Motion for Dummies
Motion for Dummies
Animatics Institute, October 2008
Contents
Magnets and Magnetism������������������������������������������������������������������������������������������������������������������������������������������������� 3
Feedback Devices����������������������������������������������������������������������������������������������������������������������������������������������������������� 5
Mechanical Systems������������������������������������������������������������������������������������������������������������������������������������������������������� 9
Understanding Actuator Loading��������������������������������������������������������������������������������������������������������������������������������� 13
Understanding Thrust Curves�������������������������������������������������������������������������������������������������������������������������������������� 14
Understanding Animatics Torque Curves�������������������������������������������������������������������������������������������������������������������� 15
Moment of Inertia Overview������������������������������������������������������������������������������������������������������������������������������������������ 17
Advanced Drive Capabilities����������������������������������������������������������������������������������������������������������������������������������������� 18
Example Applications��������������������������������������������������������������������������������������������������������������������������������������������������� 19
Motion Glossary������������������������������������������������������������������������������������������������������������������������������������������������������������ 22
Motion Formulas����������������������������������������������������������������������������������������������������������������������������������������������������������� 30
Introduction
Magnets and Magnetism covers the molecular level of magnetic flux to provide the reader with a better understanding of how
and why electrical motors operate the way they do., It gives the true “mechanical” reasons for properties of inductance and Back EMF.
Feedback Devices covers the most common means of feedback used for detecting mechanical motion. With brief descriptions and
diagrams, the reader will benefit with a more complete understanding of what is out there and how it works.
Mechanical Systems is an overview of basic actuator types and mechanical drive systems including comparison charts to aid in
proper selection for any given application.
Understanding Actuator Loading will give insight into the strengths and weaknesses of moment arm loading practices and add
to the knowledge required when properly sizing bearing loads for a given linear guide.
Understanding Thrust Curves shows the basis for limits placed on advertised thrust curves for actuators. With this in mind, a
better selection can be made when sizing up actuators for longer life and safer operation
Understanding Torque Curves like above, will show limits and the reasons for them. In addition, it shows examples of real world
operating conditions and the likely result if run under those conditions. This will greatly aid in troubleshooting systems where proper sizing
may have come into question.,
Moment Of Inertia Overview may surprise the user with alternate methods to achieve heavy load control. In a brief detailed
description, it uncovers the benefits of gear reduction and speed optimizing.
Advanced Drive Capabilities covers specific capabilities found in Animatics Smartmotors that may open up new applications and
means for improved performance in those hard to attain motion profiles.
Example Applications shows an overview of typical systems in the filed where closed loop servo motors have been used to
maintain good efficient production with repeatable quality results.
Motion Glossary and Motion Formulas is a collection of common terms and formulas used in the automation industry especially
as it applies to motion control.
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Magnetism & Magnets
Domain: A Small area of control, in the case of magnets, a small molecular level sized magnet
Permeability: This refers to how well magnetic fields can reach into or though a material.
Reluctance. : Opposite of Permeability. The magnetic field is reluctant to pass through a material.
Flux: A term given to the lines of field strength in a magnetic field. Like paths of water flow out of a shower head.
Coercivity:
Basically describes how much molecules inside a material can move around or stick together.
8 Axioms of magnetism (As it pertains to Flux)
1.Flux lines, like electrical currents, will always follow the path of least resistance. In magnetic terms, this means that flux lines will
follow the path of greatest permeance (lowest reluctance).
2.Flux lines repel each other if their direction of flow is the same.
3.As a corollary to condition two (2), flux lines can never cross.
4.As a corollary to condition one (1), flux lines will always follow the shortest path through any medium. They therefore can only
travel in straight lines or curved paths, and they can never take true right-angle turns. Meeting the terms of condition two (2), flux
lines will normally move in curved paths; although over short distances, they may be considered straight for practical purposes.
5.Flux lines will always leave and enter the surfaces of ferromagnetic material at right angles.
6.All ferromagnetic materials have a “limited ability” to carry flux. When they reach this limit, they are saturated and behave as
though they do not exist (like air, aluminum and so on). Below the level of saturation, a ferromagnetic material will substantially
contain the flux lines passing through it. As saturation is approached, because of conditions one (1) and two (2), the flux lines
may travel as readily through the air as through the material.
7.Flux lines will always travel from the nearest north pole to the nearest south pole in a path that forms a closed loop. They need
not travel to their own opposite pole; although they ultimately do if poles of another magnet are closer and/or there is a path of
lower reluctance (greater permeance) between them.
8.Magnetic poles are not unit poles. In a magnetic circuit, any two points equidistant from the neutral axis function as poles, so that
flux will flow between them (assuring that they meet the other conditions stated above).
Domain Theory
In 1907 French physicist Pierre Weiss postulated that ferromagnetic materials were fully magnetized at all times. He
attributed this to spontaneous “molecular fields” that caused total alignment of atomic magnetic moments. However, he had
to explain the absence of an apparent magnetic field when the material was not magnetized. He theorized that macroscopic
regions within the material were composed of sub regions, called domains, wherein all atomic magnetic moments are
parallel, and that domains arranged themselves randomly when no external (or internal) magneto-motive force was present.
This is analogous to world wide power struggles, and maybe even Pierre saw it this way.
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Magnetism & Magnets
Magnetic Domains
Magnetic domains function in the same way. All magnetic materials initially
have many small randomly aligned domains. Rare earth materials have strong
local forces but, unless influenced by some outside force, they live happily
with neighbors in a state of equilibrium. Externally, the material appears to
have no preferred alignment and it does not influence other objects. When
a strong outside force appears, in the guise of a magnetizing pulse, then
the magnetic domains all line up with the force and add to it, and the strong
domains grow in size.
N
S
When the strong external force goes away the domains would relax and go random again unless a strong internal force (coercivity of the
material) takes control while the strong external force is present. Internal mechanisms that develop coercivity are “anisotropy”. The four
types of anisotropy are: (a) crystal, (b) stress, (3) shape, and (d) exchange. To learn more about them please refer to a technical text.
If the material has a high flux density and a strong internal force it can influence other domains. However, domains on the periphery of the
magnet volume have fewer neighboring domains for support so they can be turned around and oppose the aligned domains if encouraged
to do so by an external force, or random energy additions. The magnet’s “king” is a magnetizing, or demagnetizing, force; flux density is
the magnet’s army; and “coercivity” is the ruler that keep domains aligned when the king goes away. A magnet’s useful strength depends
on how many domains remain aligned after the external force goes away and they have to face opposing kings and armies on their own.
A short magnetic length is like an army with a wide advancing front; it is susceptible to the opposing force everywhere, but mostly at the
edges. When the edges are neutralized by opposing external forces the rest of the magnet may be made ineffective. An army column with
a good length to width ratio, depending on its internal and external resources, is the most effective and the same is true with magnets.
External resources for a magnet would be other magnetic circuit components.
Other factors are also involved. When an external magnetizing force is applied it “moves domain walls” to make the stronger domains
larger. It takes just as much energy to move these domain walls back to where they were, so a magnet that is hard to magnetize usually
is hard to demagnetize. However, magnets do not like heat; thermal energy reduces pole strength (flux density) and the ability of domains
to remain aligned, depending on the temperature reached and intrinsic strength.
Heat first weakens the “magnetic army”; this is a flux density loss that is recovered when things cool off. Next, the outer and weaker
domains reverse and these losses are recoverable only by “the king.” The process slows as heat travels into the magnet and encounters
stronger internal domains. If a magnet gets too hot its chemistry actually changes, and it can be permanently damaged. Heating in air
initially results in oxidation; higher temperatures may result in phase changes. The temperature at which chemistry changes may begin to
occur in magnet materials is identified as the maximum operating temperature; this is usually much lower than the “Curie temperature”.
