永磁电机转矩常数的深度
永磁电机转矩常数深度分析
Abstract —The torque con stan t, together with the back-EMF co n sta n t, was origi n ally used i n perma n e n t mag n et DC commutator motors (PMDC motors) to couple the electric circuit equation s with mechan ical equation s. But it is still an open question whether the con cept of the torque con stan t an d the back-EMF con stan t can be applied to brushless DC (BLDC) motors an d perman en t magn et (PM) AC machin es. This paper presen ts an in -depth study of the two con stan ts un der various real conditions in PM machines. The torque constant at various load con dition s is computed usin g tran sien t 2D fin ite elemen t an alysis (FEA). It is shown that the torque con stan t is n ot a constant for BLDC motors and PM AC machines.Index Terms —Back-EMF constant, brushless DC motors, DC commutator machi n es, fi n ite eleme n t a n alysis, perma n e n t magnets, synchronous machines, torque constant.I. I NTRODUCTIONHE torque constant is defined as the ratio of the torquedelivered by a motor to the current supplied to it, and the back-EMF constant is the ratio of voltage generated in the winding to the speed of the rotor. In PMDC motors, they are almost constant at various load conditions. The torque constant and back-EMF constant couple the electric circuit equations with mechanical equations, and are widely used in motor control.It is of great interest to see whether the concept of the torque constant and the back-EMF constant can be applied to BLDC motors and PM AC motors. Some effort have been made in this regard [1][2]. Reference [2] indicates that an ideal BLDC motor (also called a square-wave motor), under the condition that the line-to-line back EMF waveform is trapezoidal and that the winding current waveform is ideally square, is electrically identical to a PMDC motor. The author also applies the concept of the torque constant and the back-EMF constant to sine-wave PM AC motors under the assumption that the internal power-factor angle between the back EMF and the current is fixed to zero.However, in real cases, the winding current waveform is far from the ideal square-wave in BLDC motors due to current freewheeling. And, in PM synchronous motors, the internal power-factor angle is normally not zero because the torque angle is automatically adjusted according to the changeThe authors are with Ansoft Corporation, Pittsburgh, PA 15219 USA(phone: 412-261-3200; e-mail: dlin@, ping@,zol@). in load. To this end, this paper presents an in-depth study of the torque constant and the back-EMF constant for BLDC motors and PM AC motors. The suitability of the use of the two constants in PM motors is discussed considering the following: current freewheeling, arbitrary back-EMF waveforms, salient pole, variable pulse width and trigger angle, and