DESIGN of MOTOR DRIVES with ELECTRONIC CONVERTERS · The asynchronous induction motors of...
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Valery Vodovozov DESIGN of MOTOR DRIVES with ELECTRONIC CONVERTERS
Transcript of DESIGN of MOTOR DRIVES with ELECTRONIC CONVERTERS · The asynchronous induction motors of...
Valery Vodovozov
DESIGN of MOTOR DRIVES with ELECTRONIC CONVERTERS
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Contents
Designations.............................................................................................................................................4 Symbols .............................................................................................................................4 Indexes...............................................................................................................................4 Abbreviations......................................................................................................................4
Preface .....................................................................................................................................................5 Objective...................................................................................................................................................6 Design Algorithm ......................................................................................................................................9 Calculation of Load Data ........................................................................................................................11
Travel Diagram.................................................................................................................11 Support.............................................................................................................................12 Hoist .................................................................................................................................12 Truck and Roll-Table ........................................................................................................13 Conveyer..........................................................................................................................13 Rotary Table.....................................................................................................................14 Crane ...............................................................................................................................15
Gears Dimensioning and Selection ........................................................................................................16 Motor Dimensioning and Selection.........................................................................................................17 Equipment Checking ..............................................................................................................................18 Power Converter Dimensioning and Selection.......................................................................................19 Examples of Truck Drive Fed by Industrial Mains ..................................................................................20
Input Data.........................................................................................................................20 Calculation of Load Data ..................................................................................................20 Gear Unit Dimensioning....................................................................................................20 AC Servo Drive with Complete AC/DC/AC Converter .......................................................21 Asynchronous Motor Drive with Complete AC/DC/AC Converter......................................24 DC Motor Drive with Complete AC/DC Converter .............................................................28
Examples of Truck Drive with Battery Supply ........................................................................................30 Clarifying ..........................................................................................................................30 Asynchronous Motor Drive with Desired Inverter ..............................................................31 DC Motor Drive with Desired Chopper..............................................................................34
Appendixes.............................................................................................................................................38 1. Approximate Efficiency of Transmissions......................................................................38 2. Approximate Friction Factors........................................................................................38 3. Description of “Mitsubishi Electric” Servo Drive Wiring Diagram Fig. 4 .........................38 4. Description of “Sew Eurodrive” Asynchronous Drive Wiring Diagram Fig. 6..................39 5. Description of BTU 3601 DC Drive Wiring Diagram Fig. 8 ............................................40 6. Description of Asynchronous Drive Wiring Diagram Fig. 10..........................................40 7. Description of DC Drive Wiring Diagram Fig. 11 ...........................................................41 8. Useful Links..................................................................................................................41
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Designations
Symbols
a acceleration C capacitance c cyclic duration factor e Euler constant (2.718278) F force g gravitation acceleration (9.81) I current i gear ratio J moment of inertia k gain, factor L inductance ∆l path M torque m mass P power R resistance r radius
s Laplacian operator T period, time constant t time U voltage v speed W transfer function X reactance
γ inertia ratio
η efficiency
θ friction angle
λ overload
µ friction π circle ratio (3.14159)
σ leakage factor
ϕ rotation angle
ω angular speed
Indexes
0 standstill 1 stator 2 rotor a acceleration b braking C converter rated value d dc link e electromagnetic G gear rated value I current J inertia L load M motor rated value
m mechanical max maximum o object r regulator rms root mean square S supply s steady state
µ small time constant
ϕ angle
ω speed
‘ non-converted value
* set-point
Abbreviations
ac alternating current CW clockwise rotation CCW counter-clockwise rotation dc direct current
EMF electromotive force IGBT insulated gate bipolar transistor VAC ac volts VDC dc volts
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Preface
A design is known as a stage of master training where a student gets a possibility to test and develop his private creative potential.
The spectrum of problems, soluble in the process of electromechanical systems’ project development, changes increasingly. Many of them did not enter into designing sphere some years ago, but today they are considered as the urgent problems. First of all it concerns of poorly formalizing processes of automation. Effective design of driving systems meets with a problem of such kind owing to rather complicated algorithms. A list of the integrated design tasks includes: equipment selection, structural synthesis, experiment planning, and its results processing, as well as an improving of the designed systems.
For successful project management, some famous companies have developed their specific technologies. Examples are the guides and software of “Siemens”, “Omron”, “Sew Eurodrive”, “Maxon Motors”, “Mitsubishi Electric”, etc. Commonly, in the initial stage, the area of criteria is produced. Its space dimension is defined by a number of criteria. The set of electromechanical system parameters includes: working forces, load torque, inertia, friction, speeds, accelerations, etc. Using this technology, a designer has an opportunity to choose equipment, to impose restrictions, to estimate results, and to repeat an inquiry on other conditions. Later, one can restructure a list of mechanical gears, motors, and power converters and conduct a search in appropriate databases for the goal of the optimum drive composition.
To master this approach, try to do carefully:
• understand the problem to such a degree, that provides the finding of solution conditions and ways with maximum capacity and literacy;
• do not turn on the result’s obtaining at once but foresee a number of iterations leading to the goal little by little and step by step; “a value of experience is equal to the number of errors”, thus appliances are not the same as the cook book;
• search the most rational and technological means, which are exactly what's the problem needed, avoiding the blind variants sorting out;
• learn to discovering and throwing away baffle versions;
• think out and calculate your solution so that be ready to defend it any way.
During the design, endeavor to arrange your educational process with maximum usefulness, which helps you to get the most experience in the field.
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Objective
The goal of this work is gaining of the first experience in electric drive calculation methods, equipment selection, validity checking, and topology optimization as well as the circuit diagrams development and system simulation.
The types of gears, motors, and power converters for the particular learning problems should meet the demands, which are given in the table below.
* Gear: gt – spur, gp – planetary, gs – ball screw, gw – worm; electric drive type: ma – asynchronous, ms – synchronous servo drive, md – direct current; converter: c – transistor, ct – thyristor.
** Other data: support – cutting force LF (N), hoist – motion duration Lt (s), truck –
wheel radius Lr (m), conveyer – slope angle Lθ (rad), roll-table – roll radius Lr (m),
rotary table – table radius Lr (m), crane – mechanism mass Lm (kg).
The drafts of all mechanisms and the travel diagrams of the cycling mechanisms are shown in Fig. 1.