(Curie temperature is the temperature at which an element or alloy becomes totally non magnetic.) Ceramic magnets (strontium or
barium ferrite) are the exception; they are made from oxides that do not change composition even after their magnetic temperature limit
is reached.
Magnets can be “thermally demagnetized” at moderate temperatures (less than Curie) to allow further processing after testing but,
while little or no external field is exhibited, they are far from their virgin state. So long as they have not seen a chemistry change,
these magnets will recover fully when re-magnetized. Heat treating in the magnet manufacturing process uses precise heat and
cool rates to precipitate the desired phase, a protective gas atmosphere to avoid oxidation, and usually an orienting magnetic field.
Magnet material producers use combinations of atomic elements in their magnets to make domain walls harder to move and more
resistant to heat. However, these elements take up a portion of the magnet’s volume so they produce less total flux (fewer soldiers).
“Domain wall pinning” is another factor in making domain walls harder to move; this is like driving a pile into the ground to keep the domain
wall from moving.
Domain theory is useful in understanding how magnets work. It cannot account for all observed magnetic phenomena, but it helps
scientists describe the internal cause for observed external field changes. It is interesting to note that it has become possible to see
magnetic domains with a variety of high power microscopes. So domain theory, once just a convenient way to explain how magnets work,
has a factual basis.
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Feedback Devices:
This section covers various means of feedback devices in motion control.
Contents
1.Incremental Encoders
2.Absolute Encoders
3.Linear Encoders
4.Magnetic Encoders
5.Optical Encoders
6.Potentiometers
7.Resolvers
8.Tachometers
1: Incremental Encoders
Like any other position feedback device, the incremental encoder is used to determine rotary or linear position. This term ‘incremental’
describes the type of information that the encoder sends out. There are only two options available here, either incremental or absolute.
This encoder provides relative position information. As rotation or linear translation occurs, the incremental encoder sends out one pulse
for each set incremental distance of travel. These pulses can be counted to determine the linear or rotary position relative to another
position. Motion is quantified by a certain number of pulses. Usually, the incremental encoder will come with three channels, referred to
as A,B, and Z. A typical output signal is shown to the below.
A
B
K
A and B are placed 90’ out of phase. With these two channels, the processor determines the distance traveled by the number of steps,
and the direction traveled by the leading wave form. The third channel is the reference. Usually the Z channel will have only one pulse
per revolution or per length of the encoder, so it can be used to determine an actual location, rather than just an incremental number.
These encoders can be either: magnetic, optical, contacting, or capacitive.
The disadvantage of the incremental encoder is that it is unable to determine its location upon start-up, but this problem can be overcome
by taking the time to do a homing or reference pulse sequence, and then moving the desired amount of steps from there. If this is
possible, It is recommended.
The added expense and setup time of an absolute encoder should be avoided unless completely necessary.
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Feedback Devices:
2: Absolute Encoders
The device is used to determine rotary position. The term absolute defines the type of information that is relayed to the processor. There
are only two options available here, either absolute or incremental.
The absolute encoder differs from the incremental encoder in that each angular location is represented by a different digital word. In the
case of the incremental encoder, it is only possible to know your location relative to another location. The absolute encoder solves this
problem by making each angular position unique. An image of an absolute encoder disk is shown here.
Each separate location can be represented by a binary number, determined by the sequence of light transmission or blockage as you
progress inward to the center.
The advantage of the absolute encoder is that the position is not lost in the case of power loss or
noise bursts. The disadvantage is added complexity and price.
3: Linear Encoders
This device is used to convert linear position information into an electrical output signal. The linear encoder consists of a linear tape scale
made up of glass or steel, a light source (e.g. LED, laser), and a photoreceptor. The light source, photoreceptor, and additional scale are
usually housed together. This housing either surrounds the tape scale in through beam encoders or resides on one side of the tape scale
in reflective linear encoders.
Light is projected through or off the tape scale and is detected by the photoreceptor. The fixed scale modulates the light as the
receptor and light source progress. The receptor detects these modulations and converts the input into an electrical output usually in the
form of a quadrature signal (shown below).
A
B
The two channels are always 90’ out of phase. The direction of the motion can be determined by the leading channel. The output is the
same as that of the incremental rotary encoder.
The linear version is incremental as well, which means that it tells the position of one location relative to that of the other, rather than
having a knowledge of its actual location.
A linear encoder is often preferred over a rotary encoder where linear motion is the final output of the system (e.g. conveyors, rodless
cylinders). In a linear system you are able to eliminate the inherent backlash and inaccuracies involved with mechanical systems by
measuring the linear displacement rather than a rotary displacement.
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Feedback Devices:
4: Magnetic Encoders
This device is used to convert position information into an electrical output that can be interpreted by a system controller. The two main
components of a magnetic encoder are the read head and the magnetic disc. The read head contains a magneto resistive sensor, which
is basically an inductor that detects changes in the magnetic flux. The disc is magnetically coded. The magnetic code is interpreted by
the sensor as a series of on and off states. One magnetic code is interpreted as a 0 bit value and the next as a 1 bit value. Through this
combination the magnetic encoder is able to transmit pulses representing incremental rotary motion.
The magnetic encoder offers good resolution, can operate in a wide variety of conditions, and requires low power for operation; however,
they cannot achieve very high speeds.
5: Optical Encoders
This feedback device is used to detect rotary or linear position and convert it to an electrical output. A light source, usually either an LED
or a laser, is projected through thin slits in a rotary disc for rotary encoders, or a thin tape scale for linear. The LED is adequate for most
applications, although the laser has found niches in several high precision, high resolution applications. The disk and tape can either be
made of covered glass with thin etchings in the cover, or thin metal with etchings through it. Each has appropriate applications. As light
is transmitted, a photo receptor on the opposite side of the disc or tape detects the light and converts it to an electrical output. Different
optical encoders can create a wide range of signals, (e.g. TTL, silicon cell, analog, sinusoidal).
Optical encoders offer the higher resolution and accuracy than all other encoders. Some can offer in excess of 1 million counts/
revolution. Often times the best way to decide what feedback device you should use for your application is to determine what type of
information your controller, PLC, smart drive, or other processor that you are using is capable of processing without too much trouble.
Frequently many types of feedback will fit your needs, but only a couple will be simple to integrate. Due of the different signal options
and versatility of the optical encoder, this is a very popular position feedback device.
6: Potentiometers
This device provides an output voltage proportional to angular or linear position. The image below shows a schematic of the linear and
rotary potentiometer.
Variable Resistors
Vtotal
min
Vpotentiometer
wiper
max
Vtotal
Vpotentiometer
The output voltage in both scenarios varies according to the location of the sliding contact on the resistor. Ideally, distance would be
perfectly proportional to the output voltage. Unfortunately, this is not the case due to the non linear characteristics of the resistive element
and the additional load of the sliding contact.
A potentiometer is an affordable, adequate position sensor in many applications. However, if you need accurate position monitoring,
you should look into a resolver or encoder. Potentiometers are commonly used to transmit a variable analog voltage set by a user. They
are commonly found in joysticks, tuning pots, and reference signal controllers
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Feedback Devices:
7: Resolvers
This device is an absolute position sensor with an analog output. The resolver is composed of a rotor with one winding and a stator with
two windings at right angles to each other. The winding of the rotor is excited with an AC reference voltage. This voltage induces a
current in the two windings of the stator.
Let’s look at the induced voltage of one of the stator windings.
As the rotor spins the voltage that will be induced in the stator will vary. When the windings are parallel to each other, the voltage will be
at a maximum. When they are perpendicular to each other, it will be at a minimum. Thus the induced voltage of one stator winding is
dependent on the rotor position and governed by this equation V=Vinput SinØ.
