Đồ án truyền động điện(động cơ bước có tính toán công suất) bản tiếng anh

HCMC UNIVERSITY OF TECHNOLOGY AND EDUCATION
FACULTY FOR HIGH QUALITY TRAINING


Course Project

AUTOMATIC ELECTRIC DRIVE

PROJECT TOPIC:

STUDYING ABOUT STEP MOTOR AND ITS
APPLICATION

Instructor: Dr. Nguyễn Phan Thanh
Students:
1. Lê Minh Huy

ID: 17142019

2. Ngô Hữu Lâm

ID: 17142029

Ho Chi Minh City December 2020


CONTENT
CHAPTER 1: OVERVIEW ..................................................................................................... 3
I. PROBLEM VIEWING .................................................................................................. 3
II. OBJECTIVE AND PURPOSE OF THIS PROJECT .................................................... 3
1. Objective .................................................................................................................. 3

2. Purpose of this project ............................................................................................. 4
III. RESEARCH METHOD ............................................................................................... 4
1. Theoretical basic. ..................................................................................................... 4
2. Practical application................................................................................................. 4
CHAPTER 2: THEORETICAL BASIC .................................................................................. 5
I. STEP MOTOR OVERVIEW ........................................................................................ 5
1. Stepper motor concept ............................................................................................. 5
2. Structure and working principle .............................................................................. 5
2.1. Structure. ....................................................................................................... 5
2.2. Working principle.......................................................................................... 6
3. Types of step motor ................................................................................................. 6
4. Stepper motor torque ............................................................................................... 9
II. STEP MOTOR CONTROL......................................................................................... 13
1. Stepper motor applications .................................................................................... 13
2. Stepper motor conrol method ................................................................................ 14
2.1. Wave control (Wave drive) ......................................................................... 14
2.2. Full step controller (Full step drive) ............................................................ 14
2.3. Half-stepping controller (Half-stepping drive) ........................................... 15
2.4. MicroStepping controller (MicroStepping drive) ....................................... 15
3. Stepper motor Driver ............................................................................................. 16
4. Stepper motor Driver types .................................................................................... 17
CHAPTER 3: APPLICATIONS OF STEP MOTOR ............................................................ 20
I. CHOICE OF ELECTRIC DRIVES ............................................................................. 20
II. 3D PRINTER PLAN DESIGN.................................................................................... 21
III. IMAGES OF 3D PRINTER ........................................................................................ 25
CHAPTER 4: COMMENTS AND EVALUATION ............................................................. 26
I. COMMENTS............................................................................................................... 26
1. Advantage of the project ........................................................................................ 26
2. Disadvantage of the project ................................................................................... 26
3. Practical applicability ............................................................................................ 27

II. EVALUATION THE PROJECT’S RESULT ............................................................. 27


III. SUGGESTION FOR AUTOMATIC ELECTRIC DRIVE PROJECT ....................... 28
REFERENCE......................................................................................................................... 29


INSTRUCTOR COMMENT
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HCMC, 28th, December 2020
Instructor

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THANK YOU
Our project team want to give our thanks to the teacher/professor in our ElectricalElectronic falcuty for letting us study under your care all this time. We would like to give our
most heartful thanks to Mr. Nguyen Phan Thanh has been supporting for the completion of
this course project Automatic Electric Drive.
In the process of making this course project there has been some mistake that was make
along the way, we hope that you can overlook it if possible. Because our knowledge and
practical experience are still short so our project may have been imperfect or lacking, we
hope for you to give us some insight for our project to be more completed and for our team
to gain more experience and knowledge along the way.
Thank You Very Much!

