An Experimental and Theoretical Study of Quasi-Static Behavior of Double-Helical Gear Sets

2020 ◽  
Vol 143 (4) ◽  
Author(s):  
M.R. Kang ◽  
A. Kahraman
Keyword(s):  
Load Distribution ◽  
Theoretical Study ◽  
Power Transmission ◽  
Transmission Error ◽  
Helical Gear ◽  
Static Behavior ◽  
World Congress ◽  
Helical Gears ◽  
Support Conditions ◽  
Stagger Angle

Abstract The quasi-static behaviors of a double-helical gear pair is investigated both experimentally and theoretically with the main focus on the influence of the key design and manufacturing parameters associated with double-helical gears, including nominal right-to-left stagger angle, the stagger angle deviation (error) from the nominal stagger angle, and axial gear supporting conditions. On the experimental side, a double-helical gear test setup proposed earlier (Kang, M. R., and Kahraman, A., 2015, “An Experimental and Theoretical Study of Dynamic Behavior of Double-Helical Gear Sets,” J. Sound Vib., 350, pp. 11–29). for studying dynamics of the same system is employed that allows adjustable right-to-left stagger angles, intentional stagger errors, and axial support conditions. Specific measurement systems are developed and implemented simultaneously to measure the static motion transmission error and axial motions of the gears under low-speed conditions, as well as gear root strains to determine right-to-left load-sharing factors. A test matrix that covers wide ranges of stagger angles, intentional stagger error, and axial support conditions is executed within a range of torque transmitted to establish an extensive database. On the modeling side, the measured quasi-static behavior of double-helical gear pairs is simulated by using an existing quasi-static double-helical load distribution model (Thomas, J., and Houser, D. R., 1992, “A Procedure for Predicting the Load Distribution and Transmission Error Characteristics of Double Helical Gears,” World Congress-Gear and Power Transmission, The 3rd World Congress—Gear and Power Transmission, Paris.). Direct comparison of the measurements and predictions of loaded static transmission error, axial play, root stresses, and right-to-left load-sharing factors are used to validate the quasi-static model as well as describing the measured behavior.

Gear transmission error outside the normal path of contact due to corner and top contact

1999 ◽  
Vol 213 (4) ◽  
pp. 389-400 ◽  
Author(s):  
R. G. Munro ◽  
L Morrish ◽  
D Palmer
Keyword(s):  
Dynamic Test ◽  
Theoretical Models ◽  
Transmission Error ◽  
Helical Gear ◽  
Gear Transmission ◽  
The Novel ◽  
Transmission Systems ◽  
Helical Gears ◽  
Tooth Stiffness ◽  
Top Contact

This paper is devoted to a phenomenon known as corner contact, or contact outside the normal path of contact, which can occur in spur and helical gear transmission systems under certain conditions. In this case, a change in position of the driven gear with respect to its theoretical position takes place, thus inducing a transmission error referred to here as the transmission error outside the normal path of contact (TEo.p.c). The paper deals with spur gears only, but the results are directly applicable to helical gears. It systematizes previous knowledge on this subject, suggests some further developments of the theory and introduces the novel phenomenon of top contact. The theoretical results are compared with experimental measurements using a single flank tester and a back-to-back dynamic test rig for spur and helical gears, and they are in good agreement. Convenient approximate equations for calculation of TEo.p.c suggested here are important for analysis of experimental data collected in the form of Harris maps. This will make possible the calculation of tooth stiffness values needed for use in theoretical models for spur and helical gear transmission systems.