Because the second rotor winding is at a right angle to the first, its voltage signal can be calculated using the cosine. In the valley and
peak of the sine wave there is only a slight slope, so position variations are difficult to pick up. This is the reason the second winding is
needed: to provide clearer positions signals at these points.
The analog signal needs to be translated to a digital signal for the system drive and/or controller to process it. A resolver to digital
converter can be used to accomplish this.
Resolvers are very durable. They can be used to provide a speed reference signal to close a velocity loop and a position signal to close
the position loop. In this respect they eliminate the need for a tachometer. Further the resolver is a device with very high precision
and resolution.
8: Tachometers
Often referred to as a tach or tacho-generator. The tachometer operates under the same principles as a generator; in fact it is a generator.
The basic design of tachometer is very similar to that of a small DC motor. The tachometer is either mounted externally to the motor or
is combined internally.
When the tachometer is driven by the motor, it generates an output voltage. The output voltage produced is proportional to the velocity
of the motor. The proportionality of this relationship is critical to the accuracy of the device. Designers of tachometers need to focus
their attention on ensuring that the output voltage is smooth over a wide range of speeds and that it is stable over temperature variations.
These characteristics determine the quality of the product.
A tachometer is the most common way of measuring velocity. The velocity signal can be fed to a rate indicator to display the velocity to
the operator, or it can be used to close a velocity loop. A large variety of amplifiers give the option of operating in velocity mode with the
use of a tachometer. Tachometers are also a critical component in many servo systems. When using a tachometer with a brushless
system, it is wise to use a brushless tachometer so as not to limit the life of the entire system.
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Mechanical Systems
Ball Screws, ACME Screws, Rack & Pinion, and Belt Drives, Which way do we go?
It is common to have a new task at hand of moving loads but not knowing or better yet, not realizing the proper mechanics to use .
“Which way do we go” would be better served by asking “what way do we need to go?”.
These are the questions to ask:
1.Is the load a Heavy load or a Light load?
2.Does it need to be moved fast or slow?
3.Is this a high-resolution move to a precise position?
4.Is it a very short incremental move or over a long distance?
5.Is this a vertical or horizontal application?
6.All of these questions usually come in to play even if the answers are realized without thinking about it.
No one question can be seen as over riding any of the others.
Vertical loads burden motors with continuous heat generation. It is better to have the motor sized adequately to insure a good safety
margin.
The use of Pneumatic or Electro-mechanical brakes should be used to ensure fail-safe operation on loss of power. Remember that
electrical safety brakes add additional heat to the system.
When it comes to high resolution and high speed, they are typically mutually exclusive. It is difficult to get both high resolution and high
speed. This can be compared to transmissions in automobiles. A car can go very fast in 3rd or 4th gear but it cannot move very slowly
in those gears. In the same manner, it is easy to move incrementally forward in 1st gear.
• Additional gear reduction adds higher resolution
• Less gear reduction gives higher speed.
The same rules apply to ball screws as well.
A 1mm/revolution screw will have higher resolution where a 20mm/revolution crew will have high speed.
Rules to follow for ball and ACME screws:
• Fine lead screw:
○○ heavy loads,
○○ holding vertical loads
○○ high resolution.
• Coarse Lead screw:
○○ fast speeds
○○ low resolution
○○ not as safe for holding vertical loads.
Actuator Type
Efficiency
Thrust Load
Back-Drive
Accuracy
Speed
ACME Screws
low
highest
difficult
good
medium
Ball Screws
high
high
easy
best
fast
Belt drives
medium
low
easy
ok
very fast
Rack & Pinion
medium
low
easy
bad
very fast
Note: ACME screws have the highest static thrust load capability
Ball screws have the highest driving thrust load capability.
This is due to the nature of the threads of ACME screws. They have more support for static load than do ball screw nuts. Ball screws have
re-circulating bearing that allow for lower friction and greater running thrust load capability.
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Mechanical Systems
Notes on Drive Types:
Belt Drives are typically available with speed ratings to 8 meters/second.
This is not achievable with Ball or ACME screws.
Lead screws of any type have a critical limit speed. This is the speed in RPM that, if exceeded, will result in excessive vibration or
damage.
Within a given length, most speed limitations are due to re-circulating ball paths.
Inside of both ball nuts and re-circulating bearing blocks, the small ball bearings have to be re-directed from the exit path back to the other
end. The radius of this return path on each end is the limiting factor. Larger re-circulating blocks have a higher speed rating because the
radius of the return path is larger and provides less frictional losses. As a result,, compact bearings cannot run as fast.
Gear Reduction: What does it do for you?
Often times, advantages of gear reduction are overlooked or forgotten entirely.
Higher gear reduction provides the following:
1.Increased torque
2.Higher resolution
(more encoder counts per revolution at the motor)
3.Lower speed
4.Higher acceleration capability and therefore better moment-of-inertia matching
5.Faster braking or stopping
Overview of Gear Reduction Types
Actuator Type
Efficiency
Backlash
Typical Reductions Available
Speed
Worm
low
medium
3 to 1000
medium
Spur
medium
high
3 to 100
fast
Planetary
high
low
3 to >100
very fast
Cyclical
medium
very low
10 to 200
very fast
Harmonic
medium
extremely low
30 to >500
fast
Toothed Belt
high
medium
>1 to 5
very fast
Notes on Gear Reduction
Most Servomotors use planetary gear heads where as most steppers use Spur gear heads.
Worm gear reduction is typically found on large AC Induction motors or conveyor drives.
Worm gear reduction has the advantage of not being able to be back driven This is good in cases where maintaining load on loss-of power
is concerned.
Cycloidal and Harmonic Drive gear reduction is used where extremely high repeatability is needed. They are considered “zero-backlash”.
Their limitations are in that they are not available in low gear ratios.
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Mechanical Systems
Gear Ratio Selection
When using Brushless servos proper gear ratio selection is very important.
An easy way to size ratios is to start with a few basic rules:
Most Planetary gear heads are limited to approximately 5000 RPM input speed. Giving a margin for error, and lower heat generation, it
is bet to limit them to 4000 RPM.
Integrated motor drive servos typically have a torque curve roll-off at approximately 3000 RPM.
After finding out what speed is required for an application, divide that speed into 3000 and the result is the gear ratio needed.
Example:
Suppose A maximum output shaft speed of 240 RPM is required. This is needed at 11 Nm.
3000/240=12.5. Typical gear reductions are 10:1 and 16:1
the 10:1 ratio will provide higher speeds but less torque.
The 16:1 will provide higher torque but less speed.
Since the ratio was calculated off of 3000 RPM and most planetary gears can handle 4000 to 500 RPM, the 16:1 ratio may be a good
choice.
240*16=3840RPM
11Nm/16=0.69Nm required at the motor shaft.
These are estimates and do not account for efficiency losses. You should consult the gear box manufacturer for more information.
If the application has fast start and stop moves, it is better to maximize gear ratio to gain the most acceleration and deceleration control.
Higher gear ratios always provide better start and stop motion than do lower gear ratios.
Timing Belt or Toothed Belt Reduction:
This method of gear reduction is often under-rated and overlooked. It is the cheapest means to gain more torque. It is also the absolute
fasted input speed of any means of gear reduction. Timing belts can be moved at many thousands of RPM.
When ball screws are needed for high thrust loads, where as belt drives may not work, it may be advantageous to use belt reduction into
the ball screws. This keeps the ball screw below critical speed while providing optimum torque curve performance of Brushless servos.
Most Brushless servos work optimally above 2500 RPMs, bur most ball screws cannot be run that high. By making use of belt reduction,
the best of both worlds are achieved. This method also allows the motor to be folded back under the ball screw making the mechanism
shorter.
