Helical Gear Set Research Articles

A Numerical Analysis of Materials Effects on Involute Helical Gear Set Meshing

A Numerical Analysis of Materials Effects on Involute Helical Gear Set Meshing

WEAR LOAD CAPACITY OF CROSSED HELICAL GEARS

The paper presents a wear load capacity of crossed helical gears (gear pair consists of a worm and a helical gear). Crossed helical gears are similar to worm gear pairs, and it is logical to extend the load capacity calculation approach of worm gears for the case of crossed helical gears. One of the disadvantages of crossed helical gear sets is very high running-in wear. The paper explains the transition between running-in and steady-state wear and proposes a joint wear calculation model. The paper outlines a proposal to extend the calculation method for wear load capacity from a worm gear pair to the case of crossed helical gears (a worm with a helical gear). This calculation method for determining the wear load capacity of crossed helical gears is verified for the cases when the wheel is of bronze CuSn12Ni2-C-GCB and sintered steel Fe1.5Cr0.2Mo.

Application of the Taguchi Method and Grey Relational Analysis for Multi-Objective Optimization of a Two-Stage Bevel Helical Gearbox

This paper introduces a novel approach to deal with the multi-objective optimization of a two-stage bevel helical gearbox by applying the Taguchi method and Grey Relation Analysis (GRA). The goal of the study is to find optimal main design factors that minimize the gearbox volume and maximize the gearbox efficiency. To accomplish this, five main design parameters were selected: the coefficients of wheel face width (CWFW) of the bevel and the helical gear sets, the allowable contact stresses (ACS) of the first and the second stages, and the gear ratio of the first stage. Furthermore, two single targets were investigated: minimum gearbox volumes, and maximum gearbox efficiency. Also, the multi-objective optimization problem is solved through two steps: Step 1 for closing the gap between variable levels and Step 2 for determining the optimal main design factors. The study’s findings were used to introduce the optimum values of five major design parameters for designing a two-stage helical gearbox.

Investigation of the Effect of Geometry Characteristics on Bending Stress of Asymmetric Helical Gears by Using Finite Elements Analysis

Asymmetric helical gears have been under investigation for more than two decades due to their inherent ability to handle greater bending loads than their spur counterparts of comparable size (i.e., the number of teeth and module). For this type of gear, only one side of each gear tooth in a geared mechanism is usually loaded (driving/driven side), whereas the other remains mostly unloaded (coast side). Due to the asymmetry of the tooth, a nonlinear model is used. For that reason, a numerical design procedure is introduced involving the geometrical and structural modelling of conjugate helical gear sets. This is accomplished with the tool of Finite Element Analysis (FEA) which is presented to the scientific literature. The basic geometry is initially generated in 2D and thereafter converted to a 3D shape using Boolean operations. The rigid body which is necessary for FEA software is produced from Computer Aided Design (CAD) software (SolidWorks). This paper is focused on the effect analysis of different geometry characteristics on bending loads. The effects on bending stress play a significant role in gear design wherein its magnitude is controlled by the nominal bending stress and the stress concentration due to the geometrical shape of the teeth. The analysis of this effect of the different geometrical characteristics in the load is presented in detail. Moreover, a comparison of the stresses that are developed between pairs with asymmetrical helical teeth by keeping one geometric parameter constant and modifying the values of the other two parameters is presented.

Design of a helical gear set with adequate linear tip-relief leading to improved static and dynamic characteristics

This study aims to improve the static and dynamic characteristics of a helical gear pair by optimizing the parameters of linear tip-relief. The static analysis intends to reduce the maximum contact stress to extend the service life of the gear pair, while the dynamic analysis attempts to reduce the dynamic transmission error (DTE).First, mathematical models of a helical gear pair generated by rack-cutters with linear tip-relief were developed based on the theory of gearing. Tooth contact analysis enabled us to estimate static transmission error and contact pattern of the gear pair under various assembly errors. Additionally, the contact stress contour and mesh stiffness were calculated through loaded tooth contact analysis by using finite element analysis. A dynamic model of the helical gear pair was also developed to simulate the dynamic characteristics under various rotational speeds, including DTE and vibration energy. Finally, the simulation results revealed that the high contact stress, DTE, and vibration energy of the original helical gear set were successfully reduced by the improved linear tip-relief parameters.

A study on determination of optimum gear ratios of a worm -helical gearbox

This paper introduces a new study on the optimum calculation of the gear ratios of a worm-helical gearbox. For finding the gear ratios, the cross section area of the gearbox was chosen as the objective function of the optimization problem. Moreover, the influence of the input parameters including the total gearbox ratio, the allowable contact stress and the wheel face width coefficient of the helical gear set, the output torque was investigated. For evaluation of the influence of these parameters on the optimum gear ratios, an “experiment” was designed and a computer program was built for performing the “experiment”. In addition, models for determining the optimum gear ratios of the gearbox were proposed. Based on those models, the gear ratios can achieve high accuracy with simplification.