The block circuit diagram of an electric drive is given in Fig. 2. Power supply SP enters the
circuit from the mains or from an on-board battery. The power electronic converter
Vari-ant
Loading mechanism
Drive com- position*
Mass m, kg
Speed v, m/s
Shaft radius r, m
Acceleration a, m/s2
Path ∆l, m
Cycle T, s
Other**
1 gs-ms-c 1500 0.1 – 0.2 3 35 3000
2 gs-ma-c 1250 0.15 – 0.3 2 15 2500 3
Support
gs-md-ct 1000 0.2 – 0.4 1 7 2000 4 gp-ms-c 300 – 0.025 – 1 6 5 5 gw-ma-c 400 – 0.050 2.0 2 8 7.5 6
Hoist
gt-md-ct 500 – 0.125 – 3 9 8 7 gw-ms-c 3000 0.6 0.035 – – – 0.25
8 gt-ma-c 2500 0.5 0.030 1.0 – – 0.3 9
Truck
gp-md-ct 2000 0.4 0.025 – – – 0.35 10 gp-md-ct 250 0.7 0.150 – – – 0.12 11 gt-ma-c 230 0.5 0.130 0.3 – – 0.08 12
Conveyor
gw-ms-c 210 0.3 0.110 – – – 0.05 13 gp-ms-c 500 0.9 0.020 – – – 0.2 14 gp-ma-c 1100 0.5 0.030 0.3 – – 0.04
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Roll-table
gw-md-ct 5000 0.4 0.040 – – – 0.05 16 gw-ms-c 300 – 0.500 – – 10 0.5 17 gp-ma-c 250 – 0.400 – – 8 0.6 18
Rotary table
gp-md-ct 200 – 0.300 – – 9 0.9 19 gp-ms-c 100 0.2 0.100 – 0.5 10 20 20 gw-ma-c 150 0.3 0.150 1.0 0.8 8 25
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Crane
gt-md-ct 200 0.4 0.200 – 1.0 6 30
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transforms the energy of power supply into the energy supplying the motor. In turn, the motor converts the electrical energy into the mechanical one. The gear transforms the energy induced in the motor gap into the output shaft rotation. Usually, it steps down the motor shaft angular speed and steps up the rotational torque simultaneously. The set-point velocity or angle and motion law enter the controller. Another controller inputs acquire the sensors information about the speed, current, etc. Using these data, the controller generates the input signals for the power converter.
Supply Motor Converter
ms (synchronous servo motor) ma (asynchronous squirrel-cage motor)
ac/dc/ac (transistor dc link converter)
ac (industrial
mains) md (permanent-field dc motor) ac/dc (thyristor bridge rectifier)
ma (asynchronous squirrel-cage motor) dc/ac (transistor inverter) dc (on-board battery) md (permanent-field dc motor) dc/dc (transistor chopper)
v
T
t
v
T
t
t
v
T
t
T
v
Support Hoist
Truck Conveyer Roll-Table
Rotary table Crane
Fig. 1
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Multiple possible configurations of electric drive are represented in the table. Their distinguishing features are in the supply source, motor type, and converter topology. A designer may select complete converters or propose an original design. Also, multiple controller arrangements with different number and types of regulators and adjusted variables of feedback systems are possible.
The asynchronous induction motors of high-dynamic applications usually perform with field-oriented control, which ensures that stator and rotor flux are always perpendicular to one another. This type of motor is cheap to manufacture and is able to operate in the field-weakening range. The disadvantage of the asynchronous motor is its low efficiency due to current-dependent losses occur in the rotor that require somewhat additional unit volume and higher converter output, especially in the range of lower speeds. These drives are then commonly provided with forced cooling fans or their speed control range or torque is reduced.
The permanent-field synchronous motor equipped with position encoder is more expensive. At the same time, it has low moment of inertia, simpler self-cooling as power loss occurs in the stator rather than the rotor, and greater efficiency.
The old-fashion brushes dc motors have the advantages of both mentioned machines, but less reliability and higher maintenance costs. Controlled thyristor rectifiers are the typical base of their power converters rather than the transistor inverters used for the ac drives.
The initial data for a gear selection are as follows: the required power GP , the output shaft
torque GM , the ratio i , and the output shaft angular speed Gω . The initial data for a motor
selection are: the required power MP , the shaft torque MM , moment of inertia MJ , and the
angular speed Mω . The initial data for a power electronic converter selection are: the
required power CP , current CI , and voltage CU . The track, the roll-table, and the conveyer
have a long-term mode of operation, and other mechanisms are cycling operative devices having the period T .
Calculation is possible with acceptance of permissible inertia ratio Jγ = 10 to 300; driving
mechanism efficiency L η = 0.8 to 0.9; overtorque M λ = 2.5 to 5.5; overcurrent I λ = 1.2 to 1.7;
y
P1
y*
Power converter
Fig. 2
.
Gear Motor
P2
Controller
PS PL
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factor of safety k = 1.2 to 1.5. Approximate gear efficiencies G η , sliding friction factors µ, and
rolling friction factors r µ are indicated in Appendixes 1 and 2.
The final design report should include next results:
• request for proposal with the individual input data; • timing calculation and the mechanism travel diagram;
• mechanism forces calculation and torque/power patterns;
• gear dimensioning and selection; • motor dimensioning and selection;
• optimum motor-gear set selection and checking;
• power electronic converter dimensioning and selection or design • motor drive wiring diagram;
• data and simulation results with transients of open-ended system;
• conclusion concerning the summary of the project.
Design Algorithm
A design algorithm depends on whether the complete converters will be used or the original ones are designed. The first way is more conventional due to simplicity of the project. The second way leads to higher efficiency but sometimes provides more expensive application. The flowchart of the design algorithm is depicted in Fig. 3.
At first, the mechanism travel diagram ( )tv is developed. Then, the drive loading calculation
is executed with the load torque M ′ , power LP , moment of inertia J ′ , and angular speed ω′
finding. If acceleration is restricted, the dynamic calculation is carried out right away. As a result of these calculations, a torque diagram of the load shaft ( )tM′ or power diagram of the
load ( )tPL is drawn.
After acquainting with data sheets of gears and motors that correspond to the required drive type, it is ought to select 3 to 5 gear models (with different output speeds, if possible) using the calculation results. Through these gears, the forces and mechanism speed found before will be converted to the equivalent values on motor shaft.
For each gear model, the own motor model is to be picked out, counted on the converted forces and speed. Ones the equipment framework will be found, the new problem appears: which of the suitable motor-gear combinations are optimum? To find a solution, a designer can form appropriate criteria and sort them. It may be a criterion of maximum accuracy or speed, minimum weight, power, or inertia, highest rigidity, etc. Thus, the whole scale of the electromechanical and electronic properties is gathered, from which the choice is done on the basis of judgments about preferences of that or other criterion.
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Fig. 3
Yes
Yes
No
No
No
No
No Yes
Yes
Is starting possible?
Start
Travel diagram building
System steady-state calculation
Restricted acceleration?
Gear selection
Forces converting to the motor shaft
System dynamic calculation
Gear selection
Motor matching for each gear
System dynamic calculation
Forces converting to the motor shaft
Motor matching for each gear
Cycling mode?
Asynchronous electric drive?
Permissible starting frequency calculation
Is heating valid?
Power electronic converter selection
End
Regulators design
Yes
Optimum motor-gear set selection
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Then, it is required to check the dynamic overloading of the optimum motor-gear set. For the systems with the cycling mode of operation, the equivalent load heating evaluation is necessary. For the asynchronous drives, which periodic operation includes a pause when the motor is at a standstill, the cyclic duration factor (permissible number of stops and starts per hour) is to be calculated.
A power electronic converter is picked out to the motor-gear set, which meets all requirements mentioned above. After that, the simulation of the open-loop system is carried.
On the last stage, which is not described here, the control system is designed. It includes some regulators and sensors. Their transfer functions, gains, factors, and time constants are calculated to meet the standard settings. Then, the closed-loop system testing is carried out on the model and its optimization is executed, if necessary.
Calculation of Load Data
Travel Diagram
The initial data for the travel diagram are as follows: the mechanism mode of operation, its speeds, and timing intervals of motion and standstill. The long-term mode of operation is typical for the truck, roll-table, and conveyer. The intermitted duty is the mode of operation of the support, rotary table, hoist, and crane. The support and the rotary table change their motion direction at the end of the path. The hoist moves the weight upward with the pause in the odd cycles, and then moves the weight downward with the pause in the even cycles. The crane moves downward without weight with pause and moves the weight upward with pause in the odd cycles, then moves the weight downward with pause and moves upward without weight with pause in the even cycles.
