超高速试验机动力学研究

The Research on the Dynamics of High-speed Friction and Wear Test

System in Mechanical Engineering

Key words:Ultra-high-speed rotation; Friction and wear;Scrape;Dynamics

Abstract.By researching the dynamics of high speed friction and wear test system, establish

the statics and dynamics model of high-speed dial and get the equation of motion of turntable scrapers state. Using Ansys Workbench software platform analysis the order moda l of the turntable, get the kinetic parameters of the system. Some suggestion and methods are proposed

on avoiding vibration of turntable system.

Introduction

Abradable coatings are mainly used to reduce the gap between rotating parts and machine box of the aero-engine, can effectively improve the power and thrust of the turbine engine. At present，the performance evaluation of abradable coatings including: abradability，erosion resistance, thermal shock resistance, high temperature oxidation resistance, the bonding strength between the coatings and the matrix and so on[1-2],the mainly method to evaluate coating performance is simulating the high speed and high temperature working environments,the research of the high speed friction and wear test system is aimed to evaluate coating performance. As the core components of the high speed friction and wear test system, the dynamic performance of the ultra-high speed rotary system directly affects the working stability and reliability of the whole system.

Rotating disk is one of the basic mechanical components widely used in rotating machinery. At present, the research of the dynamics of the rotor system is widely done, mainly concentrates in the method of the rotor dynamic balance and the rubbing phenomenon during rotor operation process, it aims to optimize the rotor structure to reduce the friction of vibration and dynamic balance. To realize the coating skiving experiment, high speed rotary table of the ultra-high speed friction and wear test system is not only affected by factors such as support bearing, unbalance mass and so on from the internal system, but also affected by Intermittent skiving impact.

This paper gives motion stability analysis of the ultra-high speed rotary scraping.

1. The design of ultra-high speed rotary system

1.1 Working principle of the high speed friction and wear test system

Three dimensional model diagram of the high speed friction and wear test system is shown in Fig 1. Ultra high speed friction and wear test system is mainly composed of high speed motor, high speed rotary, heating device, micro feed linear motor, feed sliding table, coating sample, the infrared pyrometer composition. It makes the coating sample and the high speed rotating blade tip contact through the high speed motor drives the wheel rotation with a tip and linear motor drives feed sliding table to fulfill trace feed of the coating sample to realize the coating scraping. Among these parts, the gas gun is placed at the lower end of the high speed rotary table to heat the contact area between rotary table and tip to reach the working temperature of 1200 ℃.

wear test system is 200m/s-350m/s, the range of rotary speed is 4777-16711r/min. It uses a Z4 high power dc motor to realize high rotation speed, through acceleration mechanism of the high-speed flat belt drives the high speed rotary in rotation. It is very important to choose the right wheel diameter for ultra-high speed friction and wear test system. As the diameter increases, the rotary speed reduces gradually. But the oversize rotary table will bring a lot of difficulties such as large volume, heavy, hard to machine and so on. Therefore the wheel diameter is 400 mm, the thickness of the rotary table is 40mm, both ends of the rotary table are supported by angular contact ball bearings, the lubrication way is the oil-gas lubrication. Open a corresponding tip card slot on the rotary table. The loading card way of tip is Mosaic type. In order to prevent tip falls off during high speed rotating and improve security, use bolt connection on the basis of Mosaic installed card. The structure of the rotary table is shown in Fig 2.

2. Dynamics model of ultra-high speed rotary system

2.1 Physical model of ultra-high speed rotary system

When high speed wheel rotates, because of the factor of the rotary table mass imbalance, the centrifugal force generated will lead to occur corresponding bending of rotary system axis. Considering the axial deformation, rotary system can be regarded as an infinite multi degree of freedom system. The dynamics model should be described using partial differential equation. The complexity of the problem will be increased significantly. For high speed rotary table, it can be seen as a combination of flexible shaft section and rigid rotary table for processing. The speed of ultra-high speed friction and wear test system is higher than those of the first order and second order critical speed. It causes system instability due to the resonance, when the rotary table goes through critical speed. At the same time inappropriate support characteristics can also cause self-excited

vibration of the system. Through the lower rotor - bearing - stand system stiffness by using flexible support, it can make the rotor-bearing system go through the critical speed with small amplitude. And this kind of flexible supporting can make the rotor bending vibration decrease in the whole range of speed [3] .Both ends of the rotary table are supported by angular contact ball bearing. Considering the actual bearing stiffness, damping characteristics, we use the vertical and horizontal spring constraints. Spring stiffness is equivalent to bearing stiffness and support stiffness. The damping spring is equivalent to bearing damping and support damping [4].