The influence of friction on the tooth normal force of spur and helical gears

The tooth normal force is one of the main influencing factors for calculating the pitting load-carrying capacity of gears. In the current standards for cylindrical gears, it is calculated without regard to the friction force’s influence. This paper presents a simple local calculation approach for determining the friction force and driving direction’s influence on the tooth normal force of cylindrical gears on the whole tooth flank. Unlike previous models, without the need to set up a dynamic model of the gear mesh and having to solve differential equations numerically. For two exemplary spur and one helical gear set, the tooth normal forces are calculated considering the friction force and the driving direction’s influence and without regard to these effects. A comparison is carried out and the results are discussed thoroughly.

Determination of optimum gear ratios of a three stage bevel helical gearbox

This paper presents a study on the determination of optimum gear ratios of a three stage bevel helical gearbox. In the study, for finding the optimum gear ratios, an optimization problem was conducted. In the optimization problem, the cross sectional area of the gearbox was chosen as the objective function. Also, the influence of input factors including the total gearbox ratio, the coefficient of the face width of the bevel and the helical gear sets, the allowable contact stress and the output torque were considered. evaluating the effect of these parameters on the optimum gear ratios, an “experiment” was designed and a computer program was constructed to perform the “experiment”. From the results of the study, the effect of the input factors on the optimum gear ratios were learned and several models for determination of the optimum gear ratios were proposed.

Dynamic modelling of differential bevel gear system in the presence of a defect

A differential bevel gear set has a pivotal role in automotive applications. Unlike spur or helical planetary gear set, up to now, far too little attention has been paid to propose an adequate analytical model to analyze the dynamic behavior of the differential due to its complexities. One of the complexities is the fact that the differential pinion possesses simultaneous angular velocities about non-collinear axes. The aim of this paper is to investigate the dynamic response of the differential system whose bearings are deemed to be flexible and gear mesh stiffnesses are computed through potential energy. The analytical model of the differential bevel gear has been developed by means of Newton-Euler formulation and utilized it to scrutinize differential’s natural frequencies and vibration modes. The sweep frequency analysis has been used to represent the dynamic response of the system. After that, we have incorporated the position error of the differential pinion into the differential model, and the obtained results have been compared with a healthy one. This work may be considered as an important threshold to get full dynamic details of the differential bevel gear set, and to offer insights for enhancing the differential design.

An approach for design optimization of helical gear pair with balanced specific sliding and modified tooth profile

A unique perspective in design optimization of helical gear pair has been emerged and presented in this article. Specific sliding needs to be balanced for enhancing wear and scuffing resistance of helical gears. Optimized modification in tooth profile has immense benefits in gear operations. Effect of profile shift and specific sliding on design optimization of helical gear pair have been studied and found to be beneficial of great importance. Preventing undercutting, balancing of wear and bending fatigue strength and centre distance adjustment are some of the advantages of profile tooth modifications. Real-coded genetic algorithm (RCGA) has been used to attain minimum volume of helical gear pair. Profile shift coefficients for gear and pinion have been included as design variables along with mostly used generic design variables, module, face width and number of teeth on pinion. Specific sliding, transverse contact ratio and face width constraint along with other strength requirements are the design constraints. The optimal design solutions obtained with and without profile shift are recorded and compared with commercially used software for validation. 3D computer-aided design (CAD) models have been developed by using the optimized results obtained from RCGA and commercially used software. These CAD models are used for performing finite element analysis (FEA) on the helical gear set for analyzing the stress developed in the gear pair. The developed stress in the helical gear pair is found to be well within the allowable stress limits for the gear pair.

Numerical study concerning the influence of contact ratio at helical involute gears

In the present paper some aspects of the influence of the overlap ratio of the gear set on its dynamic comportment was studied. In this aim, the values of angular acceleration of two helical involute gear sets having the same characteristics - excepting the face width - are determined. The study is performed using a software in the category of The Multibody Dynamics Simulation Solution for simulation the dynamic comportment for various width of the driven gear, at various torques and various angular velocities.

