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.

Mathematical Model of Unbalanced Response of Spindle System of Ultra-High Speed Grinder

2011 ◽  
Vol 175 ◽  
pp. 196-200
Author(s):  
Chang He Li ◽  
Chao Du ◽  
Yu Cheng Ding
Keyword(s):  
High Speed ◽  
Rotor Dynamics ◽  
Balance Equations ◽  
Third Order ◽  
Spindle System ◽  
First Order ◽  
The Third ◽  
Front End ◽  
Ultra High Speed ◽  
The Moment

This study was focused on the theoretical modeling and numerical simulation about the unbalanced response of spindle system of ultra-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 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 first order amplitude increased first and then decreased, and the maximum unbalance was located at the middle of the rotor; second order amplitude decreased first and then increased, and the maximum unbalance was located at the front end of the spindle; the third order amplitude decreased first and then increased, and the maximum unbalance was located at the back end of the spindle.

Numerical Investigation into Spindle System Stiffness of High-Speed Grinder

2011 ◽  
Vol 487 ◽  
pp. 490-494
Author(s):  
Chang He Li ◽  
Wei Ping Mao ◽  
Yu Cheng Ding
Keyword(s):  
Vector Field ◽  
Numerical Investigation ◽  
Transition Matrix ◽  
High Speed ◽  
Dynamic Stiffness ◽  
Theoretical Models ◽  
Static Stiffness ◽  
Spindle System ◽  
Overhang Length ◽  
The Moment

This study was focused on the theoretical modeling and numerical investigation about the dynamic and static stiffness of spindle system of high speed grinder. The moment balance and the transition matrix, the state vector, field matrix of spindle system of high speed grinder were analyzed and deduced. The theoretical models about dynamic and static stiffness were established using the transfer matrix method. The numerical results showed that increas of the preload could result in the improvement of static stiffness of spindle end within the range of its working speed; the reduction of front overhang length would improve the stiffness of spindle end, as well as the dynamic stiffness of spindle at the working speed; the stiffness of spindle end decreased with the increase of speed with different bearing spans within the range of working speed of spindle.

Analysis of Static and Dynamic Stiffness for Coupled Double-Rotor Spindle System of High Speed Grinder

2012 ◽  
Vol 522 ◽  
pp. 278-282
Author(s):  
Ya Li Hou ◽  
Wei Ping Mao
Keyword(s):  
Transition Matrix ◽  
High Speed ◽  
Dynamic Stiffness ◽  
Theoretical Models ◽  
Static Stiffness ◽  
Spindle System ◽  
Overhang Length ◽  
Static Rigidity ◽  
Dynamic Rigidity ◽  
The Moment

This study was focused on the theoretical modeling and numerical investigation about the dynamic and static stiffness of coupled double-rotor spindle system of high speed grinder. The moment balance and the transition matrix, the state vector, field matrix of spindle system of high speed grinder were analyzed and deduced. The theoretical models about dynamic and static stiffness were established using the transfer matrix method. The numerical results showed that increased rigidity of front bearing significantly increased static and dynamic rigidity of spindle end and the rigidity of front bearing increased, dynamic rigidity increased more significantly than static rigidity. Furthermore, it can be conclued that increased overhang length reduced dynamic and static rigidity of spindle end at an increasingly slower rate and the span of bearing increased, static and dynamic rigidities of spindle end were reduced

Optimization Design and Experimental Study of a Two-disk Rotor System Based on Multi-Island Genetic Algorithm

2019 ◽  
Vol 36 (1) ◽  
pp. 1-8 ◽  
Author(s):  
Jingjing Huang ◽  
Longxi Zheng ◽  
Chris K Mechefske ◽  
Bingbing Han
Keyword(s):  
Genetic Algorithm ◽  
Vibration Amplitude ◽  
High Speed ◽  
Optimization Design ◽  
Critical Speed ◽  
Optimization Method ◽  
Rotor System ◽  
Flexible Rotor ◽  
Optimum Position ◽  
Transient Experiments

Abstract Based on rotor dynamics theory, a two-disk flexible rotor system representing an aero-engine with freely supported structure was established with commercial software ANSYS. The physical model of the two-disk rotor system was then integrated to the multidisciplinary design optimization software ISIGHT and the maximum vibration amplitudes experienced by the two disks when crossing the first critical speed were optimized using a multi-island genetic algorithm (MIGA). The optimization objective was to minimize the vibration amplitudes of the two disks when crossing the first critical speed. The position of disk 1 was selected as the optimization variable. The optimum position of disk 1 was obtained at the specified constraint that the variation of the first critical speed could not exceed the range of ±10 %. In order to validate the performance of the optimization design, the proof-of-transient experiments were conducted based on a high-speed flexible two-disk rotor system. Experimental results indicated that the maximum vibration amplitude of disk 1 when crossing the first critical speed declined by 60.9 % and the maximum vibration amplitude of disk 2 fell by 63.48 % after optimization. The optimization method found the optimum rotor positions of the flexible rotor system which resulted in minimum vibration amplitudes.

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.

Wheel Suspension Related Disc Brake Judder

1997 ◽  
Author(s):  
Helena Jacobsson
Keyword(s):  
Vibration Amplitude ◽  
Critical Speed ◽  
Thickness Variation ◽  
Disc Brake ◽  
Passenger Car ◽  
Brake Torque ◽  
First Order ◽  
Geometrical Defects ◽  
Eigen Frequency

Abstract Brake judder can be explained as a dynamical amplification of brake torque variation (BTV) when passing through a critical speed of a vehicle. The BTV arises owing to different geometrical defects e.g. disc thickness variation (DTV), disc runout and dynamical effects. DTV is usually the most important source of these fluctuations. Measurements have been made on a passenger car with heavy DTV on one of its front brakes. The eigen frequency of the wheel suspension was found to be 14 Hz, corresponding to a first order critical speed of 95 km/h. These measurements qualitatively verify the brake model with a maximum caliper vibration amplitude close to 100 km/h followed by a slowly decreasing amplitude.

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.

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