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Electrical Machines and Drives for Electric, Hybrid and Fuel Cell Vehicles

Electrical Machines and Drives for Electric, Hybrid and Fuel Cell Vehicles
Electrical Machines and Drives for Electric, Hybrid and Fuel Cell Vehicles

Electrical Machines and Drives for Electric, Hybrid and Fuel Cell Vehicles

Z. Q. Zhu and D. Howe

Department of Electronic and Electrical Engineering, University of Sheffield, Mappin Street Sheffield S1 3JD, UK

Abstract - This paper reviews the relative merits of induction, switched reluctance and permanent magnet brushless machines and drives for application in electric, hybrid and fuel cell vehicles, with particular emphasis on PM brushless machines. The basic operational characteristics and design requirements, viz. a high torque/power density, high efficiency over a wide operating range, and a high maximum speed capability, as well as the latest developments, are described. Permanent magnet brushless DC and AC machines and drives are compared in terms of their constant torque and constant power capabilities, and various PM machine topologies and their performance are reviewed. Finally, methods for enhancing the PM excitation torque and reluctance torque components and, thereby, improving the torque and power capability, are described. Key words: Brushless drives, electrical machines, electric vehicles, hybrid vehicles, induction machines, permanent magnet machines, switched reluctance machines.

1. INTRODUCTION

Electrical machines and drives are a key enabling technology for electric, hybrid and fuel cell vehicles. The basic characteristics which are required of an electrical machine for traction applications include [1]-[3]:

?High torque density and power density;

?High torque for starting, at low speeds and hill climbing, and high power for high speed cruising; ?Wide speed range, with a constant power operating range of around 3-4 times the base-speed being a good compromise between the peak torque requirement of the machine and the volt-ampere rating of the inverter;

?High efficiency over wide speed and torque ranges, including low torque operation;

?Intermittent overload capability, typically twice the rated torque for short durations;

?High reliability and robustness appropriate to the vehicle environment;

?Acceptable cost.

In addition, low acoustic noise and low torque ripple are important design considerations. On an urban driving cycle a traction machine operates most frequently at light loads around the base-speed. Therefore, in general, it should be designed to operate at maximum efficiency and minimum acoustic noise in this region.

Typical torque/power-speed characteristics required for traction machines are illustrated in Fig.1. Induction machines (IM), switched reluctance (SR) and permanent magnet (PM) brushless machines, Fig.2, have all been employed in traction applications, and can be designed to exhibit torque/power-speed characteristics having the form shown in Fig. 3. In the constant torque region I, the maximum torque capability is determined by the current

rating of the inverter, while in the constant power region

II, flux-weakening or commutation phase advance has to

be employed due to the inverter voltage and current limits.

In region III, the torque and power reduce due to the increasing influence of the back-emf. However, the

power capability and the maximum speed can be enhanced without sacrificing the low speed torque capability by employing a DC-DC voltage booster [4], a technique which is employed in the Toyota hybrid system,

or by employing series/parallel winding connections, i.e.

series connection at low speed and parallel connection at

high speed, as demonstrated in [5] [6]. In general, however, the design considerations and control methods

for the three machine technologies are significantly different, as will be discussed in this paper. Electrical

machine design cannot be undertaken in isolation, but

must account for the control strategy and the application requirements, both static and dynamic. Hence, a system

level design approach is essential.

This paper describes the basic operational characteristics

and design features associated with the foregoing electrical machine technologies for traction applications,

and reports the latest developments, with particular reference to PM brushless machines, for which there are

various topologies.

Fig. 1. Torque/power requirements for traction machines.

(a) (b) (c) Fig. 2. Main traction machine technologies. (a) IM – Induction machine,

(b) SRM –Switched reluctance machine, (c) PMM –Permanent magnet

brushless machine.

Fig. 3. Idealised torque/power-speed characteristics.

2. INDUCTION MACHINES

Of the three electrical machine technologies under consideration, induction machines are the most mature. In this section, the basic characteristics of IMs are briefly reviewed and specific design features for traction applications are highlighted. Optimal flux, maximum efficiency and low acoustic noise operation are then

discussed.

2.1 Basic Characteristics

IMs are robust, relatively low cost, and have well established manufacturing techniques. Good dynamic

torque control performance can be achieved by either vector control or direct torque control. For conventional IMs, the constant power range typically extends to 2-3 times the base-speed. However, for traction machines, this can be extended to 4-5 times the base-speed, which is generally desirable [7].

The torque-speed characteristic of an IM is mainly characterized by the starting torque, the pull-out torque and the associated speed, and the maximum speed. The electromagnetic torque is given by:

???

?????+????????+=22''

22k r s s r

s

X s R R f s R mpV T π (1) and the maximum torque, i.e. pull-out torque, is:

k s k s s L X f V T 2

2max ψ∝

∝ (2) while the starting torque and corresponding phase current are given by: ()

??

????++=

22''22k r s s r

s st X R R f R mpV T π (3) ()

2

2'

k r s s

st X R R V I ++= (4) where V s and f s are the supply voltage and frequency, ψs is the stator flux-linkage, m is the number of phases, p is the number of pole-pairs, s is the slip, R s and R r ’ are the stator winding resistance and effective rotor cage resistance per phase, respectively, k s r s k L f X X X π2'

=+= and L k are the short-circuit reactance and the total stator and effective rotor leakage inductance per phase, respectively. The pull-out torque is independent of the rotor resistance, approximately inversely proportional to the total stator and rotor leakage reactance, proportional to the square of the stator flux (or voltage), and inversely proportional to the square of the supply frequency. The starting torque is proportional to the square of the supply voltage, while the lower the stator and rotor leakage reactance and the lower the supply frequency, the higher will be the starting torque.

2.2 Design for Traction Applications In addition to the general requirements cited in the introduction for traction machines, essential design parameters for IMs include the number of poles, the number of stator and rotor slots, the shape of the stator and rotor slots, and the winding disposition. The design process usually involves 3 stages:

(a) making appropriate choices for the pole number and

stator/rotor slot numbers; (b) dimensioning the machine and designing the stator winding to achieve a specified power at the base-speed within a specified volume envelope; (c) simulating the machine performance over the full

operating speed range. With an inverter fed machine, both a high starting torque and a low starting current can be achieved, since the supply voltage and frequency are variable. Thus, compared with machines designed for constant supply frequency operation certain restrictions, such as the need

for a specific rotor slot shape to achieve the required starting torque, are removed. By appropriate choice of supply voltage and frequency, the starting torque can be almost as high as the maximum torque, while a high

efficiency can be achieved by minimum slip control [8][9]. The stator slot number and rotor slot number, and their shape and size should be optimised to minimize the total leakage inductance and resistance. Generally, this favours the use of wide and relatively shallow rotor slots and parallel sided teeth, as opposed to deep-bars or double cages in conventional IMs. This results in a lower rotor leakage inductance, which, in turn, improves the power

factor and increases the peak torque. In addition, the rotor slot area is more effectively utilised. When combined

with the reduced rotor resistance, a lower leakage reactance is also beneficial in reducing the slip frequency

at rated torque, and the variation of the slip frequency with load. The speed range of an IM is limited by its pull-out torque at high speed. As will be evident from equation (2), the

pull-out torque is proportional to the square of the flux-linkage and inversely proportional to the stator and rotor leakage inductances. In the flux-weakening region, the

flux reduces with increasing frequency, the consequent reduction in the pull-out torque being exacerbated by the fall in the voltage across the magnetizing reactance due to the influence of the leakage reactance. Therefore, to order to obtain a wide speed range, it is again beneficial to

minimize the leakage reactance. In [10], for example, this was achieved by

(a) increasing the width of the stator slot openings to reduce the stator slot leakage flux;

(b) increasing the airgap length to reduce the harmonic leakage flux;

(c) employing relatively wide, open rotor slots to reduce the rotor slot leakage flux;

(d) not employing skew so as to eliminate skew leakage; (e) employing a copper cage, Fig. 4.

A significant improvement in the available torque at maximum speed was then achieved, Fig. 5.

Fig. 4. IM traction machine [10]. Rating: 120 Nm, 11.5kW at maximum

speed of 7600 rpm, 26kW at base-speed of 2020rpm.

Fig. 5. Torque-speed curve of IM for traction drive [10].

Over the maximum envelope of the torque/power-speed characteristic, encompassing both constant torque and constant power operating modes, the copper loss only varies slightly with speed. In contrast, initially the iron loss increases with speed and is a maximum at the base-speed, after which it gradually reduces as the degree of flux-weakening is increased. It is well-known that when the iron loss and copper loss are similar the efficiency will be maximized. Therefore, an IM for traction applications should be designed such that the iron loss is higher than the copper loss at around the base-speed, and vice-versa at low and high speeds [9]. In this way, a high efficiency can be maintained over the entire operating speed range by incorporating optimal flux control, i.e. by reducing the flux level at low torque, as will be discussed later, since the most frequent operating condition generally demands low torque around base-speed.

