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A linear piezo-electric ultrasonic motor using a single flexural vibrating bar for electro-discharge system industrial applications

A linear piezo-electric ultrasonic motor using a single flexural vibrating bar for electro-discharge system industrial applications
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  ORIGINAL ARTICLE A linear piezo-electric ultrasonic motor using a singleflexural vibrating bar for electro-discharge system industrialapplications M. Shafik   &  E. M. Shehab  &  H. S. Abdalla Received: 9 January 2008 /Accepted: 30 January 2009 /Published online: 20 February 2009 # Springer-Verlag London Limited 2009 Abstract  This paper provides the development process of a linear piezo-electric ultrasonic motor using a singleflexural vibrating bar. The process covers the designmethodology, conceptual design, basic configuration, mod-elling and analysis, principle of operation, motor structure,experimental examination and evaluation of the maincharacteristics of the motor. The motor comprises threemain parts: the stator, rotor and sliding element. Themechanism concept of the developed motor is based oncreating elliptical motions of surface points generated bysuperposition of longitudinal and bending vibration modesof oscillating structures. Pressing the stator against thedriving tip, the microscopic motions are transferred into arotary motion then into linear motion through the friction between parts of the motor. The developed motor providesa linear motion and can be driven with common drovingsystem with electrical signal of invariable frequency.Modelling using finite element analysis, mechanism anddesign of the component of the developed prototype are presented in this paper. The essential experimental test toimplement the motor in electro - discharge system industrialapplication was carried out, and the initial results show that the developed prototype is able to provide a reversibledirectional of motion, no-load travelling speed equal to28 mm/s, maximum load of 0.78 N, a resolution <50 μ  mand a dynamic response <10 ms. Keywords  Linear piezo-motor .Mode-coupledvibration piezo-motor .Piezo-motorindustrial application.Electro - discharge machining systems using piezo-motor  1 Introduction Many different constructions and techniques of piezo-electric ultrasonic motors have been developed for minia-turisation and high-precision industrial applications [1  –  14].Potentially, they offer a significant flexibility for positionand feed-rate control [15  –  18]. They have compact size,high force density, simple mechanical construction, lowweight, slow speed without additional gear or spindle, hightorque, non-magnetic operation, freedom for constructionaldesign, very low inertia, fast dynamic responses, direct drive, fine position resolution, miniaturisation and noise-less operation. These criteria give them the potential toreplace electro-magnetic motors in a number of industrialapplications [9, 10]. Demanding and careful examination for these applications reveals that there are apparent shortcomings. The first is in regard to the dynamicresponse of the motor and its transfer function. Whilst a piezo-ceramic element (typically PZT) expands in direct  proportion to the magnitude of the applied voltage, theultrasonic motor (USM) on the other hand accumulatesthose displacements over time. Therefore, the transfer function of the motor, relating the magnitude of the drivingsignal to the displacement, is an integrator [19], and this Int J Adv Manuf Technol (2009) 45:287  –  299DOI 10.1007/s00170-009-1955-5M. Shafik UK Intelligent System Research Institute,Pera Innovation Ltd,Melton Mowbray LE13 0PB, UK E. M. Shehab ( * )Decision Engineering Centre, Cranfield University,Cranfield, Bedford MK43 0AL, UK e-mail: H. S. AbdallaFaculty of Design, De Montfort University,Leicester LE1 9BH, UK   shows a delay in the dynamic response of the USM, but it is not nearly significant as that in an electro-magneticservomotor. The second is that because motion is trans-mitted through a friction force, it will have a dead band dueto the friction. Often, USM does not move until the input signal is greater than 10% of the maximum allowedvoltage to overcome the friction. Such a dead band limitsthe ability of a USM to accelerate quickly and positionaccurately [9, 10, 19]. This paper introduces a linear construction of a standingwave bimodal linear piezo-electric ultrasonic motor for electro - discharge machining (EDM) system industrialapplications. A whole series of machining process, each based upon the electro-discharge phenomena, have evolvedsince 1940s to date. One common feature of an electro - discharge system is to move the cutting tool towards andaway from the material being machined in a micro-secondtime period. The traditional manner to effect required rapidmovement of the electrode has been through the use a DCservomotor, which drives a ball screw arrangement that allows conversion of the rotary motion into linear motion.The nut in the ballscrew arrangement is usually fastened toa slide that is guided by a slideway; thus, linear motion can be affected. In the recent past, some electro - dischargesystems have used AC servomotors because of their better  performance but essentially the same kinematical arrange-ment of rotary motor/ballscrew/slide/slideway is in place.The particular electro - discharge machining process knownas EDM/EDT generally has a multi-rotary motor/ballscrew/ slide/slideway arrangement in a small volume. Thefunction being to focus as many electrodes on to a givenarea as possible, given the limitations of the designconstraints that is dominated by the physical size andvolume of DC or AC servomotors and the other kinematicelements required to effect rotary to linear motion. One potential advantage of the proposed feed drive using piezo-electric USM is its compact size in comparison to a DC or AC servo motor, thus allowing the possibility of bringingto fruition a design for an EDT servo head that has theability to effect many electrodes, each separately servocontrollable, on to a given area. The piezo-electric USMhas the same kinematics capability as a rotary motor/  ballscrew/slide/slideway arrangement and is controllablewithin the limits that DC/AC servos operate and EDMsystems requirements.The creation of motion of the piezo-electric ultrasonicmotor is mainly based on using the elliptic motion of displacement of a piezo - electric vibrator; this means that two vibrations are essentially required to form the motion.It is found that the longitudinal and bending vibrations aremost common and effective for elliptic motion. Based onthese phenomena, it was possible to construct few simple piezo-motors [7, 8, 26, 27]. 