www.airex.com
Linear Motor
Heat Sink Selection
201-White Paper Series Linear Motors
White Paper
David J. Carroll
10/01/07
ISO
9001:2000
Airex Corporation
White Paper
LM Heat Sink Selection
Introduction
Airex Corporation provides linear motor sizing information to system designers to
insure maximum motor performance and identify any requirement for cooling in the
motor application. With modeling information on thermal design and heat rise
information specific to the application, designers can optimize the linear motor to
their system requirement. The Linear motor, like many devices, must be optimized
in its operating environment to insure a long and service free life. The system
integrator or designer with system responsibility is tasked with the proper
application of cooling by first determining the effect of heating in operation.
Complex Linear motor applications can employ a variety of cooling solutions, and
with each method come benefits and tradeoffs. For any given system this includes;
liquid cooling, forced air convection or conduction cooling. The minimum required
thermal resistance for the cooling can be determined by subtracting the motor
thermal resistance from the total system thermal resistance. The primary focus of
this document is to discuss air-cooling via the application of a heat sink.
Background and Linear Motor Features
The Linear motor coil temperature increases with increasing power applied to the
coil. The force produced by the motor is the current times the motor force constant
and the power to be dissipated is the applied current squared times the resistance.
Note: In this paper, “resistance” denotes “electrical resistance”. Thermal resistance
will always be detailed separately. The motor force (F) is:
F = I × Kf
Where:
F =Motor force
I = Current
Kf = Force constant
The motor power to be dissipated (P) is measured in Watts and is calculated using
the following equation:
P = I2 ×R
Where:
R = Resistance
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The resistance of the coils in the motor is specified in Ohms at 20°C. The coil
resistance varies with the temperature of the copper coils. The following formula
can be used to determine the resistance of the copper coils at a specific
temperature:
R = Ri × (1 + .00394(T f − Ti ))
Where:
R = Coil Resistance
Ri = Coil Resistance Specified at 20°C
T f = Final Coil Temperature
Ti = Initial Coil Temperature
An example of the resistance change due to temperature follows:
A 2000-2 motor coil has a delta resistance of 7.57 Ohms at 20°C and is to be
installed in a 70°C ambient temperature (see definitions below) environment. Find
the resistance of the coil due to the warm environment.
R = 7.57Ohms × (1 + 0.00394 × (70°C − 20°C) = 9.06Ohms
As power is applied to the motor coils, heat is generated, which warms the copper
coils, thus increasing the coil resistance. This increase in resistance further increases
the power to be dissipated. The heat generated in the motor coils must be
dissipated fast enough or the coils will continue to heat up to a point of failure. By
design, heat is conducted from the active portions of the coil to the mounting
bracket, where the heat must be removed by external means. Using equation 2 and
the conditions from the above example; the power to be dissipated as heat when
2.5 Amps is applied continuously to the motor is:
P = 2.5 Amps 2 × 9.06Ohms = 56.6Watts
If the motor in the above example were running at its maximum rating of 125°C,
the resistance would be about 10.7 Ohms. The power dissipated with a 2.5 Amp
motor current would be just over 66 Watts. The heat to be dissipated, can be
conducted into the structure of a system, transferred to another system via a liquid
cooled heat exchanger, or dissipated by an air-cooled heat sink.
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The Airex Linear motor design (shown in Figure. 1 below), improves performance by
optimally using the coil structure to distribute and transfer heat to the mounting
bracket. Heat is transferred longitudinally across adjacent end-turns by the motor
heat sink cap, which is located opposite the mounting bracket, allowing heat to flow
into the core of the motor. The motor coil assembly sides are insulated to minimize
the heating of the surrounding magnets. In most cases, less than 10% of the motor
heat is dissipated into the magnet track, minimizing magnet heating, thus
maximizing magnet track flux production at high motor power levels.
Figure1: Linear Motor Sectional View
Motor Coil
Mounting Bracket
Magnet
Track
Thermal Insulation
Motor Coils
Heat Sink Cap
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A Little Thermodynamics
Heat is transferred by conduction, convection and radiation. Conduction relies on
good physical contact between a warm object and a cooler one to transfer heat.