2.3 Optimal Flux, Maximum Efficiency and Minimum Acoustic Noise

High efficiency operation is a very important issue for traction drives. The optimal flux level for maximum

efficiency varies directly with the torque and inversely with the speed [11]. Thus, at low torque it is advantageous to reduce the flux in an optimal manner in order to reduce the iron loss and maximize the efficiency. However, as the torque level is increased the flux must be simultaneously increased until the rated flux level is attained, otherwise the copper loss will increase excessively due to the low torque per ampere. If optimal flux control is employed a significant efficiency improvement is achieved at all loads in both constant torque and constant power modes [11]-[13]. Above base-speed, in the constant power mode, the flux naturally reduces since it is inversely proportional to the speed due to the limited inverter voltage.

Optimal flux control for maximum efficiency also results in lower acoustic noise [14], which, in general, increases with both the load and the flux. By way of example, Fig. 6 shows the variation of the sound pressure level with flux and load, for a constant stator fundamental frequency. It will be observed that

(a) under the same flux level, the sound pressure level increases with load;

(b) at light loads, a reduction in the flux can significantly reduce the acoustic noise. However, as the load is increased the noise can increase as the flux is reduced; (c) the optimal flux level for the lowest noise emissions increases with the load.

Flux (per-unit)

Fig. 6. Variation of sound pressure level with flux and load [14].

Since both vector control and direct torque control, either indirectly or directly, control the flux and torque, optimal flux control can be readily exercised. However, the optimal flux level for each specific torque and speed usually has to be determined experimentally, since no general and simple analytical method is available [11].

3. SWITCHED RELUCTANCE MACHINES

3.1 Features of SR Machines

The design and operational features of SRMs are well-documented [15][16], and may be summarized as follows: ? Simple, robust rotor structure, without magnets or windings, which is desirable for high temperature environment and high-speed operation. However, it can have a significant rotor iron loss.

? Potentially low cost, although relatively high manufacturing tolerances are required due to the need for a small airgap.

? Modest short-duration, peak torque capability as the magnetic circuit tends to be relatively highly saturated. ? Smooth operation at low rotational speeds requires relatively complex profiling of phase current waveforms and accurate measurement of rotor position.

? Unipolar operation requires non-standard power electronic modules, but SR drives have an inherent degree of fault tolerance.

? Since their operating is based on the sequential excitation of diametrically opposite stator coils in machines having the basic 6/4 and 8/4 stator/rotor pole number combinations, the acoustic noise, vibration and torque ripple tend to be relatively high. The high speed operating capability of SRMs, their relatively wide constant power capability, and the minimal effects of temperature variations offset, to some degree, their relatively lower power factor. Thus, SRMs have significant potential for use in vehicle propulsion systems [7][17-19].

Typical SR machines are shown in Fig.7, together with one phase leg of the inverter. When a stator pole is aligned with a rotor pole, the phase inductance is a maximum, while in the unaligned position the inductance is a minimum. When operated as a motor, the phase windings are excited during the period when the inductance is increasing as the rotor rotates. When operated as a generator, the phases are commutated on and off during the period when the inductance is reduced as the rotor rotates. The higher the ratio of the aligned inductance to the unaligned inductance, the higher the torque/power capability. In general, it requires the rotor pole arc to be slightly wider than that of the stator poles. Comparatively, SR machines have relatively few feasible stator/rotor pole number combinations (6/4, 8/6, and integer multiples thereof being the most common). Further, the stator poles are generally parallel-sided and carry a concentrated coil, as illustrated in Fig.7. However, several alternative SR machine topologies have been proposed, of which the long-pitched winding SR machine [20] which utilises the variation of the winding mutual inductances, rather than the variation of the phase self-inductances, to produce torque, and the segmented rotor SR machine [21] are arguably the most notable, since they may produce a similar torque density to that of

conventional SRMs.

(a) (b) (c)

Fig. 7. Typical SR machines and one phase leg. (a) 3-phase, 6/4 SRM,

(b) 4-phase, 8/6 SRM, (c) 1-phase leg of inverter.

3.2 Operational Characteristics

SRMs are usually operated in the discontinuous current mode, although continuous current operation may be advantageous under certain operating conditions. As was shown in Fig. 3, three operational modes generally exist for traction drives. Thus, in the constant torque region I, the phase currents are controlled by PWM to produce the desired output torque, the peak torque capability depending on

(a) the allowable maximum current from the inverter, (b) the rate of rise of the current after a phase winding has been commutated on,

(c) the degree of saturation in the magnetic circuit, (d) the allowable temperature rise.

Thus, a high overload capability requires thicker stator and rotor back-iron and appropriate thermal management. Above base-speed in the constant power region, when the inverter supply voltage is limited, commutation advance is required. Thus, both the turn-on and turn-off angles are gradually advanced as the speed is increased, and the machine eventually enters the single pulse mode of operation. When the machine is motoring, the peak current is determined solely by the turn-on angle, while when generating, both the turn-on and turn-off angles influence the peak current [22]. At very high rotational speeds, i.e. region III of Fig.3, further commutation advance is limited due to the influence of the back-emf and the winding inductance, since the phase current waveforms become continuous. However, as will be described later, by employing two-phase overlapping excitation and continuous conduction the power capability at high rotational speeds can be enhanced. Clearly, the foregoing operational characteristics of an SRM are appropriate for traction applications.

3.3 Constant Power Operation

An SRM is capable of extended constant power operation, typically up to 3-7 times the base-speed [23]. This is usually achieved by phase advancing the excitation until overlap between successive phase currents occurs.

The high speed performance of an SRM depends heavily on the rotor pole design, and in general, requires a compromise between the constant torque and constant power capabilities. For example, in [23] it was shown that when the leading dimensions of 6/4 and 8/6 SRMs were fixed, and the rotor pole arc was varied, the constant power range was extended to >6 times base-speed when the rotor pole arc was narrower than the stator pole arc and the depth of the rotor pole was relatively large. However, the machines under consideration had relatively low torque densities. The constant power capability also depends on the number of stator and rotor poles. When the number is increased the constant power capability and the overload capability are reduced, albeit the higher the torque/power density and the higher the power factor and efficiency. By way of example, [23] shows that a 6/4 machine exhibits a much wider constant power range (viz. up to ~ 7 times base-speed) than an 8/6 machine (viz. up to ~4 times base-speed), which compares to a constant power operating speed range of

~2 times base-speed for a 24/16 SRM [18]. Often, however, the number of stator and rotor poles is dictated by the space envelope constraints. In summary, not only is the ratio of the aligned to unaligned inductance reduced as the number of stator and rotor poles is increased, but the constant power operating speed range is compromised due to the limited scope for phase advancing, and although the constant power performance could be enhanced by reducing the number of turns per phase, this compromises the torque capability for a given inverter voltage-ampere rating.

Alternatively, the extended high speed constant power operation can be improved with continuous phase current excitation, by increasing the number of turns per phase. The torque per ampere capability below base-speed is then not significantly compromised, as has been demonstrated for a 24/16 SRM [24] and an 18/12 SRM [25], Fig.8, which shows an SRM which was developed

for a mild hybrid vehicle application.

(a)

(b) (c)

Fig. 8. SR machine with integrated flywheel and clutch for mild-hybrid vehicle [25]. Cranking: 45Nm (0-300rpm), continuous motoring: 200Nm (300-1000rpm), transient motoring: 20kW (1000-2500rpm), continuous generating: 15kW (600-2500rpm), transient generating: 25kW (800-2500rpm). (a) Schematic, (b) Rotor/stator without winding,

(c) Assembled unit.

The use of conduction overlap between two phases to increase the torque and to reduce torque pulsations is common practice [6]. Fig.9 illustrates overlapping conduction by advancing [6] or retarding [24] long-dwell commutation [15], both also incorporating phase advance.

Phase 1 Phase 2 Phase 3

Phase 1 Phase 2 Phase 3

Phase 1 Phase 2 Phase 3

(c)

Fig. 9. Overlap excitation techniques for extending constant power operating range. (a) Conventional excitation at high speed with phase

advance; (b) Overlapping excitation with commutation advanced; (c)

Overlapping excitation with commutation retarded.

Bipolar excitation, Fig.10, [6] [22] [26] can also be employed to improve the torque density and reduce torque pulsations, as well as to increase the efficiency. The long flux paths which are associated with SRMs supplied from conventional unipolar drives then become short flux paths, and the torque and efficiency are significantly enhanced at both low and high speeds. However, the improvement in performance gradually reduces as the excitation current is increased and the magnetic circuit becomes more highly saturated.

Phase 1 Phase 2 Phase 3

Phase 1 Phase 2 Phase 3

Fig.10. (a) Conventional excitation; (b) Bipolar overlapping excitation.

Finally, a control strategy which employs freewheeling diodes in parallel with the power switching devices in a conventional half-H-bridge inverter together with an appropriate zero voltage period, Fig.11, can also be used to boost the power capability when an SRM is operated as a generator [22][27].