2.2 mathematical model of ultra-high speed rotary system

The bearing is simulated by isotropic spring and damper and mass imbalance is simulated by lumped mass on the rigid rotary table, we can build the rotor model geometry structure according to it, as shown in Fig.3.

oxyz and inertia (fixed) coordinate system OXYZ. Y shaft of rotating coordinate system oxyz and rotor axis of rotation are the same, x and z axis are defined as the other two main principal axis of inertia, the origin choose in the center of the rotary table. The offset distance between the imbalance mass on the rotary table and shaft is u z ,imbalance mass is mu ,the mass of rotary table is m z , shaft mass is m. Vibration state of the rotary can be described by using geometric center position(X,Z) and angle (,)θ? that shaft relative to X,Z axis. The direction of (,)θ? is respectively from the y and z from y to x .The position of unbalance mass on the rotary table is （u x ，u y ，u z ） in the rotation coordinate system oxyz. The dynamic model that is established in the rotary system is as follows:

2222

2()22(sin cos )(cos sin )()22(cos sin )(sin cos )(cos sin )()22(sin cos z u x z x z z u x z x z x z a b b u y x z m m X cX kX m u u u u m m Z cZ kZ m u u u u u u cL kL I J I I m u u u φφφφφφφφφφφφφφφθθφψθφψφφ??+++=-++??

??+++=+--??

+++-+-=---22

2)(sin cos )()22(cos sin )x z a b b u y x z u u cL kL I J I I m u u u φφφφψψφθψφθφφφ????????

??-+++++=+??++???? (1)

Among it, k 、c are both ends bearing stiffness and damping, L is the rigid rotor shaft length(the distance between the two supporting), I a and I b are respectively the radial and axial moment of inertia, J is the rotary ’s radial moment of inertia, φ is rotation angle of the rotor, the direction is from z to x.

3 .Rotary table dynamics analysis

Among the analysis of the rotor system, the frictional contact of the rotor and the stationary part is the important reason of causing the rotating machinery vibration and noise [5]. High-speed dial rubbing is not the same phenomenon with rubbing referred in the Rotating Machinery, because the high-speed dial rubbing is not just contact in rotor and seal or bearing, the coating scraping contact friction is more important. After the impact, dial response should have rebound movement of the complex transient lateral vibration and torsional vibration. The twisting motion is caused by the impact of torque. The direction of rebound movement is depended on the relative position of the initial movement of the stationary member, the contact surface and the rotor circumferential speed. Rebound movement may be along the precession direction or in opposite directions. The movement after shock is described by the free transverse vibration, its frequency is equal to the rotor natural frequency or multiples [6].

3.1 Rotary table scraping state kinetic analysis models

When the turntable scraps the tip, the specific process is composed by preparing scraping, start scraping, scraping, out from scraping. The reaction force of the turntable and coating in the scraping includes not only radial force F r but also radial force creates friction F μ, there is also coatings tangential force F t and scraping torque M f , rotary table coating scraping force diagram is shown in Fig. 4.

center O 'is r, the exciting force model of rotary table coating scraping is:

r

t F F F F F F M F r

μτμτμ==+= （2）

F t in Formula (2) is the total tangential force by the rotary table.

When the scraping is began, rotary table stiffness will cause a large bending deformation of the rotary table axis, the amount of deformation is e=(x 2+y 2)1/2,the bending stiffness of the shaft is k, the radial direction of the rotor of the maximum amount of deformation is l, so the bending stiffness

of the system is /m k ke l =, bending stiffness coefficient of the X, Y direction is /m rr

rr k k e l =,

Stiffness is competed by k rr and additional stiffness k 0[4] , the additional stiffness is 0()/k k e l l =-, δr is the radial depth of the cut into the coating, β is the displacement of the initial angle, φ + β is the angle of scraping point with the x axis. Since each scraping of the coating of the turntable is occurred in one week in the precession, and ignore the transient process, scraping generates the excitation to the rotor is occurred in periodically step. So we can use the product of cycle step function and excitation force to the system. The cycle step function is expressed as:

1112()1/2sin(/2)cos[(/2]/n i F t t i t i t t i π

??Ω=-Ω-ΩΩ-????

∑ (3)

F requency Ω in formula (3) is equal to the frequency of the processionals motion, t 1 is the continuous impact time and slightly less than 2π / Ω.

11/()t i ααπ=Ω++ (4) 1cos()sin()

y e arctg

x e ?βα?β-Ω+=+Ω+ (5)

Where in α is the dial twist angle in scraping.

Above the excitation force and the step function is applied to the coating scraping turntable, we can achieve the differential equations of motion:

00()sin()()()cos()()()()r rr x r rr y p F Mx D x k x F t k x t F t F My D y k y F t k y t F t F J D k M t M F t ααα?βα?βααα++=-ΩΩ++++Ω++=-ΩΩ++++Ω++=-Ω (6)

In formula (6), M is a turntable quality, D r is damping coefficient for the turntable system, D α is dial torsional damping coefficient, k rr is the bending stiffness of the turntable, and K α is the torsional stiffness of the turntable, k 0 is additional stiffness, M (t) is externally applied to the power torque of the turntable system, J p turn coiled its moment of inertia when the rotation of the center origin O. if we regard the turntable as a uniform quality disc, its moment of inertia is 212p J Mr =.

