Gear Design Parameters Research Articles

Experimental Analysis of Spur Gear Pair with Geometrical and Operating Parameters

Abstract This study presents experimental work to analyze spur gear pair with geometrical and operating parameters. The spur gear pair accommodates the correction in tooth addendum, gear backlash, and linear tip relief profile modification with three levels. As per Taguchi L9 orthogonal array, nine test spur gear pairs are precisely manufactured to analyze the combined influence of these three geometrical parameters on gear dynamics. Other basic gear design parameters and operating parameters were held at a constant level. RMS acceleration in the vertical direction to quantify the dynamic response of test gear pairs. Experimental data are analyzed by using the Taguchi method to investigate the rank of influencing parameters to minimize vibration response. Finally, the confirmation test was performed by using a simulation study to validate the experimental results. The simulation results are similar to the experimental results. Similarly, 20 experiments were conducted with different speed and load combinations to check the effect of operating conditions on gear dynamics. From this experimental study, it is observed that the rank of influencing parameters and optimum level of geometrical are varied with respect to operating conditions. It may be concluded that typically optimized spur gear pair operated at one particular combination of load and speed may not show good performance at other operating conditions. Therefore, this study suggests that the realistic range of operating conditions should be considered while selecting suitable geometrical parameters.

A Grinding Method with an Innovative, Efficient, and Weight-Saving Design for Double Helical Gears

Grinding technology exerts an enormous effect on the surface quality of double helical gears, which are subject to stringent requirements in the aviation industry. This study presents a novel gear-gap-space-borrowing grinding method that diverges from existing techniques. Unlike conventional approaches, this method mitigates the design–manufacturing conflict by exploiting the opposing gear gap space. By borrowing space, the grinding wheel’s size can be enlarged to enhance machinability, diminish the width of the undercut, and align with the lightweight design imperative of double helical gears. The relationship between the grinding wheel diameter and the design parameters of double helical gears is analytically established, leading to the formulation of design rules. These rules facilitate the rapid selection of appropriate grinding wheel sizes for the space-borrowing method. Additionally, through geometric modeling and experimental validation, the optimal gear undercut width and the maximum wheel diameter are determined. The validity and accuracy of the proposed method are verified by simulations and experimental investigations. The study quantitatively evaluates the benefits of this method, including the expansion of the grinding wheel size, the reduction in double helical gear weight, and enhancements in processing efficiency and quality, providing a comprehensive comparison and discussion of these improvements.

Determining the Gear Design Parameters Which Have Strong Correlation with Gear Volume and Contact Ratio for Helical Gear Design Optimization

The market has a significant demand for low-cost, compact size, extended fatigue life and high load-carrying capacity helical gears. One way to manufacture such gears is by minimizing gear volume and maximizing contact ratio. Most researchers focus on gear design optimization, but minimal study has been conducted to identify design variables that significantly impact gear volume and contact ratio. Hence, it is crucial to determine gear design parameters that strongly correlate with gear volume and contact ratio beforehand. A single-stage helical gear train of local electric multiple units (EMU) is used as the gear model, and the calculations are done based on ISO 6336. Seven parameters have been chosen as independent variables; module, number of teeth of pinion, gear ratio, helix angle, tooth thickness factor, normal pressure angle and addendum factor. Graphs of total gear volume and contact ratio against independent variables are plotted to examine their relationship. The results indicate that normal module, number of teeth of the pinion, and gear ratio strongly correlate with the total gear volume. Meanwhile, the number of teeth of pinion, helix angle, tooth thickness factor, normal pressure angle and addendum factor strongly correlate with contact ratio. Therefore, these design parameters must be considered to improve the accuracy of the gear design optimization model, which aims to optimize gear volume and contact ratio.

Vibration optimization of spur gear based on GSA-SA algorithm.

To determine the optimal design parameters of spur gear under a specific condition, based on the basic theories of gear dynamics theory, gear meshing principle, tooth contact analysis and load tooth contact analysis, a six-degree-of-freedom vibration analysis model of spur gear pair is established, and a gravitational search-simulated annealing hybrid algorithm (GSA-SA) is used to optimize the gear addendum modification coefficient and profile modification parameters. The vibration response of the spur gear pair is evaluated through the optimization objective function established by the combination of the G1 method and variation coefficient method. The study shows that the optimized design parameters effectively reduce the level of the vibration, which proves the effectiveness of the optimization method, and the simultaneous optimization of the addendum modification coefficient and profile modification parameters of the gear has a better result than only optimizing the addendum modification coefficient or profile modification parameters. This method can be used for gear transmission system vibration optimization design in the automotive industry and shipbuilding.

