scholarly journals Research and manufacture of external non-circular gear-pair with improved cycloid profile of the ellipse

2021 ◽  
Vol 4 (2) ◽  
pp. first
Author(s):  
Thai Hong Nguyen ◽  
Trung Thanh Nguyen ◽  
Viet Hoang Nguyen
Keyword(s):  
Mathematical Model ◽  
Tooth Profile ◽  
Gear Pair ◽  
Design Scheme ◽  
Profile Design ◽  
The Mathematical Model ◽  
Gear Profile

Non-circular gears (NCGs) are known as an alternative to conventional mechanical mechanisms in continuous speed converters. In which, the gear profile is the factor that directly affects the performance and quality meshing of the non-circular gear. However, the types of curves that are being used to generating profiles of the non-circular gears still exist limited in meeting the conditions of undercutting and uniformity of tooth sizes at different positions on the centrode. To optimize the profile of the non-circular gear, the paper presents a new profile in which the traditional involute profile of the non-circular gears is replaced by an improved cycloid curve of the ellipse. The mathematical model of new profile of non-circular gear is formed by eccentric circular shaper cutter with the improved cycloid of the ellipse in accordance with the theory of gearing in consideration of undercutting conditions. Based on the mathematical model established by this research, a program was written in Matlab. On that basis, a pair of non-circular gear was designed and fabricated experimentally on a wire breaker to verify the theory. The results show that with the new tooth profile design scheme, the shortcomings of uneven teeth on the non-circular gear of the traditional studies when using the involute profile of the circle have been overcome.

scholarly journals Meshing principle analysis of 3-DOF involute spherical gear

2020 ◽  
Vol 213 ◽  
pp. 02029
Author(s):  
Baichao Wang ◽  
Xue Zhang ◽  
Litong Zhang ◽  
Xianting Lu
Keyword(s):  
Mathematical Model ◽  
Tooth Profile ◽  
Bevel Gear ◽  
Tooth Surface ◽  
Gear Pair ◽  
Tooth Surfaces ◽  
Three Degree Of Freedom ◽  
Relationship Of ◽  
The Mathematical Model ◽  
Spherical Gear

In this paper, a mathematical model of meshing motion of three degree of freedom involute spherical gear pair is constructed. The mathematical model can realize continuous meshing transmission between gear pairs without transmission principle error. Based on the meshing principle and motion analysis of the gear, the tooth profile of the spherical gear is designed by combining the two tooth surfaces of the involute ring gear and the hemispherical bevel gear. According to the conjugate motion relationship of spherical gear pair, a mathematical model of arc tooth surface of hemispherical bevel gear is established, and the mathematical description of the tooth profile of spherical gear is completed by combining the equation of ring tooth surface. It provides the basis and Reference for the meshing design of ball gear.

Research on Tooth Profile Design of Spur Gears Based on Line of Action

2013 ◽  
Vol 631-632 ◽  
pp. 817-823
Author(s):  
Jian Wang ◽  
Liang Hou ◽  
Shan Ming Luo
Keyword(s):  
Mathematical Model ◽  
Design Method ◽  
Tooth Profile ◽  
Spur Gears ◽  
On Line ◽  
Profile Design ◽  
The Mathematical Model

This paper aims to propose a design method for tooth profiles of spur gears based on given line of action. A simplified derivation of the mathematical model of tooth profiles is introduced according to the meshing theory. Tooth profiles of spur gears, using a parabola as line of action, is established. The result shows that it will be better to control the performances of a gear set by specifying the shape of the line of action rather than specifying tooth profiles of mating gear.

Valve Gear Refinement

2000 ◽  
Vol 124 (1) ◽  
pp. 86-90 ◽  
Author(s):  
Jurij Avsec ◽  
Milan Marcic ◽  
Maks Oblak
Keyword(s):  
Mathematical Model ◽  
Cam Design ◽  
Cam Follower ◽  
New Type ◽  
Cam Profile ◽  
Profile Design ◽  
Comparison Of The Results ◽  
The Mathematical Model ◽  
Valve Gear ◽  
Lubrication Properties

This paper describes a new type of valve gear cam—MULTICAM—which consists of seven curves and allows an optimum cam profile design. In order to calculate the cinematic and dynamic values and to assess the minimum oil film thickness in the valve gear, the mathematical model of an ideal valve gear was used. In addition, the comparison of the results between the polysine cam and the new MULTICAM cam design was made. By means of the new cam design the Hertz pressures were reduced at the point of contact between the cam and the cam follower and the lubrication properties at the top of the cam improved.