Fig. 11. Freewheel diode configuration and (a) ‘+1’; (b) ‘0’; and (c) ‘-1’

commutation.

3.4 Acoustic Noise, Torque Ripple and Their Reduction The acoustic noise which is radiated from an SRM is often cited as a major disadvantage. At low rotational speeds the acoustic noise is due predominantly to resonances which are induced by the torque ripples, and may be reduced by appropriate profiling of the phase current waveform. The key to obtaining the optimal current profile is an effective method for estimating the instantaneous torque. At high rotational speeds the acoustic noise is dominated by radial vibration resonances [28]. The acoustic noise becomes significantly higher at high rotational speeds and loads. However, various techniques have been proposed for reducing the vibration and acoustic noise. The most effective method is to employ a relatively thick stator yoke [29][30] since this increases the mechanical stiffness and, thereby, reduces the vibrational response. However, the outer diameter is then increased, but this, in general, is advantageous in improving the over-load capability since the stator yoke becomes less saturated. Reducing the supply voltage is also usually helpful in reducing the acoustic noise at light load. SRMs also generate significantly lower noise when operated under voltage control rather than current control, due to the fact that random switching of the current controller results in a wide-band harmonic spectra, thereby increasing the likelihood of inducing mechanical resonances [31][32]. In [33], the relationship between the vibration of the stator and the rate of change of the phase currents at turn-off was highlighted, while a current shaping algorithm to limit the rate of change of current at turn-off and, thereby, achieve a smoother radial force waveform was described in [34][35]. However, the method proposed in [36] is arguably the most effective, in that it introduced a zero-voltage loop between two step changes in the applied voltage, such that, together with a knowledge of the stator natural frequencies, anti-phase stator vibrations were induced. However, it has limitations [37], since, while it is very effective when SRMs are operated in both single pulse mode and PWM voltage control, it is much less effective with PWM current control, since this results in a varying PWM switching frequency. A fixed frequency current controller can, however, alleviate the problem. Further, the technique is less appropriate for application to SRMs which exhibit multiple resonances. The vibration and acoustic noise can also be reduced [38] by employing two-phase overlapping excitation, which, as stated earlier, is beneficial for extending the constant power operating range. In general, however, the acoustic noise emissions from SRMs remain a significant issue.

4. PERMANENT MAGNET BRUSHLESS MACHINES 4.1 Brushless DC and AC Machines and Drives

Due to the permanent magnet excitation, PM brushless machines are inherently efficient [39-48]. They are generally classified as being either sinusoidal or trapezoidal back-emf machines [48], Fig.12. The corresponding control strategies are usually classified as being either brushless DC (BLDC), or brushless AC (BLAC). In a BLDC drive, the phase current waveforms are essentially rectangular, while in a BLAC drive the phase current waveforms are essentially sinusoidal. Ideally, in order to maximize the torque density and minimize torque pulsations, it is desirable to operate a machine which has a trapezoidal back-emf waveform in BLDC mode, and a machine which has a sinusoidal back-emf waveform in BLAC mode. In practice, however, the back-emf waveforms may depart significantly from the ideal, and, indeed, irrespective of their back-emf waveform PM brushless machines may be operated in either BLDC or BLAC mode, although the performance, in terms of efficiency and torque ripple, for example, may be compromised. Similar to induction machine drives, when operating at low torque an optimal flux level exists for minimum iron and copper loss, and hence, maximum efficiency.

(a) (b)

Fig. 12. Idealised back-emf and phase current waveforms fro PM

brushless machines. (a) BLDC, (b) BLAC.

Fig.13 shows a schematic of a typical PM brushless drive. In both BLDC and BLAC drives, rotor position information is necessary, although the required position resolution is different. For BLDC drives, in which the phase currents only have to be commutated on and off, low cost Hall sensors are often employed, while for BLAC drives, in which the phase current waveforms have to be precisely controlled, a relatively high cost resolver or encoder would be generally used. In addition, however, numerous sensorless techniques have recently been developed or are under development for both BLDC and BLAC drives.

N S position

sensors

+ -

Fig. 13. Schematic of PM brushless drive.

Although various rotor topologies and stator winding dispositions may be employed, BLDC machines predominantly have surface-mounted magnets on the

rotor, and a concentrated non-overlapping, fractional-slot, stator winding, Fig.14(a). This results in short end-windings and, therefore, a low copper loss, and the potential for a high torque density, while a six-step inverter can be employed with PWM current chopping. 2-phase, 120o elec. conduction is the most common operational mode for a 3-phase BLDC machine, while maximum torque per ampere in the constant torque region and extended speed operation can realized by advancing the commutation, Fig. 15. Similar operational characteristics can be obtained in a BLAC drive by controlling the phase currents in such a way that they produce a demagnetizing component of armature reaction, Fig. 14. Stator winding dispositions. (a) Non-overlapping winding, (b)

Overlapping winding.

Various design features may be employed to obtain a sinusoidal back-emf waveform. For example, the stator slots and/or rotor magnets may be skewed, a distributed stator winding might be employed, or the permanent magnets could be appropriately shaped or magnetised, etc. However, a distributed overlapping winding, Fig. 14(b), results in longer end-windings, which results in a higher copper loss and a lower torque density, while skewing of either the stator or rotor makes manufacture more complicated. Hence, it is often preferable to either shape the magnets or impart a sinusoidal magnetisation distribution [49], which results in an essentially sinusoidal airgap field distribution, which is conducive to a low cogging torque and also a low iron loss. The rotor back-iron in a self-shielding, sinusoidal magnetized PM machine [49] is not essential since negligible flux flows within the inner bore of the magnet. This is, therefore, also conducive to a low rotor inertia, which can be an important consideration. Recently, however, there has been a trend to employ a fractional ratio of slot number to

pole number and a concentrated stator winding for BLAC motors so as to achieve a sinusoidal back-emf waveform and a low cogging torque. However, when the slot number per pole is fractional, the reluctance torque is usually relatively small with a concentrated stator winding. In order to utilize the saliency, an overlapping stator winding is usually required, Fig.14(b), as will be discussed in section 4.4.

Dq-axis theory can be used to analyze the electromagnetic performance of a BLAC machine, and the optimal relationship between the d-axis and q-axis currents in vector control and flux-weakening control strategies being determined analytically [50], BLAC motors are relatively easy to control and exhibit excellent performance, in terms of maximum torque per ampere control and optimal extended speed operation [51-53]. In

contrast, the control strategy to realize constant power

operation for a BLDC drive is generally more complex. As was shown in [54][55], above the base-speed the maximum achievable output power and torque when a machine is operated in the BLAC mode are higher than that which can be achieved when the same machine is operated in 2-phase, 120o elec. conduction BLDC mode, irrespective of whether it has a trapezoidal or sinusoidal back-emf waveform, Fig.16. At high speed, the phase current waveform will approximate to a sinusoid even in a BLDC drive, due to the influence of the winding o elec.

Speed

Fig. 15. Torque-speed characteristics of PM brushless machines.

T o r q u e /R M S c u r r e n t

Fig. 16. Comparison of torque-speed characteristics of BLAC and 3-phase, 120o elec. BLDC drives.

Speed

Fig. 17. Comparison of torque-speed characteristics which result with 2-phase, 120o elec.and 3-phase, 180o elec. conduction modes of operation.

T o r q u e /R M S c u r r e n t

Fig. 18. Torque-speed characteristics for brushless BLAC and 3-phase,

180o elec. BLDC operation.

4.2 Permanent Magnet Brushless Machine Topologies In this section, the basic topologies of PM brushless machine, classified according to the location of the permanent magnets, are described.

4.2.1 Radial-field machines - permanent magnets on rotor

A radial-field PM brushless machine may have either an internal rotor or an external rotor, while the PMs may be located either on the surface or the interior of the rotor.

(a) Surface-mounted permanent magnets (SPM) machines This is the most widely used topology for PM brushless machines, Fig. 19 (a-1). However, since the d-axis and q-axis stator winding inductances of such machines are the same, they exhibit zero reluctance torque. Further, in general, the armature reaction field is relatively small and the stator windings have a low inductance, since the magnet has a relative permeability which approximates to that of air, i.e. μr ~1, and the effective airgap is the sum of the actual airgap length and the radial thickness of the magnets. However, the magnets are exposed directly to the armature reaction field, and, hence, are susceptible to partial irreversible demagnetization. SPM machines are also generally to have a relatively limited flux-weakening capability. However, the flux-weakening capability, as well as the merits of PM machines having a fractional number of slots per pole and a concentrated stator winding, will be discussed later.

Fig.19 (a-2) shows a schematic of a motor in which the magnets are inset into the rotor surface. The magnet pole-

arc is, therefore, less than a full pole-pitch. However, since the q-axis inductance is now greater than the d-axis

inductance, a reluctance torque can be developed.