3.2 Ultra-high-speed dial static analysis

When the ultra-high-speed friction and wear testing system works, the turntable edge of the tip of the line speed can reach 350m / s, the speed of the turntable will also be up to 16711r/min. In such a high speed, the turntable will be subject to a great centrifugal force acts. Under conditions that, we assume the density of the materials is 7.85g/cm 3, calculated in accordance with the maximum intensity theory in engineering mechanics, the highest centrifugal tensile stress is 547.53MPa, this stress has exceeded the structural steel used in the ordinary dial a tensile ultimate strength of 460MPa, the turntable stress cloud under the speed of 16711r/min is shown in Fig.5.

When is the most susceptible damage part, belong to the fragile area. In turntable matrix material selection, material tensile ultimate strength should be greater than 547.53MPa, and try to choose a less dense, otherwise, the incorrect material selection will result in rotation speed to reach or exceed the speed of damage, it will cause danger to the safety of equipment and personnel. To make the turntable rotation be safe and reliable, select the high-temperature alloy GH985 as a turntable base material.

3.3 Ultra-high-speed dial kinetic analysis

Based on static analysis, do the dynamics analysis of dial system first is the modal analysis and harmonic analysis of turntable system. Mode is inherent in the mechanical structure of the vibration characteristics, each mode has a specific natural frequency, damping ratios and mode shapes. These modal parameters can be achieved by calculation or test analysis, such a calculation or test analysis process is known as modal analysis [7]. Do modal analysis of the dial overall after tip installed, the mode number is set to 10, obtain first 10 natural frequencies and the corresponding mode shapes of carousel system in the state of no external load constraints.

The sixth-order natural frequency range of the rotor is 0Hz~ 2.29e-03Hz, the seventh order natural frequency suddenly surged to 1022.4Hz, the tenth-order natural frequency up to 1183Hz. When the rotor frequency of the experimental system reaches this range, the carousel system occurs resonance. During the acceleration of the carousel system, low speed dial torsional vibration occurs more obvious, as the speed increases, the shaft produces a more significant bending vibration. The normal operating frequency of the ultra-high-speed friction and wear testing system is above 1700Hz, so, the test system can be effectively avoided resonance phenomenon in the scraping experiments.

Following the modal analysis of the rotor system, you need to do the corresponding harmonic response analysis on rotary table’s vibration frequency. The so-called harmonic response analysis is the technology that it can be used to determine the linear structure’s steady-state response when the linear structure is bearing a load with sinusoidal (harmonic) changes. During the rotary table harmonic analysis process, you need to set the frequency range of the dial system and set the external load that the rotary table system bears. Assuming the same as the rotational frequency of the rotary table and the system is 1752Hz, so the set frequency ranges 0-1752Hz. Vibration amplitude at the frequency of 1183Hz reached 2.32e-3mmm.And when the amplitude reaches the highest peak, the phase angle has risen to the highest value-180°.That means in this frequency rotary table’s torsional vibration p henomenon is strong.

4 .Conclusions

(1) When the ultra-high-speed friction and wear testing system works, turntable system is at ultra-high speed, shaft will occur significant vibration. Turntable starts from rest, in the acceleration

phase, due to the presence of angular acceleration, vibration is more intense; when the dial is rotated to achieve the required speed for constant speed rotation, the vibration is weakened.

(2) When the scraping happens between the dial and the coating, dial response should have complex transient lateral and torsional vibrations. When scraping happens between the tip and the coating, the carousel system bending vibration and torsional vibration occur simultaneously,and bending vibrations of the dial system response associates with torsional vibration, the torsional vibration response changes only relate to the time of producing coatings scraping, regardless of the bending vibration.

(3) The natural frequency of the turntable inclines to the vibration frequency when the dial works properly, but in dial accelerated process we should try to shorten the acceleration time of the turntable in the resonance region.

References

[1]Zhang Deming, Ren Xianjing, Teng Baiqiu. Research Progress on Performance Evaluation Techniques of Abradable Seal Coatings[J]. Thermal Spray Technology, 2009, 1 (2):19-22.

[2]LIU Junhai, He Jiawen, Lu Mingzhu. A New Method for Evaluation of Mechanica l Properties of Sealing Coating[J]. Materials Engineering, 1997, (11):43-44.

[3]Ke LiZONG,QImansiji. Rotor dynamics elastic support [M]. Beijing: Science Press, 1987.

[4]HAN Y anguang. The Numerical Experimentation and Analysis of Dynamic Balance for High Speed Rotors[D]. Huazhong University of Science and Technology, 2008:1-94.

[5]Edwards S, Lees A W, Friswell M I. The Influence of Torsion on Rotor/Stator Contact in Rotating Machinery[J]. Journal of Sound and Vibration, 1999, 225(4): 767-778.

[6]HU Niaoqing. Research on Identification of Nonlinear and Fault of Rub-impact in Rotors[D]. National Defenes University of Science and Technology, 2001: 24-35.

[7]PU Guangyi. ANSYS WORKBENCH 12 Basic tutorial with example explanation[M]. Beijing: China WaterPower Press, 2010, 10.