Application of the Riccati Method to Rotor Dynamic Analysis of Long Shafts on a Flexible Foundation

1986 ◽  
Vol 108 (2) ◽  
pp. 177-181 ◽  
Author(s):  
J. W. Lund ◽  
Z. Wang
Keyword(s):  
Dynamic Analysis ◽  
Natural Frequencies ◽  
Impedance Matching ◽  
Critical Speeds ◽  
Unbalance Response ◽  
Flexible Foundation ◽  
Rotor Dynamic

A method is described for calculating critical speeds, unbalance response and damped natural frequencies of long rotors on a flexible foundation. The shaft and the foundation are calculated separately and coupled at the bearings through impedance matching. Included in the analysis is also a method for representing the shaft response by an expansion in its free-free modes.

scholarly journals Rotor Dynamic Analysis of Driving Shaft of Dry Screw Vacuum Pump

2019 ◽  
pp. 436-439
Author(s):  
A. Purushotham ◽  
Shravan Kumar
Keyword(s):  
Dynamic Analysis ◽  
Natural Frequencies ◽  
Dynamic Properties ◽  
Vacuum Pump ◽  
Inertia Effects ◽  
Critical Speeds ◽  
Rotor Shaft ◽  
Gyroscopic Moment ◽  
Mass Moment ◽  
Rotor Dynamic

Rotor dynamics is the study of vibration behavior in axially symmetric rotating structures. Devices such as engines, motors, disk drives and turbines all develop characteristic inertia effects that can be analyzed to improve the design and decrease the possibility of failure. At higher rotational speeds, such as in a gas pumps, the inertia effects of the rotating parts must be consistently represented in order to accurately predict the rotor behavior. An important part of the inertia effects is the gyroscopic moment introduced by the precession motion of the vibrating rotor as it spins. As spin velocity increases, the gyroscopic moment acting on the rotor becomes critically significant. Not accounting for these effects at the design level can lead to bearing and/or support structure damage. The main objective of this project is to study the Rotor Dynamic behavior of the drive rotor shaft of the Dry screw vacuum pump. The design of the pump is considered from the one of the reputed pump manufacturing industry. The operational speed of the pump is 4500 rpm, whereas the maximum capable speed of the pump is 10,000 rpm. Rotating machinery produces vibrations depending on the unbalanced mass and gyroscopic effects. Thus an investigation is to be made on the rotor dynamic properties of the shaft to find the natural frequencies and critical speed. For this rotor dynamic analysis was carried out in ANSYS APDL and Workbench16 to find the natural frequencies and critical speeds in the range of 0 to 10000 rpm. Thus an effort is made to shift the mass moment of inertia of the shaft by varying the design of the shaft and to shift the critical frequency to the higher speeds of the shaft there by increasing the efficiency. The modal analysis is performed to find the natural frequencies and it is extended to harmonic analysis to plot the stresses and deflections at the critical speeds. The design of the rotor shaft is made in NX-CAD.

scholarly journals Rotor Dynamic Synchronous Response: A More Thorough Treatment

1993 ◽  
Author(s):  
R. N. Headifen
Keyword(s):  
Steady State ◽  
Dynamic Analysis ◽  
Transient Analysis ◽  
Critical Speeds ◽  
Speed Range ◽  
Wide Speed Range ◽  
Rotor Dynamic

Synchronous response can be a very valuable tool for rotor dynamic analysis. It allows the user to determine rotor displacements over a wide speed range without having to perform a transient analysis at every speed increment. The method is typically used to calculate steady state displacements caused by a rotating imbalance force and the location of critical speeds. While the algorithm presented to perform linear synchronous response is straight forward, there are several modifications that can be made to provide the analyst more useful information.