Computerized Tooth Profile Generation and Undercut Analysis of Gears Manufactured With Pre-Shaving Hobs

2009 ◽  
Vol 16-19 ◽  
pp. 1278-1282
Author(s):  
Xiang Wei Kong ◽  
Jing Zhang ◽  
Meng Hua Niu
Keyword(s):  
Mathematical Model ◽  
Computer Program ◽  
Gear Tooth ◽  
Tooth Profile ◽  
Design Parameters ◽  
Gear Teeth ◽  
The Mathematical Model

This paper investigated the feature of pre-shaving hob contour and the generated gear tooth profile. By tooth generation method, a complete geometry of the gear tooth can be mathematically derived in terms of the design parameters of the pre-shaving hob cutter. The mathematical model consisted of equations describing the generated fillet and involute profiles. The degree of undercutting and the radii of curvatures of a fillet were investigated by considering the model. Finally, a computer program for generating the profile of the gear teeth was developed by simulating the cutting methods. The methods proposed in this study were expected to be a valuable guidance for pre-shaving hob designers and manufacturers.

Research and Design of Pneumatic AMT Actuator

2011 ◽  
Vol 52-54 ◽  
pp. 318-323
Author(s):  
Jian Zhong Wang ◽  
Liang Chu ◽  
Xin Tian Lu
Keyword(s):  
Mathematical Model ◽  
Dynamic Model ◽  
Theoretical Basis ◽  
Structure Characteristics ◽  
Design Scheme ◽  
Heavy Truck ◽  
The Mathematical Model ◽  
Research And Design

According to the design requests of certain heavy truck, this paper introduces a design scheme of pneumatic AMT automatic shift system, which focuses on the structure characteristics and working principles of the three-position cylinder controlled by two solenoid valves. And the mathematical model of the three-position cylinder controlled by two solenoid valves is established based on pneumatic principle. The dynamic model of this mechanism was built by AMEsim software. The variety of pressure and stroke of intake/exhaust chamber was simulated under different air pressures. The theoretical basis is provided to design the AMT election-shift actuator.

A Novel Error Detection and Compensation Method of Hourglass Worm Gear Hob

2012 ◽  
Author(s):  
Q. Y. Shu ◽  
Q. Y. Qiu ◽  
P. E. Feng ◽  
L. Cao
Keyword(s):  
Mathematical Model ◽  
Error Detection ◽  
Worm Gear ◽  
Grinding Wheel ◽  
Gear Pair ◽  
Manufacturing Error ◽  
Optical Projection ◽  
Lubrication Condition ◽  
The Mathematical Model ◽  
Detecting Method

The double enveloping hourglass worm gear pair is a type of transmission, which has many traits, such as more teeth in mesh for transmission, higher contact quality, better lubrication condition and so on. Therefore, it has higher efficiency of transmission, stronger bearing capacity and longer work life. But the manufacturing difficulty of the worm gear hob has limited its popularization and application. Unlike the traditional worm gear hob which can use the principle of optical projection to detect the hob shaft section and compare with its mathematical model, currently, there is no standard mathematical model to detect the shaft section of hourglass worm gear hob. Hence, the accuracy of hourglass worm gear hob can’t be guaranteed during manufacturing process, and the accuracy of hourglass worm gear can’t be guaranteed too. Thus, the transmission performance of the manufactured double enveloping hourglass worm gear pair will be affected. The paper puts forward a novel detection method for hourglass worm gear hob on the basis of the detecting method for traditional worm gear hob and established the mathematical model of the shaft section of hourglass worm gear hob. The manufacturing error of hourglass worm gear hob can be obtained through such detection. The paper also points out that the error is mainly produced during the grinding of hob teeth, because the grinding wheel is worn out and the blank hob is thermally deformed. At last, a method for error compensation is advanced during the process of hob grinding. The paper presents a test to verify the feasibility of this method and the test result shows that the manufacturing error of hourglass worm gear hob is reduced from 30.15μm to 10.3μm.

