Effect Of Tooth Profile Modification Research Articles

Effect of Tooth Profile Modification on Tooth Root Stress of Spur Gear Pump

Effect of Tooth Profile Modification on Tooth Root Stress of Spur Gear Pump

On the stability analysis of gear pairs with tooth profile modification

This paper deals with the stability of loaded gear pairs, considering the effects of tooth profile modification. An analytical method to predict the stability of gear pairs has been developed by transforming their equations of motion to a form similar to the Mathieu equation and employing Floquet theory. The variation of (spur gear pair) teeth meshing stiffness due to tooth profile modification has been introduced, for different amounts of transmitted torque. Stability charts are obtained for different gear pairs, as well as undamped and damped conditions. The simulation results have shown that during operation, the examined gear pairs may cross regimes of unstable behaviour, thus contributing to aggressive oscillations of the gearbox. A holistic transmission design must take the above potential effects into consideration when predicting the durability of machine elements, such as gears and bearings.

Suitable Design of Tooth Profile Modification for Noise Reduction in Spur Gear Pump

This study has carried out for noise reduction of spur gear pump. The previous report was published at JSME 2021 annual conference, which reported the noise source analyses result of test gear pump. According to the report, it was concluded that the most effective way to reduce noise was to reduce the meshing vibration of gears. Therefore, the authors aimed to reduce gear meshing vibration by modifying the tooth profile. For this purpose, the effect of tooth profile modification on the tooth root stress form was investigated. Then, the appropriate tooth modification amount was decided by the tooth root stress calculation. Furthermore, several kind of function which determines the shape of tooth profile modification has applied to the calculation to make clear the most effective shape of tooth profile modification for noise reduction. The major conclusions of this research are as follows; (1) The most effective value to tooth root stress waveform was depth of tooth profile modification. (2)The type of functions which determine the shape of tooth profile modification was less effective to tooth root stress waveform.

Dynamic loading of spur gears with linear tooth profile modification: modelling and experimental comparisons

A dynamic model of a gear pair has been developed to investigate methods of decreasing dynamic loads and analysing dynamic stresses of gears in aviation engine drives. The effect of tooth profile modification on dynamic stresses in the system, as well as the effect of main gear parameters is analysed. It is shown that high level of dynamic stresses and vibrations in gears may be caused by using standard parameters of tooth profile modification. An experimental study of the dynamics of gears with various profile modification parameters has been carried out. The paper shows the necessity of changing the approach to calculating parameters of tooth profile modification of teeth.

Effect of Tooth Profile Modification on Dynamic Tooth Load of Planetary Gear Train

This paper aims at investigating the effects of tooth profile modification (TPM) on the dynamic response of planetary gear train (PGT). A numerical model is carried out to calculate two major excitation sources of PGT, time‐varying mesh stiffness (TVMS), and transmission errors (TEs). On this basis, a linear time‐varying dynamic model of a PGT considering TVMS, TEs, and TPM is developed. Dynamic deviation factor is further introduced to describe the dynamic response of the PGT. In this paper, TPM is only applied to the external meshes firstly. Effects of TPM parameters, such as amount of TPM, normalized modification angle, and modification curve, on the excitation sources and dynamic response of the PGT are discussed in detail. Subsequently, investigation on the effects of TPM only applied to internal meshes is conducted. Finally, with the aim to obtain the optimal TPM for the minimization of dynamic load of PGT in both external and internal gear meshes, the genetic algorithm (GA) is employed. This research may shed light upon design optimization of PGT with respect to improvement of vibration performance by means of optimized TPM.

Effect of tooth profile modification on the durability of planetary hub gears

Planetary systems offer the advantage of desired speed-torque variation with a lighter, compact and coaxial construction than the traditional gear trains. Frictional losses and Noise, Vibration and Harshness (NVH) refinement are the main concerns. Modification of gear teeth geometry to reduce friction between the mating teeth flanks of vehicular planetary hubs, as well as refining NVH under varying load-speed conditions is one of the remedial actions. However, implementing modifications can result in reduced structural integrity and system durability. Therefore, a contradiction may arise between assuring a high degree of durability and achieving better transmission efficiency, which necessitates detailed system optimisation. An integrated multi-disciplinary analytical approach, including tribology and sub-surface stress analysis is developed. As a preliminary step, Tooth Contact Analysis (TCA) is performed to obtain contact footprint shape of meshing gear teeth pairs, as well as contact kinematics and applied load distribution. Then, an analytical time-efficient Elastohydrodynamic Lubrication (EHL) analysis of elliptical point contact of crowned spur gear tooth is carried out to observe the effect of gear tip relief modification upon planetary hub sub-surface stresses.