internal power factor angle.II. R EVIEW OF THE T ORQUE C ONSTANT IN PMDC M OTORS In PMDC motors, the electric circuit equation isb a s V I R E V ++=(1)where V s is the applied DC voltage source, E is the back EMF, V bis the voltage drop of one-pair brushes, I is the input DCcurrent, and R a is the armature resistance. Equation (1) can be coupled with load mechanical equations by introducing⎩⎨⎧==I k T k E T mmE ω (2)where ωm is the angular velocity in mechanical rad/s, T m is theelectromagnetic (air-gap) torque in Nm, k E is the back-EMF constant in Vs/rad, and k T is the torque constant in Nm/A. The torque constant and the back-EMF constant have the following properties:i. k T = k E in the metric unit system; ii. k T and k E are constant; iii. k T and k E are measurable.Property (i) is obvious from the fact that the electric power (EI ) is equal to the mechanical power (T m ωm ) during power conversion.Property (ii) follows since: (1) PMDC motors have large air gaps due to surface mounted magnets, thus the saturation change caused by the armature reaction is negligible; (2) the brush position is mechanically fixed during operation even if it is adjustable; (3) the current in each coil completes commutating within the angle of the brush width, and the commutating duration is independent of the rotor speed; and (4) there is no reluctance torque even if the armature reaction is not aligned with the q-axis.Based on property (ii), the back-EMF constant k E can be measured at no-load condition operating in generator mode. The torque constant k T can be obtained directly from k E , orcan be measured at load operation. It is straightforward to predict the performance of PMDC motors from (1) and (2) in motor control. In-Depth Study of the Torque Constant forPermanent Magnet MachinesD. Lin, P. Zhou and Z. J. CendesT©2008 IEEE.III. T ORQUE C ONSTANT IN BLDC M OTORSEven though the torque constant and the back-EMF constant in BLDC motors are defined in the same way as those in PMDC motors as shown in (2), there are some essential differences regarding the torque constant and the back-EMF constant between BLDC motors and PMDC motors. For the sake of easy discussion, take a Y-connected three phase winding with bridge-type inverter as an example, as shown in Fig. 1. The trigger pulse width for each branch is 120 electrical degrees in turn and the inverter has 6 repeatableoperating states with the state period of 60 electrical degrees.Fig. 1. Y-connected three-phase windings with the bridge-type inverterA . Voltage equation (1) is no longer applicable The voltage equation (1) is no longer applicable in BLDCmotors due to the inductance voltage drop. In PMDC motors, the inductance induced voltage caused by the current commutating will not contribute to the voltage drop across the