2 Overall structure and principle of motionof the developed motor This research work proposed a piezo - electric USM for linear industrial applications. The developed motor has thecapability to provide linear motion, fast dynamic responseand micro-resolution. The motor principle of operation is based on converting the continuous flexure and linear force,generated externally through the flexural vibrating bar, intorotary motion then into linear motion through friction between bar and the rotor.The developed motor composed of three main parts isshown in Fig. 1, namely the stator, the rotor and the slidingelement. The stator is a single vibrating bar, made from piezo-ceramic material that has the ability to transform theapplied electrical load into mechanical vibration. The rotor is composed of the motor driving wheel and the shaft. Thesliding element is made up of rectangular tube steel. Thestator, rotor and sliding element jointly with the frame of the motor form the linear structure of the motor. The motor was implemented successfully in two different case studiesof electro - discharge system industrial applications [9, 10], which are texturing and machining. More details can also be found in Shafik [28].The overall design of the developed motor has taken intoconsideration application needs such as type of motion,degree of resolution, speed, output force required, loadcapacity, torque, compactness, integration of the parts into   Piezoelectric electrode Driving wheel Shaft Spring Slider Bearing Bearing Bearing Spring Slider Fig. 1  The developed dual mode standing wave linear piezo - electricUSM using a single flexural vibrating bar 288 Int J Adv Manuf Technol (2009) 45:287  –  299  the frame of the motor, production of the parts andmaintenance.The principle of motion is based on creating ellipticalmotions of surface points generated by superposition of longitudinal and bending vibration modes of oscillatingstructures (piezo - electric ceramic bar). However, to create astrong second bending vibration mode, the polarisationdirection of the piezo - electric vibrator perpendicular to theelectrodes, the piezo - electric ceramic vibrator bar wasarranged as illustrated in Fig. 2. The longitudinal and bending vibration modes are coupled by asymmetry of the piezo - electric ceramic vibrator [6, 20, 21]. The first surface is segmented into four sub-surfaces, which were arrangedelectrically to provide two sub-electrodes namely A and B.The second surface is connected to the earth and is labelledas electrode C. Then, a single-phase AC signal with a widefrequency band is used to investigate their natural frequen-cies. Driving the electrode A and C by a single-phase ACsignal with a frequency closer to the resonant frequency of the vibrator provides one direction of motion, and switch-ing to electrode B and C changes the bending vibrationmode by a phase shift of 180°, which leads to reversing thedirection of elliptical motion generated at the edge of thevibrator as shown in Fig. 3. The rotational motion isconverted into linear motion using the friction between theshaft and the sliding element of the motor.Few authors have used these phenomena and succeededin developing different constructions to generate linear motion [6, 7, 21, 22]. Some of them were unable to develop the motor on reversible direction of motion. Snitka [21] andAoyagi et al. [6] showed that the load of this type of motor depends on the contact point of the rotor, the dimension of the piezo - electric plate and material of the stator and therotor. Snitka [21] proved that the pre-load pressing forcesand friction between parts influence the degree of accuracyobtainable. Therefore, the material for the moving parts of the proposed motor has been carefully selected. It was alsonoticed that the slide element does not move until theexcitation voltage reaches about half wave its maximumvalue because a single driving system with constant frequency is used to excite both normal and thrust force.This greatly reduces the accuracy and resolution of themotor. The thrust force must overcome static friction result of pre-load force to allow relative motion between the stator and the rotor [15]. In the proposed design, a coil spring wasused to press the vibrating bar against the rotor. Thisenabled the pre-load force to be sensitively adjusted [8]. 