When velocity v is not referred, it should be calculated beforehand using the required motion duration Lt and distance l∆ :
Ltl
v∆
= .
The rotary rotates during TtL < along the distance Lrl 2π=∆ . In case of the limited
acceleration a , find velocity as a solution of the quadratic equation:
( )2
4 laatatv LL ∆−−=
2
.
Acceleration and deceleration times are as follows:
av
ta = ,
and the lengths of acceleration and deceleration paths are:
2
2a
aat
l =∆ .
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When acceleration is not restricted by initial data, the starting values are accepted as 0=∆= aa lt . If the mechanism travel distance is limited by the value l∆ , then its constant
speed distance should be calculated as:
as lll ∆−∆=∆ 2 ,
the time of the constant speed motion is:
vl
t ss
∆= ,
the full travel time is:
saL ttt += 2 ,
and the standstill time is:
LtTt −=0 (or LtT
t −=20 for the crane).
Support
The support static power is calculated according to the following formula:
. η
µ
+=
LLL
mgFkvP
Hoist
The static load torques for the upward and downward modes are next:
L
mgrM
η=′ , LmgrM η0 −=′ .
When the acceleration is limited, the dynamic torque of the upward motion run-up is:
La
marMM
η+′=′ ,
and for the upward braking:
Lb marMM η−′=′ .
Run-up behavior of the downward motion and the downward braking are described as:
La
marMM
η00 +′=′ ,
Lb marMM η00 −′=′ .
Static power is equal to:
LL
mgvP
η= .
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The angular speed of the shaft is:
rv
=′ω .
Moment of inertia is:
2mrJ =′ .
Truck and Roll-Table
Friction factor of these mechanisms is determined by the formula:
L
r
rrµµ
µΣ+
= .
The mechanisms’ static power is:
LL
vmgP
η
µΣ= .
In case of the slope with angle ±α:
( )αµαη
cossin Σ±=L
Lmgv
P .
The angular speed of the wheel (the roll) is described by the following formula:
Lrv
=′ω .
The static load torque depends on friction:
ω′=′ LP
M .
When the acceleration is limited, the dynamic run-up torque and the braking torque depend on friction and inertia:
L
La
marMM
η+′=′ ,
LLb marMM η−′=′ .
Moment of inertia is:
2LmrJ =′ .
Conveyer
The retarding force of the tape upward moving is:
( ))cos(
sinθ
θθ += L
L mgF
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where ( )µθ arctan= is a small friction angle of the ribbon tape on the rolls. The retarding
force of the weight downward moving is:
( )( )0
00
θ
θθ
cossin L
L mgF−
=
where ( )00 µθ arctan= is the substantial friction angle of the metal weight on the conveyer
tape. The mechanism static power is calculated as:
( )L
LLL
vFFP
η
0+= .
The angular speed of the shaft is:
rv
=′ω .
The static load torque is:
ω′=′ LP
M .
When the acceleration is restricted, the dynamic torque of the mechanism run-up is:
La
marMM
η+′=′
and the torque of braking is:
Lb marMM η−′=′ .
Moment of inertia is:
2mrJ =′ .
Rotary Table
The angular speed of the rotary table is:
Lrv
=′ω .
Its static torque depends on friction as:
L
rmgM
η
µ=′ .
The static power is:
ω′′= MPL .
The table moment of inertia is:
2
2Lmr
J =′ .
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When the acceleration is restricted, the dynamic torque of the mechanism run-up depends on inertia as follow:
La
marMM
η+′=′
and the proper braking torque is:
Lb marMM η−′=′ .
Crane
The angular speed of the shaft is:
rv
=′ω .
The static power and torque of the weight moving upward are as follows:
( )ωη
,
′=′
+= L
L
LL
PM
gvmmP
and for the weight moving downward are as follows:
( ) LLL gvmmP η 0 +−= , ω
00 ′=′ LP
M .
The static power and torque of moving upward without weight are:
ωη ,
′=′= L
L
LL
PM
gvmP
and for the moving downward without weight:
ωη 0
00 ,′
=′−= LLLL
PMgvmP .
When the acceleration is restricted, the mechanism dynamic torques of upward run-up and braking are:
L
La
armmMM
η
)( ++′=′ , LLb armmMM η )( +−′=′
and for downward run-up and braking:
L
La
armmMM
η
)(00
++′=′ , LLb armmMM η )(00 +−′=′ .
In case of no-load operation, m is not taken into account. Moment of inertia is:
( ) 2 rmmJ L+=′ .
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Gears Dimensioning and Selection
Calculation results of the driving mechanism become the basis for the gear selection requirements. For proper torque and speed conversion, the gear has to be of the low inherent mass moment of inertia and circumferential backlash as well as high rigidity and efficiency. A distinction is made, according to the direction of the power flow, between coaxial or parallel shaft gear units and right-angle gear units. With the first, like the spur or helical and planetary gears, the power flows linearly whereas with the last, like the worm and ball screw gears, the power is turned through a right angle.
Desired torque of the selected gears should exceed any of the previously calculated load torques:
, ,max baG MMMM ′′′≥ .
Desired gear power of the hoist, truck, roll-table, conveyer, and rotary table is:
iP
P GLG
ω
ω
′≥ ,
and desired power of the crane gear is:
i
PPP GLLGω
ω0 ,max
′≥
where Gω is the gear rated speed and i is the gear ratio listed in the data sheet. The desired
angular speed of the gear input shaft is:
iLG ωωω ′=≥ .
The ball screw gear of the support must pick up a velocity
vvG ≥
and power
v
vPP G
LG ≥ .
The screw with a radius Gr rotated with the angular speed
GL r
v== ′ωω
should overcome the static counter-torque
ω′=′ LP
M .
The ball screw gear run-up torque is:
G
Ga
marMM
η+′=′ ,
and the braking torque is:
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GGb marMM η−′=′ .
Thus, this gear ratio is:
G
GG
vr
iω
=
where Gω is the ball screw gear rated angular speed. Moment of the support inertia is:
2
2
ω′=′
mvJ .
All chosen gears with their data ought to be submitted in the report for consideration.
Motor Dimensioning and Selection
The mechanism torques are converted into the equivalent values on motor shaft through the gear as follows:
iM
MG
L η
′= ,
iM
MG
aLa
η
′= ,
iM
M GbLb
η′=
where G η is the gear efficiency. The hoist machines during the stopping time have a torque
iM
ML
′=0 .
For each version of gear, it is required to pick out its own motor. This motor ought to develop the rated torque
LM MM ≥ .
If the maximum motor torque maxMM is indicated in the data sheet, then this maximum value
must meet the condition:
maxmax MMM ≥
where ,maxmax LbLa MMM = . In these formulae
M
MM
PM
ω=
is the motor rated torque, MP and Mω are the motor rated power and speed. The mechanism
moment of inertia converted onto the motor shaft is equal
2iJ
JL
′= .
Often, the motor ought to have moment of inertia
J
LM
JJ
γ≥ .
The desired motor speed is:
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LM ωω >
and its power must be
LLM MP ω≥ or L
MLM
PP
ω
ω≥ for the support.
In the report, the chosen motor-gear pairs are to be picked together with their data. That motor-gear set, which has the lowest power or mass, is the best pretender for use in the designed electric drive.