Four-Order Parabolic Transmission Error Design of Helical Gear Based on Meshing Area

2013 ◽  
Vol 842 ◽  
pp. 410-414
Author(s):  
Jian Jun Yang ◽  
Jian Jun Wang
Keyword(s):  
Contact Stress ◽  
Transition Point ◽  
Design Method ◽  
Transmission Error ◽  
Helical Gear ◽  
Transmission Curve ◽  
Tooth Contact Analysis ◽  
Contact Conditions ◽  
Helical Gears ◽  
Alignment Errors

In the paper, a new transmission error design method for helical gears is presented. According to transition point position of the contact area in one meshing cycle, the proposed four-order transmission curve is able to diminish contact stress and edge contact, decrease transmission error as well. Tooth contact analysis is used to simulate contact conditions of helical gear driver with four-order parabolic modification curve. The results show that the meshing area is non-sensitive to the alignment errors.

Recent Progress and Prospect on Tooth Modification of Involute Cylindrical Gear

2021 ◽  
Vol 14 ◽  
Author(s):  
Lin Han ◽  
Yang Qi
Keyword(s):  
Load Distribution ◽  
Power Transmission ◽  
Gear Tooth ◽  
Transmission Error ◽  
Gear Pair ◽  
Cylindrical Gear ◽  
Tooth Width ◽  
Modification Method ◽  
Power Transmission Systems ◽  
Tooth Modification

Background: Recent reviews on tooth modification of involute cylindrical gear are presented. Gear pairs are widely employed in motion and power transmission systems. Manufacturing and assembling errors of gear parts, time-varying mesh stiffness and transmission error of gear pair, usually induce vibration, noise, non-uniformly load distribution and stress concentration, resulting in earlier failure of gear. Tooth modification is regarded as one of the most popular ways to suppress vibration, reduce noise level, and improve load distribution of gear pairs. Objective: To provide an overview of recent research and patents on tooth modification method and technology. Methods: This article reviews related research and patents on tooth modification. The modification method, evaluation, optimization and machining technology are introduced. Results: Three types of modifications are compared and analyzed, and influences of each on both static and dynamic performances of gear pair are concluded. By summarizing a number of patents and research about tooth modification of cylindrical gears, the current and future development of research and patent are also discussed. Conclusion: Tooth modification is classified into tip or root relief along tooth profile, lead crown modification along tooth width and compound modification. Each could be applied in different ways. In view of design, optimization under given working condition to get optimal modification parameters is more practical. Machining technology and device for modified gear is a key to get high quality performance of geared transmission. More patents on tooth modification should be invented in future.

Partial Meshing of Synchronous Belt Teeth

2007 ◽  
Author(s):  
Tomas Johannesson
Keyword(s):  
Load Distribution ◽  
Static Load ◽  
Power Transmission ◽  
Transmission Error ◽  
Distribution Model ◽  
Velocity Difference ◽  
Line Segments ◽  
Tooth Stiffness ◽  
Overlap Area ◽  
Difference Effect

Synchronous belts have been used in power transmissions where synchronization is also needed since the 1940’s. In the 1960’s overhead camshaft engines were introduced and synchronous belts were used as cam belts. This made way for a new standard for belts: improvements were made in materials and profile geometry. These new belts had lower noise emissions and, at the same time, greater durability. Often, both wear and noise are generated when a belt tooth seats or unseats a pulley. A tooth is considered to be fully meshed when the whole belt pitch forms a circular arc. This is not the case for teeth in partial mesh, which occurs in seating and unseating zones. In these zones force peaks are often present. These peaks are believed to arise mainly as a result of two phenomena: one is the overlap effect due to the belt geometry not fitting the pulley, and other is the velocity difference effect. The latter is speed-dependent while the former depends on the belt and pulley profile geometries and the belt teeth positions relative to the pulley. Although force peaks of high magnitude occur, they are present at a such small part of the engagement that their contribution to power transmission can be neglected. This indicates that the positions of the belt pitches relative to the pulley pitches can be established by the load distribution from fully meshed conditions. Although the characteristics of partial mesh teeth have been improved by the introduction of new profiles and materials, problems of durability, noise and transmission error, arising from partially meshed teeth, are still present. Therefore it is important to study belt mechanics in seating and unseating zones. This paper describes a method to calculate force peakson seating and unseating. An overlap area (geometrical interference) is formed by giving belt teeth profiles displacement and checking for interference with the pulley profile. Since it is assumed that the seating and unseating force peaks do not influence the load distribution, the positions of the first and last teeth are superimposed on belt teeth profiles using the results from a quasi-static load distribution model covering fully meshed conditions. The superimposed first and last belt teeth profiles are modelled by line segments. A pulley profile is also modelled by line segments and the profiles are checked for interference. Where interference occur an overlap area is formed. The overlap is translated to a force value via correlation with belt tooth force measurements. Results from the model show good agreement with measurements when force peaks are small. This is due to the fact that the quasi-static load distribution model produces correct belt displacements for these cases. For measured force peaks of higher amplitude the seating and unseating effects are under estimated by the method. The semicircular belt geometry in combination with the hyperelastic nature of the elastomer is probably the reason. A solution is to implement a non-linear force-overlap relation. Another effect not included is the velocity difference effect. The results are sensitive to belt tooth height and radial tooth stiffness.

