High Contact Ratio Spur Gears Research Articles

Analytical model of meshing stiffness, load sharing, and transmission error for internal spur gears with profile modification

The influence of the teeth geometry on the load distribution, transmission error, and meshing stiffness of internal spur gears is very similar to that of external gears. Therefore, the formulation of the models for strength and dynamic calculations for internal and external gears is also similar. However, the internal gears have usually greater values of the contact ratio, frequently above 1.8, even 1.9. In these cases, the lengthening of the contact interval due to the elastic deflections of the teeth may result in an effective contact ratio greater than 2, with the subsequent changes in the load sharing and transmission error. These changes are not properly described by the theoretical models for high contact ratio spur gears. In this paper, a model of load sharing, quasi-static transmission error, and time-varying meshing stiffness for internal spur gears with profile modification is presented, which has been applied to low contact ratio internal gears which, due to the transmitted load, become high contact ratio internal gears. The influence of the variations of the transmitted load on the load capacity is also studied.

Stiffness Analysis of High Contact Ratio Spur Gear with Asymmetric Teeth

The demands of high carrying capacity and low vibration of gear transmission systems in aviation, aerospace, and other areas are addressed by high contact ratio gears with asymmetric teeth, which have a wide range of potential applications. The Weber energy technique is utilized to determine the stiffness of high contact ratio spur gears with asymmetric teeth, and the effect law of the stiffness parameters is researched, due to the paucity of study on these gears. The influence of the drive side addendum factor, modulus, and pressure angle on the stiffness of asymmetric high contact ratio spur gears is investigated. The deformation of the gear will be exacerbated by an increase in the addendum factor, and the comprehensive stiffness of the gear will grow as more gear pairs participate in the meshing. The rigidity of gears may be greatly increased without ignoring modulus if the driving side pressure angle is properly increased.

Load share model based gear loss factor prediction in high contact ratio spur gear drive

Gear loss factor is considered to be a crucial parameter, and is governed by factors like contact load, sliding velocity, contact ratio, etc. Sliding power loss is a function of the gear loss factor and friction coefficient. It depends on the contact tooth load and its contact surfaces. A small decline in the gear loss factor and variation in the friction coefficient reduces the energy consumption which improves gear efficiency significantly. Hence, accurate prediction of the gear loss factor is important. This paper deliberates on measuring the contact load of High Contact Ratio (HCR) non-standard gear drive, using the finite element contact model. The input for the gear loss factor is obtained from a 2D elastic contact model using ANSYS. In the previous works the load is considered as a rigid hypothetical element, but in the real case it is varying at each instantaneous contact point. To address this, a more accurate method of predicting the power loss using the contact load share model is proposed. The effectiveness of this technique, built on the computational data and its accuracy are examined. Based on the accuracy, the load share model was suggested to be the most effective one compared to other techniques. The results show that the proposed model provides an effective tool for making reliability assessments on power loss and efficiency of high contact ratio gear drives under diverse operating conditions.

High-contact ratio spur gears with conformal contact and reduced sliding

The high-contact ratio (HCR) spur gear is a possible choice for a quiet and smooth gearing system. However, HCR spur gear of the involute type has several constraints, such as high sliding contact under large loads and interference problems in high speed reduction systems, so its benefits may not be fully offered. As a result, the primary goal of this research is to design a non-involute HCR spur gear with reduced sliding contact, enhanced fillet strength, better lubrication conditions, and no interference issues compared to the traditional HCR involute pair. A generalized mathematical model for defining the gear tooth profile and its geometrical aspects is built based on the path of contact shape. The involute curve length parameter and maximum pressure angle during the meshing cycle are only introduced to characterize this model. This model is utilized to create a new non-involute HCR gear pair that provides a free-form tooth profile to meet the design requirements. To demonstrate this method, certain case studies are provided, and the analytical results are validated using the finite element method. The new gear's performance is compared to the traditional involute gear that is currently in use. The results showed that by employing the proposed method, the HCR spur gear can achieve better surface durability and fillet strength.

Performance Evaluation of Low- and High-Contact Ratio Spur Gears: Dynamic Response and Bending Strength

Performance Evaluation of Low- and High-Contact Ratio Spur Gears: Dynamic Response and Bending Strength

Optimization of contact stress for the high contact ratio spur gears achieved through novel hob cutter

Optimization of contact stress for the high contact ratio spur gears achieved through novel hob cutter

Fracture characteristics of asymmetric high contact ratio spur gear based on strain energy release rate

Variations in design parameters and methodology have a significant effect on the fracture characteristics of spur gear. Furthermore, the geometry and load acting on the spur gear affect the propagation of fractures and the bending fatigue life. In comparison with conventional gear design, the direct design strategy is a highly efficient method for improving fracture resistance. This study attempts to investigate the fracture properties of a direct designed asymmetric high contact ratio (AHCR-DD) spur gear subjected to the mix-mode of crack failures. The stress intensity factor (SIF) and the shape factor are compared to conventional normal and high contact ratio spur gears. In addition, the fracture properties of conventional design symmetric HCR (SHCR-CD), direct design symmetric HCR (SHCR-DD), and AHCR-DD spur gears are compared. When compared to other gears, the AHCR-DD spur gear has a higher fracture resistance. A parametric study of the fracture properties of the AHCR-DD spur gear is also carried out to provide useful information for designing such gears. Variations in the contact ratio, rim thickness, number of teeth, and addendum pressure angle are used to assess fracture performance. It is observed that using a direct design technique significantly reduces the SIF. This investigative study provides valuable guidelines in the future for developing non-standard spur gears such as AHCR-DD.