Equipment Checking
For those mechanisms, which start-up acceleration is not restricted, the run-up time may be calculated as follow:
LMM
La MM
Jt
−=λ
ω or
LM
La MM
Jt
−=
max
ω
where L
LM
JJJ
η+= is the electric drive moment of inertia. The corresponding start-up path
and acceleration are:
2vt
l aa =∆ ,
atv
a = .
For the mechanisms those travel distance is restricted, the constant speed distance, motion time, full time, and stopping time require recalculation. The output shaft rotation that matches to the referred path is calculated as follow:
Ltωφ ′′ = .
These results leads to the more exact travel diagram building. For the variants with unlimited start-up acceleration, it is needed the more exact calculation of the dynamic loading of the
chosen motor. For this purpose, the torques LaM , LbM should be calculated and
maxM recalculated. In any case, when the inequalities
MM
MM
λmax≥ ,
maxmax MMM ≥
are violated, the more powerful motor is required to suit the torque demands.
In the cycling mechanisms, the heating conditions are checked using the inequality:
rmsM MM ≥ .
Here
( )020
2221tMtMtMtM
TM LaLbsLaLarms +++=
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is an effective torque. If an asynchronous motor switches off during the pause, then the permissible cycling duration factor is to be limited by the value
−=
MM
L
MM
JJ
kc
λΣ
36001 .
As a result, the finally chosen motor-gear set should comply with all described conditions.
Power Converter Dimensioning and Selection
The power converter type must associate with the motor type. It is a common practice to purchase the motor and converter of one and the same manufacturer, if possible.
The required converter power is:
LC PP ≥
and the maximum power is:
LC MP ωmaxmax ≥ .
Normally, a converter is one size larger than the motor. The motor and load parameters determine the converter current requirements as follow:
M
MLC M
IMI ≥ or
IM
MC M
IMI
λmax≥
as well as its voltage
MC UU ≥ .
For the cycling mechanisms, the converter is calculated in accordance with the average current
( )00tMtMtMtMTM
II LaLbsLaLa
M
Ms +++=
thus the converter rated current should be as follow:
sC II ≥ .
The average current of the hoist machines is calculated for the pair of cycles:
( )aLbaLaLaLbsLaLaM
Ms tMtMtMtMtMtM
TMI
I 0000222
+++++= .
The data of the chosen converter are to be included into the design report. The equipment selection is finished by the simulation of the open-ended converter-motor-mechanism system with the evaluation of the steady speed, start-up time, acceleration, and the service factor of each component. For the simulation, different software may be used such as eDrive, Simulink, pSpice, Electronic Workbench, LabView, etc. The simulation results are subjected to including into the report as well.
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Examples of Truck Drive Fed by Industrial Mains
Input Data
For the transportation application supplied through the cable line from the industrial mains with a sine-wave voltage US = 220 VAC, 50 Hz, a worm gear, electric motor, and appropriate power electronic converter need tp be selected from the complete units. Possible drive compositions should be discussed and compared. The data of the load:
m 3000 kg total moved mass; v 0.5 m/s maximum traveling velocity; r 0.03 m axle radius;
rL 0.25 m wheel radius;
rµ 0.5 mm rolling friction of wheels;
µ 0.020 sliding friction;
Jγ 100 inertia ratio.
Calculation of Load Data
Friction factor is determined as:
0.00440.25
0.030.0200.0005µµµΣ =
⋅+=
+=
L
r
rr
.
Assuming the total efficiency of the drive system L η = 0.85, calculate static power as:
760.85
0.50.00449.813000η
µΣ =⋅⋅⋅
==L
Lvmg
P W.
The angular speed of the wheel is described by the following formula:
20.250.5
ω ===′Lrv
rad / s.
Static load torque is:
382
76
ω===′
′LP
M Nm.
Moment of inertia for the pair of driven wheels is approximately:
187.50,253000 22 =⋅==′ LmrJ kgm 2.
Gear Unit Dimensioning
Required gears should meet the restrictions:
MMG ′≥ , 76238ω =⋅=′≥ ′MPG , and ωω ′≥
iG .
Particularly, the three permissible worm gears of minimum frame sizes are listed in the table below:
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# Gear GP ,
W Gω ,
rad/s GM ,
Nm i Gη ,
%
m, kg
LM ,
Nm Lω ,
rad/s LJ ,
kgm2 1 1.4g-080 570 157 160 63 69 30 0.87 126 0.047 2 1.4g-080 660 105 230 50 71 30 1.07 100 0.075 3 1.4g-080 1120 78.5 340 31,5 74 30 1.63 63 0.189
The load data have been converted onto the motor shaft using the formulae:
iM
MG
L η
′= , iL ωω ′= ,
2i
JJL
′= .
They are included into the gear table too.
AC Servo Drive with Complete AC/DC/AC Converter
When the electric drive is fed from the standard mains, choose the servo motors, which parameters match each gear as follows:
LM MM ≥ , LLM MP ω≥ , LM ωω > .
Possible variants of “Mitsubishi Electric” servo motors are listed in the table below.
# Motor MP ,
W MM ,
Nm
maxMM ,
Nm
Mω ,
rad/s MI ,
A
sMI ,
A MJ , kgm2
m, kg
1 HC-MFS 43 400 1.3 3.8 314 2.8 9.0 0.0000143 1.45
2 HC-PQ 43 400 1.3 2.92 314 2.8 6.44 0.0000146 1.42
3 HC-SFS 52 500 2.39 7.16 210 3.2 9.6 0,00066 5.0
The first of them, which has low mass and high maximum torque and starting current, may be accepted together with the first gear.
Now, select a converter MRC 10A of “Mitsubishi Electric” having CP = 100 W and CI = 6 A,
which satisfies the requirements:
76=≥ LC PP W, 1.871.3
2.80.87=
⋅=≥
M
MLC M
IMI A.
The wiring diagram for the “Mitsubishi Electric” servo drive with MRC 10A is given in Fig. 4 whereas corresponding Appendix 3 gives the functional description of the terminals.
The main circuit terminal block TE includes the power inverter supplied by the dc link voltage processed from the built-in rectifier. The inverter’s pulse-modulated voltage is applied to the motor when the servo on start signal SON is setting. The pulse width is determined by the control circuit output placed in the digital input/output section DE. This pulse-width modulated voltage generates an almost sinusoidal current in the motor, thus the rotating field is produced in the windings of the motor’s stator. This rotating field influences the rotor and exerts a force on it. Due to the magnetic coupling between stator and rotor, the rotor is accelerated into this field and runs at the same angular velocity, i.e. synchronously.
22
Because of the motor loading, a lag of the rotor rotation field in relation to the stator rotating field is produced. The poles of the rotor lag to those of the stator rotating field by a certain electrical angle, known as the load angle. The greater the load angle, the more the torque increases. If the load angle is precisely 90 degrees, i.e. the poles of the rotor lie between two stator poles, then the force operating on the rotor is at its maximum. The stator pole leading the rotor pole “pulls” the rotor and the lagging stator pole “pushes” it, producing the described effect. If the load angle is further increased, i.e. the motor is overloaded, the torque decreases again, motor operation becomes unstable, and the motor stalls and comes to a standstill with the trouble signal ALM.
