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.

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.

scholarly journals Mathematical model of energy efficiency in internal spur gears

2019 ◽  
Vol 23 (Suppl. 5) ◽  
pp. 1801-1813
Author(s):  
Predrag Dobratic ◽  
Mileta Ristivojevic ◽  
Bozidar Rosic ◽  
Radivoje Mitrovic ◽  
Dragan Trifkovic
Keyword(s):  
Mathematical Model ◽  
Load Distribution ◽  
Energy Losses ◽  
Spur Gears ◽  
Contact Ratio ◽  
Cylindrical Gear ◽  
Heating Effects ◽  
Effective Efficiency ◽  
The Impact ◽  
The Mathematical Model

The impact of geometric parameters of teeth and lubricating oils to the efficiency of involute internal spur gears, when the transverse contact ratio is 2 < ?? ?3, has been analyzed in this paper. The mathematical model and computer program for determining the current and the effective value of the efficiency have been developed. The influence of the character of load distribution and energy losses due to heating effects during the meshing period is included in the factor of load distribution. The results of computer simulation are given in the form of a diagram of the current values of the efficiency during the meshing period. Also, the values of effective efficiency for the considered cylindrical gear pairs have been calculated.

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.

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.

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.

A NOVEL DESIGN OF AN ELECTRIC POWER-ASSISTED BIKE BASED ON HELICAL GEARS

2017 ◽  
Vol 41 (5) ◽  
pp. 845-854
Author(s):  
Chung-Yu Tsai*
Keyword(s):  
Mathematical Model ◽  
Electric Power ◽  
Force Sensor ◽  
Helical Gear ◽  
Design Rule ◽  
Force Distribution ◽  
Electric Power Output ◽  
Helical Gears ◽  
Parameter Values ◽  
Novel Design

An electric power-assisted bike (EPAB) is a bicycle with an attached electric motor to assist with human pedaling, where the electric power output of the motor is provided in accordance with the pedaling-force. This makes the pedaling-force sensor (PFS), which is used to sense the human pedaling force, the critical device in the EPAB. Accordingly, the present study proposes a novel design for the PFS, comprising of a helical gear system and an annular magnet device. The study then develops a mathematical model for the force distribution on the helical gears, and provides a general design rule to determine the parameter values of the PFS which will prevent a self-lock situation. A prototype is produced to verify and demonstrate the proposed approach.

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.

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.

A GENERALIZED METHOD FOR PREDICTING CONTACT STRENGTH, WEAR, AND THE LIFE OF INVOLUTE CONICAL SPUR AND HELICAL GEARS: PART 2. HELICAL GEARS

Tribologia ◽  
2018 ◽  
Vol 277 (1) ◽  
pp. 19-23
Author(s):  
Myron CHERNETS
Keyword(s):  
Tooth Wear ◽  
Helical Gear ◽  
Cylindrical Gear ◽  
Frontal Section ◽  
Helical Gears ◽  
Optimal Correction ◽  
Maximal Contact ◽  
Gear Ring ◽  
Maximum Contact ◽  
Contact Pressures

The paper presents the results of research undertaken to determine maximum contact pressures, wear, and the life of involute conical helical gear, taking account of gear height correction, tooth engagement, and weargenerated changes in the curvature of their involute profile. We have established the following: (a) initial maximal contact pressures will be almost the same at the engagement in external and internal segments; (b) their highest meanings occur in different points of engagement depending on the coefficients of displacement; (c) the maximal tooth wear of the rings in the internal section will be a little bit lower than in the external; (d) the coefficients of displacement have an optimum at which the highest gear life is possible; and, (e) the gear life in the frontal section will be 1.25 lower than in the internal section. The calculations were made for a reduced cylindrical gear using a method developed by the authors. The effect of applied conditions of tooth engagement in the frontal and internal sections of a cylindrical gear ring is shown graphically. In addition, optimal correction coefficients ensuring the longest possible gear life are determined.

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.

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