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CHAPTER 1: OVERVIEW


I. PROBLEM VIEWING.
Nowadays in the national economy manufacturing sector, mechanization are a must
have in term of electrification and automation. To increase productivity and reduce the cost
of electrical device is two most wanted demand in automatic electric drive system. One side
demanding the use of complex system to have suitable goals and method, another is to reduce

the general equipment on the machine and some of the advanced device. Because of that the
most important part in production is the decide an automatic electric drive suitable for it.
At present, there is a lot of motor types on the market like stepper motor, encoder motor,
servo motor, a three-phase asynchronous motor etc… each type of motor have
correctsponding of different advantangeous and disadvantangeous. From those advantage and
disadvantage that we will chose and use them in different areas in daily life and production.
A system can consists a lot of motor, working together, do different task in that chain of
production. With the nonstop advancement of precision technology that has practical
application for robot arm, 3D print machine, a lazer engraving machine, CNC…, the stepper
motor has become more important and widespread. The stepper motor has contributed in
improving, research, educated our automatic electric drive course in our country to improve
and increased the productivity based on the technological knowledge we gained, we have
also save up the labor expense and still increased the production. Because of that the act of
creating a chain system that use stepper motor has been working favourably and controlling
them easier is a worthwhile business.
From the view and the practical application of the stepper motor our team has decied to
choose the project “Studying about step motor and it application” to help other know more
about step motor. From here we can use our theoretical basic to apply in practical uses.

II. OBJECTIVE AND PURPOSE OF THIS PROJECT.
1. Objectives
- Study about stepper motor.
- Learn about the working principle of stepper motor.
- Learn about stepper motor controller, stepper motor driver.
- Learn how to apply stepper motor application in real life.

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2. Purpose of this project

- Overview of the stepper motor.
- Know how to use a stepper motor in many fields.

III. RESEARCH METHOD
1. Theoretical basic
- Finding, summarize the study materials.
- Research about types of stepper motor, how to control it and what it can be use for.
2. Practical application
-In nowadays Stepper motors are widely used in machine tool such as CNC plasma
cutting machine, wood machine, engraving machine, laser cutting machine ...
In this report, we use 3D printer for the example to stepper motor.

4


CHAPTER 2: THEORETICAL BASIC


I. STEPPER MOTOR OVERVIEW
1. Stepper motor concept.
The Step motor is technically a synchronous motor that have the principle of turning
discrete electrical impulse control signals into angular rotation.

Figure 1: Step motor
A stepper motor is a particular type of DC motor that does not rotate continuously.
Instead, a full rotation is divided into a number of equal steps. A stepper motor consists of
phases, which are multiple coils that are organized into groups. By applying the energy from
the input voltage to each phase in a sequence, the stepper motor rotates by taking one step at
a time. Thus a stepper motor converts electrical energy or an input digital pulse into
mechanical shaft rotation.

2. Structure and Working principle.
2.1 Structure
Step Motor consist of 2 main part: Stator and Rotor.

Figure 2 Step motor structure.
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Like all electric motor, it has stator and rotor. The rotor is the movable part which has
no windings, brushes and a commutator. Usually the rotors are either variable reluctance or
permanent magnet kind. The stator is often constructed with multiploe and multiphase
windings, usually of three or four phase windings wound for a required number of poles
decided by desired angular displacement per input pulse.
2.2 Working principle
A stepper motor works under the principle of electromagnetism. A permanent magnet
or soft iron is used as the rotor and is surrounded by electromagnetic stators. The poles of the
rotor and stator may be teethed. When voltage is applied at the terminals, the rotor aligns
itself with the stator or moves to have a minimum gap with the stator due to the magnetic
effect. The stators are energized in a sequence and the rotor moves accordingly, giving a full
rotation that is divided into a discrete number of steps with a particular step angle.
• Advantage:
- A stepper motor is used in devices that need precise positioning and speed control.
Because it moves in precise repeatable steps, the stepper motor is used in devices like 3D
printers, camera platforms, plotters, scanners, etc. And because it has maximum torque at low
speeds, the stepper motor is also used in devices that require a low speed.
• Disadvantage:
- A stepper motor has low efficiency as its current consumption is independent of the
load, and it consumes more energy than other DC motors. Its torque is also reduced when
used in high-speed applications. Although a stepper motor can operate in open-loop control
systems, it lacks an integrated feedback system for positioning and control.

