Critical Speed and Vibration Mode for Double-rotor Spindle System of High Speed Grinder

2013 ◽  
Vol 2013 (1) ◽  
pp. 1 ◽  
Author(s):  
Meilin Li ◽  
Keyword(s):  
High Speed ◽  
Critical Speed ◽  
Vibration Mode ◽  
Spindle System

The Dynamics Modeling and Simulation of Spindle System of Ultra-High Speed Grinding Machine Tool

2011 ◽  
Vol 175 ◽  
pp. 206-210 ◽  
Author(s):  
Ya Li Hou ◽  
Chang He Li
Keyword(s):  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Performance Optimization ◽  
Matrix Method ◽  
High Speed ◽  
Critical Speed ◽  
Dynamics Modeling ◽  
Spindle System ◽  
Ultra High Speed ◽  
Grinding Machine

This study was focused on the theoretical modeling and numerical simulation about the dynamic characteristics of spindle system of ultra-high speed grinder. Based on the rotor dynamics and structural system dynamics, a dynamic model was established using the transfer matrix method and the overall transfer matrix method. The critical speeds of first three orders, the modes of variation and other dynamic characteristic parameters of the spindle system were analyzed and calculated. The results showed that the working speed of the spindle system is much lower than the primary critical speed and can therefore stay away the resonance range effectively. Furthermore, the span of the fulcrum bearing and the overhang had significant influences on the critical speed within a certain range, and the study provided the basis and guidance for the structural design and performance optimization of the spindle system.

Analysis of Unbalanced Response for Coupled Double-Rotor Spindle System of High Speed Grinder

2012 ◽  
Vol 522 ◽  
pp. 383-387
Author(s):  
Chang He Li ◽  
Sheng Wang ◽  
Yu Cheng Ding
Keyword(s):  
Vibration Amplitude ◽  
Transition Matrix ◽  
High Speed ◽  
Critical Speed ◽  
Rotor Dynamics ◽  
Balance Equations ◽  
Spindle System ◽  
First Order ◽  
Front End ◽  
The Moment

This study was focused on the theoretical modeling and numerical simulation about the unbalanced response for coupled double-rotor spindle system of high speed grinder. Based on the rotor dynamics, a theoretical model was established using the transfer matrix method. The moment balance equations, and the transition matrix, the state vector, field matrix of coupled double-rotor spindle system of high speed grinder were analyzed and calculated. The numerical results showed that the amplitude of unbalance response increased by the same multiple as that of the amount of unbalance at different locations and at different speeds. Furthermore, the position most sensitive to the unbalance was the front end of rotor 2, followed by the middle and back end of rotor 2. Rotor 2 was especially sensitive to unbalance. Moreover, the vibration amplitudes of the front end, front and back bearings of rotor 1 increased in response to unbalanced increase of rotate speed. The vibration amplitude abruptly increased at 17500r/min corresponding to first-order critical speed.

Influence of Shear and Gyroscopic Effect of Grinder Spindle on Critical Speed

2011 ◽  
Vol 305 ◽  
pp. 168-172
Author(s):  
Chang He Li ◽  
Hua Yang Zhao ◽  
Yu Cheng Ding
Keyword(s):  
Transition Matrix ◽  
High Speed ◽  
Critical Speed ◽  
Rotor Dynamics ◽  
Shear Effect ◽  
Balance Equations ◽  
Gyroscopic Effect ◽  
Spindle System ◽  
The Moment ◽  
Fifth Order

This study was focused on the theoretical modeling and numerical simulation about the shear effect and gyroscopic effect of spindle system of high-speed grinder. Based on the rotor dynamics, a theoretical model was established using the transfer matrix method. The moment balance equations, and the transition matrix, the state vector, field matrix of spindle system of ultra-high speed grinder were analyzed and calculated. The results showed that shear effect reduced the critical speed in various orders, and its influence on higher orders was more severe than on lower orders. Furthermore, it could be seen that gyroscopic effect increased the critical speed in various orders, and it was sensitive in higher orders. It could be found that the increase of fifth order critical speed reached 16.6% due to gyroscopic effect, while the minimum increase of critical speed was 1.8% due to gyroscopic effect.