brush terminals. However, in BLDC motors, the inductance voltage drop becomes comparable with the resistance voltage drop.B. k T and k E are no longer constantIn BLDC motors, E used in (2) is the average back EMF across the DC link, and its value will vary with the current freewheeling duration. In Fig. 1, assume at the previous operating state, the source voltage V s is applied to winding terminals AC via branches 1 and 2, and at the current operating state, V s is applied to winding terminals BC viabranches 3 and 2. When branch 1 is off, the phase-A currentfreewheels through branch 4, which makes winding A to connect in parallel with winding C. If the voltage drop acrossthe conducting transistor in branch 2 is the same as that acrossthe freewheeling diode in branch 4, the average back EMFduring the current operating state is])(21[10∫∫++=sf f T T BC T BC BA s dt e dt e e T E(3) where, e BC and e BA are instantaneous line-to-line inducedvoltages, T s is the state period in second (corresponding to 60electric degrees), and T f is the current freewheeling duration,as shown in Fig. 2. It is obvious from (3) that the average backEMF varies with the current freewheeling duration, andtherefore k Eis not constant for various operations.Fig. 2. Rectified back EMF from trapezoidal line-to-line induced voltagesFor the circuit of Fig. 1, as long as T f < T s , the freewheeling currents always reduce the input DC current and increase the delivered torque, and therefore, k T varies with the current freewheeling duration which in turn varies with the rotor speed.Another case in which k T is not constant is, in interior permanent magnet (IPM) motors, the reluctance torque component also contributes to the air-gap torque due to the salient-pole effects, and the reluctance torque component is not linearly proportional to the DC current. Furthermore, the trigger angle and the pulse width of the controlling signals in BLDC motors are usually controllable. This is also a casewhere k T is not constant.Fig. 3 shows the variation of k T with the speed of a typical surface mounted BLDC motor with fixed trigger angle andpulse width.Fig. 3. Variation of k T with the rotor speed C . k T is no longer equal to k EIn BLDC motors, the back EMF across DC link normally includes ripples associated with arbitrary line-to-line back-EMF waveforms. The ripples become considerable due to thecurrent freewheeling even though the line-to-line induced voltage may have a flat waveform in 60 electric degrees by aspecial design (see the solid lines inside T s in Fig. 2). Theinput current also contains significant ripples because thefreewheeling current is in nature of “generator” current. Byexamining the power conversion, one gets∫⋅⋅=s T s m m dt i e T T 01ω(4)∫⋅∆⋅∆+=sT sdt i e T EI 01where, ∆e and ∆i are the