step motor system design · step motor system design k. craig 4 overview •as stepper motors are...

Step Motor System Design K. Craig 1

Step Motor System Design


Overview

• As stepper motors are used in many different types of

applications, it is difficult to recommend a general step-

by-step design process.

• The stepper motor system design process is therefore

more of an iterative process involving experience,

analysis, and experimentation.

• What is most important to understand is that system

performance is affected by the motor, the driver, and the

load with its connection to the motor.

• Here we will consider limits to system performance, driver

performance, motor performance, system design, and

motor selection.


Limits to System Performance

• Output Torque and Power

– The output torque and power from a stepper motor are

functions of: motor size, motor heat sinking, working

duty cycle, motor winding, and type of driver used.

– In applications with low damping, the usable torque

from the stepper motor can be drastically reduced by

resonances.

– The pull-in torque curve shows the maximum friction

torque with which the motor can start, at different

stepping rates, without losing any steps. In an actual

application, this curve has to be modified to account

for the load inertia.


– The pull-out torque curve shows the available torque

when the motor runs at a constant speed at a given

frequency. In an application, this torque is used for

overcoming the load friction torque and for

accelerating the load and motor inertia.

– The driver selected has a huge influence on the output

torque and power. The output power of a motor can

be increased several times by proper driver selection.

This results from both an increased overall pull-out

torque and the increased stepping frequency range.

– NOTE: It is most important to understand what type of

driver the motor manufacturer used in developing the

pull-in and pull-out torque curves, as the torque-speed

characteristics of a motor can vary significantly

depending on the drive method used.


Torque vs. Speed Characteristics of a Stepper Motor


– Based on these curves, it is clear that to get a high-

performance stepper motor system, one must use

ramping up/down when we one starts and stops the

motor and load.

• Damping and Resonances

– In applications with low system damping, the available

output torque and power can be drastically reduced by

resonance.

– Resonance in stepper motor systems can arise at low-,

mid-, and high-stepping rates and causes a sudden

drop in torque which can result in missed steps or loss

of synchronism. It occurs when the input step pulse

rate coincides with the natural oscillation frequency of

the rotor. Often there is a resonance around the 100-

200 pps region and also one in the high-step-pulse-rate

region.


– The resonance phenomenon of a stepper motor

comes from its basic construction and therefore it is

not possible to eliminate it completely. It is also

dependent on load conditions. It can be reduced by

driving the motor in half-step or micro-stepping

modes.

– Damping also depends on the motor type. Some

driver and motor combinations have such low

damping that they do not run at certain stepping rates

without a high-damping load. This condition is known

as no-load instability.

• Resolution and Positioning Accuracy

– The resolution of a stepper motor system is affected

by: stepper-motor full-step length, selected driver

mode, e.g., half-step, and the gear ratio.


– As a result, there are many combinations that can be

used to get the desired resolution. Because of this,

the resolution problem of a stepper design can

normally be dealt with after the motor size and driver

type have been established.

• Design Time

– Using a more-flexible driver circuit, e.g., chopper

constant-current driver, can make it possible to select

a standard motor with no performance loss.

– Therefore, customization of stepper motors is usually

not necessary.

• Cost

– It is often possible to lower the total system cost by

using a more complex driver (with a slightly higher

cost) and a less-costly motor and power supply.


• Dynamic Characteristics

– Settling time becomes a very important factor in

applications where the stepper must move from one

position to another and then stop in the shortest

possible time.

– To get good dynamic behavior in an open-loop system

with variations in both load inertia and friction, it is

important to have the correct gear ratio and precise

control of the motor running and holding torque.

Single-Step Response vs. Time


Drive Circuit Fundamentals

• For a given size of a stepper motor, a limited space is

available for the windings.

• Efficient utilization of the available winding space, as well

as a matching of driver and winding parameters is of

great importance in the process of optimizing a stepper

motor system.

• Key Questions:

– What are the basic electrical characteristics of a

stepper motor winding?

– What are the basic driving configurations and current-

control methods?