Order Vibration Analysis of High-Speed Spindle System

2013 ◽  
Vol 712-715 ◽  
pp. 1653-1658
Author(s):  
Zhou Ping Wu ◽  
Bei Zhi Li ◽  
Jian Guo Yang
Keyword(s):  
Vibration Analysis ◽  
High Speed ◽  
Critical Speed ◽  
Model Analysis ◽  
Grinding Wheel ◽  
Work Piece ◽  
Spindle System ◽  
Operation Procedure ◽  
Modes Of Vibration

Before the working speed of high-speed spindle system reaches the critical speed, violent vibration which directly affects the quality of the work piece has been already discovered. To precisely study the speed at which violent vibration happens and the modes of vibration, this paper provided an order vibration approach through studying the model analysis and order of spindle system. The nature frequencies of model analysis were verified and the order of spindle system was confirmed by speed ascend experiment. The result shows that the violent vibration is caused by the manufacturing error of outer ring race of bearing and the mode of vibration mainly located on the grinding wheel which greatly affects the accuracy of spindle system. It is useful for optimizing the structure and operation procedure of high-speed spindle system.

Investigation on Critical Speed and Vibration Mode of High Speed Grinder

2011 ◽  
Vol 42 (10) ◽  
pp. 47-54 ◽  
Author(s):  
C. H. Li ◽  
Z. R. Liu ◽  
Y. Zhou ◽  
Y. C. Ding
Keyword(s):  
High Speed ◽  
Critical Speed ◽  
Vibration Mode ◽  
Structural Parameters ◽  
Variable Cross Section ◽  
Influential Factors ◽  
Variable Cross ◽  
Tightening Force ◽  
Rotor Bearing ◽  
Bearing System

The influences of the grinder spindle's major structural parameters on its vibration mode were investigated. Based on the transfer-matrix method and taking into consideration the gyroscopic couple, the shear, the variable cross-section and other influential factors, a dynamic model was established for the multi-disk rotor of the rotor-bearing system of the grinder spindle. The critical speeds of first three orders, the modes of variation and other dynamic characteristic parameters of the grinder spindle were programmed and calculated. The influences of the axial pre-tightening force of the bearing, the span of the fulcrum bearing as well as the changes in the front and rear overhangs on the critical speed of the rotor-bearing system on the grinder spindle and their pattern of changes were analyzed. The results showed that the working speed of the spindle system is much lower than the primary critical speed and can therefore stay away the resonance range effectively.

Formation of Standing Waves in Radial Tires

1984 ◽  
Vol 12 (1) ◽  
pp. 44-63 ◽  
Author(s):  
Y. D. Kwon ◽  
D. C. Prevorsek
Keyword(s):  
High Speed ◽  
Critical Speed ◽  
Unit Length ◽  
Standing Waves ◽  
Rolling Resistance ◽  
Damping Coefficient ◽  
Circular Membrane ◽  
Critical Speeds ◽  
Steel Cord ◽  
The Individual

Abstract Radial tires for automobiles were subjected to high speed rolling under load on a testing wheel to determine the critical speeds at which standing waves started to form. Tires of different makes had significantly different critical speeds. The damping coefficient and mass per unit length of the tire wall were measured and a correlation between these properties and the observed critical speed of standing wave formation was sought through use of a circular membrane model. As expected from the model, desirably high critical speed calls for a high damping coefficient and a low mass per unit length of the tire wall. The damping coefficient is particularly important. Surprisingly, those tire walls that were reinforced with steel cord had higher damping coefficients than did those reinforced with polymeric cord. Although the individual steel filaments are elastic, the interfilament friction is higher in the steel cords than in the polymeric cords. A steel-reinforced tire wall also has a higher density per unit length. The damping coefficient is directly related to the mechanical loss in cyclic deformation and, hence, to the rolling resistance of a tire. The study shows that, in principle, it is more difficult to design a tire that is both fuel-efficient and free from standing waves when steel cord is used than when polymeric cords are used.