3. Types of step motor:
The four major types of stepper motor are as follows:
❖ Permanent magnet stepper
The Permanent Magnet Stepper Motor has a stator construction similar to that of the
single stack variable reluctance motor. The rotor consists of permanent magnet poles of high
retentivity steel and is cylindrical in shape. The concentrating windings on diametrically
opposite poles are connected in series to form a two phase winding on the stator.
The rotor poles align with the stator teeth depending on the excitation of the winding. The
two coils AA’ connected in series to form a winding of Phase A. Similiarly the two coil
BB’ is connected in series forming a phase B windings. The figure below shows 4/2 Pole

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Permanent Magnet Stepper Motor.

The permanent magnet rotor with large number of poles is difficult to make, therefore,
stepper motors of this type are restricted to large step size in the range of 30 to 90⁰. They have
higher inertia and therefore, lower acceleration than variable stepper motors. The Permanent
Magnet stepper motor produces more torque than the Variable Reluctance Stepper
Motor.
❖ Hybrid synchronous stepper.
The word Hybrid means combination or mixture. The Hybrid Stepper Motor is a
combination of the features of the Variable Reluctance Stepper Motor and Permanent
Magnet Stepper Motor. In the center of the rotor, an axial permanent magnet is provided. It
is magnetized to produce a pair of poles as North (N) and South (S) as shown in the figure
below.

7

One of the main advantages of the Hybrid stepper motor is that, if the excitation of the
motor is removed the rotor continues to remain locked in the same position as before the
removal of the excitation. This is because of the Detent Torque produced by the permanent
magnet.
❖ Variable reluctance stepper.
The principle of Variable Reluctance Stepper Motor is based on the property of the flux
lines which capture the low reluctance path. The stator and the rotor of the motor are aligned
in such a way that the magnetic reluctance is minimum. There are two types of the Variable
Reluctance Stepper Motor. They are as follows:
+ Single stack variable reluctance motor.
+ Multi stack variable reluctance motor.
❖ Lavet-type stepping motor
The Lavet-type stepping motor has widespread use as a drive in electro-mechanical
clocks and is a special kind of single-phase stepping motorand requires very little power,
making a battery last for many years; the French engineer Marius Lavet is known as the
inventor for this kind of drives and described it in 1936 in his patent application FR823395.
Like other single-phase motors, the Lavet motor is only able to turn in one direction,
which depends on the geometry of its stator; the rotor is a permanent magnet. The motor can

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be built with a strong magnet and large stator to deliver high torque, but it is mostly built
small, to drive the load through a low gear ratio.
To make a Lavet motor turn, the current through its stator coil must change direction
each step (bipolar) followed by an interval without current while the rotor moves to its
reluctant position. Aside from clock drives, there are many variations of Lavet's concept. One
example are types of dashboard instruments in cars.
4. Stepper motor torque.

When selecting a stepper motor, you try to pick a motor that meets your speed and
torque requirements plus some safety margin. But how do you compare motor performance
between motor suppliers. Most suppliers provide speed – torque characteristic curves to
provide an idea of what performance can be expected from a motor. Stepper motor speed torque curves show how much torque is available from a stepper motor at a given speed when
combined with a particular driver. This means that depending on different motor and driver
combinations, different performance can be expected from the stepper motor system. This
article will describe how a speed - torque curve for a stepper motor is generated and what are
the important points to look for on a curve.
A well defined speed – torque curve, such as the ones shown below, should include the
following information.
1. Power input: This is the voltage that is supplied to the driver. For DC input voltage
drivers, this same voltage is usually applied directly to the motor windings. For AC
input voltage drivers, the AC voltage is rectified to a DC voltage before being
applied to the motor windings. For example, for an 115VAC driver, the applied
voltage to the motor windings is 162VDC.

