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

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.

scholarly journals Study of Vertical Characteristics with Changes in Prepressure of Rubber Pad Used by High-Speed EMU

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Chuanbo Xu ◽  
Mao-Ru Chi ◽  
Liangcheng Dai ◽  
Yiping Jiang ◽  
Zhaotuan Guo
Keyword(s):  
High Speed ◽  
Performance Test ◽  
Conversion Coefficient ◽  
Dynamic Stiffness ◽  
Theoretical Method ◽  
Static Characteristics ◽  
Static Stiffness ◽  
Characteristic Parameters ◽  
Precise Prediction ◽  
Train Dynamics

Rubber spring plays an important role in improving train performance, so the study of rubber spring is one of the focuses of train dynamics. The vertical characteristic parameters of rubber spring are affected by prepressure significantly, as a result of varying parameters of static stiffness, dynamic stiffness, periodic energy consumption, damping coefficient, and so on. In order to use the theoretical method to calculate the precise static stiffness and predict the dynamic characteristics and to reduce the workload of the rubber spring performance test, this paper takes the annular rubber pad as an example to study with different prepressures. In this paper, the convexity coefficient correction formula (simply called the CCCF) for static stiffness calculation and the dynamic fiducial conversion coefficient (simply called the DFCC) method based on different prepressures are proposed. Through further analysis, the accuracy of CCCF and DFCC is proved both theoretically and experimentally. The results have shown precise prediction of the variation of prepressure on rubber spring parameters by using CCCF and DFCC and can be used as the reference of accurate vertical dynamic-static characteristics of the rubber spring.

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.

scholarly journals Analysis of the dynamic characteristics of downsized aerostatic thrust bearings with different pressure equalizing grooves at high or ultra-high speed

2021 ◽  
Vol 13 (5) ◽  
pp. 168781402110180
Author(s):  
Ruzhong Yan ◽  
Haojie Zhang
Keyword(s):  
Dynamic Characteristics ◽  
High Speed ◽  
Rotation Speed ◽  
Dynamic Stiffness ◽  
Simulation Method ◽  
Perturbation Amplitude ◽  
Thrust Bearings ◽  
Supply Pressure ◽  
Ultra High Speed ◽  
Air Film

This study adopts the DMT(dynamic mesh technology) and UDF(user defined functions) co-simulation method to study the dynamic characteristics of aerostatic thrust bearings with equalizing grooves and compare with the bearing without equalizing groove under high speed or ultra high speed for the first time. The effects of air film thicness, supply pressure, rotation speed, perturbation amplitude, perturbation frequency, and cross section of the groove on performance characteristics of aerostatic thrust bearing are thoroughly investigated. The results show that the dynamic stiffiness and damping coefficient of the bearing with triangular or trapezoidal groove have obvious advantages by comparing with that of the bearing without groove or with rectangular groove for the most range of air film thickness, supply pressure, rotation speed, perturbation amplitude, especially in the case of high frequency, which may be due to the superposition of secondary throttling effect and air compressible effect. While the growth range of dynamic stiffness decreases in the case of high or ultra-high rotation speed, which may be because the Bernoulli effect started to appear. The perturbation amplitude only has little influence on the dynamic characteristic when it is small, but with the increase of perturbation amplitude, the influence becomes more obvious and complex, especially for downsized aerostatic bearing.

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