To be able to operate a synchronous motor with maximum possible torque, it must be insured that the load angle is 90 degrees. This means that the stator field should always lead by 90 degrees when the drive is motoring and lag by 90 degrees when it is regenerating. The motor control circuit calculates the three phase currents of the motor from a given torque and reads out the current set-points from a table stored in the driver’s memory. For this purpose the rotor position is sensed with the position encoder built in the servo motor. The encoder determines the absolute position of the motor shaft over one revolution. 90 degrees are added or subtracted to or from the value of the position angle dependently on the CW/CCW rotation start signals ST1/ST2, according to the direction of rotation and direction of torque, and the associated currents are then calculated. The appropriate position of the stator rotating field is determined to each rotor position, i.e. the rotor determines the magnitude and direction of the stator field. Thus the rotor “rotates” the stator field.
SG
MC
220 VAC
Gear
Fig. 4
M
Encoder
HC-MFS 43
TE
DE
FR
NFB MC
ON OFF
MC
L1
L2
P
C
BC
L1
L2
L1
L1
V
W
U
PE
V
W
U
E
B1 B2
Brake
BE
24 VDC + – SN1
12 V24 20 V+ 1
SON 17 ST1 13 ST2 14 DI1 15 ALM 2 PF 3
ZSP 4
SN3
SN2
MRC 10A
23
Moment of inertia of the drive is
0.0550.85
0.0470.0000143
η=+=+=
L
LM
JJJ kgm2.
Find the run-up time of a set, the corresponding start-up path, and acceleration as follows:
2.390.873.81260.055
max
ω=
−⋅
=−
=LM
La MM
Jt s,
0.62
0.52.392
=⋅
==∆vt
l aa m,
0.22.390.5
===atv
a m/s2.
Then, accepting ML = 5 mH and MR = 10 Ω, find the time constants and the motor constants:
0.000510
0.005===
M
Me R
LT s,
2.151.32.8
===M
MMI M
Ik , 2.15 ω =≈ MIM kk ,
2.542.152.15100.055 ω =⋅⋅⋅== MMIm kkJRT s.
Start-up transients of the servo drive without the speed feedback are shown in Fig. 5. The load speed and motor current traces display the running of the track wheels up to the set-point speed 2 rad/s. In open-ended process, the steady-state speed is less than the reference speed due to the additional voltage drop on the motor and cable resistances when the loading counter-torque is applied to the motor shaft. The motor current rises very fast due to the very low electromagnetic time constant of the servo drive. On the other hand, the speed grows slowly because of large mechanical time constant.
Fig. 5
24
Asynchronous Motor Drive with Complete AC/DC/AC Converter
Another approach to standard mains supply deals with the asynchronous electric drive fed by a dc link power converter. Again, select a group of asynchronous motors those parameters match each gear as follows:
LMs MM ≥ , LLM MP ω≥ , J
LM
JJ
γ≥ , LM ωω > .
Proper motors of 4A series (220/380 VAC) are listed in the table below.
# Motor MP ,
W MsM ,
Nm
maxMM ,
Nm
Mω ,
rad/s 1R ,
Ω 1X ,
Ω 2R ,
Ω 2X ,
Ω 12X ,
Ω MI ,
A MJ ,
kgm2
m, kg
1 4A80A 1100 13.6 14.9 138 9.62 6.25 5.45 9.62 136 2.7 0.003 18
2 4A80B 1500 18.8 20.7 141 7.42 4.82 4.26 7.42 118 3.6 0.003 20
3 4A90L 1100 20.5 24.3 72 8.17 9.42 6.91 18.8 88 3.6 0.009 29
The motor described in the second row, which has enough low mass and high maximum and starting torques, may be accepted in conjunction with the second gear.
Then, select a converter MOVITRAC 004 of “Sew Eurodrive” having CP = 400 W and
CI = 3.5 A, which satisfies the requirements:
76=≥ LC PP W, 0.41500
1573.61.07ω=
⋅⋅=≥
M
MMLC P
IMI A.
The wiring diagram for the “Sew Eurodrive” asynchronous drive with MOVITRAC 004 is given in Fig. 6 and the appropriate Appendix 4 gives the functional description of its terminals.
Variable-frequency converters of the MOVITRAC series are microprocessor-controlled devices with sinusoidal pulse-width modulation. They provide a variable three-phase output voltage up to the level of the input voltage with a proportionally rising output frequency.
The converter consists of two basic components: power section PS and processor PP. The power section is used for the power supply of the connected motor and for the voltage supply of the control electronics. The power section is based on the principle of the static voltage dc link converter, which feeds the motor via the diode rectifier, dc link, and IGBT inverter with low switching losses, simple control, low forward power losses, and high switching frequencies. The inner dc link capacitor keeps the voltage stable. The inverter adjusted by the processor controls speed and torque of the motor. Usually, the power section contains the brake chopper of the energy feedback unit and various protective features. It is a useful tradition to connect the power section to the three-phase mains through a line choke on the supply side. The supply voltage is 380 to 500 VAC. The line choke, in conjunction with design measures in power section, completely replaces other customary inrush current-limiting charging components. It minimizes noise on the supply lines and is a part of the input protection features against transient overvoltages.
25
The power section includes the following monitoring features: dc link overvoltage, mains phase failure, earth fault, overtemperature, and brake chopper overcurrent protection. A surge suppressor circuit protects the power supply section against damage that may be caused by voltage peaks in the supply lines, which occur when inductive and capacitive loads are connected to the mains.
When a drive is decelerating, kinetic energy is converted into electrical energy and this is fed back into the dc link through the inverter’s freewheeling diodes. As the capacity of the dc link capacitor is limited, the voltage in the dc link rises. To enable the drive to decelerate, the additional energy must be dissipated. MOVITRAC has a built in brake chopper, where produced energy is converted into the heat by the braking resistor, which may be external or built in the switch cabinet. The chopper transistor monitors the voltage within the dc circuit, and at a pre-determined point, switches on and off rapidly, bringing the resistor in and out of circuit, thereby dissipating the excess energy.
Processor PP contains the control electronics needed for the adjusting purposes, permanently assigned and freely programmable binary inputs and binary outputs, analogue inputs, analogue outputs, sensors interface, standardized communications interfaces, and slots for options.
Moment of inertia of the motor drive is
0.090.85
0.0750.003
η=+=+=
L
LM
JJJ kgm2.
220 VAC
Fig. 6
M
4A80B
PS
PP
NF V
W
U
24 VDC + –
X2
0 40 44
43 47 60 30
MOVITRAC 004
ND
X1
X0
1
2
3
4
5
6
8
9
BE
31 34
X3 41
42
61 62
48 49 60 30
X14
X4
26
The run-up time of a set, the corresponding start-up path, and acceleration are as follows:
0.470.8720.71000.09
max
ω=
−⋅
=−
=LM
La MM
Jt s,
0.122
0.50.472
=⋅
==∆vt
l aa m,
1.10.470.5
===atv
a m/s2.
Parameters of the asynchronous electric drive are as follows:
0.5631421183
314
23 12
12 =⋅⋅
=⋅=X
L ,
0.580.563144.82
314 121
1 =+=+= LX
L ,
0.590.563147.42
314 122
2 =+=+= LX
L ,
0.950.580.56
1
121 ===
L
Lk , 0.96
0.590.56
2
122 ===
L
Lk ,
0.080.960.95-1 1 21σ =⋅=−= kk .
In case of the stabilized rotor flax linkage,
0.050.580.08 1σ =⋅== LL H,
11.354.260.967.42 22
221 =+=+= RkRR Ω,
and the time constants and the motor constants are as follows:
0.00411.350.05
===RL
Te s,
0.341500
1413.6 ω
=⋅
==M
MMMI P
Ik , 0.79
11.353.6-220141
ω
ω =⋅
=−
≈RIU
kMM
MM ,
0.270.790.3411.350.09 ω =⋅⋅⋅== MMIm kkJRT s.