Effect of tooth profile modification on the durability of planetary hub gears

Effect of tooth profile modification on the durability of planetary hub gears

Mesh stiffness calculation of cycloid-pin gear pair with tooth profile modification and eccentricity error

Cycloid speed reducers are widely used in many industrial areas due to the advantages of compact size, high reduction ratio and high stiffness. However, currently, there are not many analytical models for the mesh stiffness calculation, which is a crucial parameter for the high-fidelity gear dynamic model. This is partially due to the difficulty of backlash determination and the complexity of multi-tooth contact deformation during the meshing process. In this paper, a new method to calculate the mesh stiffness is proposed including the effects of tooth profile modification and eccentricity error. The time-varying mesh parameters and load distribution of cycloid-pin gear pair are determined based on the unloaded tooth contact analysis (TCA) and the nonlinear Hertzian contact theory, allowing accurate calculations of the contact stiffness of single tooth pair and the torsional stiffness of multi-tooth pairs. A detailed parametric study is presented to demonstrate the influences of tooth profile modification, applied torque and eccentricity error on the torsional mesh stiffness, loaded transmission error, Hertzian contact stiffness and load sharing factor. This model can be applied to further study the lost motion and dynamic characteristics of cycloid speed reducer and assist the optimization of its precision, vibration and noise levels.

Effect of tooth profile modification on wear in internal gears

Internal gears are often used in the automotive industry when two gears are required to rotate in the same direction. Tooth shapes, slippage speeds at the beginning and end of meshing are different according to the external gears. Manufacturing of internal gears is more difficult than external gears. Thus, it is necessary to determine the working conditions and wear behavior of internal gears carefully. The profile modification method in terms of strength and surface tension of the gear mechanism are performed in order to increase the load-carrying capability. In this study, profile modification method was performed in the internal gears to reduce the wear on the teeth. For this purpose, the wear of the internal gears was theoretically investigated by adapting the Archard wear equation to the internal gears. Closed circuit power circulation system was designed and manufactured to experimentally investigate the wear in internal gears. With this system, wear tests of gears made of St 50 material without profile modification and different profile modifications were made and the results were compared. Experimental study was performed in the same loading and cycle time conditions to validate the theoretical results and it was seen that the results are compatible. According to the experimental results, it is seen that in the internal gears, when profile modification done the wear is decreased in the teeth tip region.

Effects of random tooth profile errors on the dynamic behaviors of planetary gears

In this paper, a nonlinear random model is built to describe the dynamics of planetary gear trains (PGTs), in which the time-varying mesh stiffness, tooth profile modification (TPM), tooth contact loss, and random tooth profile error are considered. A stochastic method based on the method of multiple scales (MMS) is extended to analyze the statistical property of the dynamic performance of PGTs. By the proposed multiple-scales based stochastic method, the distributions of the dynamic transmission errors (DTEs) are investigated, and the lower and upper bounds are determined based on the 3σ principle. Monte Carlo method is employed to verify the proposed method. Results indicate that the proposed method can be used to determine the distribution of the DTE of PGTs high efficiently and allow a link between the manufacturing precision and the dynamical response. In addition, the effects of tooth profile modification on the distributions of vibration amplitudes and the probability of tooth contact loss with different manufacturing tooth profile errors are studied. The results show that the manufacturing precision affects the distribution of dynamic transmission errors dramatically and appropriate TPMs are helpful to decrease the nominal value and the deviation of the vibration amplitudes.

Effects of tooth profile modification on dynamic responses of a high speed gear-rotor-bearing system

A finite element node dynamic model of a high speed gear-rotor-bearing system considering the time-varying mesh stiffness, backlash, gyroscopic effect and transmission error excitation is developed. Different tooth profile modifications are introduced into the gear pair and corresponding time-varying mesh stiffness curves are obtained. Effects of the tooth profile modification on mesh stiffness are analyzed, and the natural frequencies and mode shapes of the gear-rotor-bearing transmission system are given. The dynamic responses with respect to a wide input speed region including dynamic factor, vibration amplitude near the bearing and dynamic transmission error are obtained by introducing the time-varying mesh stiffness in different tooth profile modification cases into the gear-rotor-bearing dynamic system. Effects of the tooth profile modification on the dynamic responses are studied in detail. The numerical simulation results show that both the short profile modification and the long profile modification can affect the mutation of the mesh stiffness when the number of engaging tooth pairs changes. A short profile modification with an appropriate modification amount can improve the dynamic property of the system in certain work condition.

インボリュート平歯車の摩耗に及ぼす歯形修整の影響

インボリュート平歯車の摩耗に及ぼす歯形修整の影響

Effect of tooth profile modification on lubrication performance of a cycloid drive

A numerical study on contact performance of a cycloid drive lubricated with the grease is conducted. The effect of the tooth profile modification on lubrication performance is emphasized. Four profile modification methods are proposed and their influences on the length of the line of action, the pressure and the film thickness are compared. Results show that at a certain manufacturing accuracy, the lubrication performance of the one with a combined modification is better than the performance of the ones with single modification. The combined negative equidistant and negative radial-moving scheme has the best lubrication performance while the single negative radial-moving modification scheme has the worst lubrication performance among the selected schemes. Effect of the amount of the radial-moving modification and the amount of the combined negative equidistant with negative radial-moving modification are studied and results show that as the modification value increases, the length of LOA, the load-carrying capacity, and the film thickness decrease, which represents a worse lubrication performance. After modification, the lubrication performance of the engaging tooth pair would deteriorate. The higher the manufacturing precision, the smaller the amount of the modification, the better the lubrication performance.

