scholarly journals Dynamic Analysis of a Pendulum Dynamic Automatic Balancer

2007 ◽  
Vol 14 (2) ◽  
pp. 151-167 ◽  
Author(s):  
Jin-Seung Sohn ◽  
Jin Woo Lee ◽  
Eun-Hyoung Cho ◽  
No-Cheol Park ◽  
Young-Pil Park
Keyword(s):  
Stability Analysis ◽  
Dynamic Stability ◽  
Critical Speed ◽  
Equations Of Motion ◽  
Polar Coordinates ◽  
Response Analysis ◽  
Rotating Speed ◽  
Time Response Analysis ◽  
The Stability ◽  
Nonlinear Equations Of Motion

The automatic dynamic balancer is a device to reduce the vibration from unbalanced mass of rotors. Instead of considering prevailing ball automatic dynamic balancer, pendulum automatic dynamic balancer is analyzed. For the analysis of dynamic stability and behavior, the nonlinear equations of motion for a system are derived with respect to polar coordinates by the Lagrange's equations. The perturbation method is applied to investigate the dynamic behavior of the system around the equilibrium position. Based on the linearized equations, the dynamic stability of the system around the equilibrium positions is investigated by the eigenvalue analysis.The stability analysis provides the design requirements for the pendulum automatic dynamic balancer to achieve a balancing of the system. The efficiency of ball automatic dynamic balancer, for reducing the total vibration of the system, is better than one of pendulum automatic balancer, if the rotating speed is above critical speed. However, pendulum automatic dynamic balancer can achieve balancing even if the rotating speed is below critical speed.The time response analysis demonstrates the stability analysis from computing the radial displacement of the rotating system and the positions of pendulums. Furthermore, in order to confirm the theoretical analysis, various experiments are made on pendulum automatic dynamic balancer.

Linear Stability Analysis of a Waveboard Multibody Model With a Minimal Set of Equations

2021 ◽  
Author(s):  
A. G. Agúndez ◽  
D. García-Vallejo ◽  
E. Freire ◽  
A. M. Mikkola
Keyword(s):  
Stability Analysis ◽  
Multibody System ◽  
Equations Of Motion ◽  
Nonholonomic Constraints ◽  
Design Parameters ◽  
Multibody Model ◽  
Aspect Ratios ◽  
Holonomic And Nonholonomic Constraints ◽  
The Stability ◽  
Nonlinear Equations Of Motion

Abstract In this paper, the stability of a waveboard, the skateboard consisting in two articulated platforms, coupled by a torsion bar and supported of two caster wheels, is analysed. The waveboard presents an interesting propelling mechanism, since the rider can achieve a forward motion by means of an oscillatory lateral motion of the platforms. The system is described using a multibody model with holonomic and nonholonomic constraints. To perform the stability analysis, the nonlinear equations of motion are linearized with respect to the forward upright motion with constant speed. The linearization is carried out resorting to a novel numerical linearization procedure, recently validated with a well-acknowledged bicycle benchmark, which allows the maximum possible reduction of the linearized equations of motion of multibody systems with holonomic and nonholonomic constraints. The approach allows the expression of the Jacobian matrix in terms of the main design parameters of the multibody system under study. This paper illustrates the use of this linearization approach with a complex multibody system as the waveboard. Furthermore, a sensitivity analysis of the eigenvalues considering different scenarios is performed, and the influence of the forward speed, the casters’ inclination angle and the tori aspect ratios of the toroidal wheels on the stability of the system is analysed.

Stability of Liquid-Filled Spinning Spheroids Via Liapunov’s Second Method

1979 ◽  
Vol 46 (2) ◽  
pp. 259-262 ◽  
Author(s):  
P. C. Parks
Keyword(s):  
Stability Analysis ◽  
Nonlinear Equations ◽  
Stability Theory ◽  
Equations Of Motion ◽  
Spin Axis ◽  
Liapunov Functions ◽  
The Stability ◽  
Nonlinear Equations Of Motion

In this paper the stability theory of Poincare´ and others, expounded in the last few pages of Sir Horace Lamb’s textbook Hydrodynamics, is extended by a stability analysis using Liapunov functions to cover the full nonlinear equations of motion of spinning liquid-filled spheroids. The linearized criterion is confirmed, that is for stability c/a < 1 or c/a > 3 where the semiaxes of the spheroid are a, a, c, the c-axis being also the spin axis. The unstable motion for 1 < c/a < 3 is examined, and a conjecture that viscosity will destabilize spinning spheroids with c/a > 3 is proposed.

