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selection guide

DIRECT DRIVE
For a Direct Drive application, acceleration torque, (T
ACCEL
), and friction torque, (T
FRICTION
), must be determined. The following equations assume that the driven load is a hollow cylinder. For a solid cylinder, r
1
= 0.Assume that J
MOTOR
= 0, solve the equation, choose a motor based on your result, and then comeback and recalculate T
ACCEL
using J
MOTOR
of the motor you selected. T
FRICTION
(oz-in) can either beestimated or measured using one of the methods described in Figure 1 (See inside). After solving forT
ACCEL
and T
FRICTION
, select a motor or gearmotor that meets the following criteria:Make sure the motor or gearmotor has a starting torque capability equal to T
ACCEL
+ T
FRICTION
. Then proceed to Step 2 (See inside).
LEAD SCREW
For a Lead Screw application, acceleration torque, (T
ACCEL
), friction torque, (T
FRICTION
), breakawaytorque, (T
BREAKAWAY
), and gravity torque, (T
GRAVITY
), must be determined. T
ACCEL
may be ignoredunless acceleration time is critical.Assume that J
MOTOR
= 0, solve the equation, choose a motor based on your result, and then comeback and recalculate T
ACCEL
using J
MOTOR
of the motor you selected.T
FRICTION
can either be measured, using one of the methods in Figure 1 (See inside), or calculatedusing the equation:T
BREAKAWAY
is only a factor during starting and can either be estimated or measured using one of the methods in Figure 1 (See inside).T
GRAVITY
only needs to be considered when the lead screw is not mounted horizontally. It is a positivenumber when the load is moved upward, and a negative number when the load is moved downward.It can be calculated using the equation:After solving for T
ACCEL
, T
FRICTION
, T
BREAKAWAY
, and T
GRAVITY
,select a motor or gearmotor that meets the following criteria:Make sure the motor or gearmotor has a starting torque capability equal to T
ACCEL
+ T
FRICTION
+T
BREAKAWAY
+ T
GRAVITY
. Then proceed to Step 2 (See inside).
Determine speed and torque
The desired output speed of the motor or gearmotor is usually known. The load torquemight be measured, calculated, estimated, or arrived at using a combination of methods,depending on the type of mechanical system. Four common systems are:
Direct driveLead screwBelt drive or rack & pinionGear drive, chain & sprocket, belt & pulley
Identify which type of mechanical system is similar to yours and proceed to one of thefollowing sections to determine what torque and speed are required for your application.Note that many applications involve a combination of the basic mechanical systems.
1.1.
T
ACCEL
(oz-in) =
[
ρ
L(r
24
- r
14
)+J
MOTOR
R
2
E
]
N2469.55t
a
HP
CONT
=T
FRICTION
N1,008,400at a speed of N T
CONT
(oz-in) = T
FRICTION
at a speed of NT
ACCEL
(oz-in) =
[
d
2
W
L&C
+
ρ
Lr
4
+J
MOTOR
R
2
E
]
60V
LOAD
15239
e
2469.55
d
t
a
T
FRICTION
(oz-in) =
d
W
L&C
μ
6.28
e
T
GRAVITY
(oz-in) =
d
W
L&C
sin
ϕ
6.28
e
HP
CONT
=(T
FRICTION
+ T
GRAVITY
)60V
LOAD
at a speed of60V
LOAD
1,008,400
d d
T
CONT
(oz-in) = T
FRICTION
+ T
GRAVITY
at a speed of 60V
LOAD
d
oror
r
2
Nr
1
ϕ
V
LOAD
N
BODINEELECTRICCOMPANY
Direct DriveLead Screw
For assistance with calculations in Step 1, see DEFINITION OF TERMS on facing page.
Created by the BodineElectric Company,this Motor andGearmotor SelectionGuide is designed tohelp you specify thebest motor or gearmotor for your application.By considering threekey design criteria,you can quickly selecta drive system thatallows for productivefollow-up with themotor manufacturer’ssales engineers, sav-ing you considerabletime and expense.The three design criteria are:1. Determine speed and torque.2. Select the appropriate motortype.3. Select gearreducer, if needed.Enclosed is an easy-to-complete work-sheet that serves asthe companion to thisguide. When you areready, just fill in theblanks and return it toBodine ElectricCompany.There’s no easier way to determine the best motor for yourapplication.
BELT DRIVE or RACK & PINION
For a Belt Drive or Rack & Pinion application, acceleration torque, (T
ACCEL
), friction torque,(T
FRICTION
),breakaway torque,(T
BREAKAWAY
), and gravity torque,(T
GRAVITY
) must be determined. T
ACCEL
may beignored unless acceleration time is critical. The following equations assume a belt drive system. For arack & pinion system, substitute the word “pinion” in place of “roller”, and “rack” in place of “belt.”Assume that J
MOTOR
= 0, solve the equation, choose a motor based on your result, and then come back and recalculate T
ACCEL
using J
MOTOR
of the motor you selected.T
FRICTION
can be estimated or measured using one of the methods in Figure 1 (See inside).T
BREAKAWAY
is only a factor during starting and can either be estimated or measuredusing one of the methods in Figure 1 (See inside).T
GRAVITY
only needs to be considered when the belt is not mounted horizontally. It is a positive number when the load is moved upward, and a negative number when the load is moved downward. It can be calculated using the equation:After solving for T
ACCEL
, T
FRICTION
, T
BREAKAWAY
, and T
GRAVITY
, select a motor or gearmotor that meets the following criteria:Make sure the motor or gearmotor has a starting torque capability equal to T
ACCEL
+ T
FRICTION
+ T
BREAKAWAY
+ T
GRAVITY
. Then proceed to Step 2 (See inside).