Current-speed and torque-speed curves of the motor drive are shown in Fig. 7, a. The run-up torque, pullout torque, and stall current are depicted in these diagrams. The drive operates normally on the quasi-linear part of these traces. When the load rises, the torque and current increase but the speed decreases smoothly. If the torque overcomes the pullout value, the speed drops quickly and the motor stops.
27
The running transients of the asynchronous drive are shown in Fig. 7, b, c. Due to the load, the rotor current induces in the rotor winding. In the first instants the inrush current is very high because of very low rotor active resistance. The electromagnetic torque rises with the active current hence the flow saves its constant value. The start-up torque amplitude overcomes the pullout value. But this instant torque drops very fast and the average start-up
c. Fig. 7
a.
b.
28
torque is not high, so the speed increases slowly during the first starting instant. Then, the rotor EMF drops, and the current and torque decrease also, whenever the speed grows slowly.
Using a frequency converter eliminates a power inrush at start-up. Current starts from zero and rises as the load accelerates, with no danger of exceeding the full load current. This has two major benefits. The first is that it doesn’t matter when the units are switched on, as maximum demand will not be exceeded. The second is that as the current is properly controlled, the installation doesn’t require a sequenced start. This removes the need for additional capital equipment.
DC Motor Drive with Complete AC/DC Converter
The third application of the standard mains supply is the dc electric drive with a thyristor controlled rectifier. Choose the dc motors, which parameters match each gear as follows:
LM MM ≥ , LLM MP ω≥ , J
LM
JJ
γ≥ , LM ωω > .
Selected dc motors are listed in the table below.
# Motor MP ,
W MM ,
Nm maxMM ,
Nm
Mω ,
rad/s MI ,
A MU ,
V MR ,
Ω ML ,
mH MJ ,
kgm2
m, kg
1 PGT 1 1000 3.2 20.8 314 20.4 60 0.23 3 0.0007 64
2 PGT 1 1000 3.2 20.8 314 20.4 60 0.23 3 0.0007 64
3 PGT 2 2000 6.5 42.25 314 21.2 110 0.22 5 0.0020 79
The first of them, which has the small frame size in conjunction with the first gear, may be accepted.
A thyristor controlled rectifier BTU 3601-301 of “VNIIR” having CP = 1000 W, CI = 10 A, UC =
220 V satisfies the requirements:
76=≥ LC PP W, 5.53.2
20.40.87=
⋅=≥
M
MLC M
IMI A.
The wiring diagram for the BTU 3601 dc drive is given in Fig. 8 and Appendix 5 explains its terminals.
Moment of inertia of this set is
0.0550.85
0.0470.0007
η=+=+=
L
LM
JJJ kgm2.
Find the run-up time of a drive, the corresponding start-up path, and acceleration as follows:
0.360.8720.81260.055
max
ω=
−⋅
=−
=LM
La MM
Jt s,
29
0.092
0.50.362
=⋅
==∆vt
l aa m,
1.40.360.5
===atv
a m/s2.
Parameters of the dc electric drive are as follows:
633 =+=+= MC LLL mH,
0.630.230.4 =+=+= MC RRR Ω,
0.010.630.006
===RL
Te s,
6,3753.220.4
ω ====M
MMMI M
Ikk ,
1.46.3756.3750.630.055 ω =⋅⋅⋅== MMIm kkJRT s.
The current-speed curve of the thyristor motor drive is shown in Fig. 9, a. In the area of low loading, the current approaches discontinues mode, and the curve increases the slope significantly. The discontinuous current occurs only in the left part of the diagram and the continuous current occurs to the right. Consequently, the characteristic in the continuous current region is linear, exhibiting only a slight droop. In contrast, in the discontinuous current region the curve is strongly nonlinear with the loss in output voltage.
K3
380 VAC
Fig. 8
PGT1
X1
X2
13
14
17 18 19
BTU 3601
B1
A3
B3
C3
8
13
11
12
15 16
U V
W
F6
L1
A1
C1
20
23 24
21 22
26
29
27 28
T
M
BR
PA
PV
R1 R2 K2 K1
R3
K3
R4 R5
H3
K1 K2
30
Initial fragments of the drive start-up transients are shown in Fig. 9, b. Because of high running current, the continuous current mode occurs here. On the continuous current operation, the output current is smoothed by load circuit inductance that is the output signal has no breaks and the current’s waveform matches the voltage shape. After the starting finishing, the load current decreases and the discontinuous mode occurs. On the discontinuous current operation, the current waveform often consists of separate pulses the length of which depends on the inductance of the load circuit and a type of the rectifier.
Examples of Truck Drive with Battery Supply
Clarifying
A battery on-board source Ud = 48 VDC is discussed here. Due to low-voltage supply, the converter development or choosing starts before the motor and gear selection.
Let the application fed from the on-board source has the input data of the previous examples. Accordantly, the load data are the same. Again, the motor drive is developed including a converter, a proper electric motor, and a gear. Possible ac and dc drive compositions are discussed and compared.
b. Fig. 9
a.
31
Asynchronous Motor Drive with Desired Inverter
Commonly, the three-phase bridge inverter is used in ac drives. The asynchronous motor supply voltage is limited by the inverter output value:
2022.53
0.9532483
32
max
=⋅
−⋅
=−=k
Uq
UU CEd
C V
where Ud is the dc supply voltage, qmax is the maximum duty ratio of the transistor switches, k is the number of current-conducted transistors, UCE is the mean IGBT voltage drop. Often, there is no special low-voltage ac motor, and a common mode machine of extra power should be selected, which operates at low frequency fC proportional to the low voltage level UC:
4.55220
2050=
⋅==
M
CMC U
Uff Hz
where fM = 50 Hz – rated motor frequency and UM = 220 V – rated motor voltage. Required gears should meet the restrictions:
MMG ′≥ , 76238ω =⋅=′≥ ′MPG , and 224.5550
2ωω
=⋅⋅≥ =′C
MG
f
fi
Particularly, the three permissible planetary gears of minimum size are listed in the table below:
# Gear GP ,
W Gω ,
rad/s GM ,
Nm i Gη ,
%
m, kg
LM ,
Nm Lω ,
rad/s LJ ,
kgm2
1 3P-25-1 1500 225 68 10 70 23 5.43 20 1.88
2 1MPz2-50 1500 105 48.4 3.75 73 67 13.88 7.5 13.33
3 1MPz2-50 2200 157 46.7 3.5 78 65 13.92 7 15.31
The load data are converted onto the motor shaft using the formulae:
iM
MG
L η
′= , iL ωω ′= ,
2i
JJL
′= .
These data are included into the gear table too.
The parameters of selected asynchronous motor have to meet next inequalities:
LM MM ≥ , C
MLLM
f
fMP ω≥ ,
C
MLM
f
fωω > ,
J
LM
JJ
γ≥
Asynchronous motors with UM = 220 V matched each gear are shown in the table below.
32
The first motor, which has low mass and enough power, may be accepted together with the first gear.
Rated voltage of inverter transistors must exceed the value
86.5481.8 =⋅== dT kUU V
where k = 1.7…1.85 is the safety factor for the overvoltage protection. Transistors rated current should be more than
83.32.4 =⋅== MT kII A
where k = 2…3 is the safety factor for the overcurrent protection, and IM is the rated motor current.
