Spur Gear Sets Research Articles

Exploring Tribological Behaviors of Profile-Shifted Spur Gears: An Experimental Investigation

The tribological behavior of an addendum modified altered tooth sum optimized spur gear set were experimentally compared with that of the standard spur gear under several loading conditions including the wear morphology study and wear debris analysis. The temperature, viscosity, elastohydrodynamic oil film thickness, specific film thickness, and combined surface roughness variation under increasing operating load were analyzed experimentally. Finally, the performance impact of addendum shifted altered tooth sum optimized gear was examined. Results show that the tribological improvement strongly depends on the addendum alteration and modified tooth sum condition. The modification of the addendum in gears with a negatively altered tooth sum facilitates the transition from single-tooth contact to two-tooth contact, broadening the lubrication range while preserving optimal film thickness and improving wear resistance. However, it is reverse to decrease the film thickness and increase wear for standard and profile-modified positively altered tooth sum gear. The gear tribological performance can be significantly improved by profile modification and negatively altered tooth sum approach with a lower rate of degradation of oil and damage on the tooth contacting surface.

Multi-objective design optimization of polymer spur gears using a hybrid approach

Polymer gears are used in applications requiring small to moderate loads to effectively transmit power and use the limited place available as possible. Various commercial standards have been provided designers with the rating criteria and acquaintance of different polymer material properties for the process of design. However, the result was unsatisfactory in terms of economy, time, and the optimality of the product. Thus, classic and stochastic algorithms have been embraced to reach the best design of polymer gears. Taking advantage of the former and latter algorithm’ methods, optimal design of gears could be attained with an increased gear life span and decreased failure modes. In this study, polyoxymethylene (POM) spur gear set has been optimized combining the mathematical model from plastic standards and hybrid optimization approach of multi-objective genetic algorithm (MOGA) and sequential quadratic programming (SQP). Weight and power loss were the objective functions. Five design variables were optimized with the satisfaction of bending and contact stresses, temperature, wear, and deformation as constraints. Solutions of the problem were formulated as Pareto optimal set. The results of multi-objective were compared with previously published single-objective optimization. The results favored multi-objective optimization (82.67%, 31.39% reduction in weight and power loss respectively) as it gave the best applicable solution fitting in real life situations. The results also went hand in hand with literature confirming the efficiency of the proposed algorithm. With the variation of operating parameters, various optimal designs could be obtained where the designers can choose the design that is suitable for a particular application.

Finite Element Analysis of Spur Gear Set in Noodles-making Machine Using Different Materials and Face Widths

This paper focuses on the design and structural analysis of a spur gear set for a noodles-making machine by changing three different materials (ASTM A 536, ASTM A 220, and AISI 1020) and gear face widths. Gear corrosion occurs at contact points as a result of bending stress and contact stress. This is the major source of the gear failure of the noodles-making machine. Pitch diameters of 50mm and modules of 5mm spur gears are selected in the design of the roller gear set. In theoretical analysis, the AGMA contact stress equation was used based on the Hertzian theory. The minimum von Mises stress and effective strain are found on AISI 1020 carbon steel by using ANSYS 17.0 software. In this paper, von Mises stress and effective strain are analyzed by changing the face widths of spur gear set to 8mm, 10mm, 12mm, 14 mm, and 16mm and using finite element analysis (FEA). Although all face widths are safe for this design, 12mm is chosen in this paper due to power consumption and strength points of view.

An investigation of the wear and efficiency in non-standard internal spur gear set

In this research, a finite-element model of internal gear drives with different tooth thickness factors (non-standard gear drives) is generated in order to investigate their performance characteristics. The finite-element analysis includes a focused mixture of non-standard internal gear set under enhanced bending and contact strength conditions for an accurate assessment of wear and efficiency. The analysis comprised gear sets having higher bending strength compared to the conditions in the standard internal gear drive to evaluate the tooth wear and its efficiency. A state-of-the-art semi-analytical nonlinear contact mechanics construction is executed to model a non-standard internal gear transmission unit. The tooth thickness of the non-standard internal gear is varied concerning the stresses and is quantified as a function. The computed results also extended with internal gear sets at varying operating parameters. The results evidently specify that power loss decreases with the proper combination of operating parameters. The results are presented and strategies concerning the design of a non-standard internal gear are also deliberated.