Conduction is the most efficient means for transferring heat at the temperatures
normally encountered in Linear motor applications. Convection is the process of
transferring heat to a fluid or a gas such as air, where the fluid is self-displacing (it
moves) due to density change. Heat is also transferred by emitted radiation. The
heat escapes as electromagnetic radiation and can transmit heat from a warm
object to cooler surroundings. Radiant transfer of heat depends on temperature
difference and the properties and orientation of the object surfaces. Radiation of
heat is proportional to 5.7E-8 times the difference between the fourth power of
temperatures (°Kelvin) of the motor and the fourth power of the temperature of the
surrounding objects. Radiation works best with great differences in temperature
such as between the sun and the earth, or between a person and a fire in the
fireplace. Only small amounts of heat can be removed from the motor coil by
radiation at normally expected motor temperatures.
The conduction of heat from a hot object to a cooler object is not instantaneous; the
thermal resistance of the materials in the path limits the flow of heat. Similar to an
electrical circuit, the total thermal resistance of a system is the sum of the series
elements in the path. The thermal resistance of an object is defined as the heat rise
across an element in the circuit when a given amount of heat is flowing through the
path. The element is bounded at each end by an isothermal. An isothermal is an
interface where the temperature is assumed to be constant across the entire surface
of the interface. The thermal resistance RT has units of °C/W:
RT =
∆T
P
Where:
∆T = Temperature difference between the two
isothermals
P = Power (Heat) flowing through object
Doubling the thickness of a material in a series path doubles the thermal resistance
of the material. A table shown below lists the thermal resistance of some common
materials. Some tables of material thermal properties list thermal conductance,
which is the inverse of thermal resistance. Materials such as silver, copper and
aluminum have very low thermal resistances and are good conductors of heat. Steel
(especially stainless steel) can have thermal resistances more than 10 times higher
than copper. Materials such as G11 or air have very high thermal resistances and
are often referred to as thermal insulators.
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Every system has a maximum thermal resistance, which is calculated for the total
thermal drop in the system the power dissipated in the system. The maximum
thermal resistance is also called the system thermal resistance limit RS has units of
°C/W:
RS =
∆T S
P
Where:
∆TS = Difference temperature across the system
P = Power (Heat being dissipated)
Many Linear motor applications are cooled by convection via an attached heat sink.
The typical heat sink uses fins to greatly increase the surface area to improve the
efficiency of heat transfer to the air. Air is a relatively poor medium for transferring
heat. It is a thermal insulator and has fluidic properties that limit close interaction
with fin surfaces thus limiting heat transfer. Forced air movement can greatly
enhance the effect of convection. With convection cooling, heat from the motor
flows from the warm motor coil-mounting bracket into the core of the heat sink,
where the heat sink surface area is cooled by air through convection. For our
purposes the heat sink calculations shown here apply to air at sea level pressure.
Only radiation and conduction will directly move heat in a vacuum.
There are many buzzwords and terms used when discussing motor performance and
heat. The essential definitions follow:
•
Ambient Temperature - The maximum temperature of the air that generally
surrounds the Linear motor coil and magnet track, measured in degrees Celsius (°C).
Generally the maximum ambient temperature for the Linear motor coils,
commutation devices, cables, and magnet tracks is 90°C.
•
Heat Sink – A device with large surface area used to dissipate heat from a warm
object into the surrounding air.
•
Maximum Temperature – The temperature limit or rating of an object, specified
in °C. If the maximum temperature is exceeded, the operational life of the device
will be shortened. The maximum temperature for the Linear motor coil is 125°C,
measured as an average throughout the coil.
•
Power – The amount of heat to be dissipated in Watts.
•
Resistance – The opposition of electric current in a conductor. Measured in Ohms.
•
System Thermal Resistance Limit – The temperature rise seen in a system when
a given level of heat (power) is being transferred. Calculated as the temperature rise
divided by the dissipated power. The sum of the thermal resistance drops in the
system must be less than the system resistance limit.
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•
Temperature Rise – An increase in temperature of an object above a reference
temperature. The temperature rise is measured as the average coil temperature
minus the ambient temperature. The maximum temperature rise generally specified
for the Linear motor is 105°C.
•
Thermal Capacity – The ability of an object to absorb heat per unit temperature
rise. Thermal capacity aids in the ability of a motor to handle peak power demands
without exceeding its specified ratings.