2. Driver type: This states what type of driver was used to create the curve. Either a
unipolar or bipolar driver should be shown. The driver type will also states if the
driver is of the constant current or constant voltage type.

3. Damper use: While not required, a damper can help to create a more typical
performance curve by representing an inertial load on the motor. The curve should
state if a damper was used and what its characteristics are.
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4. Step angle: This is the step angle the motor was driven at when creating the curve.
Curves will commonly show what the basic step angle (1.8°, 0.9°, 0.72°, 0.36°) of
the motor or what driver resolution (full, half, microstep divisions) were used.

5. Motor winding configuration: This describes how the motor was connected to the
driver and what current was applied to the windings. Motor connections could be
unipolar, bipolar series, bipolar half coil and bipolar parallel.

6. Torque units: The vertical axis shows the amount of torque and in what units (e.g.
oz-in, N.m, etc).

7. Speed: The horizontal axis shows the shaft speed of the motor and in what units (e.g.
rpm, pps, Hz, etc).

8. Maximum No-load starting speed: The maximum no-load starting speed is the
maximum speed at which the motor can be started in synchronism with no load
attached and no acceleration used. It is usually shown as a tick mark labeled “fs” on
the horizontal axis.

9. Holding Torque: This is the torque that the motor will produce when the motor is at
rest and rated current is applied to the windings.

10. Pull-out Torque curve: This curve represents the maximum torque that the stepper
motor can supply to a load at any given speed. Any torque or speed required that
exceeds (goes above) this curve will cause the motor to lose synchronism.

11. Pull-in Torque curve (no load): This curve represents the maximum torque and speed
combination that an unloaded stepper motor can start or stop without any
acceleration or deceleration. Since the pull-in torque curve for a stepper motor varies
depends on the inertial load attached to the motor, the pull-in torque curves are not
shown in the speed – torque curves shown in catalogs. In order to operate above the
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pull-in torque curve, the motor must be accelerated into or decelerated out of the
slew range.

12. Pull-in Torque curve (inertial load): This curve represents the maximum torque and
speed combination that a stepper motor with an inertial load (i.e. damper) can supply
to a load and start or stop without any acceleration or deceleration. In order to
operate above the pull-in torque curve, the motor must be accelerated into or
decelerated out of the slew range.

13. Self start range (start/stop region): When in this area, the stepper motor can start,
stop or change directions in synchronism with the input pulse without the need for
acceleration or deceleration.

14. Slew range: The slew range is where stepper motors are usually operated. A stepper
motor can not be started directly in the slew range. After starting the motor
somewhere in the self start range, the motor can be accelerated into or load applied
into the slew range. The motor must then be decelerated or load reduced back into
the self start range before the motor can be stopped.

15. Maximum response frequency: This is the maximum speed the motor can be
operated when no load is applied to the shaft.

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The speed – torque curves are created by spinning a step motor up to a known speed and then
gradually applying torque to the output shaft with a brake and measured with a torque
transducer. The load is slowly applied until the motor loses synchronism (stops). At the
moment that the motor loses synchronism, the torque that was applied to the motor shaft at
that same moment is recorded. This process is repeated three times at each speed point. The

average of the three torque values is then used as the value that will be displayed on the speed
– torque curve. This process is repeated at several speed points. The torque points are then
plotted at the various speed points to create the complete curve. See figure below.

12


As

was

mentioned earlier, the speed – torque characteristics are determined by the stepper motor and
driver combination. In general, the higher the applied voltage to the motor windings, the faster
the motor will rotate. For example, in the curves below, the speed – torque curve for the
CVK245AK/CVK245BK stepper driver indicates that 24VDC is applied to the motor
windings, while the curve for the RKS545 stepper driver was created with 162VDC being
applied to the windings. As you can see, the torque at speed of the RKS545 stepper driver is
held out to a much higher speed.