Calculation of time dependent mesh stiffness of helical planetary gear system using analytical approach

Time-dependent mesh stiffness is a most important reason of vibration and dynamic excitation in gear sets. In this research, analytical formulas of the helical gear set and the planetary gear system are combined to calculate the time-dependent mesh stiffness of the helical planetary gear system. For this purpose, at the first step, the analytical equations are derived for the spur gear pair. Then by dividing a helical tooth into the several independent thin spur tooth slices, the helical gear pair mesh stiffness is extracted. Finally, these equations are extended to the helical planetary gear system. The suggested analytical results and those which obtained by the finite element method (FEM) are compared and are in good agreement when the helix angle is less than 15 degrees. Also, the helical planetary gear system mesh stiffness in different cases such as fixed carrier, fixed sun gear and fixed ring gears is calculated. These results show that the value of mesh frequency ratio in each case scales the mesh stiffness shapes in the rotation angle direction. In other words, mesh frequency ratio parameter determines the number of meshing period in each rotation of planets.

Regenerative braking algorithm for the electric vehicle with a seamless two-speed transmission

Better energy efficiency can be acquired by an appropriate shift operation during the regenerative braking process. In this work, an electric vehicle equipped with a two-speed automated transmission was used as the target vehicle. The transmission consists of two-stage planetary gear sets, a helical gear set, and two brakes. A hierarchical algorithm is presented for the electric vehicle. The upper-level algorithm was synthesized to assign braking force among regenerative braking, friction braking, front axle braking, and rear axle braking. Based on the motor external characteristic and ECE-R13 regulations, the work designed the dynamic distribution strategy for maximum use of regenerative braking. In the medium-level algorithm, the motor speed, efficiency characteristics, and assigned regenerative braking torque from upper-level algorithm were used to analyze the optimal shift points for improving regenerative efficiency. Then, a shift points table was drawn. In the lower-level algorithm, the linear control for the transmission was given to ensure seamless and smooth shifting. Finally, hardware-in-loop simulations were carried out. The results show that the proposed algorithm can improve performance in energy efficiency in the experimental braking events.

Comprehensive simulation methods for crossed helical gear sets with the main focus on the calculation of contact patterns

Crossed helical gear sets consist of two helical gears paired at an angle of intersection between Σ > 0° and Σ ≤ 90° and are characterized by point contact. Typical applications of this gear type are actuators, e. g. in automobiles or medical devices. Various materials such as steel, cast iron, bronze or plastic are used for crossed helical gears. Main advantages are easy assembly, quiet operation, variable angles of intersection and high gear ratios in a single gear stage. FZG has developed the FVA-Software SCHRAD2 which serves for the calculation and simulation of crossed helical gears. SCHRAD2 covers the following basic calculation functions: Main geometry, Tolerances (ISO 1328, DIN 3961, DIN 3974), Load carrying capacity (Niemann-Winter, Wassermann, Wendt, VDI 2736-3, Pech). Additionally, the program calculates the contact pattern. For this purpose, the program determines the geometry of the gears numerically, based on a manufacturing simulation. A modification of the tooth profile in the area of the tooth tip and tooth root is possible. Subsequently, a meshing simulation of the gears is conducted to calculate the local flank distances for a variety of meshing positions. Misalignments, for example deviations of the center distance or of the angle of intersection, can be considered in the meshing simulation. The local flank distances during meshing are used to analyse the position and size of the contact pattern without load and to check the gear stage for possible transmission errors. Furthermore, a method for calculating the load distribution of crossed helical gears has been developed by FZG. Thereby influences from deformations of the shafts, teeth, bearings and of the housing can be considered. For validation of the contact patterns, comparative worm gear sets were calculated using the FVA program SNETRA. By use of the presented calculation methods, contact patterns in without load and under load can be calculated for the first time within a short processing time. In the future, these results can be used within the design process of crossed helical gear sets. Furthermore, the load distribution forms the basis for the calculation of specific local parameters such as Hertzian stress, thickness of the lubricating film or coefficient of friction.

A Three-Dimensional Load Sharing Model of Planetary Gear Sets Having Manufacturing Errors

Planet-to-planet load sharing is a major design and manufacturing tolerancing issue in planetary gear sets. Planetary gear sets are advantageous over their countershaft alternatives in many aspects, provided that each planet branch carries a reasonable, preferably equal, share of the torque transmitted. In practice, the load shared among the planets is typically not equal due to the presence of various manufacturing errors. This study aims at enhancing the models for planet load sharing through a three-dimensional (3D) formulation of N planet helical planetary gear sets. Apart from previous models, the proposed model employs a gear mesh load distribution model to capture load and time dependency of the gear meshes iteratively. It includes all the three types of manufacturing errors, namely, constant errors such as carrier pinhole position errors and pinhole diameter errors, constant but assembly dependent errors such as nominal planet tooth thickness errors, planet bore diameter errors, and rotation, and assembly dependent errors such as gear eccentricities and run-outs. At the end, the model is used to show combined influence of these errors on planet load sharing to aid designers on how to account for manufacturing tolerances in the design of the gears of a planetary gear set.

