Industrial Brushless Servomotors Episode 1 pps

Preface The industrial brushless servomotor has developed through a remarkable combination of mechanical, electrical, power electronic and microelectronic technologies, and both the operation and application of the motor rely on many interdependent factors. I have tried to cover the fundamentals of the subject in a logical manner, taking a step-by-step approach, describing first the construction of the brushless machine itself and how it works, second, how the current is supplied, third, how the motor behaves when it is loaded and finally how it is rated and selected for a particular duty. The book covers the important motor and load characteristics which affect the design of the control system, but does not include a detailed treatment of control techniques which are well described elsewhere. The first chapter is devoted to a brief review of the brushed, permanent magnet motor. This allows the early introduction to the book of some basic groundwork using what is perhaps a more familiar machine, and also allows a clearer comparison to be made with the brushless type later on. Throughout I have been aware of the needs of engineers and students with no previous knowledge of how brushed or brushless motors work, and so both forms are explained from first principles. Theoretical analysis is developed in relation to practical examples, and rules of thumb are suggested wherever possible. Any equations for motor rating and selection are simple enough for numerical results to be found using a calculator or spreadsheet. My hope is that this publication will be of xiv Preface some help to those who are already using brushless motors in servomechanisms, as well as to those who are studying the electrical and mechanical properties which are involved. The practical nature of this book has been made possible by the generous supply of technical advice from the members of staff of SEM Ltd. I wish to acknowledge a debt of gratitude to Paul Newall for his constant support and for the many hours of his time taken up by our discussions, and also to Van Hamlin and Omar Benzaid for their readily given advice and practical help. I am also indebted to several members of staff of the University of Bristol, and wish to acknowledge here the help given by two in particular. Duncan Grant suggested the basic idea for the book and followed through with advice and encouragement from start to finish. I am also extremely grateful to have had the very willing help, particularly with the systematic solution of quartic equations, of Gordon Reece of the Department of Engineering Mathematics. Finally, I would like to give a special thanks to Paul Prater of Lewis Berl Automation. Acknowledgement The various photographs were kindly supplied by the following companies: SEM Ltd, Kangley Bridge Road, London SE 26 5AS, UK Parker Hannifin GmbH, Hauser Division, Robert-Bosch-Str. 22, 77656 Offenburg, Germany. List of units Unit symbol A oc H mH Hz J kg m mm A-turn H/m kg m 2 N Nm rad #rad/Nm S ms m/s Nm/rad Nm/rad s- T V V/rad s -1 W ~ Wb f~ Name ampere degree centigrade henry millihenry hertz joule kilogram metre millimetre ampere-turn henry per metre kilogram-square metre newton newton metre radian microradian per newton metre second millisecond metre per second newton metre per radian newton metre per radian per second tesla volt volt per radian per second watt degree centigrade per watt weber ohm List of symbols Symbol AC B C Cp d D DC e E F G H i I lrms lS J J Jm JL Jr KE K'r L LEE 1 m N N~ Definition alternating current magnetic flux density compliance profile constant screw pitch damping constant direct current base of the natural logarithm electromotive force (emf) force gear ratio magnetic field intensity instantaneous current current root-mean-square current continuous stall current imaginary operator x/~ moment of inertia motor moment of inertia load moment of inertia ratio of load to motor moments of inertia voltage constant torque constant inductance brushless motor inductance, line to line length mass number of turns number of turns on a sinusoidal winding Un/ts T #rad/Nm rn Nm/rad s -l V N A/m A A A A kg m 2 kg m E kg m 2 V/rad s -l Nm/rad s- H in kg List of symbols xvii P Psp R Rth RthT"m RLL p F SI s T TL rs rsoac Trms t tp t 1 V v x s # 0 Oo Oss Opk Oav Omin 0 0p O" Te Tm power speed-sensitive loss resistance thermal resistance motor rating coefficient brushless motor resistance, line to line profile distribution factor radius m international system of units Laplace operator s- a +jw S -l torque Nm load torque Nm continuous stall torque Nm continuous rated torque Nm required torque Nm time s duty operation time s duty cycle period s circuit input voltage V velocity m/s linear displacement m energy J magnetic flux Wb stator angle of sinewave motor conductors rad permeability H/m temperature ~ ambient temperature ~ steady-state winding temperature ~ peak, winding ripple temperature above O0 ~ average, winding temperature above O0 ~ minimum, winding