基于ANSYS8.0的永磁直線電機的有限元分析及計算

基于ANSYS8.0的永磁直線電機的有限元分析及計算,基于,ansys8,永磁,直線,電機,機電,有限元分析,計算 Development of a Novel Direct-Drive Tubular Linear Brushless Permanent-Magnet Motor 279 Development of a Novel Direct-Drive Tubular Linear Brushless Permanent-Magnet Motor Won-jong Kim and Bryan C. Murphy Abstract: This paper presents a novel design for a tubular linear brushless permanent-magnet motor. In this design, the magnets in the moving part are oriented in an NS-NS—SN-SN fashion which leads to higher magnetic force near the like-pole region. An analytical methodology to calculate the motor force and to size the actuator was developed. The linear motor is operated in conjunction with a position sensor, three power amplifiers, and a controller to form a complete solution for controlled precision actuation. Real-time digital controllers enhanced the dynamic performance of the motor, and gain scheduling reduced the effects of a nonlinear dead band. In its current state, the motor has a rise time of 30 ms, a settling time of 60 ms, and 25% overshoot to a 5-mm step command. The motor has a maximum speed of 1.5 m/s and acceleration up to 10 g. It has a 10-cm travel range and 26-N maximum pull-out force. The compact size of the motor suggests it could be used in robotic applications requiring moderate force and precision, such as robotic-gripper positioning or actuation. The moving part of the motor can extend significantly beyond its fixed support base. This reaching ability makes it useful in applications requiring a small, direct-drive actuator, which is required to extend into a spatially constrained environment. Keywords: Direct-drive DC motor, linear actuator, permanent-magnet motor, real-time digital control, tubular motor. 1. INTRODUCTON The objective of the work described in this paper is to develop a novel linear actuator capable of fast, smooth, precise positioning with a 10-cm actuation range. The direct-drive tubular linear brushless permanent-magnet motor (LBPMM) shown in Fig. 1 has a slotless stator to provide smooth translation without cogging. This design choice sacrifices the higher force capabilities that would be possible with iron slots in the stator in favor of smooth actuation. Applications for this type of actuator include precision positioning and robotic actuation needs. Linear actuators are used in robot end-effectors such as dexterous hands [1] and as the final link in multi-link robotic arms. Budig discusses many types of applications for which linear motors are appropriate [2]. Some linear actuators are comprised of hydraulic or pneumatic rams, which are good for non-precision applications requiring high force. Others use an electric rotary motor with a lead screw or other linkage to convert rotary motion to linear translation, which has serious complications including backlash and increased mass of the moving part due to connecting linkages or gears. Hence, the LBPMM, which is comprised of permanent magnets and current-carrying coils, is especially suited for precision positioning applications. There have been many contributions in the field of LBPMM’s and other direct-drive systems, in which the load is propelled directly by the motor. LBPMM’s __________ Manuscript received April 1, 2004; accepted June 9, 2004. Recommended by Editor Keum-Shik Hong. Won-jong Kim is with the Department of Mechanical Engineering, Texas A&M University, 3123 TAMU, College Station, Texas 77843-3123 USA (e-mail: wjkim@mengr.tamu. edu). Bryan Murphy is with The Boeing Company, International Space Station, Loads, Dynamics, and Mechanisms division, 13100 Space Center Blvd, Houston, TX 77059 USA (e-mail: Bryan.C.Murphy@boeing.com) Fig. 1. Assembled tubular linear motor mounted on aprecision optical table shown with brass tubeconnected to the LVDT at right. Thepermanent magnets are within the brass tube.The amplifiers can be seen in the back. International Journal of Control, Automation, and Systems, vol. 2, no. 3, pp. 279-288, September 2004 280 Won-jong Kim and Bryan C. Murphy are commonly used in single- and multi-degree-of-freedom precision positioning applications. Lequesne investigated a number of performance criteria for permanent-magnet linear motor designs with translation range from 5 to 20 mm [3]. Kim and Trumper, et. al demonstrated that a six-degree-of-freedom planar LBPMM could be used for precision nanopositioning [4,5]. This setup consists of current-carrying coils contained within a stationary base beneath a platen comprised of matrices of permanent magnets. When energized, the coils levitate the platen and allow significant translation and rotation in the plane of the base plate. Berhan, et al. discussed the use of a Halbach magnet array [6] in a novel ironless tubular LBPMM [7,8]. The Halbach array is implemented in the form of axisymmetric octagonally-oriented rectangular permanent magnets, which approximate a cylindrical Halbach array. The primary differences between the cited motor and the proposed design