Dynamic Characteristics Analysis of the Mud Transfer Pump Rotor

2013 ◽  
Vol 455 ◽  
pp. 248-252
Author(s):  
Jun Yuan Sun ◽  
Ji Ming Xiao
Keyword(s):  
Dynamic Analysis ◽  
Modal Analysis ◽  
Dynamic Characteristics ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Dam Construction ◽  
Pump Rotor ◽  
Characteristics Analysis ◽  
Rotor Dynamic ◽  
Dynamic Characteristics Analysis

The mud pump damming technology is a new idea put forward for realization of mechanization and automation of warping dam construction. A mud pump damming machine is studied, the FEM of the mud transfer pump rotor is built, modal analysis and rotor-dynamic analysis are carried out, natural frequencies and mode shapes under different constraints are obtained and the critical speeds of the pump rotor are determined, which will provide reference to improve the running reliability of the mud transfer pump rotor.

Critical Speeds of Geared Rotors by Including Mesh Stiffness and Using a Continuous System Model

1990 ◽  
Author(s):  
O. Sedat Sener ◽  
H. Nevzat Ozguven
Keyword(s):  
Dynamic Analysis ◽  
High Speed ◽  
Natural Frequencies ◽  
Continuous System ◽  
Transmission Error ◽  
System Model ◽  
Graphical Form ◽  
Critical Speeds ◽  
Gear Mesh ◽  
Dynamic Factors

Abstract Dynamic analysis of high speed gearing for the computation of critical speeds and dynamic factors is a must in a proper design, while some other dynamic characteristics of the system such as dynamic transmission error are to be determined for more critical designs. Numerous different models have been suggested for the dynamic analysis of geared systems. These models differ both in the effects included and in the basic assumptions made. A continuous system model is used in this analysis in order to determine the torsional natural frequencies of a gear shaft system composed of two gears, two shafts and two inertias representing the drive and the load. Gear mesh is modelled as a spring connected between two gears. The natural frequencies of the same system are also calculated by using a four degree of freedom classical discrete model in which shaft masses are ignored. The percentage differences in the natural frequencies calculated with the discrete and continuous system models are determined for several values of some nondimensional system parameters. The results are presented in graphical form in terms of the nondimensional parameters defined. Some conclusions which may be important for designers are drawn.

Vibration of Flexibly Mounted Gyroscopes

1973 ◽  
Vol 15 (3) ◽  
pp. 225-231
Author(s):  
L. Maunder
Keyword(s):  
Natural Frequencies ◽  
Critical Speeds ◽  
Supporting Structure ◽  
Vibrational Characteristics

Flexibility in the supporting structure of two-axis or single-axis gyroscopes is shown to have a radical effect on vibrational characteristics. The analysis determines the ensuing natural frequencies and critical speeds.

Determination of the Critical Operating Speeds of Planar Mechanisms by the Finite Element Method Using Planar Actual Line Elements and Lumped Mass Systems

1979 ◽  
Vol 101 (2) ◽  
pp. 210-223 ◽  
Author(s):  
S. Kalaycioglu ◽  
C. Bagci
Keyword(s):  
Dynamic Systems ◽  
Natural Frequencies ◽  
Dynamic Equilibrium ◽  
Large Error ◽  
Free Vibrations ◽  
Lumped Mass ◽  
Critical Speeds ◽  
Rotating Shafts ◽  
Line Elements ◽  
Kinematic Motion

It has been a well-established fact that dynamic systems in motion experience critical speeds, such as rotating shafts and geared systems whose undeformed reference geometry remain the same at all times. Their critical speeds are determined by their natural frequencies of considered type of free vibrations. Linkage mechanisms as dynamic systems in motion change their undeformed geometries as function of time during the cycle of kinematic motion. They do also experience critical operating speeds as rotating shafts and geared systems do, and their critical speeds are determined by the minima of their natural frequencies during a cycle of kinematic motion. Such a minimum occurs at the critical geometry of a mechanism, which is the position at which the maximum of the input power is required to maintain the instantaneous dynamic equilibrium of the mechanism. Actual finite line elements are used to form the global generalized coordinate flexibility matrix. The natural frequencies of the mechanism and the corresponding mode vectors (mode deflections) are determined as the eigen values and eigen vectors of the equations of instantaneous-position-free-motion of the mechanism. Method is formulated to include or exclude the link axial deformations, and apply to any number of loops having any type of planar pair. Critical speeds of planar four-bar, slider-crank, and Stephenson’s six-bar mechanisms are determined. Experimental results for the four-bar mechanism are given. Effect of axial deformations and link rotary inertias are investigated. Inclusion of link axial deformations in mechanisms having pairs with sliding freedoms is seen to predict critical speeds with large error.