ripple temperature above O0 angular displacement angle of load rotation real part of Laplace operator s electrical time constant of motor s mechanical time constant of motor s W W ~ ~ ms/W o C rad or ~ rad xviii List of symbols TM Tth Tw 02 6dm 6OL / Wc mechanical time constant of motor and load s thermal time constant of motor thermal time constant of motor winding angular velocity motor velocity load velocity constant velocity of motor constant velocity of load S S rad/s rad/s rad/s rad/s rad/s CHAPTER I BRUSHED DC MOTORS I.I Introduction Industrial brushless servomotors can be divided into two main types. One operates in a similar way to the three-phase synchronous motor and the other is a relatively simple development of the brushed DC motor. Both types of brushless motor have the same sort of construction and have an identical physical appearance. Both have many characteristics similar to those of a permanent magnet brushed DC motor, and both are operated from a source of direct current. A review of the features of the permanent magnet brushed motor is therefore a convenient first step in the approach to the brushless type. In this first chapter, the relationships between the supply voltage, current, speed and torque of the brushed motor are developed from fundamental electromagnetic principles. Attention is also given to the factors controlling the steady-state speed of the unloaded motor. The later part of the chapter is devoted to the question of DC motor rating. Only the basic ideas are covered at this stage, in preparation for the more detailed treatment in Chapter 5. The power losses which lead to motor temperature rise are identified, and the main factors affecting the final steady-state Industrial Brushless Servomoters 1.2 2 temperature are explained for both continuous and intermittent operations of the motor. The scope of this chapter is confined to cases where the losses during periods of speed change are insignificant in Comparison to those generated during the periods of constant motor speed. 1.2 Operational principles Motor construction Figure 1.1 shows the essential parts of a rudimentary permanent magnet DC motor. Two conductors are connected in series to form a winding with one turn. The winding has a depth ! and width 2r metres and is mounted between the poles of a permanent magnet. The winding is free to rotate about the dotted axis and its ends are connected to a DC source through sliding contacts to form a circuit carrying current I A. The main diagram is drawn for the moment when the conductors are passing the centre of the poles. The contacts allow the direction of current in the winding to reverse as it moves through the vertical position, ensuring that the direction of flow through the conductors is always the same relative to the direction of the magnetic field. In other words, it does not matter in the diagram which side of the winding is to the left or right when we look at how torque is produced. Torque production The torque produced by the motor in Figure 1.1 is the result of the interaction between the magnetic field and the current- carrying conductors. The force acting on each conductor is shown as F. Some simple magnetic principles are involved in the evaluation of the torque. Brushed DC motors 3 + 0 v 0 Rotating contacts T / $ / S S 4 S 4 y , 2r s i I :: ::: ;~.:: ~:~ j. S S S / View A Figure 1.1 Principle of the permanent magnet brushed DC motor Conductor Magnetic flux r The amount of magnetic flux in a magnetic field tells us how much magnetism is present. By itself, it does not give the strength of the field. The flux may be represented by lines drawn between the poles of the magnet and in the old British system the unit of flux was, in fact, the line. In the SI system Industrial Brushless Servomoters 1.2 4 the unit is the weber, denoted by Wb, where one weber is equivalent to 10 lines in the old system. Magnetic flux density B As its name suggests, the term magnetic flux density describes the concentration of the magnetic field. The SI unit of magnetic flux density is the tesla, denoted by T, where a tesla is equal to one weber per square metre. The force on a conductor When a conductor of length l, carrying a current/, is placed in a magnetic field of uniform flux density B, it is found that the conductor is acted on by a force which is at right angles to both the field and the conductor. The force is greatest when the conductor and field are also at right angles, as in Figure 1.1. In this case, the force is given by f = BlI (N) The unit of force is the newton, denoted as N. The direction of F can be found by the 'left-hand motor rule'. This states that the thumb of the left hand points in the direction of the force, if the first finger of the hand is pointed in the direction of the field and the second finger in the direction of the current. Torque Force F acts on each conductor of the winding shown in Figure 1.1. The torque produced at each conductor is T= Fr (Nm) The unit of torque is the newton metre, denoted as Nm. The radius of action of F around the axis falls as the winding moves away from the horizontal position, reducing the torque. In the figure, the winding lies in a plane between the centres of the fiat poles of the magnet, where B is greatest. With such a pole shape the flux will be less dense at other winding positions, reducing the torque still further. [...]