Stability analysis of rigid rotors supported by gas foil bearings coupled with electromagnetic actuators

2019 ◽  
Vol 234 (2) ◽  
pp. 427-443 ◽  
Author(s):  
Kamal Kumar Basumatary ◽  
Gaurav Kumar ◽  
Karuna Kalita ◽  
Sashindra K Kakoty
Keyword(s):  
Stability Analysis ◽  
Equations Of Motion ◽  
Electromagnetic Actuator ◽  
Electromagnetic Actuators ◽  
Foil Bearings ◽  
Damping Characteristics ◽  
Foil Bearing ◽  
Model Combining ◽  
The Stability ◽  
Rigid Rotors

Rotors supported on gas foil bearings have low damping characteristics, which limits its application. A possible solution could be an integration of a gas foil bearing with an electromagnetic actuator. This paper discusses the effect of electromagnetic actuators on the stability of a rotor supported on gas foil bearings. A coupled dynamic model combining the dynamics of gas foil bearing and electromagnetic actuator has been developed. The fluid film forces from the gas foil bearings and the electromagnetic forces from the electromagnetic actuators are integrated into the equations of motion of the rotor. The sub-synchronous vibration present in case of conventional gas foil bearings is reduced and the stability band of the rotor is increased due to the implementation of electromagnetic actuator.

Analysis of the Nonlinear Dynamics of a Railway Vehicle Wheelset

1973 ◽  
Vol 95 (1) ◽  
pp. 28-35 ◽  
Author(s):  
E. Harry Law ◽  
R. S. Brand
Keyword(s):  
Lateral Displacement ◽  
Equations Of Motion ◽  
Vertical Displacement ◽  
Linear Analysis ◽  
Design Parameters ◽  
Railway Vehicle ◽  
Nonlinear Variation ◽  
Constraint Equations ◽  
The Stability ◽  
Nonlinear Equations Of Motion

The nonlinear equations of motion for a railway vehicle wheelset having curved wheel profiles and wheel-flange/rail contact are presented. The dependence of axle roll and vertical displacement on lateral displacement and yaw is formulated by two holonomic constraint equations. The method of Krylov-Bogoliubov is used to derive expressions for the amplitudes of stationary oscillations. A perturbation analysis is then used to derive conditions for the stability characteristics of the stationary oscillations. The expressions for the amplitude and the stability conditions are shown to have a simple geometrical interpretation which facilitates the evaluation of the effects of design parameters on the motion. It is shown that flange clearance and the nonlinear variation of axle roll with lateral displacement significantly influence the motion of the wheelset. Stationary oscillations may occur at forward speeds both below and above the critical speed at which a linear analysis predicts the onset of instability.

Non-Linear Transient Stability Analysis of a Rigid Rotor Supported on Journal Bearings With Rectangular Dimples

2015 ◽  
Author(s):  
Ram Turaga
Keyword(s):  
Stability Analysis ◽  
Surface Texture ◽  
Transient Stability ◽  
Equations Of Motion ◽  
Journal Bearings ◽  
Pressure Curve ◽  
Rigid Rotor ◽  
Non Linear ◽  
The Stability ◽  
Transient Stability Analysis

The influence of deterministic surface texture on the sub-synchronous whirl stability of a rigid rotor has been studied. Non-linear transient stability analysis has been performed to study the stability of a rigid rotor supported on two symmetric journal bearings with a rectangular dimple of large aspect ratio. The surface texture parameters considered are dimple depth to minimum film thickness ratio and the location of the dimple on the bearing surface. Journal bearings of different Length to diameter ratios have been studied. The governing Reynolds equation for finite journal bearings with incompressible fluid has been solved using the Finite Element Method under isothermal conditions. The trajectories of the journal center have been obtained by solving the equations of motion of the journal center by the fourth-order Runge-Kutta method. When the dimple is located in the raising part of the pressure curve the positive rectangular dimple is seen to decrease the stability whereas the negative rectangular dimple is seen to improve the stability of the rigid rotor.

Stability Analysis of High-Speed Railway Vehicle Based on Multibody Dynamics Analysis

2013 ◽  
Vol 392 ◽  
pp. 156-160
Author(s):  
Ju Seok Kang
Keyword(s):  
Stability Analysis ◽  
Multibody Dynamics ◽  
High Speed ◽  
Equations Of Motion ◽  
Contact Forces ◽  
Design Parameters ◽  
Railway Vehicle ◽  
Dynamics Analysis ◽  
Contact Points ◽  
The Stability

Multibody dynamics analysis is advantageous in that it uses real dimensions and design parameters. In this study, the stability analysis of a railway vehicle based on multibody dynamics analysis is presented. The equations for the contact points and contact forces between the wheel and the rail are derived using a wheelset model. The dynamics equations of the wheelset are combined with the dynamics equations of the other parts of the railway vehicle, which are obtained by general multibody dynamics analysis. The equations of motion of the railway vehicle are linearized by using the perturbation method. The eigenvalues of these linear dynamics equations are calculated and the critical speed is found.