•
Thermal Resistance – The temperature rise seen in an object when a given level
of heat (power) is being transferred through the object, Stated as the temperature
rise divided by the dissipated power.
•
Thermistor – A resistive device embedded in the Linear motor coil, used to
evaluate the coil thermal performance. This device can be selected to have a
negative temperature coefficient (NTC) or a positive temperature coefficient (PTC).
•
Thermostat – A temperature sensitive switch, embedded in the motor
bracket. A thermostat is a device that signals the system that the motor
bracket is over temperature. Typical System Configurations:
o In moving magnet track applications, the coil can be directly attached
to a substantial machine base, which can often provide the highest
level of cooling through direct conduction. The system designer can
select the appropriate mounting material such as aluminum, as well as
a sufficient volume of material to easily conduct heat away from the
coil and dissipate it into the surroundings. Other cooling means such
as liquid cooled heat exchangers or large heat sinks are easily
integrated to the fixed coil. The weight of any heat spreading or
dissipating device such as a cooling loop has no impact on the motion
problem. The key advantages to stationary coil configurations include
the possibility of very high levels of cooling, the elimination of moving
cables / cooling hoses and a possible reduction in moving mass.
When the coil is part of the moving member, similar to the system shown on the
cover page or in Figure 2, it is necessary to critically evaluate the heat removal
means. The heat removal means has moving mass and can impact other system
components. A moving coil system can exhibit the highest levels of motion
performance, due to low moving mass. Some motion problems with a low duty cycle
can maintain a safe operating temperature, by carefully managing the thermal
capacity of the motor. The system designer must review the motion profile and duty
cycle in light of the cooling requirement. Some systems move fast enough and far
enough to make convection cooling efficient through sufficient movement of air over
the heat sink.
A Linear motor magnet track and coil can be side mounted to reduce the overall
height of a motion platform. In the configuration shown in Figure 2, good design
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practices must be used to minimize the loss in heat transfer efficiency due to the
longer thermal path between the coil mounting bracket and the heat sink. The
number of material interface boundary crossings also impacts cooling effectiveness.
The following slide configuration minimizes these issues by using a wide adaptor
block to transport motor heat to the table, which is acting as the heat sink. Also
note the lip on the adaptor block, which overlaps the side of the motor mounting
bracket to remove a few extra watts of heat. Heat sink grease must be used on all
mating surfaces to minimize losses in the thermal path.
Figure 2. Low profile slide application, heat flow shown with red arrows
Some systems localize the heat dissipation by isolating the motor and heat sink
combination from the remainder of the system. The motor/heat sink combination is
mechanically attached to system via a thermal barrier such as a block or strip of
G11. This approach minimizes conduction of heat from the hot components into the
rest of the system. In addition to isolating conducted heat from the system, the
warm air from the heat sink may need to be deflected away from thermally sensitive
components. Encoders and bearings can be especially sensitive to heat in some
applications due to differential thermal expansion, thermal drift, or the use of low
melting point materials.
Linear Motor Thermal Resistance
The Linear motor thermal resistance is specified and verified at the factory. The
specification of thermal resistance elements allows the system designer to budget
the thermal requirements of the system.
The process of thermal resistance and continuous power rating testing begins with
the measurement of electrical resistance to establish the initial test parameters. The
motor bracket is mounted to a heat sink (typically less than 0.06 °C/W thermal
resistance). The motor is energized to an initial power level and the motor power
and temperatures are monitored and the power is gradually increased. The thermal
drop between ambient and the heat sink temperature is maintained by airflow to be
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less than 10 degrees C. The test power is gradually increased until the motor is at
the maximum operating limits. The thermal limit is reached when either the average
coil temperature reaches 125 °C or the temperature rise exceeds 105 °C. The 20002 coil described in above examples was tested at a power level of 169 Watts with a
temperature rise of 105 °C. Using equation 4 above, the thermal resistance of this
Linear motor plus the attached heat sink RTH is:
RTH =
∆T
105°C
=
= 0.62°C/W
P 169Watts
The motor thermal resistance is determined by subtracting the test thermal
resistance from the measured total. The motor thermal resistance is calculated by:
RT = RTH − RS
Thus:
RT = 0.62°C/W - 0.06 °C/W = 0.56 °C/W
The application discussed above with a 2000-2 motor running at maximum
temperature dissipated just over 66 Watts. In a 70 °C ambient, the system thermal
resistance limit is
RS =
∆ T 125 °C − 70 °C
=
= 0.83 °C/W
P
66Watts
The thermal budgeting process calculates the maximum heat sink thermal resistance
RHM as follows:
RHM = RS − RT
Which for this example the thermal resistance of the heat sink is:
RHM = 0.83°C/W − 0.56°C/W = .27 °C/W
In the next sections the selection of a heat sink to achieve proper cooling will be
discussed.
