Simulation on the Rotational Vibration of Helical Gears in Consideration of the Tooth Separation Phenomenon (A New Stiffness Function of Helical Involute Tooth Pair)

1995 ◽  
Vol 117 (3) ◽  
pp. 460-469 ◽  
Author(s):  
Y. Cai
Keyword(s):  
Helical Gear ◽  
Contact Ratio ◽  
Narrow Face ◽  
Helical Gears ◽  
Face Width ◽  
Vibration Model ◽  
Rotational Vibration ◽  
The Finite Difference Method ◽  
Vibration Time ◽  
Tooth Pair

In this paper, an exact vibration model for helical gear pairs, is developed assuming no spacing error and no shaft run-out, in consideration of nonlinear tooth separation phenomenon. Inside the model, a simple modified stiffness function, including the effect of tooth numbers and addendum modification coefficients, is proposed for a helical involute tooth pair. This new stiffness function is verified by comparing its results with theoretical calculation and experiment. The rotational vibration of helical gear pairs with comparative narrow face width is simulated clearly on a 16-bit personal computer using the finite difference method in Fortran. The total contact ratio, including transverse and overlap contact ratios, is changed in the range of 1 ≤ ε ≤ 3. As a result, the simulated vibration time waveforms and their frequency characteristics agreed precisely with Umezawa’s calculation and experiment. This simulator is also used to investigate the effect of shaft deviation and pressure angle errors on the vibration of helical gears.

The Optimum Modification of Tooth Profile for a Pair of Spur Gears to Make its Rotational Vibration Equal Zero

1992 ◽  
Author(s):  
Yurong Cai ◽  
Teru Hayashi
Keyword(s):  
Static Load ◽  
Tooth Profile ◽  
Parameter Study ◽  
Exact Equation ◽  
Spur Gears ◽  
Contact Ratio ◽  
Profile Error ◽  
Vibration Model ◽  
Modification Method ◽  
Rotational Vibration

Abstract This paper develops an optimum modification method of tooth profile for a pair of spur gears to make its rotational vibration become zero by using an exact vibration model. By minimizing the equivalent exciting force, which includes the effects of the static load, time-varying stiffness, and relative tooth profile error, each optimum modification curve for each gear pair with different designed contact ratios can be obtained. The magnitude and the shape of the optimum modification curve depend upon the value of the designed contact ratio ε strongly. Especially, the concave modification curve is obtained in case of ε ≤ 1.1. The effect of the optimum modification on eliminating the vibration, is verified by the numerical calculation using an exact equation of vibration. A parameter study is presented to investigate the effect of running condition.

External High-Order Multistage Modified Elliptical Helical Gears and Design Procedure of Its Gear Pair

2014 ◽  
Author(s):  
Jiang Han ◽  
Youyu Liu ◽  
Dazhu Li ◽  
Lian Xia
Keyword(s):  
Design Procedure ◽  
Mathematical Expression ◽  
Gear Ratio ◽  
Helical Gear ◽  
High Order ◽  
Curvature Radius ◽  
Gear Pair ◽  
Contact Ratio ◽  
Helical Gears ◽  
Helical Gear Pair

In view of the limited number of the modified segments for high-order and two-stage modified elliptical helical gears, and poor adjustment capacity for gear ratio, the formation mechanism of a high-order multistage modified ellipse was studied, and a unified mathematical expression of the family of ellipses was obtained. Thus, a design procedure for the helical gear pair of the high-order multistage modified ellipse was suggested, and its transmission characteristics were discussed exhaustively. Moreover, some checking methods such as the curvature radius of the pitch curve, convexity, pressure angle, root cutting, and contact ratio were offered. Finally, two design cases, including two-order and three-stage modified elliptical helical gear pair and two-order and four-stage one, were implemented. The cases indicate that a high-order multistage modified elliptical helical gear can be utilized in practice.