Multi-objective optimisation with finite element analysis of profile shifted altered tooth sum spur gear

ABSTRACT Traditional gear design approaches provide design parameters that meet only one design requirement at a time. However, a major problem with this kind of approach is the deficit for high consistency and reliability. The objective of the article is to present a multi-objective design optimisation procedure for addendum modified spur gear with altered tooth sum. The design procedure involves implementation of Particle Swarm Optimisation (PSO) and a hybrid PSO- Teaching-learning based optimisation (PSO-TLBO) algorithm for simultaneous optimisation of the weight and contact or hertzian stress along line of action of the spur gear drive. The design optimisation was validated through stress analysis of the optimised spur gear set, using Finite element analysis (FEA) with various mesh types and grain size. Afterwards, manufacturing of the optimised non-standard gear set with metallic (EN24) and a composite (Hylum) gear material using standard tooling. This indicates that with the proposed design optimisation approach there is a possibility of meeting the requirement for efficient, compact, and reliable gear set with reduced computational cost. This study suggests that it is possible to determine a set of optimised design variables that can meet more than one design criteria at a time.

Dynamic Modeling, Optimization and Experiment for a High-Speed Spur Gear Set

This study proposed a novel methodology for reducing the vibration of a high-speed spur gear pair (up to 30,000 rpm) by performing multi-objective optimization of the peak-to-peak loaded transmission error (PPLTE) under three assembly conditions. The optimum tip relief parameters for the high-speed spur gear set were studied by considering the practical manufacturing tolerances on the gear shaft and bearing bores. First, the PPLTE under three assembly conditions was determined by loaded tooth contact analysis. Multi-objective optimization with a genetic algorithm was used to determine the optimum linear tip relief parameters, minimizing the PPLTE under three assembly conditions by 70%. Moreover, the dynamic characteristics of the original and optimum designs were simulated and compared under ideal conditions as well as axial misalignments. The optimum design exhibited a >50% reduction in the peak RMS of acceleration at the natural frequency. Finally, dynamic experiments were performed and the RMS values of the acceleration at various speeds were computed for comparison. The results from both dynamic simulation and experiment indicated that the optimum design exhibits superior dynamic characteristics to the original design.

A comprehensive study on multi-objective design optimization of spur gear

The paper presents procedure for design optimization of a spur gear set with the objective of minimization of the gear weight, contact stress along path of contact and optimum film thickness at the contact point. Particle swarm optimization, particle swarm optimization based teaching learning optimization and Jaya algorithms are presented here to ensure the remarkable reduction in weight and contact stress of a profile modified spur gear set with adequate film thickness at the point of contact. The parametric and sensitivity analysis performed here recommended the manufacturing tolerance to be maintained for the different critical design variables. The contact stress analysis using finite element method suggested the use of negatively altered tooth sum spur gear for compact design with better strength balance and scoring resistance. The optimized values of addendum co-efficient within the design space significantly improves the gear design as compared to the conventional design.

Tribodynamic studies of textured gearsets lubricated with fresh and MoS2 blended greases

The synergistic effects of surface texture and Molybdenum disulphide (MoS2) blended grease have been explored on the tribodynamic performance of spur gearsets. A texture involving ellipsoidal dimples on the face and flank of pinions’ teeth was fabricated using nanosecond pulsed fiber laser. The experiments were performed at different applied torques and a pitch line velocity of 4 m/s keeping in mind the practical application of the results. Contact resistance, vibrations, temperature rise and surface topographies have been measured and analyzed. Substantial increase (about 300%) in contact resistance and reduction (40% approximately) in vibration amplitudes at gear mesh frequency were found in the presence of texture. Reduction in interfacial temperature rise and less damage to teeth surface were also observed.

Evaluation of the gear noise reduction potential of geometrically uneven inequidistant gears

Randomizing the periodic excitation is a well-known noise reduction measure, for example in fans and tire patterns. Due to a randomized excitation the tonal components of the generated noise are reduced while broadband noise is increased in amplitude. This less tonal noise with a more broadband character is perceived less annoying. In the presented research this approach is applied to gears – called inequidistant gears. They are characterized by uneven tooth positions and uneven tooth thicknesses. The deviations from regular, perfectly even gears may be up to several millimeters in both position and thickness. In the same way as in fans and tire patterns, the uneven design of inequidistant gears leads to a less tonal and less annoying noise. In this paper the design of inequidistant gears is introduced. Equations are derived to define the uneven geometry of an inequidistant gear wheel and to exactly match a pair of meshing inequidistant gears. The presented approach is valid for spur gears, helical gears, and double helical gears, but only spur gears are considered in this paper. Furthermore, a method to calculate the gear mesh stiffness, which is the main excitation mechanism in gear noise, and a method to calculate the gear mesh forces are presented. Experimental investigations are carried out on a back-to-back gear test bench. The calculated gear mesh force and the experimentally determined sound pressure of a regular, perfectly even spur gear set are compared to those of an equivalent inequidistant spur gear set. The results reveal that inequidistant gears not only reduce the tonality but are – in contrast to uneven designs of fans and tire patterns – capable of reducing the total sound pressure level.

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.