• Winding Resistance and Inductance

– The windings of a stepper motor are made up of

several turns of copper wire.

– Resistance and Inductance are the two inherent

physical characteristics of any winding or coil. These

two characteristics also limit the possible performance

of the stepper motor.

–Resistance V = IR

• The resistance of the windings is responsible for

the major share of the power loss and temperature

rise of the motor.

• The resistance of a winding is proportional to the

square of the number of wire turns.

• The power loss is given by P = I2R.


• Size and thermal characteristics of the winding and

motor limit the maximum allowable power

dissipated in the winding.

• NOTE: A motor should be used at its maximum

power dissipation to be efficient. If a motor is

running below its power dissipation limit, it means

that it could be replaced by a smaller size motor,

which is probably less expensive.

– Inductance V = L(dI/dt)

• Inductance makes the motor winding oppose

current changes and therefore limits high-speed

operation.

• The inductance of a winding is also proportional to

the square of the number of wire turns.


LR Circuit Dynamic Behavior

e

tRt

LV V

I(t) 1 e 1 eR R

e

Ltime constant

R

The winding

is modeled

as a pure and

linear resistor

and inductor

in series, as

shown.


– What happens when a square wave voltage of

magnitude V is applied to the winding, as happens

when a two-phase stepper motor is driven in the full-

step (two phases on) and half-step (one phase on

alternating with two phases on) drive modes?

– The answer depends on the frequency of the square

wave, as shown.

Here, at a low frequency, the

current reaches its maximum value.


Above a certain frequency, the current never

reaches its maximum value.


• As the torque of the motor is approximately

proportional to the current, the maximum torque

will be reduced as the stepping frequency

increases.

• Two possibilities exist to overcome the inductance

and gain high-speed performance.

– Increase the current rise rate and/or

– Decrease the time constant

• As an increased resistance R always results in an

increased power loss (P = I2R), it is preferable to

increase the ratio V/L (increase the initial slope of

the I vs. t plot) to gain high-speed performance.

• Therefore, to drive current through the winding, we

should use as high a voltage as possible and keep

the inductance low.


• Accordingly, a low inductance / resistance motor

has a high current rating.

• As the maximum current is limited by the driver,

high performance is highly dependent on the

choice of driver.

• The limiting factor of the motor is the power

dissipation, and not the current itself. To utilize the

motor efficiently, power dissipation should be at

the maximum allowed level.


• Drive Circuit Schemes

– The stepper motor driver circuit has two major tasks:

• To change the current and flux direction in the

phase windings

• To drive a controllable amount of current through

the windings, and enable as short current rise and

fall times as possible for good high-speed

performance

– Flux Direction Control

• Stepping of the stepper motor requires an

independent change of the flux direction in each

phase. The direction change is done by changing

the current direction. This may be done in two

different ways: bipolar (unifilar) drive or a unipolar

(bifilar) drive, as shown.


Bipolar DriveThis refers to the

principle where the current

direction in one winding is changed

by shifting the voltage polarity

across the winding terminals. This method requires one winding per

phase. There are two connecting leads per phase.

Four switches per phase are required.


Unipolar DriveThe unipolar drive principle requires a

winding with a center tap. Flux

direction is reversed by moving the current from one half of the winding to the

other half. Only half the available copper volume of

the winding is used. There are three connecting leads

per phase. Two switches per phase are required.


• Current Control

– To control the torque as well as to limit the power

dissipation in the winding resistance, the current must

be controlled or limited.

– Furthermore, when half-stepping a zero current level

is needed, while microstepping requires a

continuously-variable current.

– The two main methods to limit the current are:

• Resistance-Limited Drive

• Chopper Drive

– Either of these methods may be realized as a bipolar

or unipolar driver.


Resistance-Limitation of CurrentThe current is limited by the

supply voltage and the resistance of the winding,

and, if necessary, an additional external

resistance.