Potential and Design Parameters of Polyvinylidene Fluoride in Gear Applications.

(1) Background: With the ever-increasing number of polymer materials and limited data on polymer gear calculations, designers are often required to perform extensive experimental testing in order to establish reliable operational data for specific gear applications. This research investigates the potential of a Polyvinyldene fluoride (PVDF) polymer material in gear applications, considering various loading conditions and different types of gear transmission configurations, including both self-mated mesh and steel/PVDF mesh. (2) Methods: PVDF gear samples were tested on a specially designed test rig that enables active torque control and temperature monitoring in order to obtain the necessary design parameters and failure modes. Each test for certain load conditions was repeated five times, and to fully investigate the potential of PVDF gear samples, comparative testing was performed for Polyoxymethylene (POM) gear. (3) Results: Tribological compatibility, tooth load capacity, and lifespan assessment, along with the types of failure, which, for some configurations, include several types of failures, such as wear and melting, were determined. Temperature monitoring data were used to estimate the coefficient of friction at the tooth contact of analyzed gear pairs, while optical methods were used to determine a wear coefficient. (4) Conclusions: The tribological compatibility of polymer gear pairs needs to be established in order to design a gear pair for a specific application. PVDF gear samples mated with steel gear showed similar lifespan properties compared to POM samples. Temperature monitoring and optical methods serve as a basis for the determination of the design parameters. PVDF is an appropriate material to use in gear applications, considering its comparable properties with POM. The particular significance of this research is reflected in the establishment of the design parameters of PVDF gear, as well as in the analysis of the potential of the PVDF material in gear applications, which gives exceptional significance to the current knowledge on polymer gears, considering that the PVDF material has not previously been analyzed in gear applications.

Optimization Method of Design Parameters of Hypoid Gears With Low Sliding Ratio

Abstract To reduce the wear, an optimization method of hypoid gears with the objective of minimizing the pinion sliding ratio is proposed. First, the sliding ratio model of the hypoid gear is established on the basis of the spatial gear meshing theory. Furthermore, the influence of design parameters on the sliding ratio and the relative sliding velocity is discussed, and the analysis results show that the parameters, especially the spiral angle and the pressure angle, have the most significant influence on the sliding ratio of the pinion. Additionally, the optimization model of hypoid gears is established, and the optimization objective is to minimize the sum of the absolute sliding ratios of 34 meshing points on the pinion tooth surfaces. Through comparison before and after optimization, it is found that the maximum drops of the sliding ratios for the pinion drive and coast side are 68.6% and 29.58%, respectively. Finally, the results of the running temperature tests demonstrate that the temperature of the optimized gear pair is significantly reduced and that the proposed method is effective.

A Theoretical and Experimental Study on the Power Loss of Gearbox Based on Dimensionless Analysis

Abstract A prediction model of gearbox power loss based on dimensionless analysis is proposed. First, the dimensional model of gearbox power loss is established based on similarity criterion, dimensional harmony principle, and fluid mechanics π theorem. Then, the experimental study is carried out on a power loss test bench. Based on the measured data and multiple linear regression method, the coefficients of the influencing factors are calculated, including gear design parameters, lubrication oil parameters, and operating conditions. To validate the prediction model, the gear pairs were tested under various operating conditions, and two new gear sets with different helical angles were also included. The comparison results show good consistency between the measured data and predicted values. The proposed model can be employed to effectively predict the power loss of gearbox and improve the gearbox efficiency.