Analysis of time-varying friction excitations in helical gears with refined general formulation

2015 ◽  
Vol 229 (13) ◽  
pp. 2467-2483 ◽  
Author(s):  
Hanjun Jiang
Keyword(s):  
Friction Force ◽  
Contact Line ◽  
Sliding Friction ◽  
Helix Angle ◽  
Universal Method ◽  
Time Varying ◽  
Contact Ratio ◽  
Friction Forces ◽  
Helical Gears ◽  
Face Width

Time-varying sliding friction force and friction torque are regarded as non-negligible excitation sources of vibration and noise in gears. The sliding friction force primarily excites the motion along the off-line-of-action direction, which transmits vibration to the housing through shafts and bearings and then radiates noise. Since the contact line intersects with the pitch line, and the directions of the friction forces are opposite on both sides of the pitch line, the calculation of the friction excitations in helical gears becomes more difficult, especially in the high contact ratio helical gears. However, there is no universal method for calculating the friction excitations in helical gears with different range of contact ratio. The changes of friction excitations in helical gears are highly dependent on the geometric parameters such as helix angle and face width among others. Yet, there exist very limited studies on these topics. In this study, a refined general formulation for the calculation of time-varying contact line and friction excitations is proposed by assuming uniform load distribution along the contact lines with time-varying normal force and friction coefficient. Key gear parameters such as modification coefficient, helix angle, and face width are analyzed to illustrate their effects on the time-varying contact line and friction excitations. The results demonstrate that the refined general formulation is effective for the calculation of the friction excitations in helical gears with different range of contact ratio, and the parametric analysis could supply some guidance for choosing gear parameters in the design of helical gears to reduce the friction excitations.

Parametric vibration of split gears induced by time-varying mesh stiffness

2014 ◽  
Vol 229 (1) ◽  
pp. 18-25 ◽  
Author(s):  
Dongsheng Zhang ◽  
Shiyu Wang
Keyword(s):  
Parametric Vibration ◽  
Design Parameters ◽  
Time Varying ◽  
Contact Ratio ◽  
Mesh Stiffness ◽  
Rotational Model ◽  
Helical Gears ◽  
Multi Scale ◽  
Rotational Vibration ◽  
The Relationship

Time-varying mesh stiffness is a significant excitation source within gear systems. Split gear (or laminated gear, phase gear) is an interesting design using equally phased gear-slices, which can remarkably reduce the mesh stiffness fluctuation like helical gears but completely avoid the axial force. This work examines a split gear pair to address the suppression of the mesh stiffness fluctuation and rotational vibration thereof, especially the relationship between the key design parameters including the number of slice, contact ratio, and damping, and the parametric vibration. For these aims, this work develops a purely rotational model, based on which the multi-scale method is employed to determine stability boundaries. The results imply that the unstable zones are related to the mesh phase determined by the number of slices and contact ratio, and these zones can be diminished by the damping. The analytical predictions are numerically verified by Floquet theory.

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.

External high-order multistage modified elliptical helical gears and design procedure of their gear pairs

2016 ◽  
Vol 230 (16) ◽  
pp. 2929-2939 ◽  
Author(s):  
Jiang Han ◽  
Youyu Liu ◽  
Dazhu Li ◽  
Lian Xia
Keyword(s):  
Design Procedure ◽  
Mathematical Expression ◽  
Helical Gear ◽  
High Order ◽  
Curvature Radius ◽  
Contact Ratio ◽  
Helical Gears ◽  
The Family ◽  
Pitch Curve ◽  
Helical Gear Pair

In view of the limited quantity of modified segments for high-order and two-stage modified elliptical helical gears, and poor adjustment capacity for transmission ratio, the formation mechanism of a high-order multistage modified ellipse was studied, and a unified mathematical expression of the family of ellipses was derived. Thus, a design procedure for the helical gear pairs of the high-order multistage modified ellipse was suggested, and then their transmission characteristics were discussed exhaustively. Moreover, some checking methods such as curvature radius of pitch curve, convexity, pressure angle, undercutting, and contact ratio were offered. Finally, two design cases, including two-order and three-stage modified elliptical helical gear pair and two-order and four-stage one, were implemented. The cases indicate that a high-order multistage modified elliptical helical gear can be utilized in practice.