Heat Sink Application (Practice and Nasty Realities)
The keys to proper motor cooling are the system specification and the component
thermal resistances. The total system thermal resistance is composed of a motor
thermal resistance element and a heat dissipation thermal resistance element in
series. The total of these series resistances must be low enough to allow the needed
amount of heat to flow without overheating any element in the series path. The
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following diagram illustrates a simplified thermal model with discrete thermal
elements illustrating a Linear motor coil and attached heat sink. Airflow through the
heat sink in the diagram below would be in the direction of the paper. The parallel
circuit paths for heat spreading are not shown:
Figure 3: Heat flow from the Linear motor to a convection-cooled heat sink
The power to be dissipated must be determined for your application. Remember to
follow the thermal limits shown in the motor specification. For moving coil systems
the motion calculation should include an estimate of the heat sink mass. The system
thermal resistance limit is calculated (using equation 5) by dividing the allowable
heat rise by the power that is to be dissipated. The motor thermal resistance can be
determined by dividing the 105 °C temperature rise by the continuous power rating
shown in the data sheet. The maximum limit for heat sink thermal resistance is
calculated by subtracting the motor thermal resistance from the system thermal
resistance. A search for an appropriate heat sink is the next step. Many on-line
resources are available to aid in this search. See “www.aavidthermalloy.com”. If an
appropriate heat sink cannot be found, perhaps a shorter version of a larger motor
can be specified to allow proper cooling to take place. The larger motor and new
heat sink mass must be re-checked as above.
It may be necessary to repeat the above steps to fully resolve heat sink sizing where
the mass of the heat sink is a significant portion of the moving mass. A larger motor
may need to be selected to produce the required force while maintaining an
acceptable operating temperature. At higher ambient temperatures, such as that
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used in the above calculation must derate the Linear motor force constant to
account for reduced magnet track flux. Once a heat sink has been chosen, it should
be reviewed against the motion profile for preferred mounting orientation, as this
can affect the efficiency of the heat transfer from heat sink to the air. With slow
moving applications, the heat sink can be mounted with the fins arranged transverse
to the motor, allowing additional cooling through use of the heat sink fin web to
spread heat through the heat sink. Faster moving applications should have the heat
sink fin direction parallel with the direction of travel to make best use of induced
airflow. Most “on-line” resources can predict performance for a heat sink at or about
the same width as the motor. Wider heat sinks must be used with care to account
for the additional thermal resistance caused by the longer thermal path. A high
thermal conductivity heat spreading plate may need to be added to the system to
maintain desired performance levels. The next few example calculations shown
below, use data from the AAVID web site for illustration only. AAVID part number
74925 is 4.8” wide, 1.77” high, 10” long, weighs 2.85 pounds and has a .45 °C /W
thermal resistance. Good practice dictates that at least a design margin be used
when specifying, as the manufacturer of the heat sink is specifying his best
configuration for a given type with assumes evenly distributed heat load and usually
a preferred orientation.
Heat sink performance increases as the square root of the heat sink length. The air
is warmed as it travels down the heat sink fins resulting in a smaller temperature
difference as the heat sink is increased in length. A heat sink extrusion that is cut to
5” long and properly cools a 2000-2 motor will, when applied in a 10” length to a
2000-4 motor, only provide 1.4 times the cooling. Heat sink manufacturers specify
the heat sink as if the device to be cooled covered the entire base. The specified
heat sink thermal resistance will be higher when applied to a Linear motor, as the
heat sink can be much wider than the motor. See the heat spreading discussion
below.
The system designer must avoid the temptation to use the calculations for one
vendor’s heat sink to size a different vendor’s heat sink, or worse to use a published
surface area to evaluate the effectiveness of a homemade heat sink or mounting
plate. Even small changes in web thickness; fin geometry, material alloy or surface
finish will make large changes in the effectiveness of heat transfer to the air.