For a given motor, high-speed performance is increased by increasing Vsupply. This must

be accompanied by Rext in series with the winding to limit the current to the previous level. The time

constant decreases, which shortens the current rise

time. The penalty is additional power loss.

supply

ext

VI

R R


Current Paths at Turn-Off & Phase Shift

Bipolar Drive

The inductive nature of the winding demands that a current path always exists. When

using transistors as switches, diodes have to be added to enable current flow in both

directions across the switch. For the bipolar driver shown, four diodes, one for each

switch, provide the necessary current paths. Note that there are two ways to turn the

current off, either by turning all transistors off (path 3), or turn just one of the two conducting transistors off (path 2). The

former gives a faster current decay as the energy stored in the winding inductance is discharged at a high voltage, Vsupply. The

latter gives a slower current decay as the counter voltage is only two diode voltage

drops and the resistance voltage drop across the winding. At phase shift, both conducting

transistors are turned off.


– Chopper Control

• The chopper driver provides an optimal solution

both to current control and fast current build-up

and reversal.

• The basic idea is to use a supply voltage which is

several times higher than the nominal voltage of

the motor. The current rise rate, which is initially

V/L, can increase substantially.

• By controlling the duty cycle of the chopper, an

average voltage and an average current equal to

the nominal motor voltage and current are created.

• Constant current regulation is achieved by

switching the output current to the windings. This

is done by sensing the peak current through the

winding via a current-sensing resistor connected in

series with the motor winding.


• As the current increases, a voltage develops

across the sensing resistor, which is fed back to a

comparator. At the predetermined level, defined

by the voltage at the reference input, the

comparator resets the flip-flop, which turns off the

output transistor.

• The current decreases until the clock oscillator

triggers the flip-flop, which turns on the output

transistor again, and the cycle is repeated.

• The advantage of the constant current control is a

precise control of the developed torque, regardless

of the power supply voltage variations. It also

gives the shortest possible current build-up and

reversal time. Power dissipation is minimized, as

well as the supply current.


Principle of Constant CurrentChopper Regulation

Current Waveformin the Basic Chopper Circuit


H-Bridge Configured as a Constant-Current Chopper


• Comments on the Bipolar Constant-Current Chopper

Driver

– The highest output power and motor utilization for a

given motor is achieved with the bipolar constant-

current driver.

Shown are the performance curves for a 3.75 ohm bipolar 57 mm PM-motor driven by a

constant-current driver with a chopper voltage of 20V and a winding current of 960 mA.


Designing a System & Motor Selection

• Analyzing the Load

– When designing a stepper motor system, the first

question to ask is “What are the characteristics of the

load?” This must be thoroughly understood before

selecting a motor and driver and before designing the

transmission and mechanical system.

• Inertia Loads

– If the system will have high dynamic performance, then

most of the output torque from the motor will be used to

accelerate the system’s inertia.

– The gear ratio should be designed so that the load

inertia seen by the motor is close to the motor inertia.


• Friction Torque

– It is necessary to calculate or measure the load friction

torque. For most load types, this is fairly constant at

different speeds.

– The friction torque and maximum speed of motion can

be used to calculate the load power needed, i.e., P =

Tω.

• Damping

– The usable torque from a stepper motor can decrease

at certain stepping rates due to resonance. At which

step rates, and to what extent, this torque reduction

appears depends on the application damping and

inertia. The damping of the driver also influence the

torque reduction.


– Resonances at low stepping rates can normally be

reduced by lowering driver current and voltage levels,

or by selecting half- or microstepping mode drivers.

– At medium step rates, the constant-current drivers

normally have the least problems with resonances, but

here the characteristics of the load have a large

impact.

– Low system inertia normally creates fewer problems

with resonances. However, in some applications, an

increased inertia can be used to move a resonance to

a lower frequency.

• Selecting a Concept

– After Analyzing the load, the output power needed, the

maximum and minimum stepping rates, and the

resolution are all known.


– The design is normally an iterative process, with

analysis and experimentation.

– A higher-step-rate driver and a smaller motor, together

with a suitable gearing, often gives better performance

– in efficiency and output power – than a large motor

driving the load directly.