Effects of misalignment error, tooth modifications and transmitted torque on tooth engagements of a pair of spur gears

In the last research [S. Li, Effects of machining errors, assembly errors and tooth modifications on load-carrying capacity, load-sharing rate and transmission error of a pair of spur gear, Mech. Mach. Theory 42 (2007) 698–726], effects of machining errors, assembly errors and lead crowning on tooth surface contact stresses (CS), root bending stresses, load-sharing ratios (LSR) and transmission errors of a pair of spur gears were investigated through performing loaded tooth contact analysis (LTCA) with developed finite element method (FEM) programs. But this research couldn't investigate the effects of tooth profile modification and lead relieving on tooth engagements. Also, the effects of machining errors, assembly errors and tooth modifications on tooth mesh stiffness (MS) couldn't be investigated. So, as a continuous study of the last research, this paper investigates the effects of tooth profile modification and lead relieving on tooth engagements of a pair of spur gears and the effects of misalignment error of gear shafts on the plane of action, tooth lead crowing and transmitted torque on tooth MS. An arc curve is used to modify tooth profiles of a pair of spur gears in this paper. This is because this method is used very popularly for the spur gears. Methods used in the last research are also used here to investigate the effects of the tooth profile modification, lead relieving and transmitted torque on tooth engagements. Based on the results, it is found that the tooth profile modification and lead relieving have significant effects on tooth CS, LSR and MS. It is also found that transmitted torque has a little effect on tooth MS, but has no effect on LSR of the gears. For the lead-relieved gears, calculation results show that edge-loads happened at the joint parts of the relieved part and the non-relieved part of tooth lead when the lead is relieved with straight lines. Since the edge-loads resulted in greater contact stresses at the joint parts and weakened tooth contact strength, attention must be paid to the lead relieving. It is necessary to reduce the edge-loads as small as possible through making the joint part smooth when the lead relieving is made.

Analytical investigation of tooth profile modification effects on planetary gear dynamics

This study investigates the impact of tooth profile modification on spur planetary gear vibration. An analytical model is proposed to capture the excitation from tooth profile modifications at the sun–planet and ring–planet meshes. The accuracy of the proposed model for dynamic analysis is correlated against a benchmark finite element analysis. Perturbation analysis yields a closed-form approximation of the vibration response with tooth profile modifications. The perturbation solution is used to investigate the effects of tooth profile modification. The tooth profile modification parameters that minimize response are readily obtained. Static transmission error and dynamic response are minimized at different amounts of profile modification, which contradicts common practical thinking regarding the correlation between static transmission error and dynamic response. Contrary to expectations, the optimal sun–planet and ring–planet tooth profile modifications that minimize response when applied individually may increase dynamic response when applied simultaneously. System parameters such as mesh stiffness and mesh phase significantly affect the influence of tooth profile modification.

Dynamic Modeling and Analysis of Tooth Profile Modification for Multimesh Gear Vibration

AbstractThis work studies the effects of tooth profile modification on multimesh gearset vibration. The nonlinear analytical model considers the dynamic load distribution between the individual gear teeth and the influence of variable mesh stiffnesses, profile modifications, and contact loss. The proposed model yields better agreement than two existing models when compared against nonlinear gear dynamics from a finite element/contact mechanics benchmark. These comparisons are made for different loads, profile modifications, and bearing stiffness conditions. This model captures the total and partial contact losses demonstrated by finite element. Perturbation analysis based on the proposed model finds approximate frequency response solutions for the case of no total contact loss due to the optimized system parameters. The closed-form solution is compared with numerical integration and provides guidance for optimizing mesh phasing, contact ratios, and profile modification magnitude and length.

Effect of tooth profile modification on the scoring resistance of spur gears

Using power-circulating gear test rigs, the scoring resistance of gears with tooth profile modification and gears without tooth profile modification, both of which were subjected to different amounts of addendum modification, was studied. The effect of tooth profile modification on the scoring resistance of gears with a small amount of addendum modification was significantly increased by the tooth profile modification. The critical surface temperature for scoring lies between 443 and 447 K under the conditions of tooth material and lubricant used. The scoring resistance of gears can be accurately estimated by evaluating the critical surface temperature.

Effect of tooth profile modification on the scoring resistance of heavy-duty spur gears

The effect of tooth profile modification on the scoring resistance of heavy-duty spur gears was studied on a power circulating type gear meshing apparatus using a case hardened chrome-molybdenum steel as gear material with a straight mineral oil as lubricant. The maximum surface temperature at the contact between the meshing gear teeth was estimated using the authors' previously developed experimental equation. It is shown that scoring resistance increases with increasing amount of tooth profile modification. The increase being in the ratio of 1.4 to more than 2. It is also shown that the estimated maximum surface temperature corresponding to the transition from non-scoring to scoring is in the range of 400°–500°C, which appears to correspond to the softening temperature of case hardened steels.