Additional Investigations Into the Natural Frequencies and Critical Speeds of a Rotating, Flexible Shaft-Disk System

2007 ◽  
Author(s):  
Lyn M. Greenhill ◽  
Valerie J. Lease
Keyword(s):  
Natural Frequencies ◽  
Slenderness Ratio ◽  
Rotor Dynamics ◽  
Axial Position ◽  
Disk System ◽  
Apparent Contradiction ◽  
Critical Speeds ◽  
Shaft Flexibility ◽  
Gyroscopic Effects ◽  
Lumped Masses

Traditional rotor dynamics analysis programs make the assumption that disk components are rigid and can be treated as lumped masses. Several researchers have studied this assumption with specific analytical treatments designed to simulate disk flexibility. The general conclusions reached by these studies indicated disk flexibility has little effect on critical speeds but significantly influences natural frequencies. This apparent contradiction has been reexamined by using axisymmetric harmonic finite elements to directly represent both disk and shaft flexibility along with gyroscopic effects. Results from this improved analysis show that depending on the thickness-to-diameter (slenderness) ratio of the disk and the axial position of the disk on the shaft, there are significant differences in all natural frequencies, for both forward and backward modes, including synchronous crossings at critical speeds.

Dynamic Analysis of Structures with Interval Parameters under Stochastic Process Excitation

2014 ◽  
Vol 553 ◽  
pp. 699-704 ◽  
Author(s):  
Duy Minh Do ◽  
Wei Gao ◽  
Cheng Wei Yang ◽  
Chong Ming Song
Keyword(s):  
Stochastic Process ◽  
Particle Swarm Optimization ◽  
Dynamic Analysis ◽  
Optimization Algorithm ◽  
Natural Frequencies ◽  
Particle Swarm Optimization Algorithm ◽  
Particle Swarm ◽  
Mean Square ◽  
Structural Dynamic ◽  
Swarm Optimization

This paper presents the interval dynamic analysis of structures with uncertain-but-bounded parameters under stochastic process excitations. Structural natural frequencies and mean square values of structural random responses are not deterministic values but intervals. The interval problems are converted to optimization problems. Mathematical models are developed to find the bounds of interval natural frequencies and mean square displacements. An improved particle swarm optimization algorithm, namely lower sequence initialized high-order nonlinear particle swarm optimization algorithm, is employed to capture the exact bounds of structural dynamic characteristics and random vibration responses. Numerical example is used to demonstrate the presented method. Quasi-Monte Carlo simulations are also implemented to validate the change ranges of structural natural frequencies and mean square displacements produced by the proposed method.

Critical Speeds of Turbomachinery: Computer Predictions vs. Experimental Measurements—Part I: The Rotor Mass—Elastic Model

1987 ◽  
Vol 109 (1) ◽  
pp. 1-7 ◽  
Author(s):  
J. M. Vance ◽  
B. T. Murphy ◽  
H. A. Tripp
Keyword(s):  
Research Program ◽  
Critical Speed ◽  
Natural Frequencies ◽  
Computer Programs ◽  
Elastic Model ◽  
Experimental Measurements ◽  
Critical Speeds ◽  
Improve Accuracy ◽  
Speed Computer ◽  
Rotor Mass

This is the first part (Part I) of two papers describing results of a research program directed at verifying computer programs used to calculate critical speeds of turbomachinery. This research program was undertaken since questions existed about the accuracy of calculations for the second and higher critical speeds. Part I describes improvements in computer programs and data modeling that resulted from comparing measured and calculated “free-free” natural frequencies of several shafts and rotors. Program modifications to improve accuracy include consideration of the effect of disk/shaft attachment stiffness, revised treatment of the end masses, and an improved convergence. Modifications resulting from the study are applicable to many other damped and undamped critical speed computer programs.

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