Mathematical model and meshing analysis of internal meshing gear transmission with curve element

2020 ◽  
Vol 34 (12) ◽  
pp. 5155-5166
Author(s):  
Dong Liang ◽  
Weibin Li ◽  
Bingkui Chen
Keyword(s):  
Mathematical Model ◽  
Gear Transmission ◽  
Internal Meshing ◽  
Curve Element

Geometry design and mathematical model of a new kind of gear transmission with circular arc tooth profiles based on curve contact analysis

2014 ◽  
Vol 228 (17) ◽  
pp. 3200-3208 ◽  
Author(s):  
Bingkui Chen ◽  
Dong Liang ◽  
Yane Gao
Keyword(s):  
Mathematical Model ◽  
High Performance ◽  
Plane Curve ◽  
Gear Transmission ◽  
Circular Arc ◽  
Smooth Curves ◽  
Gear Drive ◽  
Geometry Design ◽  
Meshing Equation ◽  
The Given

A new meshing relationship for gear drive to characterize the conjugation geometry is studied in this paper based on conjugate curves. Conjugate curves are described as two smooth curves always keep continuous and tangent contact with each other in given contact direction under motion law. The general principle of curve meshing is developed for the given spatial or plane curve. The meshing equation along arbitrary direction of contact angle is derived. The properties of geometric and motion of the contact of conjugate curves are discussed. According to the equidistance-enveloping method, tubular meshing surfaces are proposed to build up circular arc tooth profiles, which inherit all properties of conjugate curves. The geometry design and mathematical model of the gears are established. Three types of contact pattern of tooth profiles are generated: convex-to-convex, convex-to-plane and convex-to-concave. A calculation example for convex-to-concave tooth profiles of gears is provided. Theoretical and numerical results demonstrate the feasibility and correctness of proposed conjugate curves theory and it lays the foundation for the design of high performance gear transmission.

scholarly journals Generation and Meshing Analysis of a New Type of Double Helical Gear Transmission

2018 ◽  
Vol 2018 ◽  
pp. 1-10
Author(s):  
Dong Liang ◽  
Tianhong Luo ◽  
Rulong Tan
Keyword(s):  
Experimental Studies ◽  
Point Contact ◽  
Helical Gear ◽  
Gear Transmission ◽  
Cnc Machining ◽  
Gear Pair ◽  
Tooth Contact Analysis ◽  
Solid Models ◽  
Geometric Relationship ◽  
Curve Element

A study on the double helical gear transmission with curve element constructed tooth pairs is carried out in this paper. Generation and mathematical model of tooth profiles are proposed based on the geometric relationship. Tooth profiles equations are derived considering the developed equidistance-enveloping approach. Design of tooth profiles with point contact is conducted and numerical example is illustrated. And the solid models of double helical gear pair with curve element constructed tooth pairs are established. Computerized design and meshing simulation are also put forward. Furthermore, stress analysis of the gear pair is conducted and gear prototypes are manufactured using CNC machining technology. Further tooth contact analysis, dynamic and experimental studies on transmission properties of gear prototypes will be carried out.

Optimization Design of Planetary Gear Transmission Mechanism of Traction Unit

2013 ◽  
Vol 774-776 ◽  
pp. 164-167
Author(s):  
Li Li
Keyword(s):  
Mathematical Model ◽  
Optimization Design ◽  
Planetary Gear ◽  
Gear Transmission ◽  
Transmission Mechanism ◽  
Mining Machine ◽  
Mechanical Transmission ◽  
Gear Teeth ◽  
Design Variables ◽  
Traction Unit

In order to make the coal mining machine adapt the narrow work space underground, and the height of shearer is decided by the planetary gear transmission mechanism of traction unit. In this paper, the volume of planetary gear transmission mechanism is selected as objective function, and module of gear, teeth of sun gear, width of gear are considered as design variables based on mechanical transmission theory, and the optimized mathematical model of the planetary gear transmission mechanism of traction unit is established. The optimized mathematical model is solved by SQP(sequential quadratic programming) basd on Matlab program, the volume of planetary gear transmission mechanism reduces 20.22%, and the height of shearer decreases 11.3%.