Reliability Design of Two-Stage Planetary Gear Wheel Hub Reducer based on Multi-Objective Optimization

The mining dump truck has a large load capacity, low running speed, and the characteristics of low speed and high torque. The planetary wheel reducer can meet this demand, which is widely used in such vehicles. According to the structural characteristics of a 170-ton vehicle two-stage planetary gear reducer, the reliability of planetary gear transmission at all levels was analysed, and the system parameters were optimized on this basis. The multi-objective optimization design method was used to transform the maximum reliability of the system into the maximum reliability of the gears at all levels, and the constraints are established based on the actual processing, operation, installation, assembly and other working conditions. The MATLAB multi-objective optimization module was used to solve the analysis, and the best gear design parameters were obtained after rounding. Under different operating conditions, the planetary reducer before and after optimization was compared and analysed to obtain the reliability and service life of the entire deceleration system after optimization. The analysis results show that: after the parameter optimization of the planetary reducer, the transmission efficiency is 0.946, and the transmission ratio of the system is 30.54, which meets the actual use requirements. The reliability coefficient of the contact strength of the tooth surface of the secondary sun gear is 2.52, the reliability coefficient of the bending fatigue strength of the root of the secondary inner ring gear is 2.59, and the reliability of the secondary gear is 0.989. The reliability is obviously improved. The safety factor of the main parts is high. The service life of each gear of the whole secondary reduction system meets the design requirements. The analysis content and results provide reference for the optimization design and reliability analysis of similar planetary gear systems.

Application of Evolutionary Optimization Techniques in Reverse Engineering of Helical Gears: An Applied Study

Reverse engineering plays an important role in the manufacturing and automobile industries in designing complicated spare parts, reducing actual production time, and allowing for multiple redesign possibilities, including shape alterations, different materials, and changes to other significant parameters of the component. Using reverse engineering methodology, damaged gears can be identified and modeled meticulously. Influential parameters can be obtained in the shortest time. Because most of the time it is impossible to solve gear-related inverse equations mathematically, metaheuristic methods can be used to reverse-engineer gears. This paper presents a methodology based on measurement over balls and span measurement along with evolutionary optimization techniques to determine the geometry of a pure involute of a cylindrical helical gear. Advanced optimization techniques, i.e., Grey Wolf Optimization, Whale Optimization, Particle Swarm Optimization, and Genetic Algorithm, were applied for the considered reverse engineering case, and the effectiveness and accuracy of the proposed algorithms were compared. Confirmatory calculations and experiments reveal the remarkable efficiency of Grey Wolf Optimization and Particle Swarm Optimization techniques in the reverse engineering of helical gears compared to other techniques and in obtaining influential gear design parameters.

Modal sensitivity of three-dimensional planetary geared rotor systems to planet gear parameters

A parameter study is presented to determine effects of planet gear design parameters on the global modal behaviour of planetary geared rotor systems. The modal sensitivity analysis is conducted using a three-dimensional dynamic model of a planetary geared rotor system for the number of planet gears, planet mistuning, mass of planet gears, gear mesh stiffness and planet gear speed. These parameters have varying impacts on both natural frequencies and mode shapes, therefore the sensitivity of the planetary geared rotor vibration modes to the planet gear parameters is determined by computing the frequency shifts and comparing the mode shapes. The results show that the mass and mesh stiffness of planet gears have a larger influence on the global dynamic response. Torsional modes and coupled torsional-axial modes are more sensitive to gear mesh stiffness whereas lateral vibration modes are more sensitive to gearbox mass. Planet mistuning results in coupling between lateral and torsional vibrations. The planetary gearbox becomes more rigid in the torsional-axial modes and more flexible in the lateral modes with an increase in the number of planet gears. Planet gears are also found to be having significant gyroscopic effects inside the planetary gearbox. The main original findings in this study can be directly used as initial guidelines for planetary geared rotor design.

Effect of Gear Design Parameters on Stress Histories Induced by Different Tooth Bending Fatigue Tests: A Numerical-Statistical Investigation

The characterization of new materials for enabling gear design is definitely a fundamental objective in the gear industry and research. Single Tooth Bending Fatigue (STBF) tests can be performed to speed up this process. However, it is well known that STBF tests tend to overestimate material strength compared to tests performed directly on meshing gears (MG) which, in turn, require an excessively long test time. Therefore, it is common practice to use a constant correction factor fkorr of 0.9 to translate STBF results for designing actual MG (e.g., via ISO 6336). Recent works involving a combination of Finite Element Models (FEM) and multiaxial (non-proportional) fatigue criteria based on the critical plane concept have highlighted that the assumption of considering fkorr as a constant independent of the gear design parameters leads to inaccurate results. However, in previous studies, no correlation between fkorr and gear design parameters has emerged. In the present paper, the influence of the normal pressure angle (αn), the profile shift coefficient (x*), and the normal module (mn) on fkorr was investigated by analyzing FEM simulations with the Findley fatigue criterion. 27 gear geometries were studied by varying the above 3 parameters in 3 levels (full factorial DOE). These geometries were simulated in both MG and STBF configurations. The results of the 54 FEM simulations were analyzed by applying the Findley fatigue criterion and the corresponding fkorr were calculated. The correlation between fkorr and αn, x* and mn was investigated using the Analysis of Variance (ANOVA) technique. The results show that the only gear design parameter influencing fkorr is x* hence, a regression model for fkorr including x* has been developed. This latter has been then adopted for calculating and comparing fkorr values from other combination of the parameters found in literature, giving good correspondence.