(b) Interior permanent magnets (IPM) machines

Fig. 19(b) shows examples of brushless machines in which the magnets are accommodated within the rotor. In Fig. 19 (b-1) the magnets are radially magnetized, while in Fig. 19(b-2) they are circumferentially magnetized. Generally speaking, however, leakage flux from the

magnets is significantly greater than that in SPM machines. However, since the magnets are buried inside the rotor iron, the magnets are effectively shielded from the demagnetizing armature reaction field during flux-weakening operation. Further, since the d-axis inductance is smaller than the q-axis inductance, a reluctance torque exists, while the d-axis inductance is high compared with that of an equivalent surface-mounted magnet motor topology. Therefore, generally, such machine topologies are eminently appropriate for extended speed, constant power operation in the flux-weakening mode [48][51]. Indeed, a variant of the topology illustrated in Fig. 19(b-1) is employed in the Toyota hybrid vehicle [4], Fig.20. The V-shaped disposition of the permanent magnets serves to increase the airgap flux and the distributed stator winding enables the reluctance torque to be utilized.

(a-1) (a-2)

(b-1) (b-2)

Fig. 19. Alternative radial-field PM machine topologies with magnets on rotor. (a) Magnets on rotor surface, (b) Magnets inside the rotor.

Fig. 20. Open-circuit field distribution in PM BLAC machine in Toyota

hybrid vehicle.

Multiple layers of magnets may also be employed to further increase the saliency ratio, although, in practice, the number of layers is usually limited to ≤3. An extreme case, however, is to employ an axially laminated PM rotor in which permanent magnet sheets are sandwiched between the laminations [60]. In this way, a small volume of permanent magnet material, which is generally a bonded ferrite or rare-earth, such a machine can exhibit an extremely wide flux-weakening capability and a high torque density, without the risk of generating an

excessive back-emf should an inverter fault occur at high rotational speeds. However, such a rotor structure is relatively complex and expensive to manufacture [61][62].

A virtue of the rotor topology shown in Fig. 19 (b-2) is that, when the pole number is relatively high, flux focusing can be exploited and the air-gap flux density can be significantly higher than the magnet remanence. Hence, low cost, low energy product magnets, such as sintered ferrite, may be employed. By way of example, Fig. 21 shows a generator, which was developed for an electric vehicle auxiliary power unit [63]. Flux-focusing enables an airgap flux density of 0.6T to be achieved when sintered ferrite magnets, having a remanence of 0.38T are employed. Such a machine topology also exhibits a higher d-axis inductance since the armature reaction flux only passes through a single magnet, rather than two magnets as in the other machine topologies, making it very suitable for extended constant power

operation.

(a)

(b)

(c)

Fig. 21. Generator for EV auxiliary power unit [63]. 9kW at 4200 rpm, sintered ferrite magnets (remanence=0.38T), max. airgap flux density:

0.6T. (a) Stator, (b) Rotor, (c) Flux distribution.

4.2.2 Radial-field machines - permanent magnets on stator

When the permanent magnets are located on the stator, the rotor must have a salient pole geometry, similar to that of an SR machine, which is simple and robust, and

suitable for high-speed operation. The stator carries a non-overlapping winding, with each tooth having a concentrated coil. The permanent magnets can be placed on the inner surface of the stator teeth, sandwiched in the stator teeth, or mounted in the stator back-iron. Irrespective of their location, however, the torque results predominantly from the permanent magnet excitation torque, i.e. the reluctance torque is negligible, although the torque production mechanism relies on the rotor saliency. Compared with conventional permanent magnet brushless machine topologies, generally, it is easier to limit the temperature rise of the magnets as heat is dissipated more effectively from the stator.

(a) Permanent magnets in stator back-iron – doubly-salient PM machine

The machine topology which is shown in Fig. 22(a) is referred to as a doubly-salient permanent magnet machine. For a 3-phase machine a magnet is required in the stator back-iron for every 3 teeth, while for a 4-phase machine a magnet is required for every 4 teeth. The variation of the flux-linkage with each coil as the rotor rotates is unipolar, while the back-emf waveform tends to be trapezoidal [64]. Thus, this topology is more suitable for BLDC operation. However, the rotor may be skewed in order to obtain a more sinusoidal back-emf waveform to make it more appropriate for BLAC operation. Further, it will be noted that the airgap reluctance as seen by the permanent magnets is essentially invariant with the rotor position. Therefore, the cogging torque is not significant. However, a major disadvantage is that, due to the unipolar flux-linkage, the torque density is relatively poor compared to that of other PM brushless machines [65], although, as was reported in [66], it can still be higher than that of an

induction machine.

(a)

A+B+

C+

C-A-B-A+A+A+A-

A-

A-B+

B+B+B-B-B-C+

C+ C+

C-C-

C-

(b)

(c)

Fig. 22. Alternative radial-field PM machine topologies with magnets

on stator. (a) Magnets in stator back-iron – doubly-salient PM machine, (b) Magnets on surface of stator teeth - flux-reversal PM machine, (c)

Magnets in stator teeth - flux-switching PM machine.

(b) Permanent magnets on surface of stator teeth – flux-reversal permanent magnet machine

This machine topology is also commonly referred to as a flux-reversal PM machine, Fig. 22(a) [67][68]. Each stator tooth has a pair of magnets of different polarity mounted at its surface. When a coil is excited, the field under one magnet is reduced while that under the other is increased, and the salient rotor pole rotates towards the stronger magnetic field. The flux-linkage with each coil reverses polarity as the rotor rotates. Thus, the phase flux-linkage variation is bipolar, while the phase back-emf waveform is, again, essentially trapezoidal. Such a machine topology exhibits a low winding inductance, while the magnets are more vulnerable to partial irreversible demagnetization. In addition, significant induced eddy current loss may be induced in the magnets, which also experience a significant radial magnetic force. Further, since the airgap flux density is limited by the magnet remanence, the torque density may be compromised.

(c) Permanent magnets in stator teeth – flux-switching PM machine

This machine topology is also referred to as a flux-switching permanent magnet machine, Fig. 22(c) [69-71]. The stator consists of “U”-shaped laminated segments between which circumferentially magnetized permanent magnets are sandwiched, the direction of magnetization being reversed from one magnet to the next. Each stator tooth comprises two adjacent laminated segments and a permanent magnet. Thus, flux-focusing may be readily incorporated, so that low cost ferrite magnets can be employed [70]. In addition, in contrast to conventional PM brushless machines, the influence of the armature reaction field on the working point of the magnets is minimal. As a consequence, the electric loading of flux-switching PM machines can be very high. Therefore, since the phase flux-linkage waveform is bipolar, the torque capability is significantly higher than that of a doubly-salient PM machine [65]. The back-emf waveform of flux-switching PM machines is essentially sinusoidal, which makes them more appropriate for BLAC operation. In addition, since a high per-unit winding inductance can readily be achieved, such machines are eminently suitable for constant power operation over a wide speed range. 4.2.3 Other PM brushless machine topologies

(a) Axial-field machines

Axial-field PM machines have an axially directed airgap flux [72][73] and can comprise a single-sided stator and a single rotor, a double-sided stator and a single rotor, or a single stator and a double-sided rotor. In each case, a large axial force exists between the stator and the rotor. As with conventional radial-field PM brushless machines, the stator can be slotted or slotless, although it is more difficult to manufacture a slotted stator for axial-field machines. Thus, slotless designs are more common. However, while this eliminates cogging, it exposes the winding the airgap flux. Hence, a multi-stranded conductor or Litz wire may be required to minimize the eddy current loss. Further, since the effective airgap is large, the winding inductance is generally relatively small, which may limit the constant power speed range.

(b) Transverse-flux machine

Generally, transverse flux machines have a relatively large number of poles, all of which interact with the total ampere-conductors of each phase. This enables very high electric loadings and, hence, high torque densities to be achieved [74-78]. However, they have a significant leakage flux and a relatively high winding inductance, as well as a poor power factor [79][80]. This impacts significantly on the associated VA rating of the power electronics converter, which, has inhibited its application.

4.3 Design and Control Issues for PM Brushless Traction Machines

As stated earlier, traction machines are required to have a high torque density, a high overload capability, a wide operating speed range, and a high efficiency, while it is desirable that they have a degree of a high fault tolerance and are low cost. In this section, design considerations related to the above issues are discussed. However, they often conflict each other. For example, reduction of the cross-coupling magnetic saturation may also reduce the saliency ratio and consequently the reluctance torque; the selection of the base-speed is usually a compromise between the constant torque performance at low speed and the constant power performance at high speed.

4.3.1 Torque density and overload capability

The general torque equation for a PM brushless machine, which has both excitation torque and reluctance torque components, is given by:

[]

q

d

d

q

q

m

I

I

L

L

I

p

T)

(

2

3

?

?

