a method named modified curvature motion method is used to generate the spiral bevel gear with the predesigned transmission error. Lastly, based on TCA and LTCA, we verify the feasibility of the modified curvature motion method to generate spiral bevel gear with seventh-order transmission error, and the meshing impact of gear set with the seventh-order and second-order function of transmission error is analyzed and compared. The results of a numerical example show that the seventh-order transmission error acquired by the modified curvature motion method can effectively reduce the meshing impact of spiral bevel gears. The tooth modification method and meshing impact analysis method can serve as a basis for developing a general technique of flank modification for spiral bevel gears.

Influence of the Random System Parameters on the Nonlinear Dynamic Characteristics of Gear Transmission System

Abstract In order to analyze the influence of the random parameters of the system on the nonlinear dynamic characteristics of the gear transmission system, considering the random perturbation of damping ratio, gear backlash, meshing frequency, meshing stiffness and the low frequency excitation caused by torque fluctuation, the random vibration equations of three-degree-of-freedom gear transmission system are established according to the Newton’s law. The motion differential equations are solved by the Runge–Kutta method. The effects of different random parameters such as load ratio, tooth frequency ratio, damping ratio, gear backlash and meshing stiffness on the dynamic response of the gear transmission system are analyzed in light and heavy loads and low and high speeds.

Methods of Determining Sock Values and the Distance Between Axes of the Gearboxteething Using a Fitted Tooth Engagement

Abstract There are several constructive variants of devices built for complex control of engagement on both sides aimed at controlling both internal and external shocks, all of which featuring a standard wheel compound. By the method of forced tooth engagement fitted between the standard wheel and the measuring wheel and using the spectral analysis, constructive errors of the gear wheels can be quickly determined, especially those consisting in shocks and the variation of the distance between the axes, errors that severely impact on operation. At the National Institute of Research and Development in Mechatronics and Measurement Technique was developed a device used to control shock values and the distance between the axis of the gearboxes (for four of the gearbox speeds) by means of forced engagement and complex harmonic analysis.