... must be applied with caution, as damage to the motor may result from the flow of high current at the low speed, high torque end rpm 3000- 2000- 10 00- I 1 2 Figure 1. 9 Speed versus torque at various supply voltages 3 Torque Nm 14 Industrial Brushless Servomoters 1. 4 Small permanent magnet DC motors have a wide range of applications such as door operators, tape drives, floor scrubbers, conveyors, as well... be slightly lower to allow a small current to flow to supply the losses IO Industrial Brushless Servomoters 1. 3 VDC Figure 1. 5 Unloaded motor at steady-state 1. 3 The loaded motor at steady state The power required to supply a torque of T Nm at a speed of ~o rad/s is = (w) The unit of power is the watt, denoted by W Figure 1. 6 shows a DC motor connected to a load Current flows to the motor following... KTKE m ==.=, =,=~ ~ =J II2 IndustrialBrushless Servomoters 1. 3 from which we see that the speed of the permanent magnet brushed motor varies linearly with torque The speed-torque characteristic shown in Figure 1. 8 is plotted by drawing a straight line between two reference points At the first point, when T is zero, the no-load speed is given by V WNL = KE OI f.ONL 0 Figure 1. 8 DC motor speed-torque... axis, and the pattern of crosses and dots in Figure 1. 3 will be the same for any rotor position The reversals give a rectangular AC waveform to the current in the individual turns of the motor winding Only the brushes carry a unidirectional current : :!!ii i i ;::;i~l ~!!iiii!ii Figure 1. 2 Permanent magnet DC motors 6 Industrial Brushless Servomoters 1. 2 Commutator Conductor slot brush J, Ioc Laminated... value, and the question arises of how the limit in speed occurs To answer, we must look at a second aspect of the behaviour of a moving conductor in a magnetic field 8 1. 2 Industrial Brushless Servomoters Voltage generation Figure 1. 4 shows a conductor of length l which is being moved with velocity v metres per second (m/s) across and at fight angles to a uniform magnetic field of density B As the... Steady-state characteristics In Figure 1. 7 the motor is represented by the resistance R of the rotor winding conductors, and the back emf E The supply voltage is V= RI+E Brushed DC motors II VDC 0 o 71 r =., I I (-~ Motor m =~= m 3 I I Load L I Opposing I Output torque I torque I Figure 1. 6 The loaded motor I I= () I (~ R (~ I DC motor I I ~.,., ,.=m Figure 1. 7 Simple equivalent circuit of a DC... open closed I I I I I I I I I I I I I I I I I I Door velocity m/s i I I opening 1. = v closing Iv Door position Figure 1. 10 Velocity profile for an automatic sliding door i.4 M o t o r rating This section deals with ratings for continuous or intermittent motor operation, the work being broadly relevant to both the brushed and brushless motor The intermittent operations are limited to duty cycles in which... gives N~o E = ~ 71" Brushed DC motors 9 The voltage constant In the last equation above, all quantities except ~o are constant for any given motor and so the induced voltage is E = KE~ where KE is the voltage constant expressed in volts/radian per second or V/rad s -1 KT and KE Comparing the expressions above for T and E shows that for a two-pole motor with a single winding, N~ KT=KE = 71" The equality... R/KTKE of the speed-torque characteristic in Figure Brushed DC motors II3 1. 8 The current carried by the rotor conductors rises with the motor torque The last expression above does not take account of motor losses due to, for example, brush contact and rotor bearing friction, which in practice would cause a reduction in WNL Figure 1. 8 has been drawn for a fixed value of supply voltage For any particular... for a range of operating voltages The smallest of the motors shown in Figure 1. 2 is a two-pole, 24 V motor with the following constants" KT 0.07 N m / A KE = 0.07 V/rad R - 0.70 f~ Using these constants, the no-load speed and the torque developed at the point of stall can be found at several supply voltages up to 24 V Figure 1. 9 shows the resulting characteristics These must be applied with caution, . high torque end. rpm 3000- 2000- 10 00- I 1 2 3 Torque Nm Figure 1. 9 Speed versus torque at various supply voltages 14 Industrial Brushless Servomoters 1. 4 Small permanent magnet DC motors. allow a small current to flow to supply the losses. Industrial Brushless Servomoters 1. 3 IO VDC Figure 1. 5 Unloaded motor at steady-state 1. 3 The loaded motor at steady state The power required. the behaviour of a moving conductor in a magnetic field. 8 Industrial Brushless Servomoters 1. 2 Voltage generation Figure 1. 4 shows a conductor of length l which is being moved with velocity