To dynamically brake or not to dynamically brake?
When thinking of braking or brakes, usually mechanical brakes come to mind. There is a different mean to slow down or even stop fast
moving loads. Many conventional servo drives come with “regen resistor” options. This is a means to dump generated power in motors
back to a resistor bank. In most cases, the reason for doing this is to protect the DC bus from over voltage. integrated motors do not have
the luxury of space to fit a regeneration resistor in the controller case. This is where external voltage shunts are needed to dynamically
brake motors. When motors slow down rapidly, the load will tend to back drive the motor truing it into a generator. The bus voltage then
begins to rise which could lead to electrical damage.
Dynamic shunts provide a means to both protect the DC bus from over voltage as well as a means to dissipation power enabling faster
stops. In the extreme case internal motor shunting electronically can stop the generation at it’s source. This is the equivalent of shorting
out the motor windings.
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Mechanical Systems
Considerations when employing various drive systems
Lead Screw
Belt Drive or Conveyor
Consider Product Slippage
May require Linearity Mapping
NIP Roller
Rotary Indexing
Material may creep or slip over time
Be aware of Odd Gear Ratios
Rack and Pinion
Be aware of easy back-drive
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Understanding Actuator Loading
Consideraitons for Actuator Loading
Forces acting upon actuators consist of a combination of direct forces pushing in from any axis and a twisting force that may be applied
due to offset loads.
Direct Forces placed on the Actuator
F.t. : Thrust Force operating in the direction of travel.
Mechanically Limiting Factor: For Lead Screw Actuators, this is typically the thrust bearings and/or lead nut.
For Harmonic Belt drives, the limiting factor is typically the belt. It may be based on shear strength of the belt teeth or on the actual
tensile strength of the belt itself. In a welded belt, it would most likely be based on the weld strength of that belt.
F.st. : Side Thrust Force, acts upon the carriage from one side or the other.
The bearing support is typically the limiting factor. The choice of bearings and their orientation will greatly affect the maximum permissible
force.
F.n. : Normal Force downward.
Similar to side force, the limit is based on the bearings and their orientation. It is very common to have a much higher normal downward
force capacity than a side force capacity. Since Gravity typically plays a roll in Horizontal applications, most actuators are designed to
deal with downward force effectively.
Moment Loading Forces:
This is the twisting force similar to a Moment arm force applying a torque to the supporting bearings.
To insure long life of the actuator it is imperative to not exceed the Moment loading specifications.
In the above diagram, three Moment loads are depicted.
All three Moment loading forces may exist on a given application. It is important to remember that any offset load from the center surface
of the actuator carriage will induce one or more of these Moment forces.
While accelerating, that Moment load may increase drastically.
For Example: Suppose in the above diagram, you place a load offset from the center of the carriage in upward direction. Any time the load
is accelerated, the M.b. Moment loading will increase.
If the load is placed horizontally offset to one side or the other, dynamic motion will increase the M.c. component of Moment loading of
that actuator.
The M.a. component is the only Moment loading that will not typically change with the dynamics of load motion. However, offset side
loading is the greatest contributor to the M.a. component.
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13
Understanding Thrust Curves
Understanding Thrust Curves
Actuator Thrust Curves are very similar to Servo Torque Curves, but relate to linear motion performance instead of shaft rotation
performance. All thrust curves show continuous and peak performance based on the coupled system of Servo and Actuator together. The
following examples show the 2 exceptions to the previous statement, where the actuators limitations are taken into account.
Note: The continuous thrust region is where the system should be operated, except for short hard accelerations required in your motion
profile. Sustained Operation outside the continuous region will reduce the rated life on the actuator/integrated motor system. Please
check the specifications of each actuator for limiting factors such as mechanical critical speed and thrust limits.
Note: In this example, the maximum allowable thrust is limited
to 550 N. Exceeding that could potentially damage the actuator
even if the motor limits are not exceeded.
Limitation of Actuator’s Speed Example
The curve to the right shows that at 500 mm/sec, the thrust
abruptly goes to zero (the vertical line). This means that the
actuator has a maximum carriage velocity of 500 mm/sec usually
due to ball screw limitations.
600
C ontinuous Thrus t
P eak Thrus t
500
Thrust, N
The curve to the right shows that there is a maximum amount
of thrust the actuator can put out continuously and peak. That is
why the curve abruptly flattens out (horizontal line) at speeds less
than 150 mm/sec. This curve shows that the motor can provide
more input torque than the actuator can handle at speeds less
than 150 mm/sec.
HLD60 Single Rail/Internal Rollers
SM2316DT @ 48V, 2.5mm/rev
400
300
200
100
0
0
50
100
150
Carriage Velocity, mm/sec
200
250
VL-ST45 - SM2316D @ 48V, 6mm/rev lead ball screw
500
Continuous Duty
Peak Duty
400
Thrust, N
Limitation on Thrust Output Example
300
Note: This speed limitation is mechanically based. It may be
possible to command a servo speed in excess of the Critical
speed limits of the actuator. Doing so increases risk of damage
and will shorten the life of the actuator.
200
100
0
0
14
100
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200
300
400
Carriage Velocity, mm/sec
500
Understanding Animatics Torque Curves
Each Set of Torque curves depicts limits of both Continuous and Peak torque for the given SmartMotor™ over their full range speed.
Peak Torque Curve:
The Peak Torque Curve is derived from dyno testing and is the point at which peak current limit hardware settings of the drive prevent
further torque in an effort to protect drive stage components.
Continuous Torque Curve:
The continuous Torque Curve is also derived from dyno testing, but is instead the point at which the temperature rises from an ambient
of 25º C to the designed thermal limit.
For example: The motor will be placed on the dyno tester and set to operate at 1000 RPM continuously with the load slowly increased until
the controller reaches its maximum sustained thermal limit. This limit is either 70º C or 85º C depending on the model number.
The far lower right side of the curve is limited by supply voltage. This is the point at which Back EMF suppresses any further speed
increase. Higher supply voltages will shift the zero torque point of the curves further to the right.
Peak Torque Curve
(fit to curve)
Motor Torque
Peak Torque Range
Thermally Limited
Continuous
Torque Curve
(fit to curve)
No-Load
Maximum Speed
Continuous Torque Range
Voltage Limited
Speed (RPM)
Ambient Temperature Effects on Torque Curves and Motor Response:
If the motor is operated in an environment greater than 27º C, then it will reach its thermal limit faster for the same given load thereby
further limiting continuous torque.
Therefore any given motor torque curve MUST BE linearly de-rated for a given ambient temperature from 27º C to 70º C (optional 85º
C).
Supply Voltage Effects on Torque Curves and Motor Response:
Higher voltages have two-fold effects on torque curves. As mentioned above, raising voltage will shift the curve to the right. It will also
allow higher current into the drive. However, Torque curves depict Torque at a given velocity.
If you double supply voltage, the motor can sustain twice the original velocity. But since acceleration is the differential of velocity, it can
achieve 4 times the original acceleration. This is useful for high speed indexing and fast start/stop motion.
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15
Understanding Animatics Torque Curves
Considerations when using torque curves for motor sizing:
For any given product model number, there may be variations of as much as +/-10%.
The following diagram depicts data points collected from dyno testing of a given model motor. A best-fit torque curve is created from these
data points and is then de-rated to at least 5% below the worst case data points. The de-rated curve is what is advertized. This means that
within any given model number, EVERY motor sold will perform at or better than the advertized torque. Theoretically, ALL motors should
be no less than 5% better than advertized and may be better than 20% higher.
The diagram shows motor loading in 4 areas.
Point 1. This is ideal and depicts a load within the normal operating range of the motor. The motor should operate well and have no
problems for many years.