Dynamic Analysis of Helical Planetary Gear Sets under Combined Force and Moment Loading

The dynamic behavior of a single-stage planetary gear set with helical gears of multishaft automotive automatic transmissions has been studied, in which one component of the planetary gear set is imposed by additional external vertical and axial loading from countershaft gear pair in addition to the moment. Under these combined loading conditions, the contributions of the deflections of the ring gear and the carrier cannot be neglected. A three-dimensional nonlinear time-variant dynamic model considering not only the transverse, torsional, axial, and rotational motions of the gears but also the elasticity of the mounted shafts has been developed by combining the lumped parameter method with finite element method. The natural modes and the forced vibration responses due to static transmission errors have been obtained. The proposed dynamic model is employed to describe the effects of the combined external loading condition and positioning on the dynamic behavior of a four-planet system.

Geometrically Accurate Computer 3D Models of Gear Drives and Hob Cutters

The algorithms of constructing geometrically accurate real computer 3d models are developed. The special feature of these algorithms is that they reproduce a technological process of manufacturing components. The examples of constructing spur and helical gear sets, bevel gears, Archimedes and globoid gear pairs are given. The accuracy of construction is estimated. The construction inaccuracy doesn’t exceed a part of μm, which enables one to use the models as computer samples for production accuracy control and the algorithms as a basis for programs of components production with the help of the programmed control machine tools.The programs for implementation of the suggested algorithms are developed. The programs enable one to vary numerous model parameters and take into consideration teeth forms.The applicability of programs for the analysis of geometric properties of the models is shown. The model of a worm wheel root surface is received. The kinematic surface formed in the globoid gear is examined. The author presents the model of milling of a gear wheel, where the impact of cutting parameters on the tooth form of a manufactured wheel is examined.The models are constructed in the AutoCAD package. These programs are AutoLisp-based.

Optimization of Helical Gear Design Using Genetic Algorithm for Center Distance

The helical gears are employed to transmit motion between parallel shafts. These gears can also be used for transmitting motion between non-parallel, non-intersecting shafts. Helical gears are similar to spur gears except that the gears teeth are at an angle with the axis of the gears. In a genetic algorithm, populations of individuals, which are potential solutions to the optimization problem, undergo a sequence of unary and higher order transformations (also known as mutations and crossovers respectively). Genetic algorithms are being widely used for optimization, search and neural network synthesis. A lot of work has been conducted using genetic algorithm for different engineering problems related to scheduling and process planning in industrial engineering, network optimization in computer engineering. The work dissertation deals with the optimization of helical gear sets using genetic algorithm. Attention is focused on reducing the center to center distance of gear set subjected to constraints on bending stress, contact stress and involute interference.

Contact stress analysis of helical gear pairs, including frictional coefficients

Abstract In this paper an attempt has been made to study the contact stresses among the helical gear pairs, under static conditions, by using a 3D finite element method. The helical gear pairs on which the analysis was carried out were 0°, 5°, 15°, 25° helical gear sets. The Lagrange multiplier algorithm has been used between the contacting pairs to determine the stresses. The effect of friction was varied at the point of contact which made the problem nonlinear and complicated. To simplify the problem, a range of average static coefficients of friction, from 0 to 0.3, has been considered as the scope of study. The variation of contact stresses with helix angle and also with friction coefficients has been discussed. The commercial finite element software used was ANSYS and the results were compared with analytical calculations.

Contact Stress Analysis for Gears of Different Helix Angle Using Finite Element Method

The gear contact stress problem has been a great point of interest for many years, but still an extensive research is required to understand the various parameters affecting this stress. Among such parameters, helix angle is one which has played a crucial role in variation of contact stress. Numerous studies have been carried out on spur gear for contact stress variation. Hence, the present work is an attempt to study the contact stresses among the helical gear pairs, under static conditions, by using a 3D finite element method. The helical gear pairs on which the analysis is carried are 0, 5, 15, 25 degree helical gear sets. The Lagrange multiplier algorithm has been used between the contacting pairs to determine the stresses. The helical gear contact stress is evaluated using FE model and results have also been found at different coefficient of friction, varying from 0.0 to 0.3. The FE results have been further compared with the analytical calculations. The analytical calculations are based upon Hertz and AGMA equations, which are modified to include helix angle. The commercial finite element software was used in the study and it was shown that this approach can be applied to gear design efficiently. The contact stress results have shown a decreasing trend, with increase in helix angle.