Evaluation of the Dynamic Characteristics of Coupled Double-Rotor Spindle System in High Speed Grinder

2012 ◽  
Vol 5 (3) ◽  
pp. 208-219
Author(s):  
C. H. Li ◽  
Q. Zhang ◽  
S. Wang ◽  
Y. C. Ding
Keyword(s):  
Dynamic Characteristics ◽  
High Speed ◽  
Spindle System

Rotordynamic Performance of a Rotor Supported on Bump Type Foil Gas Bearings: Experiments and Predictions

2006 ◽  
Vol 129 (3) ◽  
pp. 850-857 ◽  
Author(s):  
Luis San Andrés ◽  
Dario Rubio ◽  
Tae Ho Kim
Keyword(s):  
High Speed ◽  
Critical Speed ◽  
Load Capacity ◽  
Test System ◽  
Foil Bearings ◽  
Rotor Imbalance ◽  
Synchronous Motion ◽  
Damping Characteristics ◽  
Rotor Surface ◽  
Stiffness And Damping

Gas foil bearings (GFBs) satisfy the requirements for oil-free turbomachinery, i.e., simple construction and ensuring low drag friction and reliable high speed operation. However, GFBs have a limited load capacity and minimal damping, as well as frequency and amplitude dependent stiffness and damping characteristics. This paper provides experimental results of the rotordynamic performance of a small rotor supported on two bump-type GFBs of length and diameter equal to 38.10mm. Coast down rotor responses from 25krpm to rest are recorded for various imbalance conditions and increasing air feed pressures. The peak amplitudes of rotor synchronous motion at the system critical speed are not proportional to the imbalance introduced. Furthermore, for the largest imbalance, the test system shows subsynchronous motions from 20.5krpm to 15krpm with a whirl frequency at ∼50% of shaft speed. Rotor imbalance exacerbates the severity of subsynchronous motions, thus denoting a forced nonlinearity in the GFBs. The rotor dynamic analysis with calculated GFB force coefficients predicts a critical speed at 8.5krpm, as in the experiments; and importantly enough, unstable operation in the same speed range as the test results for the largest imbalance. Predicted imbalance responses do not agree with the rotor measurements while crossing the critical speed, except for the lowest imbalance case. Gas pressurization through the bearings’ side ameliorates rotor subsynchronous motions and reduces the peak amplitudes at the critical speed. Posttest inspection reveal wear spots on the top foils and rotor surface.

A Study on the Method of Vibration Analysis for Korean High Speed Train by the On-Line Test

2006 ◽  
Vol 321-323 ◽  
pp. 1593-1596 ◽  
Author(s):  
Chan Kyoung Park ◽  
Ki Whan Kim ◽  
Jin Yong Mok ◽  
Young Guk Kim ◽  
Seog Won Kim
Keyword(s):  
Vibration Analysis ◽  
High Speed ◽  
Vibration Mode ◽  
Dynamic Performance ◽  
Railway Vehicle ◽  
High Speed Train ◽  
Acceleration Data ◽  
On Line ◽  
System Vibration ◽  
Line Test

The Korean High Speed Train (KHST) has been tested on the Kyongbu high speed line and the Honam conventional line since 2002. A data acquisition system was developed to test and prove the dynamic performance of the KHST, and the system has been found to be very efficient in acquiring multi-channel data from accelerometers located all over the train. Also presented in this paper is an analysis procedure which is simple and efficient in analyzing the acceleration data acquired during the on-line test of the KHST. The understanding of system vibration mode for a railway vehicle is essential to evaluate the characteristics of a dynamic system and to diagnose the dynamic problems of the vehicle system during tests and operations. Methods based on homogeneous linear systems are not realistic because real systems have nonlinear characteristics and are strongly dependent on environmental conditions. In this paper an efficient method of vibration analysis has been proposed and applied for the KHST to evaluate its vibration mode characteristics. The results show that this method is suitable to estimate the system vibration modes of the KHST.

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