Establishment of Tooth Profile Curve Mathematical Model of Varying-Coefficient-Shift-Modification Gears

2013 ◽  
Vol 391 ◽  
pp. 172-177
Author(s):  
Chuan Yan Zhang ◽  
Ji Guang Han
Keyword(s):  
Mathematical Model ◽  
Coordinate System ◽  
Tooth Profile ◽  
Gear Transmission ◽  
Profile Curve ◽  
Kinematics Analysis ◽  
Cutting Method ◽  
Varying Coefficient ◽  
Pure Rolling ◽  
The Mathematical Model

According to the law that modification coefficient changes with the position of the pitch-lines of gears, varying-coefficient-shift-modification gear is designed to eliminate backlash in gear transmission effectively. The tooth profile curve of varying-coefficient-shift-modification gears is obtained by generating rack, based on the theory of rack cutting method. The modification amount changing with the position of the pitch-lines of gears is obtained separately, and then added to standard rack, to obtain the model of generating rack. Finally,the model of generating rack and the pure-rolling model are joined together by using the established equation of no clearance mesh, to get the mathematical model of tooth profile in the coordinate system of the gear. For varying-coefficient-shift-modification gear in the transmission of eccentric involutes gears, the kinematics analysis of the model is conducted through the joint of MATLAB, Pro/E and ADAMS, to verify the effectiveness of the modeling method and the correctness of the mathematical model.

Computerized Tooth Profile Generation and Undercut Analysis of Noncircular Gears Manufactured With Shaper Cutters

1998 ◽  
Vol 120 (1) ◽  
pp. 92-99 ◽  
Author(s):  
Shinn-Liang Chang ◽  
Chung-Biau Tsay
Keyword(s):  
Mathematical Model ◽  
Computer Program ◽  
Contact Line ◽  
Relative Velocity ◽  
Tooth Profile ◽  
Gear Pair ◽  
Line Method ◽  
Envelope Method ◽  
Noncircular Gears

Pitch curves of a conjugate noncircular gear pair are derived based on kinematic considerations. A method for considering the inverse mechanism relationship and the equation of meshing, is proposed here to derive a complete mathematical model of noncircular gears manufactured with involute-shaped shaper-cutters. The proposed method is similar to the contact line method and the envelope method, but is easier to apply to the determination of tooth profiles. A computer program is developed for generation the tooth profile with backlashes. Undercutting analysis is also investigated by considering the relative velocity and equation of meshing. Finally, modified elliptical gears are presented to illustrate the tooth profile generation when the proposed mathematical model is applied, and to investigate the phenomenon of tooth undercutting.

Using a planar rack cutter with variable modulus to generate a spherical gear pair

2020 ◽  
Vol 44 (1) ◽  
pp. 108-120
Author(s):  
Hsueh-Cheng Yang ◽  
Chih-Yao Sun
Keyword(s):  
Mathematical Model ◽  
Degree Of Freedom ◽  
Gear Pair ◽  
Tooth Contact Analysis ◽  
The Family ◽  
Variable Modulus ◽  
Double Degree ◽  
Relationship Of ◽  
The Mathematical Model ◽  
Spherical Gear

In this study, an imaginary planar rack cutter with variable modulus and discrete conical teeth was used to generate a spherical gear pair with double degree of freedom. First, a geometric method was used to design the mathematical model of the imaginary planar rack cutter with variable modulus and discrete conical teeth. Next, the relationship of coordinate systems between the generating and generated surfaces was established. Then, the family of the imaginary planar rack cutter surfaces was obtained by homogeneous coordinate transformation matrix. Further, two equations of meshing between the generating and generated surfaces were determined by the two-parameter envelope theory. The mathematical model of spherical gear pair with variable modulus and discrete ring-involute teeth can be created by using the two equations of meshing and the family of the imaginary planar rack cutter surfaces. The mathematical models of the spherical gear pair with double degree of freedom and tooth contact analysis method were used to investigate the assembly errors of the gear pair in four cases.

Tooth Profile Generation and Analysis of Crowned Elliptical Gears

2009 ◽  
Vol 131 (7) ◽  
Author(s):  
Biing-Wen Bair
Keyword(s):  
Mathematical Model ◽  
Three Dimensional ◽  
Major Axis ◽  
Tooth Profile ◽  
Numerical Examples ◽  
Gear Drive ◽  
Computer Simulation Program ◽  
Geometric Relation ◽  
Contact Position ◽  
The Mathematical Model

This study develops a crowned elliptical gear drive that prevents edge contact when an elliptical gear drive has axial misalignment. According to the theory of gearing and a gear-generation mechanism with longitudinal crowing, the mathematical model of a crowned elliptical gear is derived using a rack cutter. Pointed teeth typically appear on the tips of the teeth of elliptical gears at major axis. Additionally, a three-dimensional geometric relation is applied to prevent pointed teeth from developing on elliptical gears. Moreover, a computer simulation program is employed to generate the tooth profiles of crowned elliptical gears without pointed teeth and locate the contact position for longitudinal middle tooth profiles. Two numerical examples demonstrate the design process and the tooth profile graphs.

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