scholarly journals Wear load capacity of crossed helical gears with wheel made from sintered steel

2015 ◽  
Vol 47 (2) ◽  
pp. 153-163 ◽  
Author(s):  
A. Miltenovic ◽  
V. Nikolic ◽  
M. Banic
Keyword(s):  
Power Transmission ◽  
Load Capacity ◽  
Helical Gear ◽  
Low Noise ◽  
Additional Treatment ◽  
Sintered Steel ◽  
Helical Gears ◽  
Noise Characteristics ◽  
Hardening Treatment ◽  
Important Position

Crossed helical gears have an important position in power transmission. Important advantages of the crossed helical gears are the small design, the realization of high ratios in one stage, and the low noise characteristics. The paper presents a theoretical and experimental research of mesh efficiency, tooth friction coefficient and wear for a wheel of crossed helical gears made of Fe1.5Cr0.2Mo sintered steel with sinter-hardening treatment and without additional treatment. The calculation method is also given for the determination of wear load capacity of the worm with a helical gear made of Fe1.5Cr0.2Mo sintered steel with sinter-hardening treatment. These results provide product developers with the first important clues for indicators for calculation of the worm with a helical gear.

Solution of Load Distribution on the Contact Line of Helical Gears With EHL Theory

1994 ◽  
Author(s):  
Yu Tonghui ◽  
Chen Chenwen ◽  
Wang Liqin
Keyword(s):  
Contact Line ◽  
Load Distribution ◽  
Multigrid Method ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Elastohydrodynamic Lubrication ◽  
Helical Gear ◽  
Contact Lines ◽  
Helical Gears ◽  
Special Boundary Condition

Abstract On the base of analysis of the effects of each term in Renolds equaiton on the lubrication state of helical gears, the three dimensional elastohydrodynamic lubrication (EHL) problem is discomposed into two dimensional problems to deal with. A special boundary condition for helical gear EHL problem is led in and applying multigrid method (MGM), numerical solutions for the helical gear EHL problem are accomplished along the contact line. Film shapes and pressure ditributions with typical EHL features are obtained at discreted points on the contact line. The procedure presented here to calculate the load distribution on the contact line can also be used to calculate the load shares among different contact lines.

Profile Modifications for Minimum Static Transmission Error in Cylindrical Gears

1998 ◽  
Author(s):  
Isaias Regalado ◽  
Donald R. Houser
Keyword(s):  
Load Distribution ◽  
Strong Relationship ◽  
Transmission Error ◽  
Gear Ratio ◽  
Spur Gears ◽  
Helical Gears ◽  
Involute Gears ◽  
Theoretical Advantage ◽  
Static Transmission Error ◽  
The Common

