Helical Gear Pair Research Articles

Tooth wear prediction of crowned helical gears in point contact

A tooth wear prediction methodology for helical gears in point contact is developed to evaluate their wear resistances using a lead crown. The load distribution coefficient is proposed in accordance with the elastic approach of each contact tooth pair being equal, and contact pressure are determined, and the sliding distance is obtained by adopting a generalized moving distance model. Then, the wear depth is computed in accordance with Archard’s wear equation, and the differences in tooth wear on standard and crowned helical gears are analyzed comparatively. The effects of crowned amount, fundamental geometry, and operating parameters on the wear resistance of the crowned helical gear pair are investigated. The results reveal that the tooth wear is lower on the gear surface with a moderate crowned amount than on the standard one, and that wear depths decrease with the increase in the helix angle, normal pressure angle, normal module, tooth number, or tooth width but increase with input torque rises. Furthermore, the rational lead crown, the geometric, and operating parameters optimization can be applied to wear resistance in the gear design.

Dynamic response analysis of helical gear pair considering the interaction between friction and mesh stiffness

This work investigates the dynamic responses of a pair of helical gears considering the interaction between friction and time-varying mesh stiffness (TVMS). Firstly, governing equations with 8 degree-of-freedom, including friction excitations, are established. Then, the calculation methods for friction excitation and TVMS including friction are briefly introduced and influences of working conditions such as surface roughness, transmitted load and rotating speed on coefficient of friction, TVMS of a helical gear pair are revealed. Next, dynamic responses under steady state through numerical algorithm are obtained and the effects of the interaction between friction and TVMS are discussed under different working conditions. The results indicate that the effect brought by the interaction on dynamic responses except the linear vibration displacement along off-line-of-action is not consistent in a whole meshing period, and related to specific working condition. This work provides a more comprehensive way to understand dynamics behaviors of gear pairs.

Dynamics responses analysis in frequency domain of helical gear pair under multi-fault conditions

This work aims to investigate dynamic characteristics of a helical gear pair under multiple faults condition, through model-based dynamic analysis. Two kinds of faults, tooth spalling and local breakages are considered. Firstly, influences of each kind of fault on meshing stiffness of gear pair with one or more faulted teeth were revealed. Then an 8 degree of freedom lumped-parameter model was developed to obtain dynamic responses. Furthermore, frequency spectrum analysis of the responses was conducted and compared with those under healthy condition. Results indicate that spalling or local breakage introduce different affects into mesh stiffness, and consequently displacement & velocity amplitudes of pinion appear with different waveforms, especially for the case only tooth breakages happen. This work could provide useful instructions for fault detection diagnosis of geared transmissions under multiple fault conditions.

Bending stress analysis of eccentric straight and helical curve-face gear pair

As a new type of gear transmission developed in recent years, curve-face gear transmission has not appeared before. In order to solve the problem of root bending strength of the eccentric straight and helical curve face gear, a calculating method of the tooth root bending strength was proposed. According to the principle of space meshing, differential geometry and design of machinery, the parametric equations of pitch curve was obtained, the pressure angle and the contact ratio in the meshing process were derived. The plane equivalent pitch curve was obtained, and the formula for calculating the equivalent tooth form factor and the equivalent stress correction factor was acquired. The calculation method of the bending strength of the gear pair was established, and the influence of the basic structural parameters on the bending stress was also analyzed in detail. The position of the stress hazard of the eccentric curve-face gear was determined. Through the finite element analysis and transmission experiment, the accuracy of the calculation method of strength of the gear pair was verified.

Effect of misalignment on tooth stress under varying frictional and loading conditions of polymer helical gear

The positive characteristics of polymer gears in comparison with metal gears include light weight, quiet operation, non-rusting, self-lubrication and cheaper mass production. Besides this they have drawbacks like lower load carrying capacity, tendency to hold heat, large dimensional change, and unsteady lifetime. In this study polymer gear meshed with steel gear has been analyzed considering with and without misalignment under varying loading and frictional conditions. The tooth stress of a perfectly aligned and axially misaligned helical gear pair has been studied by employing finite element method (FEM). The results show that the maximum contact stresses under varied frictional conditions increase while axial misalignments are present.