=ψ (5) where p is the number of pole-pairs, ψm is the stator winding flux-linkage due to the permanent magnets, and L d, L q and I d, I q are the d- and q-axis inductances and currents, respectively. In order to maximize the torque density, it is desirable to increase ψm by reducing the leakage flux. This can be achieved by introducing airspace flux barriers or interpole magnets, as illustrated in Fig. 23. ψm can also be increased by utilizing flux focusing [4][63], as illustrated in Fig. 24. The torque

density can also be enhanced by increasing the saliency ratio [3][81], as illustrated in Fig. 25. Further, since the short-duration torque capability is determined primarily by the demagnetization withstand capability of the magnets and the level of magnetic saturation, reducing the d- and q-axis cross-coupling magnetic saturation by incorporating air flux barries, as illustrated in Fig. 26, can

Fig. 23. Reduction of leakage flux by introducing airspace flux barriers

Fig. 25. Improvement of saliency ratio. (a) Lower reluctance q-axis Fig. 26. Reduction of d- and q-axis cross-coupling magnetic saturation.

(a) SPM, (b) IPM.

4.3.2 Flux-weakening capability

It is well known [62][82] that the maximum flux-weakening capability, defined as the ratio of the maximum speed to the base-speed, under supply inverter voltage and current limitations, can be achieved when a PM brushless machine is designed to have 1.0 per-unit d-axis inductance such that:

r

m

d I

L

ψ

= or 1

=

m

r

d

I

L

ψ

(6)

where ψm is the stator flux-linkage due to the magnets, L d is the d-axis inductance, and I r is the rated current. Although it is possible to design a PM brushless machine which satisfies the foregoing requirement, generally, for most PM machines L d I r/ψm<1, since the d-axis inductance is relatively low as a consequence of the recoil permeability of the magnets being approximately equal to 1.0. Nevertheless, the higher the ratio of L d I r/ψm the higher will be the flux-weakening capability, Fig. 27(a), which, theoretically, is ‘infinite’ when the ratio is 1.0. However, the higher the flux-linkage ψm to achieve a high low-speed torque capability, the more difficult it is to realize wide speed operation, Fig.27, [83].

In [62], it was shown that it was possible to design any PM brushless machine to achieve ‘infinite’ flux-weakening capability. Clearly, however, if the rated current is high (e.g. the machine is liquid cooled), it is much easier to satisfy equation (6), even for surface-mounted magnet machines, which have a high ψm and a

relatively low L d . For example, in [84] ‘infinite’ flux-weakening capability was achieved with an SPM machine equipped with a self-shielding, sinusoidal magnetized rotor having no back-iron, and in [85] with an SPM machine in which only alternate stator teeth carried a coil. However, in general, it is much easier to achieve a wide operating speed range with machines equipped with an interior permanent magnet rotor, since generally ψm is lower, while L d is higher.

T o r q u e (p e r -u n i t )

Speed (per-unit)

P o w e r (p e r -u n i t )

L d I r /ψm Speed (per-unit)

(a)

T o r q u e (p e r

-u n i t )

Speed (per-unit)

P o w e r (p e r

-u n i t )

Speed (per-unit)

(b)

Fig. 27. Variation of torque and power capability with machine design parameters, when L d I r <ψm . (a) Variation with L d I r /ψm , when ψm and L q /L d are constant, (b) Variation with ψm , when L q and L d are constant.

4.3.3 Demagnetization withstand capability

Operation in the flux-weakening mode is a necessary requirement for traction applications, while NdFeB is the most commonly employed permanent magnet material for PM brushless machines. However, the magnets are required to have an adequate demagnetization withstand capability at the maximum operating temperature, when they are most vulnerable to partial irreversible demagnetization. In addition to effective thermal

management, one means of enhancing the demagnetization withstand capability is to provide a low reluctance path for the demagnetizing d-axis armature reaction flux such that it does not pass through the magnets. One example of achieving this is to employ narrower stator slot openings and thick tooth-tips, as illustrated in Fig. 28(a), or thick rotor slot bridges in an IPM machine, as illustrated in Fig. 28(b). However, such features will also have an influence on ψm and L d . In general, however, it is easier to realize a high demagnetization withstand capability for IPM machines. Nevertheless, it has been shown [86] that, by careful design, the magnet working point in an SPM machine can remain reasonably high up the magnet demagnetization characteristic, even when the machine has ‘infinite’ flux-weakening capability, due to the fact that 1.0 per-unit d-axis inductance results primarily from stator slot leakage and end leakage fluxes.

4.3.4 Rotor eddy current loss

PM BLAC and BLDC machines are usually considered to have negligible rotor loss. However, the rotor loss may be important in machines equipped with surface-mounted magnets, in terms of the resulting temperature rise. Eddy currents may be induced in the permanent magnets, the rotor back-iron, and any conducting sleeve which may be employed to retain the magnets, by time and space harmonics in the airgap field. More specifically, they result from [87] (a) stator slotting; (b) stator mmf harmonics which do not rotate in synchronism with the rotor; and (c) non-sinusoidal phase current waveforms, which result from six-step commutation and PWM.

In general, however, the rotor eddy current loss is relatively small compared with the stator copper and iron losses. Nevertheless, it may cause significant heating of the magnets, due to the relatively poor heat dissipation from the rotor. In turn, this may result in partial irreversible demagnetization, particularly of sintered NdFeB magnets, which have relatively high temperature coefficients of remanence and coercivity and a moderately high electrical conductivity. It is particularly important to consider the rotor eddy current loss in (a)

machines with a high fundamental frequency, e.g. high-speed and/or high-pole number; (b) machines with large stator slot openings, e.g. transverse flux machines; (c) high power density brushless dc machines, e.g. force-cooled traction machines with a high electric loading; and (d) machines whose windings span a fractional pole-pitch and which have nearly equal pole and slot numbers [88].

If the eddy current loss is unacceptable, the magnets may be segmented, axially and/or circumferentially [89].

?

(a)

?

(b)

Fig. 28. Improvement of demagnetization withstand capability by introducing d-axis armature reaction demagnetization flux path. (a)

SPM stator design, (b) IPM rotor design.

4.3.5 Stator iron loss

Due to the fixed PM excitation, the no-load iron loss increases with the rotational speed, while the full-load iron loss in the constant torque operating range is generally around 20-50% higher. However, the iron loss which results on load in the flux-weakening mode depends on the machine topology, as illustrated in Fig.29. In general, SPM machines have the lowest full-load iron loss, and despite the increase in fundamental frequency it usually becomes much lower than the no-load iron loss as the degree of flux-weakening is increased [90]. IPM machines generally have a significantly higher full-load iron loss, which may be comparable to or higher than the no-load iron loss, since the armature reaction field has a higher harmonic content due to the small effective airgap [90][91]. However, when the magnets are simply inset into the rotor surface the harmonic content in the armature reaction field increases further, and generally results in the highest full-load iron loss [86].

S t a t o r i r o n l o s s

Speed (per-unit)

Fig. 29. Variation of iron loss in SPM and IPM machines when their

open-circuit stator iron loss are designed to be the same.

4.3.6 Fault-tolerance

An important consideration when operating in the extended speed, flux-weakening mode is the consequence of an inverter fault which results in the loss of the demagnetizing armature reaction field and an excessively high back-emf [92][93]. In this regard, IPM machines may be advantageous, since, for a given output torque, the PM excitation torque, and, hence, the volume of magnet material and the maximum back-emf are lesser. However, the consequences of an inverter fault occurring when a PM brushless machine is operating in the flux-weakening region remains a challenging issue.

4.4 Recent Developments 4.4.1 Fractional slot machines

SPM brushless machines which have a fractional number of slots per pole and a concentrated winding have been the subject of recent research. They have an inherently

low cogging torque, short end-windings and, hence, a low

copper loss, a high efficiency, and a high power density, as well as excellent flux-weakening performance [85][94-100]. The stator coils may be wound either on all the teeth or only on alternate teeth, Fig.30 [95][97]. In the latter case, the phase windings are effectively isolated, both magnetically and physically, and a high per-unit self-inductance can readily be achieved to limit the prospective short-circuit current, by utilizing the relatively high airgap inductance and the leakage flux at the slot openings. Due to the physical separation of the coils and the negligible mutual-inductance between phases, the possibility of a phase-to-phase fault is minimized. Therefore, the fault tolerance and flux-weakening capability of such machines can be significantly higher than for more conventional machine designs. Fig.31 shows a 3-phase, 24-slot, 22-pole, PM BLAC machine which was developed for a supercapacitor-based electrical torque boost system for vehicles equipped with down-sized IC engines [99]. However, since the torque is developed by the interaction of a stator space harmonic mmf with the permanent magnets a relatively high rotor eddy current loss can result from the fundamental and low order space

harmonic mmfs which rotate relative to the rotor [88][89]. As stated earlier, however, the magnets can be segmented

to reduce the eddy current loss. A further advantage of

such machines is that, due to the fractional number of

slots per pole, the cogging torque is very small without

employing design features such as skew. However, the reluctance torque component is negligible even when an

IPM rotor is employed.

(a)

(b)

Fig. 30. 3-phase, 12-slot, 10-pole, fractional slot PM machines [97]. (a)

All teeth wound, (b) Alternate teeth wound.