II. STEPPER MOTOR CONTROL
1. Stepper motor applications.
Stepper motor are diverse in ther uses, but some of the most common includes:
• 3D printing equipment
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• Textile machines
• Printing presses
• Gaming machines
• Medical imaging machinery

• Small robotics
• CNC milling machines
• Welding equipment
While these applications are the most common, they’re a fraction of what stepper motors can
be used for. Generally speaking, any application that requires highly accurate positioning,
speed control, and low speed torque can benefit from the use of stepper motors.

While servo motors have their place in industry as well as numerous advantages of their own,
stepper motors are an ideal solution in many applications. Stepper motors are a robust motion
control technology and can be found inside of many common machines and equipment
2. Step Motor control method.
2.1. Wave control (Wave drive)

This is the simplest way to control a stepper motor and it hadn’t been use much but still
worth to study for controlling stepper motor. In this method, each phase or stator that
are adjacent to each other will be activate by using a special circuit. This will magnetize
and demagnetize stator leading to stepper motor rotation.
2.2. Full step controller (Full step drive)

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In this method instead of activating each stator one time, there will be two stators
activating with short interval in between. In this mode any of the two will be activate.
This mean that the first stator turn ON and second stator will turn ON after a short time
while the first stator are still working (ON). This method resulting in high torque and
allow for high load motor control.
2.3. Half-step controller (Half-stepping drive)

This method maybe similar to the full-step controller. Here, two stators are put together

will be trigger first and the third stator will be trigger next, the first two stator will be
disable. This cycle trigger two stator first and after one stator repeat to control stepper
motor. This method resulted in the increase of engine resolution while reduce motor
torque.
2.4. MicroStepping controller (MicroStepping drive)

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This is the most uses control method because of it precision. The control circuit
provided variable step flow for the stator at sinusoidal waveform. These small steps are
improving the precision of each step. This method is widespread because it provided
high precision and reduced operating noises at high rate.
3. Stepper Motor Driver.
We have seen previously that the motor coils need to be energized, in a specific
sequence, to generate the magnetic field with which the rotor is going to align. Several
devices are used to supply the necessary voltage to the coils, and thus allow the motor to
function properly. Starting from the devices that are closer to the motor we have:
• A transistor bridge is the device physically controlling the electrical connection
of the motor coils. Transistors can be seen as electrically controlled interrupters,
which, when closed allow the connection of a coil to the electrical supply and
thus the flow of current in the coil. One transistor bridge is needed for each motor
phase.
• A pre-driver is a device that controls the activation of the transistors, providing
the required voltage and current, it is in turn controlled by an MCU.
• An MCU is a microcontroller unit, which is usually programmed by the motor
user and generates specific signals for the pre-driver to obtain the desired motor
behavior.

16

4. Stepper Motor Driver types.
There are different stepper motor drivers available on the market, which showcase different
features for specific applications. The most important charactreristics include the input
interface. The most common options are:
• Step/Direction – By sending a pulse on the Step pin, the driver changes its output such
that the motor will perform a step, the direction of which is determined by the level on
the Direction pin.
• Phase/Enable – For each stator winding phase, Phase determines the current direction
and triggers Enable if the phase is energized.
• PWM – Directly controls the gate signals of the low-side and high-side FETs.
Another important feature of a stepper motor driver is if it is only able to control the voltage
across the winding, or also the current flowing through it:
• With voltage control, the driver only regulates the voltage across the winding. The
torque developed and the speed with which the steps are executed only depend on
motor and load characteristics.
• Current control drivers are more advanced, as they regulate the current flowing
through the active coil in order to have better control over the torque produced, and
thus the dynamic behavior of the whole system.
Example for calculation Stepper motor:
Stepper motor is used often in automatic control system, they are applied in precision
control devices.
Example: Robotic control, control lighting focal distance, control position in monitoring
relation, catching control, clinging the target in the observed object, programing control in
machining and cutting devices, directional and dimensional steering mechanism in aircraft
control.
For the initial Parameter.
• Mass load: m=40kg
ã Friction coefficient of surface guide: à=0.05