ripples of the DC back EMF and theinput current, respectively. From (4), one concludes that atload conditions k T ≠ k E because T m ωm ≠ EI .D . kE is no longer measurable By measuring the air-gap torque (which is obtained from the load torque and the mechanical loss) and the DC component of the input current at load operation, k T can be determined. However, k E is no longer measurable at load conditions for BLDC motors. It cannot be measured by driving the motor as a generator and rectifying the line voltage with a rectifier as described in [2] because k E at load conditions is different from that at the no-load condition. Also it cannot directly be obtained from k T because k E ≠ k T at load conditions.IV. T ORQUE C ONSTANT IN PM AC M OTORSThe torque constant in PM AC motors can be defined as the ratio of the torque to the peak value of the input AC phasecurrents I peak , and the back-EMF constant is the ratio of thepeak value of the induced phase voltages E peak to the speed of the rotor, as expressed below [2] ⎩⎨⎧==peakT m mE peak I k T k E ω. (5) Most PM AC motors operate as synchronous motors. In PM synchronous motors, the internal power factor angle ϕ i , the angle between the back EMF phasor and the current phasor, is automatically adjusted based on the mechanical load and is normally not zero. In these cases, the delivered mechanical power is E peak peak T m m k E I k T /⋅=ωi rms rms i E T E mI mk k ϕϕcos cos 2⋅= (6) where I rms and E rms denote RMS values of sine-wave phasecurrent and back EMF, and m is the number of phases. For thepower conversion, the mechanical power must be equal to theelectric power, that ism m T ωi rms rms E mI ϕcos =. (7) As a resulti E T k mk ϕcos 2=. (8)One concludes from (8) that k T is not constant for PM synchronous motors even though K E may be constant when the saturation effects can be ignored. It varies with the internal power angle which in turn varies with the mechanical load.Equation (8) is derived under the assumption that the spatial harmonics of the air-gap magnetic fields produced bythe permanent magnets and the phase currents are ignored. Inorder to show the effects of the spatial field harmonics on thetorque constant, a three-phase 4-pole PM synchronousmachine, as show as in Fig. 4, is analyzed using 2D transientfinite element method (FEM). To focus on observing thevariation of the torque constant with the internal power factorangle, the change in saturation caused by armature currents isignored, and thus linear materials are used for all components.Fig. 4. The one-pole geometry layout of the three-phase 4-pole PM synchronousmachine Three-phase windings are applied with DC currents as follows⎪⎩⎪⎨⎧−=−==IAm I IAm I IAmI CB A *5.0*5.0 (9) where IAm is set to be 0 and 1A via parametric analysis. Therotor speed is set to