Point 2. The load is very close to the operating limit. The motor will run quite warm as compared to Point 1.
Point 3. The load exceeds the advertized operating limit of the motor. However, due to data scatter and de-rating, there may be some
motors that will work and others that do not.
Why? Because it is in the area of +/-10% variation expected in motors for a given size. This can become a major problem.
Imagine designing a machine that operates in this range. Then you replicate that machine with many of them running on a
production floor.
One day, a motor at the lower end of the +/-10% expected variation would be placed on a new machine and that motor would get spurious
drive faults.
It would appear as though the motor is malfunctioning because…. “all the other motors work just fine”.
This is unfortunate because in reality, all motors were undersized and operating outside of their advertized limits.
This is why it is important to properly calculate load torque to insure the correct motor is designed into the application. Never assume that
without proper load calculation and motor sizing, testing of one motor means all of that size may work. This is simply not the case. Try to
keep operating conditions below the advertized limits to insure reliable long-life operation.
Point 4. The load exceeds the advertized level and exceeds +10% expected range of possible torque capabilities. In this case, the
motor will most likely either overheat quickly and fault out or immediately get a position error because it simply does not have enough
power to support the load demand.
4
3
Dat
aP
oi n
ts
f
1
De rate
da
dv
ert
is
Dy
no
ed
to
rq
ue
c
ve
ur
Motor Shaft Speed (RPM)
16
Te
s
g
tin
Motor Torque
2
rom
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Moment of Inertia Overview
Moment Of Inertia:
A basic understanding of Moment of Inertia serves well in insuring proper motor sizing. It is one thing to look at static points on torque
curves, but it is altogether different when considering the dynamic aspects of loads being accelerated at high rates.
The Inertial mass of an object is a measure of its resistance to a change in its velocity.
The Moment of Inertia of an object is at a point of reference of rotation, which is at the pivot point or axis of rotation.
The Moment of Inertia can therefore be thought of as a measure of the resistance to any change in rotational speed.
For linear systems, the rate of change of speed, (acceleration) is proportional to the force applied. Double the mass and the force needs
to be doubled for the same acceleration. Similarly for rotational systems, the angular acceleration of the load is proportional to the
torque applied. Double the Moment of Inertia and the torque needs to be doubled for the same angular acceleration. Moment of Inertia
is therefore a measure of a load’s resistance to angular speed change; of how much effort (torque) is required to cause acceleration or
deceleration.
Matching Motor To Load:
A common rule of thumb for SmartMotor™ sizing is that the load should have no more than 10 times the Moment of Inertia of the motor
rotor that is driving it. This gives a good starting point and typically allows for safe sizing over a wide range of applications.
Since a rotating load wants to maintain the same velocity, then when a motor attempts to accelerated or decelerate the load, it must
overcome the Moment of Inertia of that load by applying enough torque to accelerate it or decelerate it.
It takes more torque to change speed than it does to maintain a given speed.
In the same manner, for the motor to slow down a load, the load’s Moment of Inertia will keep the motor going the same speed and will in
effect, back drive the motor turning it into a generator.
In extreme cases, this can result in over voltage damage to the Drive stage.
How to improve Moment of Inertia Ratio Between Motor and Load :
Adding gear reduction to a motor gives it more leverage to prevent back driving and also gives it a better advantage in accelerating a load
up to speed.
For any given change in gear reduction, you get a proportional change in speed and static torque but you get a squared change in
acceleration and dynamic rate of change of torque. The result is that by adding gear ratio you gain a squared decrease in the ratio of
Moment of Inertia between motor and load.
Therefore the motor has a greater advantage in both accelerating and deceleration the load. It adds protection against damage to the
system as a whole.
Lower System Cost
To give an idea of how much effect you get from additional gear reduction, take a look at the example below. This is an actual photo of
the before-and-after drive system of a given application. The larger motor with low gear reduction and larger pulley was replaced by the
smaller Animatics SmartMotor™ with much higher gear reduction and smaller pulley. The result was a smoother operating machine with
higher resolution and better acceleration.
Before
Optimize gear
reduction to
improve load
dynamics and
motor efficiency
& reduce system cost
After
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17
Advanced Drive Capabilities (PLS and PS2 Firmware Only)
Mode Torque Brake (MTB)
Intended as a means to quickly stop shaft motion in the event of drive fault or drive disable.
• Dynamically shunts windings for quick stops
• 60% peak overload stopping power
• In other words, the motor has 60% more stopping power than its peak advertised torque at stall when MTB is activated
• Automatically engaged under any shaft protection fault :
• Position Error (Following Error)‫‏‬
• Travel Limit Error
• Over Temperature
• RMS Over current
By connecting the travel limits to the E-stop circuitry, the motor can be quickly driven to a stop without the need of complete power
removal. MTB only requires control power, not drive power.
Note: MTB can produce Peak torques as much as 60% beyond advertised stall torque of any given applicable Animatics SmartMotor™.
It is imperative that any gear head or other shaft loads be capable of handling such a peak torque.
Trajectory Overshoot Braking (TOB)
NOTE: Must specify -PS2 firmware
Allows for smooth controlled deceleration and stabilization of high moment-of-inertia mismatch loads.
• PWM controlled Dynamic braking
• >30% better slowing power to prevent overshoots in speed or deceleration during the entire trajectory path
• Provides protection against exceeding critical speed limits of lead screws
T0
T1
T2
T3
(Light Grey Areas above Indicate where TOB takes Effect)‫‏‬
18
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T4
Example Applications
Process Tension Control
By the use of Phase Offset moves while Electronically gearing
Master to Slave, the controllers allow for easy tension control
between two sets of nip rollers. Tension can be regulated by
pre-test measurement or live analog, serial or digital feedback
providing proper control of tension through varying speeds and
up or downstream loads.
High Speed Traverse & Take-up Spool Winders
Use of Programmable Software Travel Limits, Electronic Gearing,
and Special Firmware drive control, Winders can be set up to
wind unlimited variations in spool width, wind angle and end-point
dwell as well as step wind, stack wind and tapered wind.
With low inertia motors and high speed acceleration, very precise
winding can be achieved in such applications as edge-wound
voice coils, guitar strings, catheters and standard textile spool
winding.
Programmable Cut To Length Saw Stop or Back Stop
Gage
With the ability to program up to 1000 subroutines and 32K of
extra data storage, the system can be programmed for hundreds
of back stop positions and sequences.
No external PLC or PC would be required. A simple HMI can be
utilized for interfacing
Parallel Axis Gantry
In wide gantry applications, the base axis can be moved with two
motors, one Master, one Slave. Additionally, the master axis can
follow product flow under the gantry for operations such as flying
shears, material cutoff, cross-cut saws, etc.
Proper fault handling will prevent racking of the gantry in the
event that either the Master or Slave faults out during a move.
Homing is done only once at power-up. The Master and Slave
sync up maintaining perfect alignment.
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19
Example Applications
Concepts and Capabilities of the Animatics Product Range:
3-Position Parts Diverter
Simple servo upgrade from existing pneumatic systems, the
Animatics SmartMotor™ can be placed into any system to replace
2 or 3 position air cylinders to allow for multi point programmable
positioning while maintaining simple I/O trigger control from any
PLC.
The SmartMotor is placed into Position Mode and programmed to
move to a given set point upon I/O input trigger from the PLC.
Input / Output Stacker
Utilizing Subroutines and variable counter, both Absolute and
Relative Position Mode moves allow for start of stack and
incremental stack shifts while maintaining parts counts. Having
localized I/O within the Integrated Controls, the entire handling of
parts can be dealt with by the stacker motor itself.
True Distributed control at a fraction of the cost and footprint.
Programmable Rotary Index Table
Typical Mechanical CAM based rotary Index Tables are fixed
index and dwell devices. The Index distance cannot be changed
and dwell is fixed as a function of assumed constant input RPM.