When initially considering a heat sink, a rough approximation of the heat sink
“block” volume to thermal resistance is 500 to 800 cm3 °C/W. As an example we will
try to estimate the thermal resistance of the heat sink published above. The volume
based thermal resistance, RT is calculated for the AAVID heat sink described above:
RT = V / Vc
Where:
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V = Heat sink volume in cm3
Vc = Volume to thermal resistance reference
constant of 650 cm3 °C/W
The above heat sink is about 1350 cubic centimeters (cm3) in volume. The thermal
resistance is calculated as shown:
Rt = 650 cm3 °C/W / 1350 cm3 = 0.48 °C/W
This value is very close to the published .45 °C/W thermal resistance.
Altitude can affect convection cooling performance. The system designer must
derate heat sink performance for increasing altitude. A typical efficiency scaling
value for altitude is 75% at 12,000 feet.
It is also important to note the location of the Linear motor heat sink relative to
nearby sources of heat as well as heat sensitive devices such as encoders and
interferometers. Heat sources adjacent to the Linear motor can interfere with heat
removal.
The correct motor mounting practices must be employed to achieve the calculated
cooling capacity. The motor bracket must be securely attached to a mounting
surface that is at least the full length of the motor coils. The mounting surface must
be flat and must have a fine surface finish. High quality thermal grease must be
used at every transition surface and the mounting screws should be evenly
tightened. The motor coil should be mounted as centered as possible in the track to
avoid transfer of heat to magnets due to accidental contact, as magnets will
demagnetized when heated above their maximum operating temperature.
A transition or heat spreading plate (sometimes made from copper) can be used to
allow the heat to spread from the relatively narrow motor bracket to a wider heat
sink. This approach must be used with care as it increases both the mass and the
path length that heat must travel through to be dissipated. Low thermal resistance
material must be used in the construction of the spreading plate. The following table
lists the thermal conductivities (inverse of the thermal resistance) for several
materials. The practices recommended for motor cooling must be carefully followed
to gain benefit from the spreading plate. Remember: flat surfaces, smooth surface
finish, thermal grease, evenly and fully and evenly tighten all fasteners. The
following table lists the thermal conductivities (inverse of the thermal resistance) for
several materials:
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Material
Thermal Conductivity (W/”/°C)
Copper
9.6
Aluminum
5.52
Epoxy
0.004
The thermal resistance of a spreading plate can be determined with the following
simplified formula:
θ =
1
  A  2l + B 
ln  
2 k ( A − B )   B  2 l + A 
Where:
θ = Thermal Resistance for the plate in °C/W
k = Thermal conductivity of the material
A , B = The width and length of the plate
l = The thickness of the plate
Thermal Monitoring
It is very important to maintain the motor temperature at or below the maximum
safe operating temperature. There are many ways to verify this: First, the ambient
temperature coil resistance and increase in resistance with motor under power can
be used to calculate the average operating temperature. Advanced controls and
some amplifiers can monitor the voltage and current to allow operation up to a set
point, which when exceeded causes a correction back to the safe operating point.
The thermistor is a resistive device that produces a continuous resistance
proportional to the motor temperature. A resistance measurement of the thermistor
is often done while the system is being set-up and tuned. Some control systems can
monitor the thermistor through the use of an ADC. Two thermistor types are
available; 1) a NTC type that has a room temperature resistance of typically 10 kOhms, decreasing non-Linearly to about 300 Ohms for a hot motor; 2) a PTC type
that has a room temperature resistance of 100 Ohms, Linearly increasing resistance
with temperature. See the following graphs (figures 4 and 5) for PTC and NTC
temperature to resistance conversion reference:
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Positive Tc Thermistor
160
Resistance, ohms
150
140
130
120
110
100
0
20
40
60
80
100
120
140
100
120
140
Temperature, *C
Negative Tc Thermistor
14
Resistance, Kohms
12
10
8
6
4
2
0
0
20
40
60
80
Temperature , *C
Figure 4 and Figure 5 Thermistor temperatures to resistance conversion
graphs
A thermostat is often located in the motor bracket (replaces the thermistor) for
thermal protection. The switch activates when the bracket temperature reaches a
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critical limit. Thermostat switches are specified as “Close on rise” or “Open on rise”.