ã Lead screw transmission efficiency: η=0.9
• Lead screw diameter: Db=15[mm]
• Lead screw mass: Mb=0.84[kg]
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• Screw step: Pb=15[mm]
• Coupling mass: Mk=0.5[kg]
• Outside diameter coupling: Dk=40[mm]
• Machine table accuracy: Δl=0.03[mm/step]
• Machine table displacement: l=180[mm]
• Safety factor: Sf=2
1. The necessary resolution for step motor.
2. The necessary motor rotation Nm[r/m]
3. Total inertia torque affected on motor axis Jl [kg.m2]
4. Total torque affected on motor axis, Tm [N.M]
5. Calculate working power, P0 and accelerating power Pa[W]
6. Conclusion find a suitable step motor.
SOLUTION
1.The necessary resolution for step motor. 𝜽s (degree):
𝜃s =

∆𝑙. 360° 0.03.360°
=
= 0.72°
𝑃𝑏
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2. The necessary motor rotation Nm[r/m]
f = 10000 (Hz)

Nm=

𝜃𝑠 .60.𝑓
360°

=

0.72°.60.10000
360°

= 1200(r/min)

3. Total inertia torque affected on motor axis Jl [kg.m2]
Jt = Jtv + Jtw + Jm
* Torque of lead screw:
Jtv = ½.Mb.(

𝑃𝑏2
22

) = ½.0.84.( 0.0152/4 ) = 2.3625.10-5[kg.m2]

* Torque of the machine table and details to act on the screw:
Jtw = (mt + mw).(

𝑃𝑏2
4𝜋 2

) = 40.( 0.0152/4𝜋 2 ) = 2.28.10-4 [kg.m2]

Jm = J0 = 380.10-7 [kg.m2]

 Jt = Jtv + Jtw + Jm = 2.3625.10-5+ 2.28.10-4 + 380.10-7 = 2,89.10-4[kg.m2]
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4. Total torque affected on motor axis, Tm [N.M]
Tm = (Ta + Tl).Sf
*Torque impact on motor due to friction between machine table and guide bar
Tt =

𝑃𝑏
2𝜋

. 𝜇. (𝑚. 𝑔 + 𝐹𝑧) =

0,015
2𝜋

. 0,05(40.9,81 + 0) = 0.0468 (𝑁. 𝑚)

*Torque shaft moment of inertia:
Ta = J.𝜖 = (𝐽0 + 𝐽𝑡 ).



𝜋.𝑓.𝜃𝑠
𝑇1 .180°

= (380. 10−7 + 2,89. 10−4 ).

𝜋.10000.0,72
0,2.180°

= 0.205 (𝑁. 𝑚)

Tm = (Ta + Tt).Sf = (0.205 + 0,0468).2 = 0.5036 (N.m)

5. Calculate working power, P0 and accelerating power Pa[W]
P0 = Tm.Nm.
Pa = Ta.Nm.

2𝜋
60

2𝜋
60

= (0.5036.1200).
= (0.205.1200).

2𝜋
60

2𝜋
60

= 63.28 (W)

= 25,76 (W)

6. Conclusion, find a suitable step motor.
Stepper motor that we chose must have a torque Tm=0.5036[N.m] and the time accelerating
is Ta=0.2s.

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CHAPTER 3: APPLICATIONS OF STEP MOTOR