A real time wear measurement system for tripod type constant velocity joints

A real-time wear measurement system for tripod type Constant Velocity (CV) joints is proposed in this study. Adhesive wear on tripod type CV joints is very crucial to the life time of CV joints but it is very difficult to measure the wear depth of a tripod type CV joint separate from the drive shaft assembly. The wear measurement system developed in this study can measure the wear depth of a tripod type CV joint in real-time as it applies kinematics and forces to the CV joint.In order to apply the same motions as the motions of an actual CV joint, kinematics of the CV joint has been analyzed. As a result, reciprocating stroke and yaw motions have been completely implemented in the system. The wear measurement system comprises four parts. The first part is for applying normal forces to a set of spherical roller and housing track. One servo motor, spur gear and ball screw sets were employed to generate and augment the normal forces. The second and third parts are for applying reciprocating stroke and yaw motions, respectively. These parts synchronize with each other to make the same motion profiles as the actual CV joint. The fourth part is for measurement. This part consists of load cell and rotary encoder to measure the surge normal forces caused by the flaking phenomena and the wear depth caused by the adhesive wear. In the case of the encoder, the wear depth is augmented by the ball screw and spur gear sets so 0.18°/μm of measurement resolution can be achieved.For the validation of the system, a tripod type CV joint was selected, and its wear depth was measured by the system and the results were compared with the wear depth measured by a profilometer.

An exploration of the performance behaviors of lubricated textured and conventional spur gearsets

Abstract This paper reports the experimental investigations on the performance behaviors of the conventional and textured gearsets. The vibration behaviors, temperature rise and surface topography of gearsets have been investigated for different loads (PH) and pitch line velocities. The texture comprising of micro-cylindrical dimples of non-uniform diameter was created by chemical etching process on teeth surface. The vibration results obtained employing conventional and textured gearsets have been compared and analysed in time and frequency domains. Moreover, the surface topography and temperature rise have been measured. Based on the experimental results, it is found that in the presence of texture on gear teeth, the vibration amplitudes, oil film temperature rise and teeth surface damage have substantially reduced.

Design optimization of spur gear using SA and RCGA

Gear size is one of the most important criteria in design optimization of gear set used in automotive, aeronautical and various other applications. Smaller gear size results in requirement of less material and hence reducing manufacturing cost. This paper aims at minimizing center distance of spur gear set to obtain its corresponding optimal design variables. Design variables included in this study are diametrical pitch and number of pinion teeth. Real Coded Genetic Algorithm and simulated annealing are employed for performing design optimization procedure. In this study, along with constraints on bending strength, contact strength, interference and contact ratio, scoring has been added as design constraint in design problem. All the design factors included in design procedure are considered as per AGMA standards. The recommended optimization techniques are implemented on a design example and optimum values of design variables are obtained. The obtained results are compared with those obtained by traditional design procedure to find the better solution as well as better optimization technique. Variations in input power and gear ratio have been done to verify their effect on the objective function and to further investigate a more useful optimization technique for gear design.

Stress Analysis of Parallel Misaligned Spur Gear Pair

Gears are highly engineered machine elements that are designed to transmit the torque and speed. The misalignment of gear is a common problem during power transmission, which leads to extra load on gear tooth. Analysis of such misaligned gear pair become more critical, in order to interpret the possible increase in induced stress value to avoid premature failure of gear. The variation of the stress with various parallel misalignments is performed on spur gear set using ANSYS software. Model is developed for various parallel misalignments and effect of parallel misalignment on stress distribution is analyzed. The results obtained are validated by AGMA and Hertz’s stress equation for contact stress and also by Lewis bending equation for principle stress. The results show that the value of induced stresses increases slowly for smaller parallel misalignment. As misalignment increased further the contact stresses increases rapidly. It is needed to keep misalignment within permissible limits or no misalignment to avoid pre-mature failure of gear due to excessive stress.

A Generic and Modular Modeling Approach for Automotive Drivetrains Using a Coordinate Partitioning Method

Drivetrain models play an important role in state-of-the-art automotive drivetrain and control concept development. Based on a proposed set of elementary drivetrain components, this article contributes a generic straightforward approach to compute state-space models for various geared drivetrain layouts, including complex hybrid multi-mode transmissions. The modular approach follows Lagrange formalism: The free motion of rigid shafts is subsequently constrained, considering connecting elements like spur and planetary gear sets. The generalized coordinates are determined by a coordinate partitioning method, ensuring a physically reasonable coordinate system. The proposed approach features high potential for automation. This enables drivetrain modeling by non-experts in the field of mechanical engineering.