On the Dynamic Stability of Self-Aligning Journal Gas Bearings

1977 ◽  
Vol 99 (4) ◽  
pp. 434-440 ◽  
Author(s):  
M. J. Cohen
Keyword(s):  
Dynamic Stability ◽  
Journal Bearing ◽  
Equations Of Motion ◽  
Stability Boundary ◽  
Initial Condition ◽  
Small Motion ◽  
Gas Bearings ◽  
Loading Case ◽  
The Stability ◽  
Small Disturbances

The report presents an investigation of the dynamic stability behaviour of self-aligning journal gas bearings when subjected to arbitrary small disturbances from an initial condition of operational equilibrium. The method is based on an approach similar to the nonlinear-ph solution of the author for the quasi-static loading case but the equations of motion of the journal are the linearized forms for small motion in the two degrees (translational) of freedom of the journal center. The stability domains for the infinite journal bearing are presented for the whole of the eccentricity (ε) and rotational speed (Λ) ranges for any given bearing geometry, in the shape of stability boundaries in that domain. It is shown that a given bearing will be stable within a corridor in the (ε, Λ) parametral domain having as its lower bound the so called “half-speed” whirl stability boundary and as its upper bound another whirling instability at a higher characteristic (relative) frequency, the instability occurs generally at the higher eccentricities and lower rotational speeds.

scholarly journals An Analytical Study of Self-Compensating Dynamic Balancer with Damping Fluid and Ball

1995 ◽  
Vol 2 (1) ◽  
pp. 59-67 ◽  
Author(s):  
Jongkil Lee
Keyword(s):  
Dynamic Stability ◽  
Critical Speed ◽  
Analytical Study ◽  
Equations Of Motion ◽  
Circular Disk ◽  
Lagrangian Method ◽  
The Self ◽  
Rotating System ◽  
Stability Investigation ◽  
Low Viscosity

The self-compensating dynamic balancer (SCDB) is composed of a circular disk with a groove containing ball and a low viscosity damping fluid. The equations of motion of the rotating system with SCDB were derived by the Lagrangian method. To consider dynamic stability of the motion, perturbation equations were investigated. Based on the results of stability investigation, ball positions that result in a balanced system are stable above the critical speed with small damping (β′>3.8 case). At critical speed the perturbed motion is said to be stable for large damping (β′>2.3 case). However, below critical speed the balls cannot stabilize the system in any case.

Dynamics and Stability of a Nonlinear Brake Model

2001 ◽  
Author(s):  
Jörg Wauer ◽  
Jürgen Heilig
Keyword(s):  
Stability Analysis ◽  
Lyapunov Exponent ◽  
Nonlinear Model ◽  
Numerical Evaluation ◽  
Critical Speed ◽  
Initial Conditions ◽  
Brake Disc ◽  
Disc Brake ◽  
Brake Pad ◽  
The Stability

Abstract The dynamics of a nonlinear car disc brake model is investigated and compared with a simplified linear model. The rotating brake disc is approximated by a rotating ring. The brake pad is modeled as a point mass which is in contact with the rotating ring and visco-elastically suspended in axial and circumferential direction. The stability analysis for the nonlinear model is performed by a numerical evaluation of the top Lyapunov-exponent. Several parameter studies for the nonlinear model are discussed. It is shown that dynamic instabilities of the nonlinear model are estimated at subcritical rotating speeds lower than 10% of the critical speed. Further, the sensitivity of the nonlinear model to the initial conditions and the stiffness ratios is demonstrated.

scholarly journals Implicit Subspace Iteration to Improve the Stability Analysis in Grinding Processes

2020 ◽  
Vol 10 (22) ◽  
pp. 8203 ◽  
Author(s):  
Jorge Alvarez ◽  
Mikel Zatarain ◽  
David Barrenetxea ◽  
Jose Ignacio Marquinez ◽  
Borja Izquierdo
Keyword(s):  
Stability Analysis ◽  
Dynamic Stability ◽  
Time Domain ◽  
Grinding Processes ◽  
Subspace Iteration ◽  
Efficient Calculation ◽  
Chatter Vibrations ◽  
Stability Maps ◽  
Iteration Methods ◽  
The Stability

An alternative method is devised for calculating dynamic stability maps in cylindrical and centerless infeed grinding processes. The method is based on the application of the Floquet theorem by repeated time integrations. Without the need of building the transition matrix, this is the most efficient calculation in terms of computation effort compared to previously presented time-domain stability analysis methods (semi-discretization or time-domain simulations). In the analyzed cases, subspace iteration has been up to 130 times faster. One of the advantages of these time-domain methods to the detriment of frequency domain ones is that they can analyze the stability of regenerative chatter with the application of variable workpiece speed, a well-known technique to avoid chatter vibrations in grinding processes so the optimal combination of amplitude and frequency can be selected. Subspace iteration methods also deal with this analysis, providing an efficient solution between 27 and 47 times faster than the abovementioned methods. Validation of this method has been carried out by comparing its accuracy with previous published methods such as semi-discretization, frequency and time-domain simulations, obtaining good correlation in the results of the dynamic stability maps and the instability reduction ratio maps due to the application of variable speed.

Sign in / Sign up

Export Citation Format

Share Document