be 1500rpm, and the rotor initial position is set to such a position that the phase-A winding has positive maximum induced voltage at time = 0. The computed torques at IAm = 0 and 1A are shown in Fig. 5. It can be seen from Fig. 5 that the torque at IAm = 1A consists of two components: one is the component producedby the phase currents, and the other is the cogging torque component which is produced by the permanent magnets at 0phase currents. Because linear materials are used, the torque component produced by the phase currents can be directlyderived from the result of the torque at IAm = 1A minus thetorque at IAm = 0, as shown in Fig. 6. By definition, the curvein Fig. 6 shows the torque constant because the torque isproduced by unit phase currents. One notes that the torqueconstant is not a constant as had been anticipated and istherefore not suitable for use with PM AC machines.Fig. 5. Torques at different phase currents varying with the internal power factor angle ϕ i (time=20ms corresponds to ϕ i =360 electric degrees)Fig. 6. Torque produced by unit phase current varying with the internal power factor angle ϕ i (time=20ms corresponds to ϕ i =360 electric degrees)V. C ONCLUSIONThe torque constant and the back-EMF constant which were originally used in PMDC motors are generally not suitable for BLDC motors and PM synchronous motor analysis. Detailed computations of both constants with real motors reveal that they are no longer constant but, instead, vary significantly with load conditions.R EFERENCES[1]Electro-Craft Handbook, Fifth Edition, August 1980, ISBN 0-960-1914-0-2.[2]J.R. Hendershot Jr, and T. J. E. Miller, Design of Brushless PermanentMagnet Motors, Magna Physics Publishing and Clarendon Press, Oxford, 1994.Din gshen g Lin received his B.S. and M.S. degrees in Electrical Engineering from Shanghai University, Shanghai, China, in 1982 and 1987, respectively. He is currently a Senior Research and Development Engineer at Ansoft Corporation, Pittsburgh, PA. Before he joined Ansoft in 1999, he was an Associate Professor of electrical engineering at Shanghai University. His research interests include design and optimization techniques of electrical machines and electromagnetic field computation. He received the third prize of the Chinese National Award of Science and Technology, in 1987, and two second prizes of the Shanghai City Award of Science and Technology, in 1986 and 1989.Ping Zhou received his M.S. degree from Shanghai University, China in 1987 and his Ph.D. degree from Memorial University of Newfoundland, Canada in 1994. He was with Shanghai University as a lecturer after his undergraduate study in the same university in 1977. He was a Visiting Scholar of Memory University of Newfoundland from 1989 to 1991. Since 1994, he jointed Ansoft Corporation