is that the proposed motor has a simpler mover made up of cylindrical permanent magnets, is more compact in size, and is much easier in construction. Ishiyama, et al. designed a tubular LBPMM that can be used to drive a carriage in an image reading device and other applications [9]. This design entails an array of hollow radially-magnetized permanent magnets, with the poles of each magnet aligned with the attractive poles of the adjacent magnets. This configuration is repeated to produce a relatively long tubular array of magnets, which constitutes the fixed part of the motor. The primary differences between this design and the design proposed herein are the magnetization direction of the magnets and the configuration of the motor. The cited design also embodies a fixed array of magnets, with the outer coils as the moving part. This is substantially different from the motor discussed in this paper, as in the latter the tube, which encompasses the permanent magnets, is free to extend out well beyond the support of the base. Zhu, et al. constructed a tubular LBPMM and discussed cogging minimization [10]. In this design multiple motor topologies are discussed. Radially-magnetized magnets similar to those in [9] and axially-magnetized magnets as in the authors’ design were both proposed as options for the embodiment. This design uses an iron core in the stator, which instigates cogging forces into the system. The primary performance goal discussed in [10] is to maximize the force-per-current and force-per-volume ratios. In the proposed design herein, while output force is of appreciable concern, the primary desire is for precise positioning. Liaw, et al. developed an LBPMM with robust position control [11]. Shieh and Tung designed a controller for an LBPMM used in a manufacturing system [12]. Brückl discussed the use of a linear motor for ultra-precision machine tools [13], which is also a possible application for our design. Basak and Shirkoohi used a software package to compute the magnetic field in DC brushless linear motors with NdFeB magnets [14]. Lee demonstrated a cylindrical linear motor design using toothed sections which makes assembly easier and prevents overheating [15]. Trumper, et al. discussed electromagnetic arrays capable of generating field patterns in two and three dimensions by varying current density in the winding [16]. Ishiyama presented a stator design for a cylindrical linear motor in which opposing faces of ring shaped permanent magnets are adjacent and positioned close to each other using a tightening mechanism [17]. Akmese, et al. described computer-aided analysis of machine parameters and the magnetic cogging force using finite element techniques [18]. Eastham, et al. discussed the optimum design of brushless tubular linear machines [19]. The concepts given in the aforementioned papers, particularly those discussed in [7-10], incorporate qualities similar to the design proposed here, but with significant differences. The proposed design allows for compact actuation of a slender cylindrical tube, which is free to extend beyond the support base. As the design is ironless and slotless, there is no cogging, which allows smooth translation. The downside of this ironless design is that there is no iron yoke to concentrate the magnetic field, so the efficiency suffers. The compact design of the motor makes it applicable to space-constrained robotics applications. The potential resolution of the system lends itself to applications in precision positioning. In the following sections, a presentation of the electromechanical design is given with the governing equations and motor sizing discussed. Next, the design of controllers for particular motion requirements is presented, as well as the steps taken to optimize the controllers for two specific robotic-actuation needs. Several experimental results are given illustrating the system response to various inputs, some including externally applied loads. The maximum force for which the motor is capable is also determined. This work is also discussed in detail in [20]. 2. ELECTRO-MECHANICAL DESIGN 2.1. Design concept Fig. 2 represents the conceptual configuration without particular dimensions assigned to the magnets and coils. Cylindrical permanent magnets are placed in an NS-NS—SN-SN fashion with spacers between pairs. The magnet pitch is required to match the coil pitch, and arranging magnets (which were conveniently available) together in pairs allowed the magnet Development of a Novel Direct-Drive Tubular Linear Brushless Permanent-Magnet Motor 281 zdpwhcZRxyρ BCA' B'C' ABCz, z'θ' coil polycarbonate spacer aluminum spacer magnetMOVER o' r θ o r' STATOR 3 2 5 7 4 6 1 8 Fig. 2. Section view of coils and magnets with brass tube hidden. Coordinates are given for the mover frame (primed frame) as well as the stator frame (unprimed frame) that is stationary in space. Fig. 3. Parameters between permanent magnet (left) and current-carrying coil (upper right). The