기어시스템에서 설계변수에 따른 전달오차와 물림강성 해석

The gear has a wide range of transmitted force as various gear ratios are possible using a combination of teeth. It can transmit power reliably and cause relatively little vibration and noise. For this reason, the application of reducers of electric vehicles is being expanded. Vibration noise generated from gears is propagated into the quiet interior of a vehicle, causing various claims. In most gear studies, transmission error has been pointed out as the main cause of vibration noise of gears. Transmission errors have various causes, including design factors, manufacturing factors, and assembly factors. In general, when predicting transmission error through finite element analysis, design factors play an important role without considering manufacturing factors or assembly factors. In this study, relationships among important design variables (gear module, compensation rate, load torque, and transmission error) in gear design were investigated using analytical and experimental methods. In addition, a method of predicting gear meshing stiffness through the predicted gear transmission error was proposed to obtain variation of meshing stiffness due to changes of gear design parameters.

Influence of cycloid-pin gear design parameters on bearing capacity and optimized design

Influence of cycloid-pin gear design parameters on bearing capacity and optimized design

Analysis method for factors influencing gear hobbing quality based on density peak clustering and improved multi-objective differential evolution algorithm

ABSTRACT For addressing the problem that the quality indicators of gear hobbing are complicated and the influencing factors are unknown, a characteristic processing method combining improved multi-objective differential evolution (IMODE) and clustering based on peak density (DPCA) is proposed. This method can extract the characteristic parameters that strongly influence gear hobbing quality for multi-process parameters and multi-quality indicators, and quantify their importance to the comprehensive quality indicators. First, based on correlation analysis of the quality inspection parameters by DPCA, a set of relatively independent gear hobbing quality inspection indicators is obtained, and the dimensions of the quality inspection parameters are reduced for more effectively reflecting the hobbing processing quality. Next, multi-threshold Birch (IBirch) clusters are obtained for different gear hobbing quality inspection data under different process parameters to obtain cluster labels. Finally, Rough Sets theory and IMODE are used to reduce the gear hobbing process parameters and design parameters. Feature parameters that significantly affect the hobbing process quality are extracted from the process parameters and their importance is quantified. The validity and practicability of the method are verified by processing experiments, and the advantages of the proposed method are proved.

Effect of design parameters on stresses occurring at the tooth root in a spur gear pressed on a shaft

Gears are commonly used in transmission systems to adjust velocity and torque. An integral gear or an interference fit could be used in a gearbox. Integral gears are mostly preferred as driving gear for a compact design to reduce the weight of the system. Interference fit makes the replacement of damaged gear possible and re-use of the shaft compared to the integral shaft. However, internal pressure occurs between mating surfaces of the components mated. This internal pressure affects the stress distribution at the root and bottom land of the gear. In this case, gear parameters should be re-considered to assure gear life while reducing the size of the gear. In this study, interference fitted gear-shaft assembly was examined numerically. The effects of rim thickness, profile shifting, module and fit tolerance on bending stress occurring at the root of the gear were investigated to optimize gear design parameters. Finite element models were in good agreement with analytical solutions. Results showed that the rim thickness of the gear is the main parameter in terms of tangential stress occurring at the bottom land of the gear. Positive profile shifting reduces the tangential stress while the pitch diameter of the gear remains constant. Also, lower tolerance class could be selected to moderate stress for small rim thickness.