The typical Linear motor thermostat Activates at 105°C and deactivates at 100°C.
The thermostat is an on/off device and can only indicate when the system is already
in trouble. Thermostats must be used with care, as they can give short false
indications when subject to acceleration and vibration. A thermostat must not be
used to carry much current as the device self heats when handling large currents.
Linear Motor Application Examples
A 2000-1 motor coil is installed in a 20°C ambient temperature environment. It is
moving at 1 mm/s. The application requires a force of 14.4 pounds, which requires a
current of 3.6 Amps. The motor can run at the maximum temperature. Specify a
suitable heat sink:
1. Find the resistance of the coil.
R = 3.79Ohms × (1 + .00394 × (125°C − 20°C) = 5.36Ohms
2. Find the power to be dissipated by the system and the system thermal
resistance limit.
P = 3.6 Amps 2 × 5.36Ohms = 69.5Watts
RS =
∆ T 125 °C − 20 °C
=
= 1 .51 °C/W
P
69 .5Watts
3. Find the maximum heat sink resistance by subtracting the motor thermal
resistance from the system thermal resistance.
RHM = 1.51°C/W − 1.24°C/W = .27 °C/W
The search for a suitable heat sink located an AAVID Part number 68290. Heat
spreading for this wide heat sink is an issue but the thick heat sink base plate could
allow for sufficient cooling. The thick base could also act as a structural member for
the motion system components. At the slow speed used in this example, the heat
sink weight will have little impact on the motion. An output from the AAVID web site
product search engine can be seen in Figure 6:
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Figure 6. AAVID Heat sink selection
A 2000-2 motor coil is installed in a 20°C ambient temperature environment. It is
moving at 1 m/s. The application requires a force of 14.4 pounds, which requires a
current of 3.6 Amps. The motor can run at the maximum temperature. Specify a
suitable heat sink:
4. Find the resistance of the coil.
R = 3.79Ohms × (1 + .00394 × (125°C − 20°C) = 5.36Ohms
5. Find the power to be dissipated by the system and the system thermal
resistance limit.
P = 3.6 Amps 2 × 5.36Ohms = 69.5Watts
RS =
∆ T 125 °C − 20 °C
=
= 1 .51 °C/W
P
69 .5Watts
6. Find the maximum heat sink resistance by subtracting the motor thermal
resistance from the system thermal resistance.
RHM = 1.51°C/W − 1.24°C/W = .27 °C/W
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The search for a suitable heat sink located an AAVID Part number 68290. Heat
spreading for this wide heat sink is an issue but the thick heat sink base plate could
allow for sufficient cooling. The thick base could also act as a structural member for
the motion system components. At the slow speed used in this example, the heat
sink weight will have little impact on the motion.
The following is an application example where a 2000-4 Linear motor is used at a
75-Watt power level where the maximum heat rise of the coil must not exceed 55
Degrees C. The machine maximum ambient temperature is 40 Degree C. The motor
achieves a velocity of 2 meters per second for a 50% duty cycle.
1. The differential between the ambient and the motor is [40 + 55 = 95 degrees
C]. The resulting temperature is below the motor maximum operating
temperature of 125 degrees C.
2. The system thermal resistance is [55 degrees C / 75 Watts = .733 Degrees
C/Watt]
3. Subtracting the motor specified thermal resistance of 0.311 Degrees C/Watt
(for the 2000-4 motor) from the system thermal resistance of .733 Degrees
C/Watt, the maximum heat sink thermal resistance is .422 Degrees C/Watt.
4. A search for a suitable heat sink on the AAVID web site yields 4 pages of heat
sink shapes. Many of these are heavy or very large. P/N 67860 is 7.2” wide,
by 2.83” tall. This unit weighs 6.08 pounds.
5. The movement of the coil allows some forced cooling to take place. A search
for small heat sinks with a thermal resistance slightly higher than .4 Degrees
C/Watt located part # 74925 (4.8” wide, 1.77” tall, 10” long, 24 fins, weighs
2.85 pounds). This unit has a thermal resistance of about 0.25 Degrees
C/Watt with an average airflow of 1 meter per second (based on the 50%
duty motion). If the heat-sink mass is an issue this is clearly an interesting
option.
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