A new dynamic model of a cylindrical gear pair with localized spalling defects

Accurate assessment and modeling of the effects of tooth defects on the vibration response of gear systems is beneficial for the early detection and diagnosis of gear faults and failures. This paper presents a new dynamic model of a cylindrical gear pair with localized tooth spalling defects. Depending on the depth and extent of a spall, the resulting contribution of the spall to the gear dynamics can be classified in terms of mesh stiffness reduction and displacement excitation. The main improvement of the proposed model, relative to previous similar models which assume a linear line contact between mating tooth pairs, is that modification coefficients are introduced to account for the effects of nonlinear elliptical tooth surface contact pattern on the influencing mechanisms of the spalls on the gear dynamics. It was found that the modification coefficients are dependent on the transmitted load, the dimensions of the spall, and the amount of tooth crowning. Experimental vibration responses of several 1:1 ratio spur gear pair sets with different dimensions of spalling defects working under various load and speed conditions were measured to compare with the simulated results based on the proposed model and previous similar models in terms of the time-history acceleration, power spectrum and some statistical indicators. The results validate the superiority of the proposed model against previous similar models.

An approach to weight optimization of a spur gear

Lightweight is one of the most important criterion in the optimum design of gear set for motorsport and aerospace application. A tradeoff between optimum weight and failure modes of gear is a subject of interest for researchers and the industry. In the present work weight of a single-stage spur gear set is optimized. This nonlinear constrained optimization formulation has been solved by using differential evolution algorithm. A total of six design variables corresponding to gear geometry and material property are considered. The results obtained are compared with those of published heuristics like genetic algorithm, simulated annealing, and particle swarm optimization algorithm, respectively. The optimization is performed in such a way that the design variables satisfy all constraints at optimum solution. Apart from this, several constraints related to scoring are included in the optimization. The constraint violation study is performed to prioritize the constraints. The sensitivity analysis is carried out to see the effect of manufacturing tolerances of design variables on weight of the gear set. The optimality of the solution has been ensured through the convergence study. The optimization reveals that the reported results are also encouraging in terms of objective function values and CPU time. In addition, the optimum design variables obtained through the weight optimization of spur gear set are used for preparation of a CAD model. Then the stress analysis using finite element analysis is performed on the gear set to identify the critical stress region in the optimized gear set.

Efficiency and Durability Predictions of High Performance Racing Transmissions

Efficiency and durability are key areas of research and development in modern racing drivetrains. Stringent regulations necessitate the need for components capable of operating under highly loaded conditions whilst being efficient and reliable. Downsizing, increasing the power- to-weight ratio and modification of gear teeth geometry to reduce friction are some of the actions undertaken to achieve these objectives. These approaches can however result in reduced structural integrity and component durability. Achieving a balance between system reliability and optimal efficiency requires detailed integrated multi-disciplinary analyses, with the consideration of system dynamics, contact mechanics/tribology and stress analysis/structural integrity. This paper presents an analytical model to predict quasi-static contact power losses in lubricated spur gear sets operating under the Elastohydrodynamic regime of lubrication. Tooth Contact Analysis (TCA) is used to predict variations in contact loads, local surface curvature and rolling and sliding velocities. This is combined with an extrapolated oil film thickness formula available in literature, to predict instantaneous lubricant film thickness and sub-surface stresses. Subsequently, viscous and boundary friction are estimated, enabling calculation of power losses. The presented methodology has been used to investigate the effects of parabolic tip relief on power loss and induced sub-surface stresses. The results of this investigation are also presented.

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.

Modeling and monitoring of tooth fillet crack growth in dynamic simulation of spur gear set

This study integrates a linear elastic fracture mechanics analysis of the tooth fillet crack propagation into a nonlinear dynamic model of spur gear sets. An original formulation establishes the rigidity of sound and damaged teeth. The formula incorporates the contribution of the flexible gear body and real crack trajectories in the fillet zone. The work also develops a KI prediction formula. A validation of the equation estimates shows that the predicted KI are in close agreement with published numerical and experimental values. The representation also relies on the Paris–Erdogan equation completed with crack closure effects. The analysis considers that during dN fatigue cycles, a harmonic mean of ΔK assures optimal evaluations. The paper evaluates the influence of the mesh frequency distance from the resonances of the system. The obtained results indicate that while the dependence may demonstrate obvious nonlinearities, the crack progression rate increases with a mesh frequency augmentation. The study develops a tooth fillet crack propagation detection procedure based on residual signals (RS) prepared in the frequency domain. The proposed approach accepts any gear conditions as reference signature. The standard deviation and mean values of the RS are evaluated as gear condition descriptors. A trend tracking of their responses obtained from a moving linear regression completes the analysis. Globally, the results show that, regardless of the reference signal, both descriptors are sensitive to the tooth fillet crack and sharply react to tooth breakage. On average, the mean value detected the crack propagation after a size increase of 3.69 percent as compared to the reference condition, whereas the standard deviation required crack progressions of 12.24 percent. Moreover, the mean descriptor shows evolutions closer to the crack size progression.