General Mathematical Model of Internal Meshing Spiral Bevel Gears for Nutation Drive

2011 ◽  
Vol 101-102 ◽  
pp. 708-712 ◽  
Author(s):  
Zheng Lin ◽  
Li Gang Yao
Keyword(s):  
Mathematical Model ◽  
3D Modeling ◽  
Gear Tooth ◽  
Spiral Bevel Gears ◽  
Bevel Gears ◽  
General Mathematical Model ◽  
Spiral Bevel ◽  
The Mathematical Model ◽  
Crown Gear ◽  
Internal Meshing

The general mathematical model of internal meshing spiral bevel gears for nutation drive is studied. Based on conventional enveloping theory and transmission principle, the meshing of two spiral bevel gears in nutation drive was substituted by the meshing of an imaginary rotating crown gear engaging with the external and internal bevel gear respectively. The general mathematical model of crown gear was established. Then the general mathematical model of internal meshing spiral bevel gears is obtained by matrix transformation, which is suitable for a variety of gear tooth profiles. Finally, the mathematical model and 3D modeling of double circular-arc spiral bevel gears are developed.

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.

Electromechanical Coupling Modeling in Permanent Magnet AC Servo-Driven Precision Gear Transmission System

2011 ◽  
Vol 52-54 ◽  
pp. 1375-1381
Author(s):  
Wei Zhou ◽  
Li Hong Lin ◽  
Xiao An Chen
Keyword(s):  
Mathematical Model ◽  
Permanent Magnet ◽  
Electromechanical Coupling ◽  
Coupling Effect ◽  
Permanent Magnet Synchronous Motor ◽  
Transmission System ◽  
Gear Transmission ◽  
Ac Servo ◽  
Gear Transmission System ◽  
Driven System

Electromechanical coupling effect must be considered in the dynamic analysis of permanent magnet AC servo-driven precision gear transmission system. According to the global coupling and local coupling analysis in servo-driven system, the global electromechanical coupling relation diagram of whole system and the local electromechanical coupling relation diagram of the permanent magnet synchronous motor-precision gear transmission subsystem are established. For this subsystem, a physical model is built up. And a mathematical model is constituted by using Lagrange-Maxwell equation, that is the dynamic equation of the subsystem. The mathematical model can provide theoretical basis for follow-up researches.

An Optimization Design Method of Gear Transmission

2013 ◽  
Vol 712-715 ◽  
pp. 1729-1733
Author(s):  
Hai Ning Yu
Keyword(s):  
Mathematical Model ◽  
Optimization Design ◽  
Optimization Problems ◽  
Design Method ◽  
Helix Angle ◽  
Gear Transmission ◽  
Integer Variable ◽  
Model Study ◽  
Tooth Width ◽  
Tooth Number

For solving the continuous and integer variable optimization problems in gear transmission, this article to establish a gear transmission optimization mathematical model, study the influence of modulus, tooth width, helix angle and tooth number on objective function by genetic algorithm, and the digit results is well.

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 Quality Improvement of a Gear Transmission by Means of Genetic Algorithm

2019 ◽  
Vol 1 (1) ◽  
pp. 386-393
Author(s):  
Paweł Lempa ◽  
Edward Lisowski ◽  
Fumito Masui ◽  
Grzegorz Filo ◽  
Michal Ptaszynski ◽  
...  
Keyword(s):  
Genetic Algorithm ◽  
Mathematical Model ◽  
Genetic Algorithms ◽  
Quality Improvement ◽  
Optimization Method ◽  
Gear Transmission ◽  
Flow Pulsation ◽  
Reduced Flow

Abstract The article deals with the issue of quality improvement of a gear transmission by optimizing its geometry with the use of genetic algorithms. The optimization method is focused on increasing productivity and efficiency of the pump and reducing its pulsation. The best results are tested on mathematical model and automatically modelled in 3D be means of PTC Creo Software. The developed solution proved to be an effective tool in the search for better results, which greatly improved parameters of pump especially reduced flow pulsation.

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