3 Modelling of the developed motor using finite elementanalysis Piezo - electric USMs have many complex non-linear char-acteristics. Normally, two methods of analysis can be usedto simulate and model piezo - electric USMs [23  –  25]. Thesemethods are the analytical analysis and finite element analysis (FEA) [23  –  25]. In the current developed USM,ANSYS (FEA software) was employed in the motor design process to investigate the material vibration modes (longi-tudinal and bending modes). Furthermore, two types of finite elements analysis were used, model analysis andharmonic analysis, to determine and investigate the major technical parameters required for modelling the motor.These offer two types of loads, the nodal and the pertainingto the element. In the nodal case, the loads were applied tonodes of the element that do not have direct links withelement properties. Fig. 2  Basic configuration of the rectangular vibrating bar in a piezo-ceramic material and method used to generate two modes of vibrations Fig. 3  Principles of creating bidirectional motionInt J Adv Manuf Technol (2009) 45:287  –  299 289  A model for the developed motor was constructed basedon a full translation of the motor boundary condition. The piezo - electric electrode (stator) was defined to be the activeelement, and the rotor (driving wheel) was defined to be the passive element.Figure 4 shows the variation of displacement of thevibrating bar against exciting frequency, for linear con-struction, of the motor using FEA model. The figuresillustrate that the change of amplitude at a resonant frequency of the current model was found to be 42.2 kHz.This initially shows the operating frequency and theresponse time of the developed piezo - electric USM motor.The analysis shows clearly the influence of the slidingelement and friction force on the vibrating bar deformationand the displacement. The displacement of the bar changedfrom 10.1125 to 3.0999 μ  m due to sliding element andfriction force between the sliding element and the shaft.Modelling also enabled to assess the material vibrationmodes and the distribution of the maximum and minimumvibration step of the bar. This can be used to avoid designerrors and avoid mishandling of the material deformation,which can produce a jerking effect that affects the degree of accuracy of the motor. Consequently, it could restrict the potential applications for the motor.The model-vibration modes for different input signalwere determined. Figures 5 and 6 show two modes of  vibration (transverse bending mode (1) and longitudinalextension mode (2)) at the drawn operating frequency, for motor. 4 Mechanism and design of the motor 4.1 Mechanism of the developed motor The developed motor was designed using standing wavevibrations, which has a fixed wave length. The concept is toutilise two oscillation modes to obtain desired motion of the piezo - electric element longitudinal and transverse (bending)vibrations. One vibration produces a normal force, whilst theother vibration generates thrust force, which is perpendicular to the normal force, resulting in an elliptical trajectory of theelement edge by attaching the piezo - electric ceramic plateedge to a driving wheel using a coil spring. The ellipticaltrajectory was converted into a rotary motion as shown inFig. 3. As the combination of two modes of vibrationscreated a friction-based driving force between the stator andthe rotor at the contact edge, a movement in forward or  backward direction was created depending on the method-ology used to excite the piezo - electric ceramic bar and togenerate two modes of vibrations. The linear motion wasdeveloped using the friction based driving force between theshaft and the sliding element as shown in Fig. 1.4.2 Design of the motor component The design and dimensions of stator for the proposed motor were based on the ratio of frequency of the longitudinalmode  f   L  and bending mode  f   B ,  f   L /   f   B =2.0 and  d/l  =0.1 because internal non-linear coupling of parametric vibration Fig. 4  The amplitude (displace-ment) variation against excitingfrequency for the developed piezo - electric USM (AC 50 V)290 Int J Adv Manuf Technol (2009) 45:287  –  299   between two resonance modes was generated under thesecondition [6]. The capacitance ratio and direction of vibratory displacement were also considered.Using the model shown in Fig. 7a and the relation betweenthe torque  T   and various acting forces on the rotor components gives: T   ¼  F  R   D 2  ¼  F  r  d  2  ð 1 Þ where  F  R   is the elliptical force produced using piezo - electricvibrating bar,  F  rs  is the driving force transferred to the shaft using torque factor   A r   ¼  Dd  ,  D  is the diameter of the drivingwheel and  d   is the shaft diameter.The torque factor of the motor and the diameter of therotor, including driving wheel and the shaft, were obtained.The transferred force to the shaft was determined using thetorque factor relation:  F  r   ¼  F  R   Dd   ð 2 Þ This relation also shows that the torque factor   A r   has to be carefully considered during the design process of themotor since it influences the efficiency of the driving force produced by the piezo - electric vibrating bar, the resolutionof the motor and maximum travelling speed.The length of the shaft   l  s  was determined according to theallowable ratio of the  l  s = d  s , where  d  s  is the shat diameter of the shaft. This is to meet the conceptual view of the designfor the proposed construction. This considered the propertiesof the material used to produce the shaft and the moment of inertia of the rotor. The moment of inertia of the rotor wasconsidered to be small for fast dynamic response and toobtain a maximum efficiency of the transferred driving force.The pre-load force acting in the shaft and locations of  bearings of the sliding element was determined using thedynamic model shown in Fig. 7c. X  F   x  ¼  0 : 0  F  sb  ¼  F  sh  þ  F   b  ð 3 Þ Where  F  sb ,  F   b  and  F  sh  are the side spring slider, bearing andshaft acting forces, respectively. From the model shown inFig. 7c, the bearing acting force  F   b  was obtained from therelation:  F  sb  X   ¼  F   b l  sl  ð 4 Þ Consequently, the bearing acting force was found to be:  F   b  ¼  F  sb  X l  sl ð 5 Þ Substituting  F   b  into slider acting force:  F  sb  ¼  F  sb  X l  sl þ  F  sh  ð 6 Þ Then,theshaftactingforcewasdeterminedusingtherelation:  F  sh  ¼  F  sb ð 1    X l  sl Þ ð 7 Þ Fig. 5  Motor model deformedshape at determined operating parameters (transverse bendingvibration mode)Int J Adv Manuf Technol (2009) 45:287  –  299 291
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