coil is represented with a rectangular cross-section. pitch to match the coil pitch. The magnets are fixed within a freely sliding brass tube which constitutes the mover. Electromagnetic coils are configured in three phases labeled A, B, and C. Each coil has one lead from the outermost turn and one from the innermost turn. The coils are arranged in sequence such that every third coil is in the same phase. The coils constitute the stator, and the mover is placed within the stator. As the coils are powered, they exert a force upon the permanent magnets according to the Lorentz force equation, which causes translation of the mover. The length (along the z-axis) of the magnets is set to be equal to that of the coils. Therefore the required design parameters are the length of the magnets/coils, the outer radius of the magnet and the inner radius of the coil (this pair determines the air gap between them), and the outer radius of the coil. The magnet array is fixed within a brass tube, space for which must be accommodated in the air gap between the magnet and coil arrays. 2.2. Motor force calculation and sizing To determine the particular values for the design parameters, some quantified desired performance criteria must be established. In this case, the conceptual design guarantees the smooth translation requirement, as there are no iron slots, which would introduce cogging. The remaining performance parameter of interest is the maximum output force. The Lorentz force equation, f = ∫ (J × B) dV governs the interaction of the coil current and permanent magnet. The output force is the volumetric integral of the cross product of the current density in the coil with the magnetic flux density generated by the permanent magnet over the whole coil volume. The force of primary interest is the interaction of a single magnet with a single coil current. Upon further expansion and simplifications due to symmetry, the Lorentz force equation becomes (1). Some geometric parameters are given in Fig. 3. A thorough derivation is given in [20], in which material from [21,22] was quite helpful. The coil inductance and resistance are 0.500 mH and 0.552 ?, respectively, per coil. A maximum current of 3 A flow through each coil. The magnets chosen for evaluation were cylindrical neodymium iron boron (NdFeB) magnets. Their maximum energy product (BHmax) is 0.4 MJ/m3(50 MGOe). The magnets chosen are 10.0-mm (0.395”) in diameter, 2222022 200022222 200()4( / 2) 2 cos( )...(/2) 2cos()hwZcRzwhcZRJM df dddrzd r rd d r d dz drzd r rπππμ ρθ ρπρρθφρθρ φρρθφ++??????=??????++? ??????+++? ??∫∫∫ ∫∫∫∫(1)282 Won-jong Kim and Bryan C. Murphy 9.53-mm (0.375”) long, and have a minimum remanence of 1.20 T. To allow adequate space for the 11.1-mm (7/16”) O.D. (outer diameter) brass tube to house the magnets and slide freely without contact within the coils, the I.D. (inner diameter) of the coils was chosen to be 12.2 mm, with an O.D. of 33.2 mm. The length (in the z-direction) was selected to be 9.53 mm to match that of the magnets. Using AWG #21 wire, 179 turns of wire fit within the design envelope. Based on these dimensions, the force per current between a single magnet and single coil as a function of relative displacement (Z) can be determined using (1). MathCAD was used to solve for this force per current for numerous values of Z. These results are illustrated in Fig. 4. The points given in the figure are from iterations solved in MathCAD. The lines connecting the points into a continuous line are from linear interpolation between these points. 2.3. Mechanical design The stator consists of nine coils (three per each phase), corresponding to 1? pitches. To provide the desired travel range of 10-cm, several pitches of magnets are included, so that there are always magnets within appreciable force range on both sides (axially) of each coil. Aluminum spacers were used between pairs of magnets so that the magnets could be glued together. The magnets and spacers were glued in place by coating PC-7 epoxy on the outer surfaces. The magnet pitch consisting of four magnets with two spacers is 63.3 mm. A brass tube was chosen to house the magnets and spacers. The tube has an 11.1-mm (7/16”) O.D., wall thickness of 0.356 mm (0.014”) and is 305 mm (12.0”) in length. The magnets and spacers are positioned in the brass tube in an NS-NS—SN-SN orientation. The magnets within the brass tube will translate through the nine-coil assembly, as shown in Fig. 2. Nylon bearings which support the brass tube are held in Delrin housings fixed to both ends of the stator. When gluing the coils together face-to-face, 0.787-mm-thick multi-layer polycarbonate spacers were used to leave a gap between coils for the lead wire from the innermost coil winding to run along the face of the coil to the outside of the coils. A notch was cut from the inner diameter to the outer diameter of each of the spacers to leave room for the lead wire. The spacers were trimmed so that the inner diameter of the spacers was larger than that of the coils and so that the outer diameter of the spacers was smaller than that of the coils. This allowed the brass tube to slide freely through the coils, and also left room for the wire leads on the outside of the coils to be wrapped around to the appropriate location. The effective thickness of the added polycarbonate spacer (including the glue line on both faces) was 1.03 mm. Thus, the stator pitch consisting of six coils with six spacers is 63.3 mm, the same as the magnet pitch. 