Abstract The theoretical advantage of conjugate action in involute gears is lost due to the deflection of the teeth under load and due to manufacturing and assembling errors. These factors produce instantaneous variations in the gear ratio commonly referred to as transmission error. The transmission error has been proven to have a strong relationship with the noise emitted by the transmission. In order to reduce the transmission error, the contacting surfaces of the gears are modified to compensate for the deflections and errors. These modifications may be performed in the direction of the profile, the lead or in a more general sense it may be topographical (defined point by point). This paper describes a non-iterative procedure for the calculation of the modifications for minimum transmission error based on a predefined load distribution. The results presented agree with the common practice for spur gears of tip relief in the direction of the profile and crowning in the direction of the lead, but for helical gears the need for a more complicated modification is observed.

The Effect of Tooth Wear on the Dynamic Transmission Error of Helical Gears with Smaller Number of Pinion Teeth

2014 ◽  
Vol 657 ◽  
pp. 649-653 ◽  
Author(s):  
Virgil Atanasiu ◽  
Cezar Oprişan ◽  
Dumitru Leohchi
Keyword(s):  
Dynamic Contact ◽  
Tooth Wear ◽  
Transmission Error ◽  
Analytical Investigation ◽  
Helical Gear ◽  
Wear Depth ◽  
Contact Ratio ◽  
Mesh Stiffness ◽  
Helical Gears ◽  
Dynamic Transmission Error

The paper presents an analytical investigation of the effect of the tooth wear on the dynamic transmission error of helical gear pairs with small number of pinion teeth. Firstly, the dynamic analysis is conducted to investigate only the effect of the time-varying mesh stiffness on the variation of dynamic transmission error along the line of action. Then, the tooth wear effect on the dynamics of helical gear with small number of pinion teeth is being researched. In the analysis, instantaneous dynamic contact analysis is used in wear depth calculations. A comparative study was performed to investigate the relation between total contact ratio, mesh stiffness and dynamic transmission error of helical gear pairs with small number of teeth.

The Influence of the Pinion-Shaft Deflection on the Dynamic Characteristics of Helical Gear Pairs

2014 ◽  
Vol 658 ◽  
pp. 17-22
Author(s):  
Virgil Atanasiu ◽  
Cezar Oprişan ◽  
Dumitru Leohchi
Keyword(s):  
Dynamic Characteristics ◽  
Transmission Error ◽  
Helical Gear ◽  
Time Varying ◽  
Comparison Analysis ◽  
Mesh Stiffness ◽  
Helical Gears ◽  
Shaft System ◽  
Shaft Deflection ◽  
Shaft Flexibility

This study presents a dynamic model of helical gears for analyzing the effect of pinion-shaft flexibility on the dynamic behavior of helical gears. In the analysis, the time-varying mesh stiffness is determined in relation with the geometry of the gear pair and incorporates the deflection of the pinion–shaft. A comparison analysis is presented for the dynamic transmission error response of gear pairs supported with a rigid and a flexible shaft system. The results show that the pinion-shaft deflection must be included in the dynamic analysis since they can strongly affect the dynamic characteristics of helical gear pairs.

Analysis of Plastic Helical Gear

2006 ◽  
Author(s):  
Toni Jabbour ◽  
Ghazi Asmar ◽  
Chadi Ghaith
Keyword(s):  
Mathematical Model ◽  
Real Number ◽  
Modulus Of Elasticity ◽  
Load Distribution ◽  
Large Deformations ◽  
Tooth Wear ◽  
Helical Gear ◽  
Contact Ratio ◽  
Helical Gears ◽  
The Real

The objective of this work is to present a mathematical model which studies helical gears made of a material with a small modulus of elasticity, when one or more pairs of teeth mesh prematurely during engagement. This phenomenon may lead to the modification of the load distribution on the teeth which are initially in contact and to a kind of interference causing additional tooth wear of the gear. In this case, the calculation of the contact ratio must account for the real number of pairs of teeth in contact. This is especially important when large deformations occur as is confirmed in the results presented to confirm the validity of the proposed method.

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