Control of transmission error of high contact ratio spur gears with symmetric profile modifications

This paper presents a study on the influence on the quasi-static transmission error of symmetric long profile modifications on high contact ratio spur gears. A previously developed model for the load sharing ratio and quasi-static transmission error, based on the hypothesis of equal delay interval in all the teeth in simultaneous contact, has been used. The simple formulation of the model allows to obtain the equation of the required profile modification to ensure a preestablished function of load sharing ratio or quasi-static transmission error. From this model, the tip reliefs for minimum peak-to-peak amplitude of quasi-static transmission error and for minimum dynamic load, have been obtained. In both cases, the optimum length of modification has been expressed as a function of the contact ratio.

Load sharing model for high contact ratio spur gears with long profile modifications

The start of contact between loaded involute gear teeth occurs before reaching the theoretical inner point of contact due to the load-induced deflections of previous tooth pairs in contact. This sooner contact occurs outside the pressure line and produces a shock between the driving tooth root and the driven tooth tip, which induces noise, vibrations and dynamic load. To avoid these undesirable effects profile modifications are often used, which through a suitable tip relief at the driven tooth delay the actual start of contact until locate it at the theoretical inner point of contact. However, the length and shape of profile modification have also influence on the curves of load sharing and quasi-static transmission error. Specifically, long tip relieves, beyond the interval of minimum tooth pair contact, which are unsuitable for standard contact ratio spur gears, may reduce drastically the load at the inner points of the path of contact of high contact ratio gears, though a peak of load arises at the outer interval of two pair tooth contact. Since the determinant contact stresses are usually located at the inner points of the contact interval and the determinant tooth-root stresses at the outer ones, long tip relieves can be used for balancing both determinant stresses and improving the load capacity.

Bending Stress Analysis of High Contact Ratio Spur Gear

Bending Stress Analysis of High Contact Ratio Spur Gear

Study of the tooth contact for high contact ratio spur gears with long tip relief

Profile modifications are commonly used to avoid shocks between meshing gear teeth produced by the delay of the driven gear, and the subsequent sooner start of contact, due to the teeth deflections. A suitable tip relief at the driven tooth shifts the start of contact to the proper location at the theoretical inner point of contact. The shape of the relief governs the loading curve of the tooth pair, while the length of relief determines the intervals in which this actual loading curve differs from the theoretical one of unmodified teeth. As at least one tooth pair should be in contact at the unmodified involute profile interval, the length of modification should be smaller than the length of the intervals of two pair tooth contact; otherwise, a shock at the end of contact of the previous pair is unavoidable. However this problem does not occur for high contact ratio spur gears, in which at least two couples of teeth are in contact at any moment. In this work, a study on the load sharing and the quasi-static transmission error for high contact ratio spur gears with long profile modification has been performed, and a model for the tooth contact has been developed.

Evolution of balanced root stress and tribological properties in high contact ratio spur gear drive

Tooth bending and surface wear are the two major causes of failure modes which occur due to inadequate bending and contact strength. In a gear drive, when the gear ratio is more than one the bending strength of the pinion and gear it is different. Consequently gear drive with an equivalent bending strength in the gear and pinion is called as a balanced gear drive. This can be attained by providing non-standard tooth thickness at the pitch circle in High Contact Ratio (HCR) spur gears. Non-standard HCR spur gear drive is one in which the tooth thickness at the pitch circle of the gear and pinion is not same. In the present study, tooth wear over the contacting surfaces for non-standard HCR spur gear drive is probed numerically through finite element analysis (FEA). In addition, the tooth load, contact stress, film thickness and sliding distance are also estimated for a balanced non-standard HCR spur gear drive. Also the effect of different gear parameters like pinion teeth number, pressure angle, addendum height and gear ratio on tooth wear along the line of action on non-standard HCR spur gear has been evaluated and discussed.

Influence of gear ratio on wear depth of nonstandard HCR spur gear drive with balanced fillet stress

In this paper, the wear depth of a nonstandard High Contact Ratio (HCR) spur gear drive is investigated using contact analysis considering the load share between the tooth in contact, fillet stress and contact stress for number of mesh cycles in steel gears. The fillet stresses obtained using finite element method is balanced by varying the tooth thickness along the reference line. This method of changing the tooth thickness is referred as nonstandard HCR spur gear drive. Using this method, an improved nonstandard HCR spur gear drive is obtained in terms of bending strength. In this enhanced nonstandard HCR spur gear drive the wear depth is estimated analytically for balanced fillet stress. Also, this paper explores the influence of gear ratio over wear depth of nonstandard HCR spur gear drive and finally the results are discussed.