in the R&D department. Currently, he is the manager of Electromechanical R&D group at Ansoft. His research interests include finite element numerical field computation, circuit coupling, multi-physics coupling and electrical machine modeling.Zoltan Cendes is Founder and Chairman of Ansoft Corporation, Pittsburgh, PA, and is an Adjunct Professor at Carnegie Mellon University, Pittsburgh, PA. In addition to his role at Ansoft, Dr. Cendes has served as a Professor of Electrical and Computer Engineering at Carnegie Mellon University, as an Associate Professor of Electrical Engineering at McGill University, Montreal, Canada, and as an Engineer with the Corporate Research and Development Center of the General Electric Company in Schenectady, NY. Dr. Cendes received his M.S. and Ph.D. degrees in Electrical Engineering from McGill University and his B.S.E. degree from the University of Michigan.。
电机转矩系数
电机转矩系数1. 介绍电机转矩系数是描述电机性能的重要参数之一。
它反映了电机在给定工作条件下产生的转矩大小与输入电流之间的关系。
电机转矩系数越大，表示电机的输出转矩相对较大，具有较好的负载能力和动力性能。
在工业和家用电器领域，电机转矩系数的优劣直接影响到设备的效率和稳定性。
2. 电机转矩系数的计算电机转矩系数可以通过以下公式计算：K t=T I其中，Kt表示电机转矩系数，T表示电机的输出转矩，I表示输入电流。
根据这个公式，我们可以看出电机转矩系数是通过将电机的输出转矩除以输入电流来得到的。
3. 影响电机转矩系数的因素电机转矩系数受到多种因素的影响，主要包括以下几个方面：3.1 磁通磁通是电机转矩的产生者，磁通的大小与电机的磁场强度和磁路特性有关。
当电机的磁场强度增大或磁路特性改变时，磁通的大小也会随之改变，从而影响电机的转矩系数。
3.2 动态特性电机的动态特性包括惯性、动态响应能力等。
电机的惯性越大，转矩系数越小；反之，惯性越小，转矩系数越大。
此外，电机的动态响应能力也会影响转矩系数的大小，响应能力越强，转矩系数越大。
3.3 电流与电压电机的输入电流与电压也会对其转矩系数产生影响。
一般来说，输入电流越大，电机的转矩系数也越大。
而对于输入电压，如果电压过高或过低，都会对电机的转矩系数产生不利影响。
3.4 磁阻势能电机的磁阻势能是指电机通过改变磁场强度来改变转矩的能力。
磁阻势能越大，电机的转矩系数也越大。
4. 提高电机转矩系数的方法为了提高电机的转矩系数，可以采取以下几个方法：4.1 优化磁路设计通过优化电机的磁路设计，可以增加电机的磁通密度，从而提高转矩系数。
4.2 优化磁场控制通过优化电机的磁场控制方式，使得磁场强度更加均匀，从而提高转矩系数。
4.3 优化电机的结构通过优化电机的结构设计，可以减小电机的惯性，提高转矩系数。
4.4 提高电机的输入电流与电压通过增加电机的输入电流与电压，可以提高电机的转矩系数。
永磁电机齿槽转矩及其计算方法探究
永磁电机齿槽转矩及其计算方法探究随着环保意识和节能理念的普及，永磁电机作为一种高效、可靠、节能的电机，被广泛应用于工业和民用领域。
永磁电机不仅拥有优良的速度控制性能和负载响应性能，还能在补偿系统和传动系统中发挥非常重要的作用。
但是，在永磁电机的性能设计和有效应用中，齿槽转矩的计算是至关重要的。
一、永磁电机的齿槽转矩齿槽转矩是永磁电机的一种特殊转矩，是由于永磁体和锯齿型铁芯之间的相互作用所引起的。
在同步运行电机中，锯齿型铁芯中的齿槽产生磁场，而永磁体中的磁场被磁通链裹着，如果有些磁通链与锯齿型铁芯中的齿槽产生剪切，则会发生永磁体的转动。
这个现象就是齿槽转矩。
二、齿槽转矩计算方法1、永磁电机的齿槽转矩计算可以通过齿槽系数来实现。
齿槽系数是指永磁电机中锯齿型铁芯的齿槽数目与角度之比。
齿槽系数越大，齿槽转矩就越大。
可以通过调整永磁电机的齿槽系数提高转矩的质量和性能。
2、永磁电机的齿槽转矩还可以通过计算磁场分布来估算。
磁场分布是模拟器得到的理论计算值，可以提供永磁电机转矩的数值。
通常情况下，计算磁场分布需要使用有限元分析方法，因此需要使用各种软件进行计算。
3、另外一种方法是使用电机参数来计算永磁电机的齿槽转矩。
这种方式根据公式：T=K×Bp×Imax×A；其中，T是电机的齿槽转矩，K是系数，Bp是永磁体磁场密度，Imax是电机的电流峰值，A是永磁体和铁芯之间的面积。
这种方法可以快速计算永磁电机的齿槽转矩，但是需要知道有关永磁体参数和电路参数。
三、永磁电机齿槽转矩的影响因素1、永磁体的磁场强度和形状。
永磁体的磁场密度和形状对齿槽转矩的大小和效果有很大影响。
磁场强度越大，齿槽转矩越大。
2、永磁体和铁芯之间的面积。
面积越大，齿槽转矩越大。
3、电流峰值大小。
电流峰值越大，齿槽转矩越大。
四、结论永磁电机齿槽转矩的计算是永磁电机性能设计的一个重要步骤。
齿槽转矩的大小直接影响永磁电机的转矩质量和性能。
永磁交流伺服电动机转矩常数和反电势常数的规范化应用
永磁交流伺服电动机转矩常数和反电势常数的规范化应⽤摘要：本⽂分析了永磁交流伺服电动机在⾏业应⽤中，对转矩常数、反电势常数产⽣很多误解、混淆的原因，并给出了有效解决问题的办法。
同时，在应⽤过程中如何利⽤好这两个常数，也给出了探讨。
为便于⼯程师理解应⽤，对GB/T30549-2014中Kt=Ke的结论还给出了详细的演算过程。
另外，特别指出永磁交流伺服电动机机械转矩与电磁转矩的区别。
