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.

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.

Modeling and Calibration of Grid Structured Light Based 3-D Vision Inspection

1999 ◽  
Vol 122 (4) ◽  
pp. 734-738 ◽  
Author(s):  
Guangjun Zhang ◽  
Liqun Ma
Keyword(s):  
Mathematical Model ◽  
Coordinate System ◽  
Structured Light ◽  
Calibration Method ◽  
Experimental Results ◽  
Image Feature ◽  
Feature Analysis ◽  
Calibration Process ◽  
Vision Inspection ◽  
The Mathematical Model

The principle of structured light 3-D vision is introduced, and using projective and perspective transformations, the mathematical model of grid structured light based 3-D vision inspection is established in homogeneous coordinate system in this paper. Based on the image feature analysis of grid structured light, a calibration method of grid structured light based 3-D vision inspection is proposed, and experimental results are also presented. This method is easy, efficient and fast to carry out. It simplifies the calibration process while guaranteeing its accuracy. [S1087-1357(00)00703-6]

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 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.

Study of the Dynamic Behavior of Face Gear Transmission System

2012 ◽  
Vol 268-270 ◽  
pp. 1063-1066 ◽  
Author(s):  
Zhi Wang ◽  
Qing Chen ◽  
Jia Chun Lin ◽  
Li Li Yang
Keyword(s):  
Mathematical Model ◽  
Static Load ◽  
Transmission System ◽  
Gear Transmission ◽  
Tooth Surface ◽  
Cyclic Loads ◽  
Face Gear ◽  
Static Loads ◽  
Gear Transmission System ◽  
The Mathematical Model

According to the gear meshing theory, the tooth surface equation of orthogonal face gear is derived and the mathematical model is established. Also the model was provided for simulating the bevel gear transmission system concerning the time variant stiffness and face gears errors under static load and cyclic loads. Through the model the computerized analysis of speed, angle and acceleration of gear real tooth surface could be accomplished. Rattle as discussed under condition of different static loads and the constant cyclic loads.

scholarly journals STUDY OF TRANSIENT AND STATIONARY OPERATION MODES OF SYNCHRONOUS SYSTEM CONSISTING IN TWO MACHINES

2017 ◽  
Vol 60 (3) ◽  
pp. 228-236
Author(s):  
V. S. Safaryan
Keyword(s):  
Mathematical Model ◽  
Steady State ◽  
Power System ◽  
Mathematical Models ◽  
Coordinate System ◽  
Electric Power ◽  
Electric Power System ◽  
Machine System ◽  
Transient Regimes ◽  
The Mathematical Model

The solution of the problem of reliable functioning of an electric power system (EPS) in steady-state and transient regimes, prevention of EPS transition into asynchronous regime, maintenance and restoration of stability of post-emergency processes is based on formation and realization of mathematical models of an EPS processes. During the functioning of electric power system in asynchronous regime, besides the main frequencies, the currents and voltages include harmonic components, the frequencies of which are multiple of the difference of main frequencies. At the two-frequency asynchronous regime the electric power system is being made equivalent in a form of a two-machine system, functioning for a generalized load. In the article mathematical models of transient process of a two-machine system in natural form and in d–q coordinate system are presented. The mathematical model of two-machine system is considered in case of two windings of excitement at the rotors. Also, in the article varieties of mathematical models of EPS transient regimes (trivial, simple, complete) are presented. Transient process of a synchronous two-machine system is described by the complete model. The quality of transient processes of a synchronous machine depends on the number of rotor excitation windings. When there are two excitation windings on the rotor (dual system of excitation), the mathematical model of electromagnetic transient processes of a synchronous machine is represented in a complex form, i.e. in coordinate system d, q, the current of rotor being represented by a generalized vector. In asynchronous operation of a synchronous two-machine system with two excitation windings on the rotor the current and voltage systems include only harmonics of two frequencies. The mathematical model of synchronous steady-state process of a two-machine system is also provided, and the steady-state regimes with different structures of initial information are considered.

A Mathematical "Screw-Nut" Connection Model for the Universal Software to Analyse Dynamical Systems

2017 ◽  
pp. 1-12
Author(s):  
V. A. Martynyuk ◽  
V. A. Trudonoshin ◽  
V. G. Fedoruk
Keyword(s):  
Mathematical Model ◽  
Coordinate System ◽  
Dry Friction ◽  
Local Coordinate System ◽  
Direction Cosine ◽  
The Body ◽  
Global Coordinate System ◽  
Elastic Model ◽  
Screw Axis ◽  
The Mathematical Model

The article deals with a mathematical model of the "screw-nut" connection adapted for using in universal software systems to analyse dynamic characteristics. This article is sequel to a number of earlier authors-written articles devoted to object simulation of 3D mechanics. Such a model available in the library of mathematical models of the modelling system will significantly extend the list of simulated mechanisms. The mathematical model of "screw-nut" connection suggests such a connection between absolutely rigid bodies. The "screw-nut" connection parameters are the following:thread pitch by the radian of the angle of pitch;coordinates of the point on the axis of the screw in the local coordinate system of the body 1;direction cosines of the screw axis in the local coordinate system of the body 1.Note that the connection parameters have constant values. Two drawbacks of this model should be noted.1. Some expressions of the mathematical model involve dividing by direction cosine  of the screw axis thereby eliminating "division by zero" when the axis of the screw is perpendicular to the x-axis of the global coordinate system. The software-based way allows eliminating this shortcoming.2. The model does not include coordinates of mass centres of bodies tied by connection. This can lead to a significant "mismatch" in the position of the bodies in modelling of multi- periodic transient processes. However, adding an elastic model to the mathematical model can eliminate this drawback.The article demonstrates the "screw-nut" connection model to simulate a jack using the PA8 system and comparing its results with those obtained with help of the NX10 complex. Gives, in addition, the results of influence in terms of dry friction in the "screw-nut" connection. Taking into consideration the dry friction allows us to reflect the effect of "self-stopping" in the jack.

scholarly journals A Mathematical Model for Parametric Tooth Profile of Spur Gears

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Guodong Zhai ◽  
Zhihao Liang ◽  
Zihao Fu
Keyword(s):  
Mathematical Model ◽  
Spur Gear ◽  
Parametric Modeling ◽  
Tooth Profile ◽  
Modeling Method ◽  
Spur Gears ◽  
Profile Curve ◽  
Traditional Design ◽  
Mathematical Equations ◽  
Involute Curve

Spur gears are widely used transmission components. In the traditional design process, the noninvolute part of the tooth profile curve is difficult to describe with mathematical equations. This article puts forward a new parametric modeling method, which can describe the modified involute part of spur gears and parameterize and optimize the transition part of the involute curve of the spur gear. And this model of the spur gear can be created by parameters which is input in Scilab software and the spur gear graphic can be completed correspondingly. The experiments show that this modeling method can more quickly produce the standard spur or modified spur gear, and it also improves the efficiency and accuracy of spur gear modeling.

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.

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