The three-phase IGBT module CPV 364M4U from “International Rectifier” may be chosen to satisfy the application requirements. Its rated collector-emitter voltage, collector current, and direct voltage drop are: UT = 600 V, IT = 20 A, UCE = 2.1 V.
The wiring diagram of the ac drive built on the CPV 364M4U is shown in Fig. 10 and the functional description of its components is given in Appendix 6. Here, the battery voltage supplies the power inverter. The associated triggering driver circuit switches the inverter’s power transistors so that a pulse-modulated voltage feeds the motor. The pulse width is determined by the controller output. The controller compares the set-points ant actual values and uses a PWM to generate the control signals that are routed to the control stages of the individual power transistors of the inverter. The desired waveform is built up by switching the output transistors on and off at a fixed frequency. The modulated voltage produces a current in the motor, which is almost sinusoidal because of the motor and cable inductances. Nevertheless, the current waveform consists of a series of low frequency harmonics, and this may in turn cause voltage harmonic distortion, depending on the supply impedance.
A diode is connected in parallel to each power transistor. These freewheeling diodes prevent self-induced voltages from damaging the power inverter. These occur with inductive output loads at the moment of switching. The diodes feed the stored energy back to the input of the inverter. They also exchange reactive energy between the motor and the inverter.
Moment of inertia of this set is
2.210.851.88
0.002 η
=+=+=L
LM
JJJ kgm2.
The run-up time of a drive, the corresponding start-up path, and acceleration are as follows:
Motor
4A
MP
kW MsM
Nm maxMM
Nm Mω
rad/s 1R
Ω 1X
Ω 2R
Ω 2X
Ω 12X
Ω MI
A MJ
kgm2
m, kg
80A 1.5 9.5 11.7 300 5.60 3.4 3.27 5.4 167 3.3 0.002 18
112M 3 54.3 67.9 100 2.53 2.2 1.88 3.0 566 7.4 0.017 56
112M 3 54.3 67.9 100 2.53 2.2 1.88 3.0 566 7.4 0.017 56
33
75.4311.7202.21
max
ω=
−⋅
=−
=LM
La MM
Jt s,
1.7520.57
2=
⋅==∆
vtl aa m,
0.077
0.5===
atv
a m/s2.
Parameters of the asynchronous electric drive having the stabilized rotor flax linkage are as follows:
0.831421673
314
23 12
12 =⋅⋅
=⋅=X
L ,
0.810.83143.4
314 121
1 =+=+= LX
L ,
T/Itrip
HinU
HinV
HinW
LinU
LinV
LinW
V+
LeU
LeV
LeW
Fig. 10
VT4 VT5 VT6
VT1 VT2 VT3
M
VbU
VbV VbW U V W
Controller
Driver
Rg4 Rg1 Rg5 Rg2 Rg6 Rg3
Rsh
GND
15VDC
34
0.810.83145.4
314 122
2 =+=+= LX
L ,
0.9850.810.8
1
121 ===
LL
k , 0.9850.810.8
2
122 ===
L
Lk ,
0.030.9850.985-1 1 21σ =⋅=−= kk ,
0.0240.810.03 1σ =⋅== LL H,
8.773.270.9855.6 22
221 =+=+= RkRR Ω.
The time constants and the motor constants are as follows:
0.0038.770.024
===RL
Te s,
0.661500
33.3 ω
=⋅
==00
M
MMMI P
Ik , 1.57
8.773.3-220300
ω
ω =⋅
=−
≈RIU
kMM
MM ,
201.570.668.772.22 ω =⋅⋅⋅== MMIm kkJRT s.
DC Motor Drive with Desired Chopper
Required gears should meet the restrictions:
MMG ′≥ , 76238ω =⋅=′≥ ′MPG , and ωω ′≥
iG .
Particularly, the three permissible planetary gears of minimum frame sizes are listed in the table below:
# Gear GP ,
W
Gω ,
rad/s GM ,
Nm i Gη ,
%
m, kg
LM ,
Nm Lω ,
rad/s LJ ,
kgm2
1 3P-25-1 750 125 64 10 70 14 5.43 20 1.875
2 1MPz2-50 1100 78 57.3 4.35 68 70 12.85 8.7 9.9
3 3P-28-1 1100 125 95 10 70 18 5.43 20 1.875
The load data have been converted onto the motor shaft using the formulae:
iM
MG
L η
′= , iL ωω ′= ,
2i
JJL
′= .
They are included into the gear table too.
One of the most popular circuits for dc motor supply is a four-quadrant forward dc/dc converter. The average output voltage of the chopper with symmetrical control is:
Ud out = qmaxUd – kUCE = 0.95 · 48 – 2 · 2.5 = 40.6 V
where Ud is the dc supply voltage, qmax is the maximum duty ratio of the transistor switches, k is the number of current-conducted transistors, UCE is the mean IGBT voltage drop.
35
Choose the dc motors, which parameters match each gear as follows:
outdM UU ≥ , LM MM ≥ , LLM MP ω≥ , J
LM
JJ
γ≥ , LM ωω > .
Selected dc motors are listed in the table below.
# Motor MP ,
W
MM ,
Nm
maxMM ,
Nm
Mω ,
rad/s MI ,
A MU ,
V MR ,
Ω ML ,
mH MJ ,
kgm2
m, kg
1 PGT 2 2000 6.5 42.25 314 21.2 110 0.2 5 0.0020 79
2 PGT 4 4000 13 84.5 314 21 220 0.3 10 0.0007 109
3 PGT 2 2000 6.5 42.25 314 21.2 110 0.22 5 0.0020 79
The first motor, which has low mass and enough power, may be accepted together with the first gear.
Rated voltage of the chopper transistors must exceed the value
86.5481.8 =⋅== dT kUU V
where k = 1.7…1.85 is the safety factor for the overvoltage protection. Transistors rated current should be more than
5121.22.4 =⋅== MT kII A
where k = 2…3 is the safety factor for the overcurrent protection, and IM is the rated motor current.
The IGBT full bridges SK 50 GD066ET from “Semikron” may be chosen to satisfy the application requirements. Its rated collector-emitter voltage, collector current, and direct voltage drop are: UT = 600 V, IT = 51 A, UCE = 1.45 V.
The wiring diagram of the dc drive built on the SK 50 GD066ET is shown in Fig. 11 and the functional description of its components is given in Appendix 7.
Four-quadrant chopper is the base of the fast response reversible variable speed drive. As a rule, the discontinuous current is avoided here by increasing the switching frequency or by adding the inductance in series with the motor.
Chokes may be fitted to the output of the converter to allow operation with long cables. The choke compensates for the stray capacitance of the cables.
Speed and current controllers use the information from the user such as the set-point speed to control the drive functionality and to develop the required speed and torque at the motor shaft. They also protect the drive when circumstances dictate, and provide information to the user on the drive status. By accurately controlling the voltage applied to the motor, user is assured of process or product performance.
Moment of inertia of this set is
2.210.85
1.8750.002
η=+=+=
L
LM
JJJ kgm2.
36
Find the run-up time of a set, the corresponding start-up path, and acceleration as follows:
1.25.4342.2522.21
max
ω=
−⋅
=−
=0
LM
La MM
Jt s,
0.320.51.2
2=
⋅==∆
vtl aa m,
0.421.20.5
===atv
a m/s2.