By adding an Animatics Integrated SmartMotor™ to any servo
rated Worm Gear box or flange output gear reducer, the system
becomes a fully programmable rotary index table and can be
programmed to any practical number of indexes and dwell times.
Given the I/O and control capabilities, the dwells can be based
on end-of-process contrary to fixed mechanical CAM thereby
speeding up over all production cycle times.
Programmable Force Press-To-Fit
Animatics’ integrated approach to drives and controls allows
for closely regulated positioning and position error control. This
results in the ability for highly repeatable torque limited machine
cycles. The result is a very good solution for pressing parts
together or any other force limited application where both cycle
time and proper force must be tightly regulated.
20
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Example Applications
Drill & Tap/Nut Runner
Set rotating Motor as master and have the linear axis electronically
gear off of it to provide high speed drill and taps and screw feed
control with limited torque. Adding proper torque detection, the
unit can detect when a drill or tap has worn or become dull. As
a nut/screw runner, it can pick up on cross thread, broken or
stripped thread, missing part or jammed part.
High Speed Parts Counter and Verification
The External Encoder Input can be used to read Quadrature
Incremental Encoders, Step and Direction Input or just as a counter
where input pulses can be counted at a rate up to 2 Megahertz.
As a result, the motor can both feed parts and verify part count
even at high rates of speeds and short distance between parts.
Multi-Axis Pick & Place
Up to 100 individually addressed motors can be placed on a
communications bus allowing for easy synchronisation of multiple
axis applications such as Pick & Place machines, Palletizers,
Cross axis cutters, sorters, etc.
Print and Die Cut alignment on-the-fly
When using Electronic Gearing, phase offset adjustment moves
can be achieved to properly align die cut processes with printed
registration marks. This same technique can be used to insure
over mold and multi-layer print alignment and even pocketed
blister pack parts placement.
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Motion Glossary
Acceleration
A change in velocity as a function of time. Acceleration usually refers to increasing velocity, and deceleration to decreasing velocity.
Accuracy
A measure of the difference between expected position and actual position of a motor or mechanical system. Motor accuracy is usually
specified as an angle representing the maximum deviation from expected position.
Ambient temperature
The temperature of the cooling medium, usually air, immediately surrounding the motor or another device.
Angular accuracy
The measure of shaft positioning accuracy on a servo or stepping motor.
Back EMF
The voltage generated when a permanent magnet motor is rotated. This voltage is proportional to motor speed and is present
regardless of whether the motor winding(s) are energized or de-energized.
Bipolar chopper driver
A class of step motor driver which uses a switch mode (chopper) technique to control motor current and polarity. Bipolar indicates the
capability of providing motor phase current of either polarity (+ or -).
Breakaway torque
The torque required to start a machine in motion. Almost always greater than the running torque.
Brushless motor
Class of motors that operate using electronic commutation of phase currents, rather than electromechanical (brush-type) commutation.
Brushless motors typically have a permanent magnet rotor and a wound stator.
C-face mounting
A standard NEMA mounting design, where the mounting holes in the face are threaded to receive the mating mount.
Class B insulation
A NEMA insulation specification. Class B insulation is rated to an operating (internal) temperature of 130°C.
Class F insulation
A NEMA insulation specification. Class F insulation is rated to an operating (internal) temperature of 155°C
Class H insulation
A NEMA insulation specification. Class H insulation is rated to an operating (internal) temperature of 180°C.
Closed loop
A broadly applied term, relating to any system in which the output is measured and compared to the input. The output is then adjusted
to reach the desired condition. In motion control, the term typically describes a system utilizing a velocity and/or position transducer to
generate correction signals in relation to desired parameters.
Cogging (Cogging torque)
A term used to describe non-uniform angular velocity. Cogging appears as a jerkiness, especially at low speeds.
Commutation
1.A term which refers to the action of steering currents or voltages to the proper motor phases so as to produce optimum motor
torque. In brush type motors, commutation is done electromechanically via the brushes and commutator. In brushless motors,
commutation is done by the switching electronics using rotor position information obtained by Hall sensors, a Tachsyn, or a
resolver.
2.Commutation of step motors is normally done open loop. Feedback from the motor is not required to hold rotor position precisely.
Continuous rated current (ICR) (Amperes)
The maximum allowable continuous current a motor can handle without exceeding the motor temperature limits
22
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Motion Glossary
Continuous rated torque (TCR) (lb-in.)
The maximum allowable continuous torque a motor can handle without exceeding the motor temperature limits
Continuous stall current (ICS) (Amperes)
Amount of current applied to a motor (at locked rotor conditions), which results in rated temperature rise. Refer also to definition of
“Continuous stall torque”
Continuous stall torque (TCS) (lb-in.)
The amount of torque at zero speed, which a motor can continuously deliver without exceeding its thermal rating. Determined by
applying DC current through two windings with rotor locked, while monitoring temperature. Specified with motor windings at maximum
rated temperature, with motor in 25 degrees C ambient, mounted to a heat sink. Refer to individual specs for heat sink size.
Controller
A term describing a functional block containing an amplifier, power supplies, and possibly position-control electronics for operating a
servomotor or step motor.
Current at peak torque (IPK) (Amperes)
The amount of input current required to develop “peak torque”. This is often outside the linear torque/current relationship.
Current, Rated
The maximum allowable continuous current a motor can handle without exceeding motor temperature limits.
D-flange mounting
This type of mount has clearance holes on the flange, and the mounting bolts stick out through the flange from the motor side. This
mount is common in cases where the motor is integral to the machine.
Demag current
The current level at which the motor magnets will start to be demagnetized. This is an irreversible effect, which will alter the motor
characteristics and degrade performance. Also known as peak current.
Detent torque
The maximum torque that can be applied to an unenergized step motor without causing continuous rotating motion.
DPBV – Drip-proof Blower Ventilated
Type of motor cooled by blowing air through the inside of the motor using an attached blower.
Drive
An electronic device that controls torque, speed and/or position of an AC or brushless motor. Typically a feedback device is mounted on
the motor for closed-loop control of current, velocity and position.
Driver
Electronics which convert step and direction inputs to high power currents and voltages to drive a step motor. The step motor driver is
analogous to the servomotor amplifier’s logic.
Duty cycle
For a repetitive cycle, the ratio of on time to total cycle time.
Duty cycle (%) = [On time / (On time + Off time)] x 100%
Dynamic braking
A passive technique for stopping a permanent magnet brush or brushless motor. The motor windings are shorted together through a
resistor which results in motor braking with an exponential decrease in speed.
Efficiency
The ratio of power output to power input.
Electrical time constant (te) (Seconds)
The time required for current to reach 63.2% of its final value for a fixed voltage level. Can be calculated from the relationship te=L/R
where L is inductance (henries) and R is resistance (ohms).
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23
Motion Glossary
Encoder
A feedback device which converts mechanical motion into electronic signals. The most commonly used, rotary encoders, output digital
pulses corresponding to incremental angular motion. For example, a 1000-line encoder produces 1000 pulses every mechanical
revolution. The encoder consists of a glass or metal wheel with alternating transparent and opaque stripes, detected by optical sensors
to produce the digital outputs.
Feedback
A signal which is transferred from the output back to the input for use in a closed loop system.
Ferrite
A type of permanent magnet consisting of ceramic compounds made up of oxides of iron, barium and strontium.
Form Factor
The ratio of RMS current to average current. This number is a measure of the current ripple in a SCR or other switch-mode type of
drive. Since motor heating is a function of RMS current while motor torque is a function of average current, a form factor greater than
1.00 means some fraction of motor current is producing heat but not torque.
