Analysis On Ultrasonic Bearing Reducing Friction

A lot of work has been done on ultrasonic bearing in my laboratory. Manytypes of ultrasonic thrusting bearing and radial bearing has been designed. Thetheory on ultrasonic bearing anti-friction has been mainly carried in this paper,providing the support for the following research on new ultrasonic bearing.The paper consists of six chapters, given as follows:Chapter 1 IntroductionBearing is the essential important spare part in mechanical products, mainlyused to support rotation components and reduce the friction between the relativemotion components. To design the bearing having small friction coefficient andreliable performance is very important in the mechanical industry development.Firstly the friction classification is introduced in this chapter. The frictionincludes the static friction force, the skidding friction force and the rolling frictionforce. Then the research scope of friction and the development of ultrasonicanti-friction are introduced. Finally the main research content of this paper isoutlined.Chapter 2 The influence of radiation pressure to friction coeffientThe difference between linear and non-linear acoustics theories is introducedin this chapter. There is a statical pressure P0 and a statical density ρ 0 in anypoint in the room on the equilibrium state. The disturbances of the media will leadto acoustical field, the pressure will change to P in any point in the room. Theexcess pressure is p=P-P0.The linear acoustics theory is used to study ultrasonicswhen the sound energy density is not big. The sound pressure is sometimespositive and sometimes negative following the medium takes compression andsparse turn in turn. The energy of the acoustic is directly proportional to theacoustic frequency so the energy of ultrasonic is much larger than common soundand the energy can affect on matter and organism. But the nonlinear acousticstheory should be used to analyze ultrasonic when the sound energy density is greatas the sound pressure everywhere in the sound field, the medium density and theparticle speed are nonlinear. In this condition the convective acceleration ormigrant acceleration in the motion equation of p and the speed u should not beignored in high sound intensity, so some important appearances such as acousticradiation pressure takes place. The accoustic radiation pressure includes two kinds.One is the langevin pressure resulted in convective acceleration. The expression isT 2 200 0p= 1pdt p c? T ∫ = ρ =εThe other is the Rayleigh pressure resulted in the non-linear of matterequation and the expression is: p=-12? γ ε.The two pressures are directly proportional to the acoustic energy density andbeacon the propagation direction, which have the suspending ability.The radiation pressure expression of concave shape radiating surface isconcluded,12 2 12 2b10 0 1 2 2 12 121 11p(z) j u q(R ) exp[ jk z R RA z]R dRz R RA zωρ? + +=+ +∫This expression provides the foundation for the quantitative evaluation ofradiation pressure. The pressure gas blanket in the bearing contact face is higherthan the exterior barometric pressure which is similar to the high pressure gasblanket in the gas bearing. Compared with gas bearing, the ultrasionc bearing hasthe advantageous of simply structure, stable performance.Chapter 3 The influence of the area and time of contact to friction coeffientThe classicality theory of rubbing friction F = fWis based on experimentsand has much limitation in practice and only can be used in engineeringcalculation. Then the glue theory of friction was suggested by Bowden whichmaintains the contact surface is plastic contact condition and the friction alwaystakes place on peak dots. The friction coefficient is related to the real contact areaand the deformation of the peak dots and has no relationship with the apparentcontact area. The real contact area is part of apparent contact area. The glue theoryof friction is introduced which maintain the friction coefficient is related to thenumber and the size of contact points, the time of contact.When the viberator is viberating in high frequency ,the surface of theviberator and the shaft do not fully contact. Assoclation and breakup happen inturn during the viberating process. The motion between the viberator and shaft issmooth in macrocosmic but intermittent in microcosmic and the force of friction issometimes great and sometimes small based on the viberator modes analyzed byANSYS. Sometimes the shaft is rising, which the friction is much smaller thancommon contacting friction according to the glue theory. The abrupt change of thefriction cannot be seen in macrocosmic because of the high frequenvy. The frictionof macroscopics is the average of friction of microcosmic. The antifriction ofultrasonic bearing is best when resonance takes place.Chapter 4 The influence of extrusion effect and air-dynamic lubricating tofriction coeffientThis chapter introduces the extrusion effect and air-dynamic lubricationwhich are both produced by the relative motion between the bearing contact face.The relative motion includes two movements, one is the movement of shaft centerpoint relative to the viberator. The air between the contact faces is repeatedlyextruded as the high-frequence of the viberator, which produces the extrusionmembrane lubrication. The Reynolds equation can be changed to:h 3 p h 3p 12h?? ??? i ??x ??? + ??y ??? i ??y ???=η??tThe boundary condition is2θ = ± π p=0θ = π ddθp = 0The bearing capacity is13 22 2 2 3 212 2 1(1 ) (1 ) 1W R arctgdL c dtη ε ε εε ε ε= ???? ? + ? ??? +????????If the velocity of the axis can be measured, the bearing capacity can beachieved.The other movement is the rotation of the shaft. Wedge shape gap existsbetween the bearing contact face because of the installation error which canproduce air-dynamic lubrication.From the Reynolds equation3 30h p h p 12V 6Uhxη x y ηy x?? ??? ?? ??? + ?? ??? ?? ??? = +??And sommerfeld boundary conditions2θ = ± π p=0θ = π ddθp = 0The expression of sound pressure can be achieve22 L22 2p 6 ( R ) { 2 cos ( 2 2 d) sinc (1 cos ) dt21 [ 1 1 ] d}(1 cos ) (1 )dtη εε θθ ω ω ψ εεθεε ε θ ε= ++ ? ?++ + ?+The air-dynaminc lubrication effect of the ultrasonic bearing is better thancommon air-dynamic lubrication because the pressure between the contact surfaceis higher than the atmosphere pressure. The pressure values of extrusion effect andair-dynamic lubrication in the clearance between bearing and shaft are separatelycalculated using Helmholtz Equation and Neumann conditions which explain theinfluence of extrusion effect and air-dynamic lubricating to friction coeffient.Chapter 5 The structure and experiment of ultrasonic bearingThe friction moment is caught through the experiment, then the kineticfriction coefficient is figured out. The system will move from inaction toaccelerated motion with the load. The time t1 and t 2 of the displacements S1and S 2 can be achieved, so the acceleration of the load and the rotaryacceleration of the shaft can be acquired. The experimental result shows that thefriction coefficient of ultrasonic is much smaller than double-gulley ball bearing.The combined type of ultrasonic and ball bearing is designed. When theviberator doesnot work, the contact surfaces of the viberator and the outeraluminum barrel are common contact. The shaft and the balance weight run withthe motor while the outer aluminum barrel doesnot rotate. The force of slidingfriction of ball bearing is smaller than the peak static friction between the viberatorand the aluminum barrel.If the viberator is applied energy, the contact surfaces of the viberator and theouter aluminum barrel are ultrasonic bearing, the shaft , the outer aluminum barreland the balance weight will run together. There is no sliding movement betweenthe shaft and the alumimum barrel, which shows that the sliding friction of theultrasonic bearing is smaller than the peak static friction of the ball bearing.This structure shows that the ultrasonic bearing friction coefficient is smallerthan ball bearing friction coefficient intuitionistically.Chapter 6 Conclusion and expectationThis chapter gives the main conclusion obtained in this paper and theprospect for next research.