Parameters of the dc electric drive are as follows:
550 =+=+= MC LLL mH,
0.30.2202.1
2=+=+= M
T
CE RI
UR Ω,
0.0170.3
0.005===
RL
Te s,
Fig. 11
50 VDC
GND
+12 VDC 12 VDC
-12 VDC
+M
-M
ES
SCC/PWM
TS
FVC
E R MN
+SET
–SET
+TACH
–TACH
ENA ENA\ ENB
ENB\
+ VT1 VT2
VT3 VT4
CS
PGT2
M
C
37
3.266.521.2
ω ====M
MMMI M
Ik k ,
73.263.260.32.21 ω =⋅⋅⋅== MMIm kkJRT s.
38
Appendixes
1. Approximate Efficiency of Transmissions
2. Approximate Friction Factors
3. Description of “Mitsubishi Electric” Servo Drive Wiring Diagram Fig. 4
220 VAC Power supply 24 VDC Power supply of digital input/output section NFB No-fuse breaker MC Magnetic contactor FR Option power factor improving reactor or line filter TE Main circuit terminal block DE Digital input/output section CN1 Junction terminal block to connect the control signals (I/O signal connector) CN2 Rotor position encoder connector CN3 RS-232C option unit, which matches a personal computer P, C, BC Brake option and option braking resistor B1, B2, BE Option electromagnetic brake L1, L2 Power input terminals U, V, W Servo motor power supply and power input terminals of the servo motor M Motor PE, E Protective earth terminal
Transmission Gη Transmission Gη
Gear units 0.94…0.98 Frictional 0.70…0.80
Planetary 0.75…0.95 Belt 0.80…0.95
Worm 0.40…0.85 V-belt 0.88…0.93
Screw 0.77…0.95 Rope 0.91…0.95
Chain 0.90…0.96 Pulley, winch, polyspast 0.92…0.98
Sliding elements µ Rolling elements µ rµ , mm
Bronze on bronze 0.06 Steel gears 0.005 0.1
Steel on steel 0.09 Roll-tables 0.010 0.3
Steel on bronze 0.08 Running wheels 0.020 0.5
Cast-iron on bronze 0.15 Polymer on steel 0.150 2
Belts on steel 0.25 Polymer on concrete 0.250 3
Steel on polymer 0.25 Hard rubber on concrete
0.500 10
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SG Power supply common terminal for connection the negative terminal of external power supply
V24 Interface power input 24 VDC, 200 mA or more for external power supply V+ Digital output power terminal, which supplies power for driving the digital
output section SON Servo on start signal terminal ST1, ST2 CW/CCW rotation start signals DI1 Low/high rotation speed selection ALM Trouble signal output terminal PF Positioning finished up-to-speed output signal ZSP Zero speed output signal
4. Description of “Sew Eurodrive” Asynchronous Drive Wiring Diagram Fig. 6
220 VAC Power supply 24 VDC Power supply of digital input/output section PS Power section PP Processor M Motor ND Option line choke NF Option input filter HF Option output filter BE Option braking resistor X0 Grounding terminal X1…X14 Junction terminal blocks 1, 2, 3 Connection terminals to the supply 4, 5, 6 Motor cable terminals 8, 9 Option braking resistor connection 31 10 VDC for set-point potentiometer 34 Set-point input 0 Ground 10 VDC 40 External power supply 24 VDC for inverter diagnosis with the mains off 44 Auxiliary power supply output 24 VDC for external command switches 41 CW/stop binary input 42 CCW/stop binary input 43 Enable/rapid stop binary input 47 Ramp generator binary input 30 Ground 24 VDC 60 Reference terminal for binary inputs 61 Brake released binary output 62 Fault binary output 48 Low speed binary input 49 High speed binary input X4 Slot for option keypad, RS-232, and RS-485 serial interfaces
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5. Description of BTU 3601 DC Drive Wiring Diagram Fig. 8
X1 Power section junction terminal X2 Control section junction terminal M Motor BR Tacho generator T Power transformer L1 Smoothing choke PA, PV Load ammeter and voltmeter R1, R2, R3 Reference resistors K1, K2 CW/CCW selection relays R4, R5, K3 Resistors and relay of the current restriction F6 Circuit breaker A1, B1, C1 Control system supply terminals A3, B3, C3 Secondary winding of the supply transformer terminals 8, 13 Motor terminals 11, 12, 13 Load ammeter and voltmeter terminals 14, 16 External load terminals fed by 24 VDC
15, 17, 18 Speed reference terminals fed by ±15 VDC 19, 16 External load terminals fed by -24 VDC 20, 15 Terminal for relay contact for the regulators’ blocking release 21, 22 Speed reference 23, 22 Tacho generator terminals 26, 14 Alarm signal lamp terminals 27, 17 Limiting current resistor terminals 28, 15 Pin terminals for current restriction 29, 22 Addition signal inputs for the speed reference
6. Description of Asynchronous Drive Wiring Diagram Fig. 10
M Motor VT1…VT6 Power switches U, V, W Power outputs V+ Power input LeU…LeW Power inputs 15VDC Control circuit supply GND Grounding VbU…VbW Phase current sensors HinU…HinW High switches gate signals
LinU…LinW Low switches gate signals T/Itrip Heat and overload protection data
Rg1…Rg6 Gate current limiters Rsh Shunt resistors
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7. Description of DC Drive Wiring Diagram Fig. 11
VT Power switches 50 VDC Supply voltage GND Power ground 12 VDC Internal supply
±12 VDC 12 VDC outputs
±M DC motor output voltage, 45 VDC
±SET Set-point inputs
±TACH Tacho inputs EN A…B\ Encoder inputs E Enable input signal R Ready output signal MN Monitor output PS MOSFET power stage PWM PWM control and protection circuit SCC Speed/current controller C Option choke ES EMF sensor CS Current sensor TS Tacho sensor FVC Frequency-voltage converter
8. Useful Links
Electronic converters and power electronics manufacturers:
“ABB” – http://www.abb.com/ “Advanced Power Technology” – http://www.advancedpower.com/ “Danfoss” – http://www.danfoss.com/products/ “International Rectifier” – http://www.irf.com/product-info/ IXYS – http://www.ixys.com/ “Maxon Motor” – http://www.maxonmotor.com/ “Mean Well” – http://www.meanwell.com/ “Mitsubishi Electric” – http://www.mitsubishielectric.com/ “National Semiconductor” – http://www.national.com/ “Nihon Electronic” – http://www.niec.co.jp/ “Omron” – http://www.omron.com/ “Schneider Electric” – http://www.schneider-electric.com/ “Semikron” – http://www.semikron.com/ “Sew-Eurodrive” – http://corporate.sew-eurodrive.com/ “Siemens” – http://www.siemens.com/ “Symmetron” – http://www.symmetron.ru/suppliers/ “Texas Instruments” – http://www.ti.com/ “Toshiba” – http://www.toshiba.com/taec/
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Drivers and components manufacturers:
“Advanced Micro Devices” – http://www.amd.com/ “American Microsystems” – http://www.amis.com/ “Analog Devices” – http://www.analog.com/ “Fujitsu” – http://www.fujitsu.com/global/ “General Instrument” – http://www.antiquetech.com/companies/GI.htm “Hitachi” – http://www.hitachi.com/ “Intel” – http://www.intel.com/ “Motorola” – http://www.motorola.com/ NEC – http://www.nec.com/ RCA – http://www.rca.com/ “Rockwell” – http://www.rockwellautomation.com/ “Samsumg” – http://www.samsung.com/ “Siliconix” – http://www.1stcallelectronics.com/ “Tyco Electronics” – http://www.tycoelectronics.com/ “Zilog” – http://www.zilog.com/