• Stepper Motor Performance

– Key Questions:

• How much torque can the motor produce while

accelerating, decelerating, or running at a constant

speed?

• Can the motor produce sufficient torque to

overcome the load torque and accelerate the load

inertia?

• What is the maximum speed at which the motor

can drive the load?

– The answers to these questions are supplied in a

graph: the pull-out torque / speed characteristic. It

shows the maximum torque (the pull-out torque) which

the motor can develop at each operating speed.


– If the load torque exceeds the pull-out torque, the rotor

is pulled out of synchronism with the magnetic field

and the motor stalls.

– For a given load the maximum operating speed is

referred to as the pull-out rate.

– The complete torque / speed characteristic can be

divided into several regions:

• Low speeds (e.g., < 100 steps per second): current

is quickly established in the windings when a

phase is turned on and stays near its rated value

for a substantial part of the time for which the

phase is excited. The basic pull-out torque / speed

characteristic in this region can be deduced from

the static torque / rotor position characteristic.


• High speeds (e.g., > 100 steps per second): the

time constant for current rise and decay becomes

a significant portion of the total phase excitation

time. The phase current cannot be maintained at

its rated value and therefore the torque produced

by the motor is reduced.


Low-Speed Region High-Speed Region

Typical

Pull-out Torque /Speed Characteristic

Sharp dips at speeds near 20 and

40 steps per second are caused

by mechanical resonance in the

motor- load combination.


– The most important performance parameter for a

stepper motor is steady torque output.

– The figure shows a typical torque-speed plot. The

curves do not define specific operating points but outline

regions where the motor will operate satisfactorily.

– Step motors develop their highest torque at standstill.

As the step rate is increased, winding inductance

prevents the current from reaching its steady-state value

and torque decreases with the step rate.

– Pull-In Torque (or start-without-error torque) is the

maximum torque at which the stepper will start from rest

(or stop without the loss of a step) when operating at the

given stepping rate. Pull-in torque data includes rotor

inertia torque.


– Pull-in torque is not the maximum torque delivered by

steppers. Part of the drive torque is used to

accelerate motor inertia. Once running speed is

reached, inertia torque is available for friction torque.

– Pull-Out Torque (or running torque) is the maximum

frictional torque that can be applied to the motor while

running at a steady rate.

– The difference between the pull-in torque curve and

the pull-out torque curve at a fixed rate is the torque to

overcome motor inertia.

– The area between the two curves is called the slew

range.

– There are two aspects to the design problem which

need to be discussed before using torque-speed

curves.


• First, load frictional torque is known (fixed).

Therefore, its intersection with the pull-in torque curve

gives the maximum step rate to move the load from

rest. Any lesser step rate is also acceptable. The

design torque intersection with the pull-out torque

curve gives the maximum step rate (slew rate)

possible after the motor is running at pull-in step rate.

However, the motor must be carefully accelerated to

this speed and decelerated to a stop again if any

steps are not to be missed. Stepping rates outside

the pull-out torque curve will cause the motor to stop,

oscillating about its fixed position.

• Second, speed-torque curves do not account for load

inertia. We would not expect the pull-in torque curve

to be very helpful although the pull-out torque curve is

still valid.


• There is a simple solution to this problem. Since

the vertical distance between the two curves is a

motor inertia torque, a reflection of this torque on

the downside of the pull-in torque gives the new

pull-in torque curve for the combined moment of

inertia.


Starting and Running Torque Range for a Stepper Motor


• Stepper Motor Selection

– Stepper motor selection cannot be made on the basis

of geometric parameters alone. Torque and speed

considerations are often more crucial in the selection

process. The effort required in selecting a stepper

motor for a particular application can be reduced if the

selection is done in an orderly manner. The following

steps provide some guidance for the selection

process:

– Step 1

• List the main requirements for the particular

application, including speeds, accelerations,

required accuracy and resolution, and load

characteristics such as size, inertia, fundamental

natural frequencies, and resistance torques.