Macro geometry optimization of a helical gear pair for mass, efficiency, and transmission error

When designing helical gears, the goal is to optimize gear weight, efficiency, and noise while simultaneously achieving the required strength. In this study, the macro geometry of a helical gear pair was optimized for low weight, high efficiency, and low noise; further, trends of optimal solutions for five combinations of the three objectives were analyzed. The gear mass and efficiency were directly used as the design objectives. However, since the calculation of the gear noise is generally very complicated and time-consuming, the gear noise has not been directly used as the design objective, and the peak-to-peak static transmission error (PPSTE), which is the main source of the gear vibration, was selected as the design objective for the gear noise in the optimization. The objectives exhibited a trade-off relation between each other in the optimal space. If one of them was omitted, the objective considerably deteriorated. To analyze the results, the objectives were normalized and scored. As a result, most of the top ranks were from the optimal solutions considering the mass, efficiency, and PPSTE. Therefore, all three objectives should be considered in the gear optimization for low weight, high efficiency, and low noise.

Modeling the effect of misalignment and tooth microgeometry on helical gear pair in mesh

Understanding the effect of misalignment and microgeometry is important for gear designers and those have the main interest is gear manufacturing and maintenance. Unavoidable misalignment and microgeometry are both important factors to be considered in gear design which influence the resulted stresses, transmission error, and dynamic response. Analyzing the stress concentration on the tooth root and tooth flank areas is important to predict the failure modes that may occur. The current research work concentrates on modeling engaged gear teeth, analyzing the generated stresses and shows the importance of introducing the micro-geometry modifications. To do so, three different cases have been studied. The first case (case 1) considers the basic microgeometry modifications, the second case (case 2) considers the misalignment effect, and the last case (case 3) is to add some more micro-geometry modifications to compensate for the misalignment effect.It was observed that the gear calculating tools resulted in significantly higher stresses than the FE software. The obtained results from different software tools have been discussed to understand the differences for the three studied cases. However, the results from case 2 as compared to case 1 showed that the introduced misalignment results in shifting the stress pattern into one side of the gear tooth and significantly higher stresses than case 1. Case 3 showed that the use of micro-geometry modifications can result in compensating the effect of the misalignment in operation.

Research on Dynamic Model of Double Helical Gear Pair Based on TCA and LTCA

Numerous dynamic models of spur gears, helical gears, bevel gears, and face gears can be found in various studies. However, studies that focus on the dynamic model of a double helical gear pair are quite limited. The author proposed a model of a double helical gear pair by only considering the axial vibration. The author did not consider the friction and multiple backlashes in the proposed model. The friction force of the tooth surface and backlash are important factors that can cause complex non-linear phenomena in gear pairs. Therefore, a dynamic model of a double helical gear pair that takes into consideration the axial vibration, friction and multiple backlashes is proposed. Firstly, based on the tooth contact analysis (TCA) of a double helical gear pair, the path of contact and meshing time from engagement to disengagement are obtained. The formula for determining the sliding friction coefficient is introduced. Based on TCA and the dynamic meshing force provided by the subsequent dynamics model of double helical gear pair, the sliding friction coefficient of the tooth surface is calculated. Secondly, the stiffness excitation, gear-into impact excitation and error excitation (including the axial displacement caused by the errors of manufacture and installation under low speed) are calculated according to the existing research results. Following this, a dynamic model of a double helical gear pair that takes into consideration the axial vibration, friction and multiple backlashes is both built and solved. Finally, an example is presented to verify the corresponding results.

Thermal elastohydrodynamic lubrication analysis of helical gear pair under starved lubrication condition

AbstractIn the present study, thermal starved elastohydrodynamic lubrication (EHL) model is developed for a helical gear pair. The influences of inlet oil‐supply layer, input speed, lubricant viscosity, and surface roughness on the lubrication behaviour are investigated. The minimum film thickness, temperature rise of teeth surfaces and oil film, and the friction coefficient are predicted along the line of action (LOA). Results show that the effects of inlet oil‐supply layer, input speed, and lubrication viscosity on the tribological performance are remarkable. Under the starved lubrication, the influence of inlet oil supply on the temperature rise is insignificant. Meanwhile, the effect of surface roughness has been discussed. It reveals that the roughness texture along the entrainment velocity direction has significant influence on the lubrication characteristics. The results provide the tribological guidance for design of a helical gear pair in engineering.

Analysis of nonlinear local contact deformation of gear pair using multilevel multi-integration method

For the non-conforming contact problem of spur and helical gear pair, the total deformation of gear pair is usually separated into a linear global term and a nonlinear local term. To calculate the local contact deformation, the Hertz solution is widely used while lubrication is ignored. In order to account for the effect of elastohydrodynamic lubrication, the local contact deformation of helical gear pair is calculated on the basis of multilevel multi-integration method in this work. Through comparison with results obtained by analytical method and general numerical integration method, the effectiveness of the presented method is verified and it lays foundation for further analysis of transmission error of gear pair.