A C C

B -B --

C C C A A B -A A

A A

-B A -A A

-

C C

-C C

C

-C B

B

B B

B B C

C

C -C C

-

A A

-A A

A

-A B

-B B

B

-B B

(a)

(b)

Fig. 31. 3-phase, 24-slot, 22-pole, PM BLAC machine with modular stator winding and IPM rotor [99]. Rated output power=18.5kW, rated speed=1700rpm, rated torque=105Nm. (a) Cross-section of 3-phase, 24-slot, 22-pole IPM BLAC machine, (b) Machine test rig.

4.4.2 Hybrid PM and current excitation

Since the PM excitation is fixed in a PM brushless machine, the current phase angle has to be progressively advanced as the speed is increased above base-speed so that a demagnetizing d-axis current component is produced which reduces the flux-linkage ψm with the stator winding. Ultimately, however, this may cause partial irreversible demagnetization of the magnets. At the same time, due to the inverter voltage and current limits, the torque-producing q-axis current component has to be reduced correspondingly. Consequently, the torque and power capability are limited. Thus, a compromise has to be made between the low speed torque capability and high speed power capability.

Hybrid permanent magnet and field current excitation has been shown to be beneficial in improving the power capability in the extended speed range, enhancing the low speed torque capability, and improving the overall operational efficiency. There are several ways of realizing such hybrid excitation. For example, DC winding may be located on the rotor [101] or the stator

[102-107], which is preferable since it does not require slip-rings. The magnetic circuit associated with the DC excitation may be either in series or in parallel with the magnetic circuit associated with the PM excitation. However, although series excitation is simple it requires a higher excitation mmf due to the low recoil permeability of the magnets. On the other hand, parallel excitation is more effective electromagnetically but leads to a more complex machine structure. Fig.32 shows three examples of PM brushless machines equipped with hybrid excitation, based on doubly-salient pole [102], consequent-pole [103-105], and claw-pole [106][107] machine topologies. The DC excitation winding enables the airgap flux, and, hence, the torque capability, to be enhanced at low speed, to be reduced at high speed to facilitate extended speed operation, and to be optimized over the entire speed range to improve the efficiency. It also reduces the likelihood of an excessively high back-emf being induced at high speed in the event of an

inverter fault.

(a)

(b)

Stationary DC Stator winding S-pole rotor

excitation coil DC coil supporter

(c)

Fig. 32. Hybrid excited PM machines. (a) Hybrid excitation based on doubly-salient pole structure [102], (b) Hybrid excitation based on consequent pole structure [105], (c) Hybrid excitation based on claw-pole structure [106].

5. CONCLUSIONS

The operational characteristics, design features and control requirements for induction machines, switched reluctance machines, and permanent magnet brushless machines for vehicle propulsion systems have been reviewed, with emphasis on their low speed torque and high speed power capability. Given that they offer the highest efficiency and torque density, particular emphasis has been given to permanent magnet brushless machines. Various PM brushless machine topologies have been highlighted, and their relative merits have been briefly described. In general, however, all three machine technologies can meet the performance requirements of traction drives, and each of machine technology has merits.

ACKNOWLEDGEMENTS

The authors acknowledge the contributions of colleagues in the Electrical Machines and Drives Group, University of Sheffield, UK, and also the support of industrial organizations, in particular, IMRA UK Research Centre, Centro Ricerche Fiat, Volvo Technology Corporation, and FEV Motorentechnik GmbH.

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Z. Q. Zhu (M’90, SM’00) received the B.Eng. and M.Sc. degrees from Zhejiang University, Hangzhou, China, in 1982 and 1984, respectively, and was awarded the Ph.D. by the University of Sheffield, Sheffield, UK, in 1991, all in electrical and electronic engineering.

From 1984 to 1988 he lectured in the Department of Electrical Engineering at Zhejiang University. In 1988, he joined the University of Sheffield, initially as a Research Associate. He was subsequently appointed to an established post as

a Senior Research Officer/Senior Research Scientist. Since 2000 he has been Professor of Electrical Machines and Control Systems. His current major research interests include the application, control and design of permanent magnet machines and drives.

David Howe received the B.Tech and M.Sc. degrees from the University of Bradford, in 1966 and 1967, respectively, and a Ph.D. from the University of Southampton in 1974, all in electrical power engineering.

He has held academic posts at Brunel and Southampton Universities, and spent a period in industry with NEI Parsons Ltd working on electromagnetic problems related to turbo-generators. He is currently Professor of Electrical Engineering at the University of

Sheffield, where he heads the Electrical Machines and Drives Research Group. His research activities span all facets of controlled electrical drive systems, with particular emphasis on permanent magnet excited machines. Prof. Howe is a Fellow of the Royal Academy of Engineering and a Fellow of the IEE, UK.

螺纹联结与螺旋传动试卷(带答案)

螺纹联结与螺旋传动 一、单项选择题(从给出的A、B、C、D中选一个答案) 1 当螺纹公称直径、牙型角、螺纹线数相同时,细牙螺纹的自锁性能比粗牙螺纹的自锁性能。 A. 好 B. 差 C. 相同 D. 不一定 2 用于连接的螺纹牙型为三角形,这是因为三角形螺纹。 A. 牙根强度高,自锁性能好 B. 传动效率高 C. 防振性能好 D. 自锁性能差 3 若螺纹的直径和螺旋副的摩擦系数一定,则拧紧螺母时的效率取决于螺纹的。 A. 螺距和牙型角 B. 升角和头数 C. 导程和牙形斜角 D. 螺距和升角 4 对于连接用螺纹,主要要求连接可靠,自锁性能好,故常选用。 A. 升角小,单线三角形螺纹 B. 升角大,双线三角形螺纹 C. 升角小,单线梯形螺纹 D. 升角大,双线矩形螺纹 5 用于薄壁零件连接的螺纹,应采用。 A. 三角形细牙螺纹 B. 梯形螺纹 C. 锯齿形螺纹 D. 多线的三角形粗牙螺纹 6 当铰制孔用螺栓组连接承受横向载荷或旋转力矩时,该螺栓组中的螺栓。 A. 必受剪切力作用 B. 必受拉力作用 C. 同时受到剪切与拉伸 D. 既可能受剪切,也可能受挤压作用 7 计算紧螺栓连接的拉伸强度时,考虑到拉伸与扭转的复合作用,应将拉伸载荷增加到原来的 倍。 A. B. C. D. 8 采用普通螺栓连接的凸缘联轴器,在传递转矩时,。 A. 螺栓的横截面受剪切 B. 螺栓与螺栓孔配合面受挤压 C. 螺栓同时受剪切与挤压 D. 螺栓受拉伸与扭转作用 9 在下列四种具有相同公称直径和螺距,并采用相同配对材料的传动螺旋副中,传动效率最高的是。 A. 单线矩形螺旋副 B. 单线梯形螺旋副 C. 双线矩形螺旋副 D. 双线梯形螺旋副 10 在螺栓连接中,有时在一个螺栓上采用双螺母,其目的是。 A. 提高强度 B. 提高刚度 C. 防松 D. 减小每圈螺纹牙上的受力

课程设计齿轮传动设计

3.2高速级齿轮传动的设计 3.2.1传动齿轮的设计要求 1)齿轮材料:软齿面齿轮传动 小齿轮:45号钢,调质处理,齿面硬度为240HBS; 大齿轮:45号钢,正火处理,齿面硬度为200HBS。 2)轴向力指向轴的非伸出端; 3)每年300日,每班8小时,两班制 4)齿宽系数; 5)螺旋角; 6)中心距取整,分度圆直径精确计算(保留小数点后两位)。 3.2.2选择齿轮类型,精度等级及齿数 1)参考表10.6,取通用减速器精度等级为7级精度 2)取小齿轮齿数为,齿数比,即大齿轮齿数 ,取; 3)选择斜齿圆柱齿轮,取压力角°; 4)初选螺旋角. 3.2.3按齿面接触疲劳强度设计 1.计算小齿轮的分度圆直径,即 ≥ 1)确定公式中的各参数值 a)试选载荷系数=1.3 b)计算小齿轮传递的转矩

=9.55*?=9.55**4.496/1450(N?mm)=2.96*N?mm c)取齿宽系数=1.0 d)由图10.20查得区域系数=2.433; e)由表10.5查得材料的弹性影响系数=189.8 f)计算接触疲劳强度用重合度系数 =arctan(tan/tan)=arctan(tan20/tan14)=20.562° =arccos =arccos[24*cos20.562/(24+2*1*cos14)]=29.974 =arccos = 22.963 = =[24*(tan29.974-tan22.963)+115*(tan22.963-tan20.562)]/2 =1.474 ==1*24*tan14/=1.905 = g)螺旋角系数===0.985 h)计算接触疲劳许用应力 由图10.25c,d查得小齿轮和大齿轮的接触疲劳极限分别为 =500MPa,=375MPa 应力循环次数分别为 =60=60*1450*1*(2*8*300*8)=3.341*