Approximate equations for the meshing stiffness and the load sharing ratio of spur gears including hertzian effects

In this paper, the meshing stiffness of spur gear pairs, considering both global tooth deflections and local contact deflections, is evaluated at any point of the path of contact and approximated by an analytical, simple function. With this function, the load sharing ratio is calculated and compared with previous results obtained from the hypothesis of minimum elastic potential energy (MEPE model), considering the tooth deflections, but neglecting the hertzian deflections. Critical bending and contact stresses from both models are also compared both for standard and high contact ratio spur gears.

Investigation of load carrying capacity of asymmetric high contact ratio spur gear based on load sharing using direct gear design approach

The Direct Gear Design® approach is one of the many gear designing methods available to improve load carrying capacity of the gear pairs. For customized gear pairs, the direct gear design approach is more advantageous over conventional design. In this paper, a parametric study is carried out for asymmetric high contact ratio spur gears based on load sharing method to determine the improvement in load carrying capacity. A finite element model for multi-pair contact is adopted to determine the non-dimensional fillet and contact stresses which quantify the load carrying capacity of the gear pairs. The results of direct designed symmetric and asymmetric high contact ratio spur gears are compared with the conventional symmetric high contact ratio spur gears. Also, the influence of gear parameters such as addendum pressure angle, gear ratio, teeth number and backup ratio of non-dimensional stresses is analyzed in detail. The results show significant improvement in gear pair performance for all parameters analyzed.

Optimization of fillet stress to enhance the bending strength through non-standard high contact ratio spur gears

The present study aims to determine the improvement in the bending strength of the non-standard high contact ratio spur gears based on the balanced (optimum) fillet stress of the pinion and gear. The average number teeth in contact is more than two for high contact ratio gear drives. In the non-standard high contact ratio spur gears, the rack cutter tooth thickness factor is more than 0.5, whereas the standard rack cutter tooth thickness factor is 0.5. The maximum fillet stresses of the pinion and gear is not equal for non-standard high contact ratio spur gear drives when the gear ratio increases. In order to avoid the fatigue failure of the gear, the fillet stresses of the pinion and gear should be balanced. This balanced stress is predicted as the optimum fillet stress. Hence, the present study focuses to optimize the fillet stress with respect to the rack cutter tooth thickness factor of the pinion and gear through finite element analysis. Also, a parametric study is carried out to obtain the influence of some gear parameters, such as gear ratio, teeth number in the pinion, pressure angle, addendum height and corrected gear drives (S+, S− and So) on the optimum fillet stress with respect to the rack cutter tooth thickness factor of the pinion and gear.

An Alternative Approach to the Definition of Profile Modifications in High-Contact-Ratio Spur Gears

An alternative formulation for the definition of profile modifications in high-contact-ratio (HCR) spur gears is presented which makes it possible to select optimum relief with regard to transmission error (TE) fluctuations over a range of loads. General guidelines are presented which can help design optimum relief with minimum effort. It is also confirmed that two-slope profile relief can improve the dynamic behavior of HCR spur gears.

Effect of Drive Side Contact Ratio on Direct Design Asymmetric High Contact Ratio Spur Gear Based on Load Sharing

The aim of this paper is to determine the effect on direct design asymmetric high contact ratio spur gear based on tooth load sharing. A unique Ansys parametric design language code is developed for this study. The load sharing based bending and contact stresses are determined for different drive side contact ratios. In addition to that the location of critical loading point is determined. Because the critical loading point for high contact ratio spur gear not lies on fixed point like normal contact ratio spur gears namely highest point of single tooth contact. In conclusion an increase in drive side contact ratio leads to increase in the load sharing based bending stress and decrease in the contact stress at the critical loading point.

Optimum Profile Shift Estimation on Direct Design Asymmetric Normal and High Contact Ratio Spur Gears Based on Load Sharing

Abstract In direct design method, gear pair is selected from area of existence diagram. This area of existence diagram gives N number of possible gear pairs. From this possible gear pairs it is important to optimize the fillet strength of pinion and gear with respect to the optimum profile shift. Optimum design of gear drive means the maximum fillet stresses developed at the pinion and gear are to be equal. Hence the present work attempts for a reasonably accurate estimation of optimum profile shifts based on pinion and gear tooth fillet strength for a load at critical loading point considering the load sharing between the gear pair on asymmetric normal and high contact ratio asymmetric spur gear through direct design.

Tooth-root stress calculation of high transverse contact ratio spur and helical gears

In this paper, a non-uniform model of load distribution along the line of contact of spur and helical gears, obtained from the minimum elastic potential criterion, has been used, combined with the equations of the linear elasticity, to evaluate the tooth-root stress of high transverse contact ratio gears. The values of both critical stress and load conditions have been obtained and a complete analysis of the tooth bending strength has been carried out. As the load per unit of length at any point of the line of contact and any position of the meshing cycle has been described by a very simple equation, a complete study of the location and the value of the tooth-root stress has been carried out. From this study, a recommendation for the calculation of the bending load capacity of high transverse contact ratio spur and helical gears is proposed.