Experiments on Root Stresses of Helical Gears With Lead Crown and Misalignments

2008 ◽  
Vol 130 (7) ◽  
Author(s):  
M. Hotait ◽  
A. Kahraman
Keyword(s):  
Helical Gear ◽  
Strain Gages ◽  
Helical Gears ◽  
Gear Teeth ◽  
Face Width ◽  
The Face ◽  
Bending Stresses ◽  
Contact Models ◽  
Gear Contact ◽  
Different Levels

In this study, the results of an experimental parametric study of the combined influence of shaft misalignments and gear lead modifications on the load distribution and tooth bending stresses of helical gear pairs are presented. A set of helical gear pairs having various amounts of total lead crown was operated under loaded, low-speed conditions with varying amounts of tightly controlled shaft misalignments. Gear teeth were instrumented through strips of strain gages along the face width of gears at the tooth fillet region at a roll angle that is near the start of the active profile. Variations of root strains along the face width were quantified for different levels of shaft misalignments and gear lead crown. The results presented demonstrate the direct link between the lead crown and gear misalignments as well as the effectiveness of the lead crown in preventing edge loading conditions due to misalignment. The results presented here form a database that should be available for a validation of gear contact models in terms of their ability to simulate misalignments.

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.

Optimization Design of Double-Helical Gear with High Contact Ratio

2012 ◽  
Vol 248 ◽  
pp. 91-94
Author(s):  
Ning Zhao ◽  
Peng Yuan Qiu ◽  
Sheng Wen Hou
Keyword(s):  
Genetic Algorithm ◽  
Optimization Design ◽  
Original Data ◽  
Helical Gear ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Contact Ratio ◽  
Helical Gears ◽  
Numerical Examples

Fast Elitist Non-dominated Sorting Genetic Algorithm is introduced in this paper to optimize the performance of double helical gears with high contact ratio.It is effective and timesaving. Numerical examples that illustrate the developed theory are provided. Feasibility of it is validated by analysis of contrast between Pareto optimal solutions and original data.

scholarly journals Geometry and parameter design of novel circular arc helical gears for parallel-axis transmission

2017 ◽  
Vol 9 (2) ◽  
pp. 168781401769095 ◽  
Author(s):  
Zhen Chen ◽  
Huafeng Ding ◽  
Bo Li ◽  
Linbo Luo ◽  
Liang Zhang ◽  
...  
Keyword(s):  
Helical Gear ◽  
Space Curve ◽  
Parameter Design ◽  
Contact Ratio ◽  
Circular Arc ◽  
Helical Gears ◽  
Pure Rolling ◽  
Meshing Equation ◽  
Gear Mechanism ◽  
The Impact

Based on the space curve meshing equation, in this article, a geometry design of a novel circular arc helical gear mechanism with pure rolling for parallel transmission was presented. Different from conventional circular arc gears, the meshing points of circular arc helical gears were limited at the instantaneous centre of rotation. The parameter equations describing the contact curves for both the driving gear and the driven gear were deduced from the space curve meshing equation, and parameter equations of the concave–convex circular arc profiles were established both for internal meshing and external meshing. Furthermore, a formula for the contact ratio was presented, and the impact factors influencing the contact ratio were discussed. Then, the parameter design was presented for the geometry parameters of tooth profiles, such as normal pitch, tooth height and tooth thickness. Using the deduced equations, several numerical examples were then considered, and prototype samples were produced to experimentally validate the contact ratio equation and the theoretical kinematic performance. The circular arc helical gear mechanism investigated in this study showed a high gear transmission performance such as a pure rolling meshing, a high contact ratio and a large comprehensive strength, when considering engineering applications.

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