单级圆柱齿轮减速器的高速级齿轮传动设计

优秀设计 单级圆柱齿轮减速器的高速级齿轮传动设计

目录 一、传动方案的拟定及电动机的选择 (2) 二、V带选择 (4) 三.高速级齿轮传动设计 (6) 四、轴的设计计算 (9) 五、滚动轴承的选择及计算 (13) 六、键联接的选择及校核计算 (14) 七、联轴器的选择 (14) 八、减速器附件的选择 (14) 九、润滑与密封 (15) 十、设计小结 (16) 十一、参考资料目录 (16)

数据如下: 已知带式输送滚筒直径320mm ,转矩T=130 N ·m ,带速 V=1.6m/s ,传动装置总效率为?=82%。 一、拟定传动方案 由已知条件计算驱动滚筒的转速n ω,即 5.953206 .1100060100060≈??=?= π πυωD n r/min 一般选用同步转速为1000r/min 或1500r/min 的电动机作为原动机,因此传动装置传动比约为10或15。根据总传动比数值,初步拟定出以二级传动为主的多种传动方案。 2.选择电动机 1)电动机类型和结构型式 按工作要求和工作条件,选用一般用途的Y (IP44)系列三相异步电动机。它为卧式封闭结构。 2)电动机容量 (1)滚筒输出功率P w kw n T 3.19550 5.951309550P =?=?= ωω (2)电动机输出功率P kw d 59.1% 823 .1P P == = η ω 根据传动装置总效率及查表2-4得:V 带传动?1=0.945;滚动轴承?2 =0.98;圆柱齿轮传动 ?3 =0.97;弹性联轴器?4 =0.99;滚筒轴滑动轴承?5 =0.94。 (3)电动机额定功率P ed 由表20-1选取电动机额定功率P ed =2.2kw 。

基于MATLAB的齿轮传动系统优化设计

基于MATLAB的齿轮传动系统优化设计 摘要:某高速重载齿轮进行了优化设计,在分析齿轮在各工况下的弯曲强度后,根据齿轮的优化设计原则,选择齿轮体积最小为优化设计原则,对传动齿轮中的小齿轮进行了优化设计,设计模数、齿数、齿宽系数、螺旋角为变量,根据各参数的设计要求来确定约束条件,同时根据齿根弯曲疲劳强度和齿面接触疲劳强度进行条件约束,最后用MATLAB进行编程计算,最后得出优化后的结果,该结果满足要求。本文的研究对机械系统的优化设计具有指导意义和工程应用价值。关键词:齿轮;优化设计;MATLAB; 0引言 优化设计是近年发展起来的一门新的学科,也是一项新技术,在工程设计的各个领域都已经得到了更为广泛的应用。通过实际的应用过程表明:工程设计中采用优化设计这种新的科学设计方法,不仅使得在解决复杂问题时,能够从众多纷繁复杂的设计方案中找到尽可能完善的或者最适合的设计方案,而且,采用这种方法还能够提高设计效率和设计质量,使其的经济和社会效益都非常明显。优化设计的理论基础是数学规划,采用的工具是计算机。 优化设计具有一般的设计方法所不具备的一些特点。优化设计能够使各种设计参数自动向更优的方向进行调整,直到找到一个尽可能完善的或最适合的设计方案。一般的设计方法只是依靠设计人员的经验来找到最佳方案,这样不足以保证设计参数一定能够向更优方向调整,也不能够保证一定能找到最适合的设计方案。优化设计的手段是采用计算机,在很短的时间内就可以分析一个设计方案,并判断方案的优劣、是否可行,因此就能够从大量的方案中选出更加适合的设计方案,这是常规设计所不能比的。 1 机械系统优化设计方法概述 许多机械工程设计都需要进行优化。优化过程可以分为三个部分:综合与分析、评价、改变参数三部分组成。其中,综合与分析部分的主要功能是建立产品设计参数与设计性能、设计要求之间的关系,这也就是一个建立数学模型的过程。评价部分就是对该产品的性能和设计要求进行分析,这就相当于是评价目标函数是否得到改善或者达到最优,也就是检验数学模型中的约束条件是否全部得到满足。改变参数部分就是选择优化方法,使得目标函数(数学模型)得到解,同时根据这种优化方法来改变设计参数。 在许多机械工程设计问题中,优化设计的目标是多种多样的,按照所追求的目标的多少,目标函数可以分为单目标函数和多目标函数。以多级齿轮传动系统设计过程为例,要求在满足规定的传动比和给定最小齿轮、大齿轮直径的条件下,追求系统的转动惯量最小,箱体的体积最小,各级传动中心距和最小,承载能力最高,寿命最长等,这就是一个多目标函数。目标函数作为评价方案中的一个很重要的标准,它不一定有明显的物理意义、量纲,它只是代表设计指标的一个值。所以,目标函数的建立是否正确是优化设计中很重要的一项工作,它既要反映用户的需求,又要敏感地、直接地反映设计变量的变化,对优化设计的质量及计算难易程度都有一定的影响。表2.1给出了常用优化设计中的可供选择的优化目标。 优化设计问题的前提是选择优化设计方法,选用哪个方法好,这就主要是由优化设计方法的特性和实际设计问题的具体情况来决定。一般来讲,评价一种优

(整理)3 高速级齿轮设计.

3 高速级齿轮设计 3.1 选定齿轮类型,精度等级,材料及齿数 3.1.1 压力角 选定直齿圆柱齿轮,属于一般用途的齿轮传动,压力角取20°。 3.1.2 精度选择 带式输送机为一般工作机器(通用减速器),参考表10-6[2],选用7级精度。 3.1.3 材料选择 由表10-1[2],选择小齿轮材料为40Cr (调质),齿面硬度280HBS ,大齿轮材料为45号钢(调质),齿面硬度为240HBS 。硬度差为40HBS 。 3.1.4 齿数选择 闭式齿轮传动,试选小齿轮齿数z 1=20,大齿轮齿数z 2为: 21=z u z ? (3-1) 式中:z 1 ——小齿轮齿数; u ——Ⅰ轴与Ⅱ轴之间的传动比。 故由式3-1,得大齿轮齿数z 2: 2=4.8320=96.6z ? 取z 2=97。 3.2按齿面接触疲劳强度设计 3.2.1 试算小齿轮分度圆直径 小齿轮分度圆直径d 1t 可由下式近似计算: [] 2 131 21 Ht H E d H K T Z Z Z u d m u m ε φσ?? +=?? ? ??? (3-2) (1)确定公式中的各参数值 ①试选K Ht =1.3。

②小齿轮传递的转矩T 1为: 6 19.5510 I I P T N mm n =?? (3-3) 式中:P Ⅰ ——Ⅰ轴的输入功率,单位:kW ; n Ⅰ ——Ⅰ轴的转速,单位:r/min 。 故由式3-3,得小齿轮传递的转矩T 1: 6 411 9.5510 2.38110T P N mm N mm n =??=?? ③因为小齿轮相对支承非对称布置,所以由表10-7[2],可查得齿宽系数Φd =1。 ④由图10-20[2],可查得区域系数Z H =2.5。 ⑤由表10-5[2],可查得材料的弹性影响系数Z E =189.8MPa 1/2。 ⑥接触疲劳强度用重合度系数Z ?为: 3 4α εε-= Z (3-4) 式中:?α——端面重合度,按下式计算: 11* 122* 21122cos arccos[]2cos arccos[]2(tan tan )(tan tan ) 2a a a a a a z z h z z h z z αα αα αααααεπ =+=+-+-= (3-5) 式中:z 1 ——小齿轮齿数; z 2 ——大齿轮齿数; h a * ——齿顶高系数; α ——压力角,单位:°。 故由式3-4、3-5,得接触疲劳强度用重合度系数Z ?:

传动比计算

126 §5-6 定轴轮系传动比的计算 一、轮系的基本概念 ● 轮系:由一系列相互啮合的齿轮组成的传动系统; ● 轮系的分类: 定轴轮系: 所有齿轮轴线的位置固定不动; 周 转轮系:至少有一个齿轮的轴线不固定; ● 定轴轮系的分类: 平面定轴轮系:轴线平行; 空间定轴轮系:不一定平行; ● 轮系的传动比: 轮系中首、末两轮的角速度(或转速)之比,包括两轮的角速比的大小和转向关系。 传动比的大小:当首轮用“1”、末轮用“k ”表示时,其传动比的大小为: i 1k = ω1/ωk =n 1/n k 传动比的方向:首末两轮的转向关系。 相互啮合的两个齿轮的转向关系: 二、平面定轴轮系传动比的计算 特点: ●轮系由圆柱齿轮组成,轴线互相平行; ●传动比有正负之分: 首末两轮转向相同为“+”,相反为“-”。 1、传动比大小 设Ⅰ为输入轴,Ⅴ为输出轴; 各轮的齿数用Z 来表示;