1.引⾔选好⽤好永磁交流伺服电动机的转矩常数和反电势常数（以下称两常数）对于装备制造业⽤户⾮常重要。
每⼀台永磁⽆刷电动机都具有双重⾝份，把驱动电流为⽅波的称为永磁⽆刷直流电动机（以下称BLDCM），但驱动电流为正弦波的则有⼏种叫法，在英美的⽂献中，把这类正弦波驱动的称为“永磁同步电动机(PMSM)”或者“⽆刷交流电动机(BLACM)”，在⽇本和欧洲则⼤多数情况下称为“交流伺服电动机(ACservo)”，国内基本上也多数采⽤ACservo的名称。
本⽂采⽤2014年版GB/T30549《永磁交流伺服电动机通⽤技术条件》（以下称GB/T30549-2014）的叫法—PermanentMagnetACServoMotor（以下简称ACServo）。
在采⽤国际单位制时，BLDCM的两常数是相等的(成⽴条件：续流回路的电流相对很⼩可以忽略时)，⽽在ACServo中有的倍数关系，但⽬前有的⼯程师还未重视这⼀区别，另外，不少ACServo公司的产品⼿册上经常出现两常数相互⽭盾的情况，导致⾏业应⽤的不少⿇烦。
为⽤户理解和应⽤好两常数起了⼀定警⽰作⽤，GB/T30549-2014对两常数的定义清晰规范，起到了积极的引导作⽤，但观察近两年国内的ACServo资料，两常数存在问题、⽭盾的还是不少，⽤户碰到这种情况则很困惑、迷茫。
在中国制造2025的⼤背景下，装备制造业（如⼯业机器⼈、加⼯中⼼、⾃动化⽣产线等）的ACServo应⽤越来越⼴泛，因此很有必要为ACServo 正确选型和应⽤进⼀步普及这⽅⾯的知识。
永磁电机转矩常数的深度
In Depth Study of the Torque Constant for Permanent-Magnet Machines
指導老師：黃昌圳 學生：陳育俊
摘要
介紹 PMDC馬達的轉矩常數回顧 BLDC馬達的轉矩常數 PM交流馬達的轉矩常數 轉矩常數的其他定義方式 結論
輸入電流因為也包含顯著的漣波。藉由功率轉 換的定理，可以得到
1 Tmm Ts
0
Ts
1 e i dt EI Ts
0
Ts
e i dt
(4)
Δe和Δi是直流反電動勢和輸入電流的漣波，相 對地，從由上式，得知因為Tmωm≠EI所以在負 載情況kT≠kE。
D. kE在負載下不再被精確測量
交流永磁馬達的轉矩常數被定義為轉矩與交流 輸入相電流Ipeak的峰值的比例，並且反電動勢 常數為感應相電壓Epeak與動子轉速的比例
E peak k E m T k I m T peak
(5)
大部分交流永磁馬達操作如同同步馬達。在永 磁同步馬達，內部的功率因素角ψi是反電動勢 相量和電流相量之夾角，從機械負載的觀點， 夾角會隨著負載自動被調整，因此一般不是零。 在這些情況，傳送的機械功率為
(13)
R1是相繞組電阻，Ld和Lq是在dq軸上的繞組同步 電感，p代表d/dt，並且 . eq -md -(nppmd) m (14)
λmd是由永磁轉換成d軸的繞組磁通交鏈，ωm是 rad/s的機械角速度，npp是馬達的極對數。 以N· m的轉矩為 Tm n pp (Lq - Ld )idiq - mdiq (15) 大部分的表面型永磁馬達 Lq=Ld，因此轉矩為
6000v永磁电机技术条件 12618
6000v永磁电机技术条件随着社会的不断发展，电气化水平逐渐提高，对电机技术的要求也随之增加。
作为一种全新的电机技术，6000v永磁电机技术已经受到广泛关注。
在这个背景下，本文将从技术条件的角度来探讨6000v永磁电机的相关问题。
一、电机技术条件的概念电机技术条件是指在特定电气系统中，电机在运行过程中所能满足的技术要求和标准。
对于6000v永磁电机技术条件来说，主要包括以下几个方面：1. 额定功率：6000v永磁电机在正常运行条件下所能提供的功率大小。
额定功率是评价电机性能的重要指标，也是用户选择电机的重要参考依据。
2. 额定转矩：6000v永磁电机在额定工况下所能输出的最大转矩。
转矩是电机输出功率的直接体现，对于某些需要高扭矩的应用场景来说，额定转矩是非常重要的。
3. 效率：6000v永磁电机在不同负载和转速下的能量利用率。
高效率是各种电机的追求目标之一，6000v永磁电机技术条件要求在不同工况下都能保持高效率。
4. 联接方式：6000v永磁电机的联接方式通常有直联、带脉冲联接和间接联接等。
不同的联接方式对电机的性能和安全都有一定影响，需要根据具体情况来选择。
5. 起动方式：6000v永磁电机的起动方式通常有直接起动、星角起动、软启动等。
不同的起动方式对电机的启动性能和对电网的影响也不同。
二、6000v永磁电机技术条件的必要性6000v永磁电机技术条件的制定和遵循对于电机的正常运行和用户的安全使用都是必要的，主要体现在以下几个方面：1. 保证电机的安全运行：电机在运行过程中需要正常输出功率和扭矩，遵循技术条件可以有效保证电机的安全运行。
2. 提高电机的利用率：6000v永磁电机技术条件的合理制定能够提高电机的利用率，降低能耗，减少生产成本。
3. 增强电机的稳定性：通过遵循技术条件，可以增强电机的运行稳定性，延长电机的使用寿命，减少维护成本。
4. 保障用户的安全：6000v永磁电机技术条件的遵循可以保障使用者的人身和财产安全，降低某些意外事故的发生几率。
永磁电机转矩常数的深度课件
電樞反應影響的飽和度變化可以被忽略 。
b)在運作時電刷位置被機械固定即使他可以被調整 。 c)在電刷寬度的角度內每個線圈的電流完成換相，並
且換流持續時間不受轉子速度的影響。
d)即使電樞阻抗並沒有排列在q軸，也沒有磁阻轉矩。
由特性3)的觀點，反電動勢kE可以在發電機模 式無載情況下被測量，轉矩常數kT可以直接從 kE獲得，或者從負載操作下獲得。
A. 固定電樞磁場旋轉轉子
三相繞組是用於直流由下表示
IIba
Im -0.5
Im
(9)
Ic -0.5 Im
Im經過參數分析設定為0和1A。轉子轉速設定 為1500rpm，轉子的起初位置設定在a相繞組在
t=0時有正的最大感應電壓的位置。
在Im為0和1A時，轉矩顯示下圖。
我們可以看到Im=1A的轉矩包括兩個成分： 其中一個成分由相電流產生，另一個頓轉轉矩
永磁电机转矩常数的深度
摘要
介紹 PMDC馬達的轉矩常數回顧 BLDC馬達的轉矩常數 PM交流馬達的轉矩常數 轉矩常數的其他定義方式 結論
介紹
Tm=kTI。
E=kEωm。 kT和kE 將電路方程式與機械方程式結合一起，
並且廣泛使用在馬達運動控制。 兩個常數使用在PM馬達必須討論以下：
馬達控制可以很簡單的從上面兩式預測永磁直
流馬達的特性。
BLDC馬達的轉矩常數
低速大扭矩永磁同步电机参数
低速大扭矩永磁同步电机参数
