Dynamic Characteristics and Load Coefficient Analysis of Involute Spline Couplings

2014 ◽  
Vol 889-890 ◽  
pp. 450-454
Author(s):  
Xiang Zhen Xue ◽  
San Min Wang
Keyword(s):  
Dynamic Model ◽  
Fourth Order ◽  
Dynamic Characteristics ◽  
Dynamic Load ◽  
Dynamic Equations ◽  
Kutta Method ◽  
Meshing Stiffness ◽  
Runge Kutta Method ◽  
Spline Coupling ◽  
Involute Spline

As one of the important components of aviation and space transmission systems, dynamic characteristics of involute spline couplings influence its lifetime and reliability seriously. Here, taking the backlash of spline joint into account, considering the meshing stiffness varying with the teeth engaged, established the dynamic model with varying stiffness and dynamic equations, and calculated the number of actual meshing teeth and comprehensive meshing stiffness while bearing the varying torque, then, solved dynamic equations using the fourth order Runge - Kutta method, finally, get the teeth meshing number is 23,and the maximum dynamic load coefficient gets smaller from 1.19 to1.15 with the decrease of . This provides a numerical basis for wear`s studying and lifetime`s forecasting of involute spline coupling.

Application of the piecewise constant method in nonlinear dynamics of drill string

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Jialin Tian ◽  
Jie Wang ◽  
Yi Zhou ◽  
Lin Yang ◽  
Changyue Fan ◽  
...  
Keyword(s):  
Nonlinear Dynamics ◽  
Dynamic Model ◽  
Dynamic Characteristics ◽  
Drill String ◽  
Vibration Velocity ◽  
Kutta Method ◽  
Time Step ◽  
Piecewise Constant ◽  
Runge Kutta Method ◽  
Runge Kutta

Abstract Aiming at the current development of drilling technology and the deepening of oil and gas exploration, we focus on better studying the nonlinear dynamic characteristics of the drill string under complex working conditions and knowing the real movement of the drill string during drilling. This paper firstly combines the actual situation of the well to establish the dynamic model of the horizontal drill string, and analyzes the dynamic characteristics, giving the expression of the force of each part of the model. Secondly, it introduces the piecewise constant method (simply known as PT method), and gives the solution equation. Then according to the basic parameters, the axial vibration displacement and vibration velocity at the test points are solved by the PT method and the Runge–Kutta method, respectively, and the phase diagram, the Poincare map, and the spectrogram are obtained. The results obtained by the two methods are compared and analyzed. Finally, the relevant experimental tests are carried out. It shows that the results of the dynamic model of the horizontal drill string are basically consistent with the results obtained by the actual test, which verifies the validity of the dynamic model and the correctness of the calculated results. When solving the drill string nonlinear dynamics, the results of the PT method is closer to the theoretical solution than that of the Runge–Kutta method with the same order and time step. And the PT method is better than the Runge–Kutta method with the same order in smoothness and continuity in solving the drill string nonlinear dynamics.

Simplified Dynamics Modeling of Seat-Passenger in Vehicle Frontal Crash

2014 ◽  
Vol 597 ◽  
pp. 544-550
Author(s):  
Yao Yuan Wang ◽  
Zhuo Yang Lyu ◽  
Liang Liang Wang ◽  
Zhen Hua Yan
Keyword(s):  
Differential Equation ◽  
Dynamic Model ◽  
Fourth Order ◽  
Dynamics Analysis ◽  
Kutta Method ◽  
Analysis Method ◽  
Dynamics Modeling ◽  
Frontal Crash ◽  
Runge Kutta Method ◽  
Initial Stage

To quickly predict the performance of the seat in frontal crash during the initial stage of the seat development, in this paper a simplified coupled dynamic model of seat-passenger interaction is established according to the dynamics analysis method of Lagrange, and the fourth order Runge-Kutta method is used to resolve differential equation. Moreover, the simulation of Madymo testifies the simplified coupled dynamic model of seat-passenger interaction in frontal crash. Therefore, this model will be effective and feasible in predicting the performance of the seat in frontal crash during the initial stage of the seat development, for example, the performance of anti-submarining protection.

Dynamic Characteristics of a Rigid Spindle Supported by Water-Lubricated Bearings

2013 ◽  
Vol 401-403 ◽  
pp. 121-124
Author(s):  
Hui Hui Feng
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Dynamic Characteristics ◽  
Equations Of Motion ◽  
Journal Bearings ◽  
Dynamic Equations ◽  
Kutta Method ◽  
Static And Dynamic Characteristics ◽  
Runge Kutta Method ◽  
Unbalance Force

In this paper, a rigid spindle supported by two identical water-lubricated journal bearings is proposed. The dynamic equations of motion are presented to predicate the performance of the spindle. Under the assumption of linearity, the responses of the rotor excited by constant external force and unbalance force are comprehensively discussed by the fourth Runge-Kutta method. To analyze the static and dynamic characteristics of the water-lubricated bearings, the bulk flow turbulent theory is used and numerically solved by finite difference method. Results of this investigation contribute a better understanding of the performance of a water-lubricated bearing-rotor system.

scholarly journals Numerical Study on Phase-Fitted and Amplification-Fitted Diagonally Implicit Two Derivative Runge-Kutta Method for Periodic IVPS

2021 ◽  
Vol 50 (6) ◽  
pp. 1799-1814
Author(s):  
Norazak Senu ◽  
Nur Amirah Ahmad ◽  
Zarina Bibi Ibrahim ◽  
Mohamed Othman
Keyword(s):  
Fourth Order ◽  
Initial Value Problems ◽  
Numerical Experiments ◽  
Numerical Study ◽  
Kutta Method ◽  
Initial Value ◽  
First Order ◽  
Runge Kutta Method ◽  
Runge Kutta ◽  
The Stability

A fourth-order two stage Phase-fitted and Amplification-fitted Diagonally Implicit Two Derivative Runge-Kutta method (PFAFDITDRK) for the numerical integration of first-order Initial Value Problems (IVPs) which exhibits periodic solutions are constructed. The Phase-Fitted and Amplification-Fitted property are discussed thoroughly in this paper. The stability of the method proposed are also given herewith. Runge-Kutta (RK) methods of the similar property are chosen in the literature for the purpose of comparison by carrying out numerical experiments to justify the accuracy and the effectiveness of the derived method.

Elastohydrodynamic Lubrication in Rolling and Sliding Contacts

1972 ◽  
Vol 94 (4) ◽  
pp. 324-329 ◽  
Author(s):  
C. M. Rodkiewicz ◽  
V. Srinivasan
Keyword(s):  
Film Thickness ◽  
Quadrature Formula ◽  
Fourth Order ◽  
Elastohydrodynamic Lubrication ◽  
Experimental Film ◽  
Kutta Method ◽  
Sliding Contacts ◽  
Runge Kutta Method ◽  
Runge Kutta ◽  
Good Agreement

A solution to the elastohydrodynamic lubrication problem for the case of two rolling cylinders, at different speeds, is presented. The lubricant is assumed compressible throughout the region. The fourth-order Runge-Kutta method for the lubricant and an improved quadrature formula for the elastic calculations are used. Pressure and film-thickness profiles are presented for different rolling velocities. There is a good agreement with the experimental film thickness data, available in literature.

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