Four quadrant
Refers to a motion system which can operate in all four quadrants; i.e., velocity in either direction and torque in either direction. This
means that the motor can accelerate, run, and decelerate in either direction.
Friction
A resistance to motion caused by contact with a surface. Friction can be constant with varying speed (Coulomb friction) or proportional
to speed (viscous friction).
Hall sensor
A feedback device which is used in a brushless servo system to provide information for the amplifier to electronically commutate the
motor. The device uses a magnetized wheel and hall effect sensors to generate the commutation signals.
Holding torque
Sometimes called static torque, holding torque specifies the maximum external torque that can be applied to a stopped, energized
motor without causing the rotor to rotate. Generally used as a figure of merit when comparing motors.
Horsepower
An index of the amount of work a machine or motor can perform. One horsepower is equal to 746 watts. Since power is equal to torque
multiplied by speed, horsepower is a measure of a motor’s torque and speed capability; e.g., a 1 HP motor will produce 36 lb-in. at
1,750 rpm.
Formula:
HP = Torque (lb-in.) x Speed (RPM)/63,025
or
HP = Torque (lb-ft.) x Speed (RPM)/5,252
or
HP = Volts x Amps x Efficiency/746
Note: 1 HP = 746 Watts
Hybrid step motor
A motor designed to move in discrete increments of steps. The motor has a permanent magnet rotor and a wound stator. Such motors are
brushless. Phase currents are commutated as a function of time to produce motion.
Idle current reduction
A step motor driver feature that reduce the phase current to the motor when no motor motion is commanded (idle condition) for a
specified period of time. Idle current reduction reduces motor heating and allows high machine throughputs from a given motor.
24
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Motion Glossary
Indexer
Electronics which convert high level motion commands from a host computer, PLC or operator panel into step and direction pulse
streams for use by the step motor driver. Indexers can be broadly divided into two classes. A preset indexer typically accepts distance,
velocity and ramp time inputs only. The more sophisticated programmable indexer is capable of complex motion control and includes
program memory.
Inductance (L) (mH - millihenries line-to-line)
The electrical equivalent to mechanical inertia; that is, the property of a circuit, which has a tendency to resist current flow when no
current is flowing, and whencurrent is flowing has a tendency to maintain that current flow. Pacific Scientific measures inductance (lineto-line) with a bridge at 1000 Hz and with the rotor positioned so the back-EMF waveform is at the peak of the sinusoid.
Inductance (mutual)
Mutual inductance is the property that exists between two current carrying conductors or coils when magnetic lines of force from one
link with those of the other.
Inertia
The property of an object to resist change in velocity unless acted upon by an outside force. Higher inertia objects require larger torques
to accelerate and decelerate. Inertia is dependent upon the mass and shape of the object.
Inertial match
For most efficient operation, the system coupling ratio should be selected so that the reflected inertia of the load is equal to the rotor
inertia of the motor.
Insulation Class
The rating assigned to the maximum temperature capability of the insulating components in a motor or other piece of equipment.
Microstepping
An electronic technique for increasing a step motor’s position resolution and velocity smoothness by appropriately scaling the phase
currents. Microstepping is also a technique used to reduce or eliminate the effects of system resonance at low speeds.
Note: Microstepping beyond 16 microsteps per step only smooths motion, linearity becomes sinusoidal with amplitude of the sine
effects increasing with higher microsdtep resolutions.
Mid-range instability
A phenomenon in which a step motor can fall out of synchronism due to a loss of torque at mid-range speeds. The torque loss is due to
the interaction of the motor’s electrical characteristics and the driver’s electronics. Some drivers have circuitry to eliminate or reduce the
effects of mid-range instability.
NEMA - National Electrical Manufacturer’s Association
Acronym for an organization which sets standards for motors and other industrial electrical equipment.
Neodymium iron boron
A type of rare-earth permanent magnet material.
NTC - Negative Temperature Coefficient
A negative temperature coefficient thermistor is used to detect and protect a motor winding from exceeding its maximum temperature
rating. Resistance of the device decreases with an increase in temperature.
Open-loop
A system in which there is no feedback. Motor motion is expected to faithfully follow the input command. Stepping motor systems are
an example of open-loop control.
Overload capacity
The ability of a drive to withstand currents above its continuous rating. It is defined by NEMA as 150% of the rated full-load current for
“standard industrial DC motors” for one minute.
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25
Motion Glossary
Peak torque (Tpk) (lb-in.)
The maximum torque a brushless motor can deliver for short periods of time. Operating permanent magnet motors above the maximum
torque value can cause demagnetization of the rare-earth magnets. This is an irreversible effect that will alter the motor characteristics
and degrade performance. This is also known as peak current. Not to be confused with system peak torque, which is often determined
by amplifier peak current limitations, where peak current is typically two times continuous current.
Poles
Refers to the number of magnetic poles arranged on the rotor of the brushless motor. Unlike an AC motor, the number of poles has no
direct relationship to the base speed of the motor.
Power
1.The rate at which work is done. In motion control, power is equal to torque multiplied by speed.
2.The rate of doing work or expending energy. It may be written as: Power (watts) = force x distance/time. Expressed in electrical
terms it is voltage x current = power (watts)
Power factor
Ratio of true power (kW) to apparent power (kVA).
Pull-out Torque (Poll Slip)
The maximum friction load, at a particular inertial load, that can be applied to the shaft of a synchronous motor (running at constant
speed) and not cause it to lose synchronism.
Pulse rate
The frequency of the step pulses applied to a step motor driver. The pulse rate, multiplied by the resolution of the motor/driver
combination (in steps per revolution), yields the rotational speed in revolutions per second.
Pulse Width Modulation (PWM)
1.A PWM controller (amplifier) switches DC supply voltage on and off at fixed frequencies. The length of the on/off interval or
voltage waveform is variable.
2.Pulse width modulation (PWM), describes a switch-mode (as opposed to linear) control technique used in amplifiers and drivers
to control motor voltage and current. PWM offers greatly improved efficiency compared to linear techniques.
Regeneration
The action during motor braking, in which the motor acts as a generator and takes kinetic energy from the load, converts it to electrical
energy, and returns it to the amplifier.
Repeatability
The degree to which a parameter such as position or velocity can be duplicated.
Resistance, Hot (RH)(Ohms line-to-line)
The motor’s terminal resistance value specified at the hot winding temperature, which is at the motor’s maximum rated temperature.
Resolution
The smallest increment into which a parameter can be broken down. For example, a 1000 line encoder has a resolution of 1/1000 of a
revolution.
Resolver
An electromagnetic feedback device which converts angular shaft position into analog signals. These signals can be processed in
various ways, such as with an RDC (resolver-to-digital converter) to produce digital position information. There are two basic types of
resolvers; transmitter and receiver. A transmitter-type is designed for rotor primary excitation and stator secondary outputs. Position
is determined by the ratio of the sine output amplitude to cosine output amplitude. A receiver-type is designed for stator primary
excitations and rotor secondary output. Position is determined by the phase shift between the rotor output signal and one of the primary
excitation signals.
26
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Motion Glossary
Resonance
Oscillatory behavior caused by mechanical or electromechanical harmonics and limitations.
Restart torque
The maximum friction load, at a particular inertial load, that can be applied to the shaft of a synchronous motor without causing it to lose
synchronism when
accelerating to a constant speed from standstill.
Ringing
Oscillation of a system following a sudden change in state.
RMS Current - Root Mean Square Current
In an intermittent duty cycle application, the RMS current is equal to the value of steady state current which would produce the
equivalent motor heating over a period of time.
RMS Torque - Root Mean Square Torque.
In an intermittent duty cycle application, the RMS torque is equal to the value of steady state torque which would produce the equivalent
motor heating over a period of time.