In digital motion control, the stepper motor is a particularly effective actuator, as it can
faithfully execute commands given in digital form. This type of motor is currently widely
used in the automation industry, especially the equipment that requires precise control.
Stepper motors are widely used in machine tool such as CNC plasma cutting machine, wood
machine, engraving machine, laser cutting machine ...
In this report, we use 3D Printer for the example to stepper motor.
I. CHOICE OF ELECTRIC DRIVES
There are Servo motors and Stepper motors, and Servo motor is better than stepper motor in
many ways. Servo motor is a DC motor but with an encoder to provide position feedback. A
circuit (can be a computer) then compares the actual position (from the encoder) against the
commanded position and uses the error to determine how much power to put to the motor.
Some of the advantages of servos:
• The encoders on the motor often have thousands of counts per revolution so they are
accurate.
• They are a great choice for controlling a large mass. When beginning a motion, the
control loop can detect that more power is required when the encoder does not respond
as fast as expected thus putting more power to the motor. This will them automatically
reduce as the motor reaches speed and no longer needs the acceleration torque. Also,
the servo loop can also apply reverse torque when trying to slow down the large mass
to limit overshot.

Some of the disadvantages of servos:
• The DC Motors used for servos reach peak power at thousands of RPM. That means
to use them on a printer you will need to gear them down. This adds to the expense.
• You need electronics to PWM the power to the DC Motor and to close the servo loop
(usually at least 1 KHz). This can require a lot of the CPU.
• The servo loop tuning can cause the motor to buzz when it is holding position on an
unloaded axis. This could cause print issues.
Stepper motors on the other hand:
• They are really cheap
• Don't require complicated drive circuits or control loops

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• Hold position without a load.
Their downside is that their rotational accuracy is limited by the physical poles of the motor.
This can be improved using micro-stepping.
In summary, servos are great for some applications; but, for low cost situations like 3D
printing, steppers are hard to beat. It is likely servos needed for milling CNCs because the
cutting head is much more massive than an extruder or laser and the servo control loop is
needed to provide accurate motion for the higher mass. From all reasons above, to build a 3D
printer (especially in university, for a course project), Stepper motor is the best choice.
II. 3D PRINTER PLAN DESIGN
❖ For X and Y axis:
Calculate for each axis (X and Y axis are used nearly the same engine), however the X axis
carries the direct extruder and the Z axis, so we use the Y for calculation.
We have:
Mass: m = 3 kg
Acceleration: a = 1800 mm/s2 = 1.8 m/s2
Max print speed: v = 200 mm/s = 0.2 m/s

Use GT2 T16 pulley which have a diameter of 9.4mm
then the arm length L = 9.4mm/2 = 4.7mm = 4.7*10-3 m
Figure 3.1. GT2 T16 (9.4mm / 2mm)

and its pitch is 2mm.
Motor has 𝜃s = 1.80 full step angle
Solution:
According to second Newton’s law the force:
𝐹 = 𝑚 ∗ 𝑎 = 3 ∗ 1.8 = 5.4 𝑁
Torque T is:

𝑇 = 𝐹 ∗ 𝐿 = 5.4 × 4.7 ∗ 10−3 = 0.0253 𝑁. 𝑚
The motor’s steps for a full rotation:

3600
1.80

= 200 𝑠𝑡𝑒𝑝/𝑟𝑒𝑣 (step per revolution)

Calculate linear displacement for each step:
16 𝑡𝑜𝑜𝑡ℎ ∗ 2𝑚𝑚 𝑝𝑖𝑡𝑐ℎ = 32 𝑚𝑚/𝑟𝑒𝑣

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32 𝑚𝑚/𝑟𝑒𝑣
= 0.16 𝑚𝑚/𝑠𝑡𝑒𝑝
200 𝑠𝑡𝑒𝑝/𝑟𝑒𝑣
Max step speed is
𝑁𝑚 =

200 𝑚𝑚/𝑠
60
= 1250 𝑠𝑡𝑒𝑝⁄𝑠 𝒐𝒓 1250 ∗
= 375 𝑟𝑝𝑚
0.16 𝑚𝑚/𝑠𝑡𝑒𝑝
200

Look at this picture, you can see that when Nm = 375 rpm (curve 12 Vdc) is about 48 %
(0.23/0.48), from this then our need torque become:
0.0253
= 0.0527 𝑁. 𝑚
48%
Because we use driver with micro step, using microstep bring to a huge lost of torque.

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