127 角速度用ω表示; 首先计算各对齿轮的传动比: 所以: 结论: 定轴轮系的传动比等于各对齿轮传动比的连乘积,其值等于各对齿轮的从动轮齿数的乘积与主动轮齿数的乘积之比; 2、传动比方向 在计算传动比时,应计入传动比的符号: 首末两轮转向相同为“+”,相反为“-”。 (1)公式法 式中:m 为外啮合圆柱齿轮的对数 举例: (2)箭头标注法 采用直接在图中标注箭头的方法来确定首末两轮的转向,转向相同为“+”,相反为“-”。 举例: 12 2112z z i ==ωω322233 3 2z i z ωωωω''' = = = 334 34443z i z ωωωω' '' ===4 55 445z z i = = ωω1 1211) 1(--== k k m k k z z z z i ω ω

机械设计—螺纹联接与螺旋传动计算题

例13-1 如图所示,用8个M24(d 1=20.752 mm )的普通螺栓联接的钢制液压油缸,螺栓材料的许用应力][σ=80 MPa ,液压油缸的直径D =200 mm ,为保证紧密性要求,剩余预紧力为P Q '=1.6F ,试求油缸内许用的的最大压强P max 。 1.先根据强度条件求出单个螺栓的许用拉力Q ; 2.在求许用工作载荷F 。 解:根据: ][ ≤4 3.1= 2 1σπ σd Q ca , 解得: Q ≤][ 3.1×4 2 1σπd =80×3 .1×4752.20 2π =20814 N 依题意: F F F F Q Q P 6.26.1=+=+'= 由: 2.6F = 20814,解得:F = 8005 N 汽缸许用载荷: F Σ = z F = 8F = 64043 N 根据: 6404342 max ==∑D p F π 解得: 04.220064043 442 2 max =??= = ∑ ππD F p MPa 例13-5 如例13-5图1所示螺栓联接,4个普通螺栓成矩形分布,已知螺栓所受载荷R = 4000 N ,L =300mm ,r =100mm ,接合面数m =1,接合面间的摩擦系数为f = 0.15,可靠性系数K f = 1.2,螺栓的许用应力为][σ=240MPa ,试求:所需螺栓的直径(d 1)。 解:(1) 将R 简化到螺栓组形心,成为一个横向载荷R 和一个转矩T ,如例13-5图2所示,其中: 510123004000?=?==RL T Nmm (2) 求每个螺栓联接承受的分力 R 的分力:F SR = R/z = 4000/4 =1000 N T 的分力:3000100410125 =??===∑zr T r T F i ST N (3求F S max ?++=45cos 22 2max ST SR ST SR S F F F F F = ???++45cos 3000100023000100022= 3774 N (4) 据不滑移条件:Q P f m ≥K f F S max 所需预紧力Q P : fm F K Q S f P max ==1 15.037742.1??= 30192 N (5) 根据强度条件:2 14 3.1d Q P ca π σ= ≤][σ 例13-5图2

齿轮系传动比计算 (1)

齿 轮 系 传 动 比 计 算 C 1 齿轮系的分类 在复杂的现代机械中,为了满足各种不同的需要,常常采用一系列齿轮组成的传动系统。这种由一系列相互啮合的齿轮(蜗杆、蜗轮)组成的传动系统即齿轮系。下面主要讨论齿轮系的常见类型、不同类型齿轮系传动比的计算方法。 齿轮系可以分为两种基本类型:定轴齿轮系和行星齿轮系。 一、定轴齿轮系 在传动时所有齿轮的回转轴线固定不变齿轮系,称为定轴齿轮系。定轴齿轮系是最基本的齿轮系,应用很广。如下图所示。 二、行星齿轮系 若有一个或一个以上的齿轮除绕自身轴线自转外,其轴线又绕另一个轴线转动的轮系称为行星齿轮系,如下图所示。 1. 行星轮——轴线活动的齿轮. 2. 系杆 (行星架、转臂) H . 3. 中心轮 —与系杆同轴线、 与行星轮相啮合、轴线固定的齿轮 4. 主轴线 —系杆和中心轮所在轴线. 5. 基本构件—主轴线上直接承受 载荷的构件. 行星齿轮系中,既绕自身轴线自转又绕另一固定轴线(轴线O1)公转的齿轮2形象的称为行星轮。支承行星轮作自转并带动行星轮作公转的构件H 称为行星架。轴线固定的齿轮1、3则称为中心轮或太阳轮。因此行星齿轮系是由中心轮、行星架和行星轮三种基本构件组成。显然,行星齿轮系中行星架与两中心轮的几何轴线(O1-O3-OH )必须重合。否则无法运动。 根据结构复杂程度不同,行星齿轮系可分为以下三类: (1)单级行星齿轮系: 它是由一级行星齿轮传动机构构成的轮系。一个行星架及和其上的行星轮及与之啮合的中心轮组成。 (2)多级行星齿轮系:它是由两级或两级以上同类单级行星齿轮传动机构构成的轮系。 (3)组合行星齿轮系:它是由一级或多级以上行星齿轮系与定轴齿轮系组成的轮系。 行星齿轮系 根据自由度的不同。可分为两类: 1450rpm 53.7rpm 1 2 H 3 1 2 3 4 H 5 1 2 H 3

偏心齿轮传动的快速优化设计要点

机械设计课程设计 设计题目:偏心齿轮传动的快速优化设计学校: 专业:机械设计与制造2012级秋 姓名: 指导老师: 完成设计时间:

目录 摘要 (2) 绪论 (3) 1 偏心齿轮简介化原理 (4) 2 偏心齿轮快速优化设计 (5) 2.1 偏心齿轮传动设计计算公式推导 (5) 2.2 偏心齿轮优化设计模型的建立 (6) 2.3偏心齿轮优化设计的程序实现 (8) 2.4偏心齿轮优化设计示例 (9) 结论 (10) 参考文献 (11)

摘要 偏心齿轮虽然在制造上与普通渐开线齿轮无异,却属于变传动比的非圆齿轮传动,设计计算十分复杂。本文将优化设计概念引入非圆齿轮设计,使非圆齿轮设计方法从传统的基于分析的设计发展为基于综合的设计,避免了带有较大盲目性的参数试凑和反复校验过程, 提高了非圆齿轮传动设计的科学性和一次成功率。 关键词:偏心齿轮非圆齿轮优化目标规划

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螺纹连接和螺旋传动练习题

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443 高速级齿轮传动设计

目 录 一、传动方案的拟定及电动机的选择 (2) 二、V 带选择 (4) 三.高速级齿轮传动设计 (6) 四、轴的设计计算 (9) 五、滚动轴承的选择及计算 (13) 六、键联接的选择及校核计算 (14) 七、联轴器的选择 (14) 八、减速器附件的选择 (14) 九、润滑与密封 (15) 十、设计小结 (16) 十一、参考资料目录 (16)

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计的齿轮传动质量差,可靠性低,承载能力小。因此,为了使齿轮传动设计既贴近实际工况,又有最优方案,提出将优化设计和可靠性设计理论有机结合起来的设计方法,该方法无论对缩小尺寸,减轻质量,提高承载能力和保证设计可靠性均有现实意义。可靠性设计方法认为作用在齿轮上的载荷和材料性能等都不是定值,而是随机变量,具有明显的离散性质,在数学上必须用分布函数来描述,由于齿轮的载荷和材料性能等都是随机变量,所以必须用概率统计的方法求解。齿轮可靠性设计认为齿轮存在一定的失效可能性,并且可以定量地回答齿轮在工作中的可靠程度,从而弥补常规设计的不足,它已成为质量保证,安全性保证,产品责任预防等不可缺少的依据和手段。 1 齿轮传动可靠性优化设计的数学模型 设计一对齿轮传动(目标函数为体积或质量最小),已知条件:传递功率N=20 KW,小齿轮转速n=1000rpm,传动比u=3,小齿轮材料为40Cr,齿面淬火,大齿轮材料为45钢,调质处理, 齿轮制造精度为8级,中等冲击,单向传动, 每年工作300天,工作十年,要求齿轮强度的可靠度为0.98以上。 1.1 可靠性优化设计模型的建立方法 根据已知条件和设计要求,齿轮传动的可靠性优化设计数学模型的建立可选用均值模型。 求 X=|1,2 |T x x xn min E{f(X,ω)} s.t. p{g n(X,ω)30}3a n (n=1,2,3 n p) (1)

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10. 润滑密封设计 11. 联轴器设计 1.传动装置总体设计方案: 1. 组成:传动装置由电机、减速器、工作机组成。 2. 特点:齿轮相对于轴承不对称分布,故沿轴向载荷分布不均匀, 要求轴有较大的刚度。 3. 确定传动方案:考虑到电机转速高,传动功率大,将V带设置在高速级。 其传动方案如下: 初步确定传动系统总体方案如:传动装置总体设计图所示。 选择V带传动和单级圆柱斜齿轮减速器。 η 传动装置的总效率 a η=η1η2η32η4=0.876; η(为V带的效率)=0.95,η28(级闭式齿轮传动)=0.97 1 η(弹性联轴器)=0.99 η3(滚动轴承)=0.98, 4 2.电动机的选择

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