2.4. Commutation In order to provide balanced three-phase current to the motor, a commutation equation relating force and current based on position was required. For convenience, the coordinate convention designated in Fig. 2 was chosen to correlate with that defined in [8] so that the commutation equation would be applicable without significant modification. The commutation equation from said paper is given in (2), where C replaces a quotient of geometric parameters. 101020cos13 .sin13AB zdCiziC fziγγ??????????=???????????????(2) The variables iA, iB, and iCcorrespond to the three-phase currents applied to the coils. The parameter γ1is the magnitude of the spatial wave number of the first harmonic, γ1= |2π/l|, where l is the pitch of the motor (63.3 mm). The relative lateral displacement of the mover with respect to the stator is denoted z0, and fzdis the desired axial thrust. Equation (2) provides three equations for only one unknown, C, as the currents are given, and the displacement and force can be readily determined. To find an appropriate value for C, analytical and experimental procedures were executed. In each instance, balanced three-phase currents and a displacement (z0) were fixed. Upon statistical investigation of the data for C, the median value was selected. Once C is determined, the controller output can be converted to the three desired output currents as follows. The output from the controller is force, which is multiplied by the geometric quotient C and the appropriate sinusoidal displacement dependency as in (2). The maximum swing of the current to the coils is ±3 A, proportional to the output voltage from the controller board. Hence the transconductance Fig. 4. Theoretical force per current as a function ofrelative displacement for one magnet with onecoil. -0.70-0.60-0.50-0.40-0.30-0.20-0.100.000 0.005 0.01 0.015 0.02 0.025 0.03 0.035Relative Displacement (m)Force/Current(N/A)Numerically Determined Data PointsLinearly Interpolated PointsDevelopment of a Novel Direct-Drive Tubular Linear Brushless Permanent-Magnet Motor 283 Table 1. Analytical force output. Coil in Phase A Coil in Phase B Coil in Phase CMagnet Distance Force/ Current Distance Force/ Current DistanceForce/Current(mm) (N/A) (mm) (N/A) (mm) (N/A)1 -36.55 0.00 -26.00 -0.05 -15.45 -0.232 -27.03 -0.05 -16.48 -0.20 -5.93 -0.583 -4.90 -0.53 5.65 -0.57 16.20 -0.204 4.63 -0.52 15.18 -0.24 25.73 -0.065 26.75 -0.05 37.30 0.00 47.85 0.006 48.85 0.00 59.40 0.00 69.95 0.00Force/Current (N/A) -1.16 -1.06 -1.07Multiplied by 3 Coils -3.47 -3.17 -3.21Current to Coils (A) -3.00 -3.00 -3.00Force per Phase (N) 10.40 9.51 9.62Total Force (N) 29.60 amplifier gain is 0.333 A/V. To analytically determine the force capabilities of the motor, the individual contributions for each magnet-coil interaction must be summed. Since the pitch of the coils matches the pitch of the magnets, the force contribution from each coil in a single phase is identical. Thus the force per current for each phase is multiplied by three, as there are three coils in each phase. From Fig. 4, it is clear that for magnets beyond 30 mm, the force contribution is negligible, so only the six closest magnets to each coil are taken into consideration. Table 1 enumerates the force contributions between the six nearest magnets and a single coil in each phase. The magnet number corresponds to the magnets as labeled in Fig. 2. The force per current is summed for each representative coil, then multiplied by three because there are three coils in each phase. This force-per-current value for each phase is multiplied by the current sent through that phase to find the force output. The total force is found by adding the force outputs from each phase. Table 1 represents the position and current condition for maximum force output, which relaxes the balanced three-phase condition. The maximum force is determined to be 29.6 N. With the balanced three-phase condition in place, the maximum force is 19.4 N. 2.5. Experimental setup and instrumentation The experimental setup is depicted in Fig. 5. The linear variable differential transformer (LVDT) is connected to the mover of the motor through a threaded rod. The LVDT outputs the analog position signal to the conditioning circuit, which shifts and filters it, then sends it to an analog-to-digital (A/D) channel of the DS1104 controller board. The controller board processes the position signal, and outputs appropriate control signals to the