Balancing of Rotors Supported on Bearings Having Nonlinear Stiffness Characteristics

1994 ◽  
Vol 116 (3) ◽  
pp. 718-726 ◽  
Author(s):  
A. Turpin ◽  
A. M. Sharan
Keyword(s):  
Nonlinear System ◽  
Linear System ◽  
Equations Of Motion ◽  
Real Life ◽  
Influence Coefficient ◽  
Rotor Systems ◽  
Equivalent Linear ◽  
Influence Coefficient Method ◽  
Stiffness Characteristics ◽  
Equivalent Linear System

In real-life applications, multi-disk-rotor systems are supported on bearings with nonlinear flexibility. The balancing of such systems at high speeds is a challenging task. This work presents a method of balancing such systems. The dynamic equations of motion for a nonlinear system are derived first using the influence coefficient method and then Lagrangian equations. An equivalent linear system is found using the optimization principles. Finally, the correct balance weights for the nonlinear system are obtained based on the equivalent linear system. The results thus obtained establish the utility of such a method of balancing nonlinear systems.

Formulation of Stochastic Linearization for Symmetric or Asymmetric M.D.O.F. Nonlinear Systems

1980 ◽  
Vol 47 (1) ◽  
pp. 209-211 ◽  
Author(s):  
P-T. D. Spanos
Keyword(s):  
Nonlinear Systems ◽  
Linear System ◽  
Solution Procedure ◽  
Stationary System ◽  
System Response ◽  
Equivalent Linear ◽  
Stochastic Linearization ◽  
Equivalent Linear System

A formulation of the method of stochastic linearization so that it is applicable for symmetric or asymmetric nonlinear systems is presented. Formulas for the generation of the equivalent linear system are given. The solution procedure for determining nonstationary or stationary system response statistics is outlined.

scholarly journals Random Excitation of a System With Bilinear Hysteresis

1960 ◽  
Vol 27 (4) ◽  
pp. 649-652 ◽  
Author(s):  
T. K. Caughey
Keyword(s):  
Linear System ◽  
Random Excitation ◽  
Viscous Damping ◽  
Equivalent Linear ◽  
The Mean ◽  
Equivalent Linear System

An analysis is made of the response of a system with bilinear hysteresis to random excitation. It is shown that for moderately large inputs, the additional damping created by the bilinear hysteresis decreases the mean squared deflection compared with that for a linear system with the same viscous damping. However, for large inputs, the decrease in the stiffness of the system due to the bilinear hysteresis causes the mean squared deflection to increase over that for the equivalent linear system.

Developing software tools that automate the conversion nonlinear systems to equivalent linear system in form Brunovsky

2014 ◽  
Vol 0 (35) ◽  
Author(s):  
В.Д. Дмитриенко ◽  
А.Ю. Заковоротный ◽  
А.О. Нестеренко
Keyword(s):  
Nonlinear Systems ◽  
Linear System ◽  
Software Tools ◽  
Equivalent Linear ◽  
Equivalent Linear System

Nonlinear Dynamic Behaviors of Rotor Systems for Ball End Milling

2008 ◽  
Author(s):  
Ting-Nung Shiau ◽  
Kuan-Hung Chen ◽  
K. H. Huang
Keyword(s):  
Nonlinear System ◽  
Linear System ◽  
Cutting Force ◽  
Nonlinear Dynamic ◽  
End Milling ◽  
Depth Of Cut ◽  
Dynamic Behaviors ◽  
Ball End Milling ◽  
Critical Speeds ◽  
Rotor Systems

The nonlinear dynamic behaviors of rotor-bearing system for ball end milling are studied in this paper. The rotor system is supported by bearings with nonlinear spring effects. The nonlinear cutting force can be calculated by using the Tlusty proposed 3/4 rule for chip thickness. The effects of design parameters on system dynamic behaviors including critical speeds and stability under the dynamic cutting forces are numerically investigated in the time domain. For linear system case or the nonlinear system with small depth-of-cut or feed per tooth under linear cutting force, the results show that the critical speeds of system are proportional to the corresponding system natural frequencies, but inversely to the cycle number of tool vibration multiplying by the number of flutes during the cutting time from one flute to another. With large depth-of-cut or feed per tooth, the differences of the critical speeds become larger between linear and nonlinear rotor systems and so are the dynamic responses at critical speeds milling. The critical speed under nonlinear cutting force milling is found to be always higher than that under linear cutting force. Furthermore, the chatter stability lobes are studied for various cutting conditions. The intervals between critical speeds increase gradually, and the axial depths of cut of nonlinear system for stability are lower than those of linear system.

scholarly journals Observer-Based Controllers for Two-Wheeled Inverted Robots with Unknown Input Disturbance and Model Uncertainty

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Khanh G. Tran ◽  
Nam H. Nguyen ◽  
Phuoc D. Nguyen
Keyword(s):  
Linear System ◽  
Taylor Series ◽  
Model Uncertainty ◽  
Disturbance Observer ◽  
System Stability ◽  
Unknown Input ◽  
Input Disturbance ◽  
Equivalent Linear ◽  
Compound Disturbance ◽  
Equivalent Linear System

In this paper, two controllers with a compound disturbance observer are proposed for a two-wheeled inverted robot (TWIR) with model uncertainty and unknown input disturbance. First, an equivalent linear model of the TWIR with uncertainty and input disturbance is proposed using the Taylor series expansion for the nonlinear model of the TWIR at an equilibrium point, in which the nonlinear part of the Taylor series and the model uncertainty are combined with unknown input disturbance as compound input disturbance. Then, the compound input disturbance is estimated by using the Newton method and reference model. As the estimated compound disturbance is used to compensate for the compound disturbance, the equivalent linear system becomes closely definite without compound input disturbance. Finally, two controllers are proposed using the equivalent linear system. Stability analysis of the proposed control methods is also given. To illustrate the proposed methods, some simulations for the TWIR are performed and compared with the existing methods. The main contribution of this work includes the following: (i) simple controllers based on compound input disturbance observer for trajectory tracking and balancing of TWIRs with unknown input disturbance and model uncertainty are proposed; (ii) the stability of proposed closed-loop control systems is proved; (iii) our proposed methods are simulated and compared with the existing methods.

EFFECTS OF EXCITATION CHARACTERISTICS ON THE EQUIVALENT LINEAR SYSTEM OF A BUILDING STRUCTURE WITH MR DAMPERS

2007 ◽  
Author(s):  
J.-H. PARK ◽  
S.-K. LEE ◽  
S.-H. LEE ◽  
K.-W. MIN ◽  
B.-W. MOON ◽  
...  
Keyword(s):  
Linear System ◽  
Building Structure ◽  
Mr Dampers ◽  
Equivalent Linear ◽  
Equivalent Linear System
Sign in / Sign up

Export Citation Format

Share Document