Improving Gerotor Pump Performance Trough Design, Modeling and Simulation

Gerotor pumps are well known by a compact design, simple structure and low noise level, which makes them suitable for use in the automotive industry, and especially in hydraulic systems for engine lubrication. One of the main disadvantages of gerotor pumps is the inability to adjust to wear, which significantly reduces the pump efficiency. In order to mitigate the negative effect of the inevitable wear process, this paper presents a methodology for determining the optimal combination of trochoid gears design parameters for a defined aspect. An appropriate mathematical model has been developed to analyze the effect of changes in gear design parameters in relation to maximum contact stresses, pressure changes in gerotor pump chambers and wear rate proportional factor (WRPF). Verification of the developed models was performed by realizing physical pairs of gears and laboratory experiments with simulation of pump operating conditions. The results and conclusions presented in this paper, with an emphasis on the actual work processes, bring very important perspectives for the gerotor pumps design with improved performance.

Computerized determination of the qualified region of main design parameters of face-milled hypoid gears with low shaft angle

The influence of main design parameters of hypoid gears with low shaft angle, namely, the offset, shaft angle, cutter radius, gear ratio, and the spiral angle of wheel, on the geometrical morphology the gear tooth surfaces has been investigated. Checks for obtaining appropriate top-land widths and spiral angles at the toe and heel sides have been developed and applied. The limits for the main design parameters that yield non-adequate tooth surfaces because- of top-land pointing, undercutting, or having a negative value of the spiral angle of wheel at the toe side have been investigated based on the results obtained by the simulation of a large number of cases of design. A specific computerized flow chart has been designed to iterate among the main design parameters to obtain a qualified region for them. With those results, a limiting graph has been proposed to get the list of recommended values of main design parameters and provide a reference for their selection. Finally, the results of loaded tooth contact analysis of two cases of design arbitrarily chosen from the proposed limiting graph of recommended values are shown to verify its applicability to yield to successful designs with favorable conditions of meshing and contact.

Principal stress lines based design method of lightweight and low vibration amplitude gear web

<abstract> <p>A lightweight and low vibration amplitude web design method was investigated to reduce gear weight and noise. It was based upon the relationship between length and orthogonality that the principal stress lines were designed at the gear web. By constructing a vibration control model with gear design parameters, the optimal distance was calculated. By offsetting the principal stress lines at the optimal distance, the lightweight gear web with the low vibration amplitude was then generated. A vibration experimental platform was built to verify the novel gear vibration performances, and it was compared with other gears with the same web's porosity to verify loading performance. The experimental results indicated that compared with the solid gear, the novel gear is 20.50% lighter and with a 29.46% vibration amplitude reduction.</p> </abstract>

A novel method to predict static transmission error for spur gear pair based on accuracy grade

This paper proposes a novel method to predict the spur gear pair’s static transmission error based on the accuracy grade, in which manufacturing errors (MEs), assembly errors (AEs), tooth deflections (TDs) and profile modifications (PMs) are considered. For the prediction, a discrete gear model for generating the error tooth profile based on the ISO accuracy grade is presented. Then, the gear model and a tooth deflection model for calculating the tooth compliance on gear meshing are coupled with the transmission error model to make the prediction by checking the interference status between gear and pinion. The prediction method is validated by comparison with the experimental results from the literature, and a set of cases are simulated to study the effects of MEs, AEs, TDs and PMs on the static transmission error. In addition, the time-varying backlash caused by both MEs and AEs, and the contact ratio under load conditions are also investigated. The results show that the novel method can effectively predict the range of the static transmission error under different accuracy grades. The prediction results can provide references for the selection of gear design parameters and the optimization of transmission performance in the design stage of gear systems.

A Modified Wear Model Considering Contact Temperature for Spur Gears in Mixed Elastohydrodynamic Lubrication

In this study, a modified wear model considering contact temperature for spur gears in mixed elastohydrodynamic lubrication (EHL) is proposed. The contact temperature consists of bulk temperature and flash temperature. The bulk temperature is determined by the thermal network model, whereas the flash temperature is estimated through the published method. The bulk temperature, which was rarely included in the previous works, substantially has a considerable influence on the tooth wear in mixed EHL. It is also found that the lower contact temperature contributes to the reduction of gear wear depth. Furthermore, the effects of gear basic geometrical parameter and operating parameter on wear depth are investigated. The results show that the wear depth decreases with the increased tooth width, module, pressure angle and rotational velocity but increases with the surface roughness and torque. It indicates that wear resistance of tooth surfaces can be enhanced by optimising the design parameters of gear drives.