Rotor
The moving part of the motor, consisting of the shaft and magnets. These magnets are analogous to the field winding of a brush-type
DC motor.
Settling time
The time required for a parameter to stop oscillating or ringing and reach its final value.
Shock loading
A load that produces extremely high peak torques for very short durations. This type of load is associated with conveyorized grinding,
crushing and separation processes.
Speed
Describes the linear or rotational velocity of a motor or other object in motion.
Stall Torque
The amount of torque developed with voltage applied and shaft locked, or not rotating. Also known as locked-rotor torque.
Stator
The non-moving part of the motor. Specifically, it is the iron core with the wire winding in it that is pressed into the frame shell. The
winding pattern determines the voltage constant of the motor.
Step angle
The angular distance the shaft rotates upon receipt of a single step command.
Stiffness
The ability to resist movement induced by an applied torque. Stiffness is often specified as a torque displacement curve, indicating the
amount a motor shaft will rotate upon application of a known external force when stopped.
Synchronism
A motor rotating at a speed corresponding correctly to the applied step pulse frequency is said to be in synchronism. Load torques in
excess of the motor’s capacity (rated torque) will cause a loss of synchronism. This condition is not damaging to a step motor.
TENV - Totally Enclosed Non-Ventilated
Acronym describing a type of motor enclosure, which has no outside air going into it. It is cooled only by convection to the frame, which
is usually finned.
Thermal protection
A thermal sensing device mounted to the motor to protect it from overheating. This is accomplished by disconnecting the motor phases
from the drive in an over temperature condition.
Animatics Corporation
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27
Motion Glossary
Thermal resistance (Rth) (°C/watt)
An indication of how effectively a unit rids itself of heat; a measure of temperature rise per watts lost. In Pacific Scientific literature, it is
the specified value from the motor windings to the ambient, under locked rotor conditions.
Thermal time constant (tth) (minutes)
The time required for a motor to attain 63.2% of its final temperature for a fixed power input.
Thermostat
A temperature sensitive pilot duty device mounted on the interior of the motor to protect it from overheating.
Torque
A measure of angular force which produces rotational motion. This force is defined by a linear force multiplied by a radius; e.g. lb-in.
Torque is an important parameter of any motion control system. Formula: Torque (lb-ft.) = 5,250 x HP/RPM
Torque Constant (KT = lb-ft./A)
An expression of the relationship between input current and output torque. For each ampere of current, a fixed amount of torque is
produced.
Torque-to-inertia ratio
Defined as the motor’s holding torque divided by the inertia of its rotor. The higher the ratio, the higher a motor’s maximum acceleration
capability will be.
Torque constants ARE NOT linear over the operating range of a motor.
They apply best at ~75% of no load maximum speed or where the peek and continuous torque curves meet.
Unipolar driver
A step motor driver configuration that uses a unipolar power supply and is capable of driving phase current in only one direction. The
motor phase winding must be center tapped (6 or 8 lead) to operate with a unipolar driver. The center tap is used instead of providing
the current reversal of a bipolar driver.
Velocity
The change in position as a function of time. Velocity has both a magnitude and sign.
Viscous Damping (KDV) (lb-in./kRPM)
Inherent losses are present in all motors which result in lower torque delivered at the output shaft than developed at the rotor. Losses
which are proportional to speed (i.e. speed dependent terms such as windage, friction, eddy current) are related through the motor’s
“viscous damping” constant, measured as the slope of the damping curve.
Voltage constant (KE) (V/kRPM peak, line-to-line)
May also be termed back-EMF constant. When a motor is operated, it generates a voltage proportional to speed, but opposing the
applied voltage. The shape of the voltage waveform depends upon the specific motor design. For example, in a brushless motor, the
waveshape may be trapezoidal or sinusoidal in nature. All Pacific Scientific brushless motor designs have a sinusoidal voltage constant.
For a sine waveform, the voltage constant can be measured from line-to-neutral or line-to-line and expressed as a peak value or “RMS”
value.
28
Animatics Corporation
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Motion Glossary
Calculating Power : the Real Story
Symbol Definition
SI
English
Unit of electrical power where : Watts =(volts)(amps) or W=V*A
Watts are a unit consisting of time since amps are a measure of
electron flow per unit time
CG
Circumference of Gear
m (or cm)
in (or ft)
CP: 1, 2, 3
Circumference of Pulleys, 1, 2, or 3
“
“
D
Diameter of cylinder or . . .
m (or cm)
in (or ft)
For this reason, Torque cannot be directly equated with Watts or
Horse Power without consideration of RPM where Revolutions
per min contains time that would cancel out the time in watts
to give you torque. This is why Horsepower is a useless unit of
measure when sizing motors for motion control applications!
DG
...(pitch dia.) of Gear
“
“
DPM
...(pitch dia.) of Pulleys on Moto
“
“
DP:1, 2, 3
...(pitch dia.) of Pulleys 1, 2, or 3
““
e
efficiency of mechanism or reducer
%
%
F
Forces due to
N
lb
One horsepower equals 746 watts and has nothing to do
with torque by itself!!!!!
FFr
...friction (Ffr = mWL cos g)
“
“
Fg
...gravity (Fg = WL sin g)
“
“
Fp
...Push or Pull forces
“
“
g
gravity accel constant
9.80
m-s-2
386 in-s-2
J
mass moment of inertia for
kg-m2
lb-in2
JB→M
...Belt reflected to Motor
or
or
JC
...Coupling
g-cm2
oz-in2
JG
...Gear
etc.
or
JL
...Load “ in-lb-s2
JL→M
...Load reflected to Motor
“
or
JM
...Motor
“
in-oz-s2
JPL
...Pulley on the Load
“
etc.
JPM
...Pulley on the Motor
“
“
JPL→M
...Pulley on Load reflected to Motor
“
“
JP: 1, 2, 3
...Pulley or sprocket 1, 2, or 3
“
“
Jr
...reducer (or gearbox)
“
“
JTotal
...Total of all inertias
“
“
Formula for Power to Torque:
Power (HP)
=
Power (Watts) = Power (HP)
=
Power (Watts) x746
N (RPM) x T(ft-lbs)
7.04
N (RPM) x T(ft-lbs)
5252
Torque required will be:
T (ft-lbs
=
T (ft-lbs)
=
Power (Watts) x 7.04
N(RPM)
Power (HP) x 5252
N(RPM)
All references on the right side of this page are
used in the formulas on the pages that follow
JS
...lead Screw
Nr
Number ratio of reducer
Nt
Number of teeth on gear, pulley, etc.
PG
““
none
none
Pitch of Gear, sprocket or pulley
teeth/m
teeth/
inch
PS
Pitch of lead Screw
revs/m
revs/inch
T
Torque...(for “required” Calculations)
Nm
in-lb
TL
...at Load (not yet reflected to
motor)
“
“
TP .
..due to Preload on screw nut, etc.
“
“
WM
angular/rotational velocity of Motor
“
“
WL
Weight of Load
N (or kg)
lb
WB
Weight of Belt (or chain or cable)
“
“
WT
Weight of Table (or rack & moving
parts
“
“
Ө
rotation...
radians
revs
Өa, c, or d ... rotation during accel, decel, etc.
“
“
ӨL
...rotation of Load
“
“
ӨM
...rotation of Motor
“
“
µ
coefficient of friction
none
none
‫ץ‬
load angle from horizontal
degrees
degrees
ШM
Maximum Speed (servos &
steppers)
“
“
Animatics Corporation
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29
Motion Formulas
Motion Mechanism and Motion Equations
Inertia, Torque Equations
Reducer
Rack & Pinion
Conveyer
Leadscrew
30
Animatics Corporation
tel: 408.748.8721 • fax: 408.748.8725 • www.animatics.com
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