– Step 2

• Compute the operating torque and stepping rate

requirements for the particular application.

Newton’s Second Law is the basic equation

employed in this step. The required torque rating

is given by:

– Step 3

• Using the torque vs. stepping rate curves for a

group of commercially available stepper motors,

select a suitable stepper motor. The torque and

speed requirements determined in Step 2 and the

accuracy and resolution requirements specified in

Step 1 should be used here.

maximumresis tance equivalentT T J

t


– Step 4

• If a stepper motor that meets the requirements is not

available, modify the basic design. This may be

accomplished by changing the speed and torque

requirements by adding devices such as gear systems

and amplifiers (e.g., hydraulic amplifiers).

– Step 5

• Select a drive system that is compatible with the motor

and that meets the operational requirements in Step 1.

For simple applications, an open-loop system

consisting of a pulse source (oscillator) and a

translator could be used. For more complex transient

tasks, a microprocessor or customized hardware

controller may be used to generate the desired pulse

command. Closed-loop control is an option for

demanding tasks.


– The single most useful piece of information in

selecting a stepper motor is the torque vs. stepping

rate curve. Other parameters that are valuable to

know are:

• Number of steps per revolution

• Starting torque of motor when powered with rated

voltage

• Maximum slew rate (maximum steady-state

stepping rate possible at rated load)

• Motor torque at maximum slew rate (pull-out

torque)

• Maximum ramping slope (maximum acceleration

and deceleration possible at rated load)

• Motor time constants (no-load electrical time

constant and mechanical time constant)


• Motor natural frequency (without an external load

and near detent position)

• Motor size (dimensions of poles, stator and rotor

teeth, air gap and housing, weight, rotor moment of

inertia)

• Power supply capacity (voltage and power)


Supplementary Slides with Sample Manufacturer’s Data


Unipolar Step Motor

• NMB PM55L-048-KSD5 Hybrid Step Motor

• Unipolar, Bifilar, Two Phases

• 12 Rotor Teeth (Pole Count N = 12)

• 7.5° per step, 48 steps per revolution in full-step mode (4

Electrical States per Electrical Cycle)

• 3.75° per step, 96 steps per revolution in half-step mode

(8 Electrical States per Electrical Cycle)

• Motor Data from Manufacturer and Testing


• Motor Parameters

– Drive Voltage: 42.3 V-DC

– Drive Current: 370 mA

– Rotor Inertia: 4.3E-6 kg-m2

– Winding Resistance: 19.75 Ohms

– Winding Inductance: 16 mH

– Holding Torque (two phases on, 400 mA/phase):

1.165E-1 N-m

– Motor Torque Constant: 0.1918 Nm/A

– Detent Torque: .0019 N-m

– Max Slew Speed: 2270 pps

– Position Error: 1.5°

– Step-to-Step Error: 1.5°


Bipolar Step Motor

• NMB PM42L-048-XRL7A Hybrid Step Motor

• Bipolar, Unifilar, Two Phases

• 12 Rotor Teeth (Pole Count N = 12)

• 7.5° per step, 48 steps per revolution in full-step mode (4

Electrical States per Electrical Cycle)

• 3.75° per step, 96 steps per revolution in half-step mode

(8 Electrical States per Electrical Cycle)

• Motor Data from Manufacturer and Testing


• Motor Parameters

– Drive Voltage: 38 V-DC

– Drive Current: 400 mA

– Rotor Inertia: 2.2090E-6 kg-m2

– Winding Resistance: 19.57 Ohms

– Winding Inductance: 30 mH

– Holding Torque (two phases on, 400 mA/phase):

1.1374E-1 N-m

– Motor Torque Constant: 0.2386 N-m/A (calculated)

– Detent Torque: 0.0004 N-m

– Max Slew Speed: 2782 pps

– Position Error: 0.342°

– Step-to-Step Error: 0.409°

step motor system design · step motor system design k. craig 4 overview •as stepper motors are...

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