Experimental and numerical investigations on dynamic characteristics of gear-roller-bearing system

In the present study, dynamic characteristics of gear-roller-bearing system is investigated by use of experimental test and theoretical modeling. In terms of experiment, a new test set-up dedicated to offset press is developed to measure the acceleration within a wide range of speed. After the completion of data acquisition, the vibration signals obtained from different conditions are analyzed both in time domain and frequency domain, thereby capturing the source of vibration excitation. For theoretical modeling, a novel dynamic model of gear-roller-bearing system including time-varying properties and contact nonlinearities is proposed based on the fundamental idea of finite element method, divided into the helical gear pair model, dynamic model of roller and shaft, bearing elements, shoulder iron and rubber contact elements. The unconditionally stable algorithm, known as Newmark-β method, is employed to solve the governing equations, and then the validity of mathematical model in predicting dynamic response is demonstrated by comparison with experimental results. Experimental and numerical results indicate that the proposed method can be utilized as a useful tool for parameter design and performance analysis of gear-roller-bearing system.

A Novel Gear Honing Machine Parameter Design and Finite Element Analysis Based on the Principle of Dislocation Axis Line Contact

The characteristics of the dislocation axis line contact gear space transmission was analyzed in order to study the new precision gear honing machine prototype which could be clamped and formed at one time, and a pair of dislocation axis involute helical gears in space was designed from the most basic principle of involute gear meshing. The vertical dislocation axis line contact the worm and worm gear (helical gear) transmission mechanism were formed, when two gears had equalent normal base diameter and the sum of their base-circle spiral angles was equal to 90°. According to worm drive relationship of the vertical dislocation axis line contact, the helical gear tooth surface was honed through the worm could be used as a grinding wheel of the honing machine. Grinding wheels with different parameters could be used to machine bevel gears with different modulus, different numbers of teeth and different tooth widths. The finite element analysis and optimization showed that the prototype of the machine tool was reasonable, and the first-order natural frequency is 341.8Hz, which was much higher than the working frequency of 30Hz to avoid resonance.

Static and Dynamic Transmission Error Measurements of Helical Gear Pairs With Various Tooth Modifications

This paper presents a set of motion transmission error data for a family of helical gears having different profile and lead modifications operated under both low-speed (quasi-static) and dynamic conditions. A power circulatory test machine is used along with encoder and accelerometer-based transmission error measurement systems to quantify motion transmission behavior within wide ranges of torque and speed. Results of these experiments indicate that the tooth modifications impact the resultant static and dynamic transmission error amplitudes significantly. A design load is shown to exist for each gear pair of different modifications where static transmission error amplitude is minimum. Forced response curves and waterfall plots are presented to demonstrate that the helical gear pairs tested act linearly with no signs of nonlinear behavior such as tooth contact separations. Furthermore, static and dynamic transmission error amplitudes are observed to be nearly proportional, suggesting that static transmission error can be employed in helical gear dynamic models as the main gear mesh excitation. The data presented here is intended to fill a void in the literature by providing means for validation of load distribution and dynamic models of helical gear pairs.

Multi crack detection in helical gear teeth using transmission error ratio

Gear systems are used to transmit power in the industry when accuracy and synchrony are needed and helical gear systems are used in more accurate and high-speed industries. It is important to ensure that these systems work faultlessly, therefore the detection of the crack location and situation is very efficient in the gear systems. In this research, a new approach is proposed to detect the multi crack location and length in the helical gear teeth. To this end, after giving an explanation of helical gear mesh stiffness and demonstrating the helical gear pair dynamic modeling, the transmission error ratio method is used to detect the cracks locations and lengths. Then, according to solved examples, when the cracks locations are far enough that their effects on the transmission error are completely separated, the cracked teeth and the lengths of cracks can be detected exactly, and when the cracks are in adjacent teeth, according to the cracks lengths and depths and their effects overlap, the number of cracks and their lengths can be detected exactly, approximately or absolutely undetectable.

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.

Enhanced application limits for crossed helical gearboxes using new geometries for smaller sliding paths or smaller contact pressures

Crossed-axis helical gear units are used as actuators and auxiliary drives in large quantities in automotive applications such as window regulators, windscreen wipers and seat adjusters. Commonly gear geometry of crossed helical gears is described with one pitch point. This article deals with an extended calculation method for worm gear units. The extended calculation method increases the range of solutions available for helical gears. In general, for a valid crossed helical gear pair, the rolling cylinders do not have to touch each other. In mass production of many similar gears, individual gears can be reused because they can be paired with other centre distances and ratios. This also allows the use of spur gears in combination with a worm, making manufacturing easier and more efficient. By selecting design parameters, for example the axis crossing angle or the helix angle of a gear, positive effects can be achieved on the tooth contact pressure, the overlap ratio, the sliding paths, the lubrication condition, the tooth stiffness and, to a limited extent, on the efficiency of the gearing. It can be shown that for involute helical gears, in addition to the known insensitivity of the transmission behaviour to centre distance deviations, there is also insensitivity to deviations of the axis crossing angle. This means that installation tolerances for crossed helical gearboxes can be determined more cost-effectively.