低速大扭矩永磁同步电机参数包括：
1. 额定功率：一般在几千瓦至数十千瓦之间。
2. 额定电压：电机的额定电压一般是直流电，其值一般在几百伏特至数千伏特之间。
3. 极数数目：这个参数决定了电机的运转速度，其值一般在6极至20极之间。
4. 最大转矩：也就是电机在额定负载下所能输出的最大转矩，它一般是额定扭矩的两倍至三倍。
5. 效率：电机的效率也是衡量其性能的一个重要指标。
一般来说，永磁同步电机的效率要比异步电机高。
6. 精度：电机的控制精度对于不同的应用场景是不同的，一般来说，低速大扭矩永磁同步电机的控制精度要比高速电机高。
7. 过载能力：由于低速大扭矩永磁同步电机往往需要应对复杂的工作环境和负载条件，因此其过载能力也是需要考虑的一个因素。
8. 数据接口：现在很多永磁同步电机都具备了数据通信接口，以便于工程师们使用这些数据进行更精细的控制及优化。
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• 下圖顯示表面型無刷直流馬達(固定不變的觸發 角和脈波寬度)隨著速度改變的kT。
C. kT再也不等於kE
• 在無刷直流馬達，跨於直流端的反電動勢一般 包含與任意線對線反電動勢波形相關的漣波。 即使線對線感應電壓可能藉由一個特殊的設計， 在60°電機角有一個平坦的波形，電流飛輪二 極體漣波仍需要被考慮。
• 輸入電流因為也包含顯著的漣波。藉由功率轉
換的T定m理m， 可T1s 以0T得s e 到i dt
• 一個3相4極的永磁同步電 機，如右圖所示，使用2D 暫態有限元素方法(FEM) 分析可以指出轉矩常數隨 著內部功率因素角度而改 變。為了觀察隨著內部功 率因素角度而改變的轉矩 常數，電樞電流造成的飽 和變化可以被忽略，如此 線性材料被使用於所有元 件。
A. 固定電樞磁場旋轉轉子
• 三相繞組是用於直IIba流由-I0m.下5表Im示
PM交流馬達的轉矩常數
• 交流永磁馬達的轉矩常數被定義為轉矩與交流
輸入相電流Ipeak的峰值的比例，並且反電動勢 常數為感應相電壓Epeak與動子轉速的比例
Epeak kEm
Tm
k T I peak
(5)
• 大部分交流永磁馬達操作如同同步馬達。在永 磁同步馬達，內部的功率因素角ψi是反電動勢 相量和電流相量之夾角，從機械負載的觀點，
6
2
4
6
ab ac bc ba ca cb
A. 電壓方程式再也不能應用
• 電壓方程式在無刷直流馬達因為自感壓降再也 不被應用。在永磁直流馬達，由電流換相造成 的自感感應電壓並非有助於電刷兩端的電壓降。 然而，在無刷直流馬達，自感壓降可以比擬成 電阻壓降。
B. kT和kE再也不是常數
• 在無刷直流馬達，E是跨於直流端的平均反電 動勢，他的值將會隨著電流飛輪二極體的導通 時間而改變。
• Irms 和Erms代表弦波相電流和反電動勢的根均方 值(rms)，m是相數。為了能量轉換，機械功率
一定等於電機功率，也就是說
Tmm mI rmsErmscos i (7)
其中
kT
m 2
kEcos i(8)kTm 2
kEcos i
• 由上式可以得到一個結論，即使當飽和效應
可以被忽略時，kE可能是常數。但是永磁同 步馬達的kT不是常數。kT隨著內部功率角而 改變，功率角隨著機械負載不同而改變。
永磁電機轉矩常數的深度討論
In Depth Study of the Torque Constant for Permanent-Magnet Machines
指導老師：黃昌圳 學生：陳育俊
摘要
• 介紹 • PMDC馬達的轉矩常數回顧 • BLDC馬達的轉矩常數 • PM交流馬達的轉矩常數 • 轉矩常數的其他定義方式 • 結論
EI 1 Ts
Ts e i dt
0
(4)
• Δe和Δi是直流反電動勢和輸入電流的漣波，相 對地，從由上式，得知因為Tmωm≠EI所以在負 載情況kT≠kE。
D. kE在負載下不再被精確測量
• 藉由測量氣隙轉矩和負載運轉下的輸入電流的 直流成分，kT可以被決定。然而，無刷直流馬 達的kE在負載下再也不精確地測量。因為kE在 負載情形不同於在無載情形，所以不能藉由驅 動一個馬達作為發電機並且使用整流器整流線 電壓。因為在負載情況下kT ≠ kE，所以kE不能 直接地從kT獲得。
• Vs是供應直流電壓源，E是反電動勢，Vb是一 對電刷的電壓降，I是輸入直流電流，並且Ra 是電樞電阻。
•
可以將機械方程式E 結k合E在m 一起。
Tm
kTI
(2)
• ωm是在rad/s的機械角速度，Tm是在N·m的電 磁(氣隙)轉矩，kE是在V·s/rad的反電動勢常數， kT是在N·m/A的轉矩常數。
介紹
• Tm=kTI。
• E=kEωm。 • kT和kE 將電路方程式與機械方程式結合一起，
並且廣泛使用在馬達運動控制。 • 兩個常數使用在PM馬達必須討論以下：
電流飛輪二極體、任意的反電動勢波形、凸極、 任意的脈波寬度和觸發角和內部功率因素角度。
PMDC馬達的轉矩常數回顧
• 在PMDC馬達，電路方程式為 (1) Vs=E+RaI+Vb
且換流持續時間不受轉子速度的影響。
d)即使電樞阻抗並沒有排列在q軸，也沒有磁阻轉矩。
• 由特性3)的觀點，反電動勢kE可以在發電機模 式無載情況下被測量，轉矩常數kT可以直接從 kE獲得，或者從負載操作下獲得。
• 馬達控制可以很簡單的從上面兩式預測永磁直
流馬達的特性。
BLDC馬達的轉矩常數
1
3
5
• kE和kT 有以下的特性： 1)在度量單位下， kE=kT 。 2) kE和kT 是常數。 3) kE和kT 可以測量。
• 特性1)可以從 EI= Tm ωm得證。
• 特性2)有以下四點： a)永磁直流馬達由於表面型磁石有高氣隙，因此，因
電樞反應影響的飽和度變化可以被忽略 。
b)在運作時電刷位置被機械固定即使他可以被調整 。 c)在電刷寬度的角度內每個線圈的電流完成換相，並
E 1
Ts
Tf 0
1 2
e
ba
ebc dt
Ts Tf
e
bc
dt
(3)
• 很明顯的知道平均反電動勢隨著電流飛輪二極
體導通時間而改變，因此kE在不同的操作並不 是定值。
• 只要Tf<Ts，飛輪二極體的電流總是會減少輸入 的直流和減少轉矩，因此kT隨著電流飛輪二極 體的導通時間而改變，導通時間隨著轉子速度 改變。
夾角會隨著負載自動被調整，因此一般不是零。
在這些情況，傳送的機械功率為
Tmm kTIpeak Epeak /kE
2k T
mk Ecos i
mI rmsErmscos i
(6)
Tmm kTIpeak Epeak /kE
2k T
mk Ecos i
mI rmsErmscos i