A comparative study of tribological performance of helical gear pair with various types of tooth surface finishing

PurposeThis paper aims to compare the tribological performances of four different types of tooth surface finishing, namely, form grinding, generating grinding, super finishing and grinding and coating, and to reveal the details at dry contact nodes.Design/methodology/approachReal measured roughness is input to a finite line contact mixed elastohydrodynamic lubrication model developed for helical gear pairs. Their tribological performances are compared. The variation throughout one meshing period is analyzed. The influence of the root mean square (RMS) is studied. The textures are also scaled to the same RMS values to make comparisons while excluding the influence of roughness amplitude.FindingsRoughness is directly reflected in pressure and film thickness. Average film thickness sees major changes while entering and leaving the single-tooth-contact region. The textures have different performances even under the same RMS. Roughness peaks incurring dry contact are those higher than the smooth-situation film thickness plus the sum of variation in normal approach and elastic deformation compared with the smooth situation. To lower dry contact severity, the surface finishing process should take care of both the overall amplitude and the portion of peaks with maximum height. When RMS value is the same, the latter plays a decisive role.Originality/valueThis paper interprets the differences between the tribological performances of four different types of tooth surface finishing from the aspect of roughness features and presents a way to analyze the details at dry contact nodes.

On the mixed EHL characteristics, friction and flash temperature in helical gears with consideration of 3D surface roughness

PurposeThe purpose of this study is to investigate the tribological performance of helical gear pairs with consideration of the properties of non-Newtonian lubricant and the real three-dimensional (3D) topography of tooth flanks.Design/methodology/approachBased on the mixed elastohydrodynamic lubrication (EHL) theory for infinite line contact, this paper proposes a complete model for involute helical gear pairs considering the real 3D topography of tooth flanks and the properties of non-Newtonian lubricant. Film thickness, contact load and contact area ratios at the mid-point of contact line are studied for each angular displacement of pinion. Both the total friction coefficient and surface flash temperature are calculated after obtaining the values of pressure and subsurface stress. Then, the influences of input parameters including rotational speed and power are investigated.FindingsDuring the meshing process, contact load ratio and area ratio of the two rough surface cases first increase and then decrease; the maximum flash temperature rise (MFTR) on the gear is lower than that on the pinion first, but later the situation converses. For cylindrical gears, on the plane of action, there is a point or a line where the instantaneous friction reduces to a minimum value in a sudden, as the sliding–rolling ratio becomes zero. When rotational speed increases, film thickness becomes larger, and meanwhile, contact load ratio, coefficient of friction and MFTR gradually reduce.Originality/valueA comprehensive analysis is conducted and a computer program is developed for meshing geometry, kinematics, tooth contact, mixed EHL characteristics, friction, FTR and subsurface stress of involute helical gear pairs. Besides, a numerical simulation model is developed, which can be used to analyze mixed lubrication with 3D machined roughness under a wide range of operating conditions.

Mesh stiffness calculation of helical gears with profile modification

Time-varying contact line and mesh stiffness are important parameters for dynamic investigation of helical gear pair with profile modification; however, the calculation methods of the time-varying mesh with high accuracy and high efficiency are also very limited currently. A new mesh stiffness calculation method for helical gear pairs with profile modification is proposed. The new method is conducted by cutting the helical gear tooth into slices to obtain the change of the contact line and the time-varying mesh stiffness with considering the change of each slice's engagement performance introduced by the profile modification. Then, the mesh stiffness of the assumed three different modification cases is calculated by using the proposed method. The calculated results indicate that the proposed method can be used to calculate the mesh stiffness of helical gear pairs, especially of those with tooth profile modification.

Kinematic Errors on a C-Type Gear with a Parabolic Surface

Abstract An asymmetric tooth is used to develop a mathematical model of an imaginary skewed rack cutter. Using this imaginary skewed rack cutter and the theory of gearing, a pair of helical gears with asymmetric, straight teeth and a parabolic surface is created. Using tooth contact analysis, this mathematical model of a pair of helical gears with a parabolic surface is used to study the kinematic errors that occur because of assembly errors. Using a computer-aided software package to simulate the scenario, the kinematic errors for the gear set when it is ideally assembled and inaccurately assembled are presented. The contact pattern between the pair of helical gears is obtained. A pair of helical gears is created by rapid prototype machining and is used to observe the actual contact conditions of the gears.