GEAR DRIVE, CHAIN & SPROCKET, BELT & PULLEY
For a Gear Drive application, acceleration torque, (T
ACCEL
), breakaway torque, (T
BREAKAWAY
),and reflected load torque, (T
REFLECTED
), must be determined. T
ACCEL
may be ignored unless accelerationtime is critical. The same equations can be used for chain & sprocket or belt & pulley systems. Justreplace the word “gear” with “sprocket” or “pulley.”The value for J
LOAD
depends on what is connected to the output of GEAR 1. Refer to the equations for the other types of mechanical systems to solve for J
LOAD
.T
FRICTION
can be estimated or measured using one of the methods in Figure 1 (See inside).T
BREAKAWAY
is only a factor during starting and can either be estimated or measured using one of the methods in Figure 1 (See inside).T
LOAD
depends on what is connected to the output gear. Refer to the equations for the other mechanical systems to solve for T
LOAD
.After solving for T
ACCEL
, T
BREAKAWAY
, and T
REFLECTED
, select a motor or gearmotor that meets the following criteria:Make sure the motor or gearmotor has a starting torque capability equal to T
ACCEL
+ T
BREAKAWAY
+ T
LOAD.
Then proceed to Step 2 (See inside).
HP
CONT
=T
REFLECTED
N
1
Gat a speed of N
1
G1,008,400T
CONT
(oz-in) = T
REFLECTED
at a speed of N
1
G
d
=
lead of screw (inch/rev)E= gearmotor gearing efficiency (see Table 3)
e
= mechanism efficiency (see Table 3)G = ratio of input speed to outputspeedJ
LOAD
= inertia of driven load(oz-in-sec
2
)J
MOTOR
= motor inertia (oz-in-sec
2
)L= length of cylinder or lead screw(inches)N = angular velocity of load (RPM)n = number of rollers
ϕ
= angle of screw or belt fromhorizontal (degrees)
ρ
= density of cylinder or lead screw(oz/in3) (see Table 1)R = gearmotor gear ratior = radius of roller, screw, gear, or pulley (inches)ta= time to accelerate (seconds)T
LOAD
= load torque (oz-in)
μ
= coefficient of frictionV
LOAD
= linear velocity of load (inch/sec)W
BELT
= weight of belt or roller(ounces)W
GEAR 1
= weight of gear 1 (ounces)W
GEAR 2
= weight of gear 2 (ounces)W
L&C
= weight of load & carriage(ounces)W
LOAD
= weight of load (ounces)W
ROLLER
= weight of roller (ounces)
or
T
GRAVITY
(oz-in) = rW
LOAD
sin
ϕ
T
ACCEL
(oz-in) =
[
W
LOAD
r
2
+nW
ROLLER
r
2
+W
BELT
r
2
+J
MOTOR
R
2
E
]
V
LOAD
tr683277683
a
T
CONT
(oz-in) = T
FRICTION
+ T
GRAVITY
at a speed of9.55V
LOAD
rHP
CONT
=(T
FRICTION
+T
GRAVITY
)V
LOAD
at a speed of9.55V
LOAD
rr295,501
or
T
ACCEL
(oz-in) =
[
J
LOAD
+W
GEAR1
r
12
+W
GEAR2
r
22
+J
MOTOR
R
2
E
]
N
1
G
e
G
2
772G
2
7729.55t
a
T
REFLECTED
(oz-in) =T
LOAD
e
(G)
V
LOAD
r
ϕ
N
ϕ
V
LOAD
rN
r
N
2
r
112
N
r
N
2
r
112
N
Definition of terms
Belt & PulleyGear DriveRack & PinionBelt Drive
The equations used in this selection guide have been derived from fundamen-tal motion control formulas. For more application-specific information, pleasecontact the Bodine Electric Company.
(see Table 2)
The String and Pulley Method
Affix a pulley to the shaft of the machine tobe driven (see Figure A). Secure one endof a cord to the outer surface of the pulleyand wrap the cord around it. Tie the otherend of the cord to a spring scale. Pull onthe scale until the shaft turns. The force, inpounds indicated on the scale, multipliedby the radius of the pulley (in inches) givesthe breakaway torque in pound-inches.
Torque Wrench Method
A simple torque wrench can be applied tothe shaft of the machine to be driven. Turnthe wrench as you would an ordinary pipewrench, and when the shaft begins torotate, read the value for T
BREAKAWAY
(in ounce-inches or pound-inches) on thetorque wrench gauge.
“Test” Motor method
Both AC and DC test motors or gearmo-tors can be used to measure breakawaytorque, (T
BREAKAWAY
),and friction torque,(T
FRICTION
). This method requires moretime and instrumentation, but can be wellworth the expense in the long run. It is thebest way to optimally match machine anddrive unit, and is popularly used for allhigh volume OEM (srcinal equipmentmanufacturer) applications. After usingthese methods, contact the motor manu-facturers’ sales engineer for help in inter-preting the data.
“Test” With An AC Drive
Use a torque wrench or “string and pulley”to find the approximate size of the testmotor or gearmotor needed. An AC motoror gearmotor whose rated output speed isclose to the desired “final” speed of themachine should be obtained. Next, hookup the AC drive, along with a variableautotransformer to the load (See Figure B).With a voltmeter connected to the line,increase the voltage supplied by the auto-transformer until it starts and acceleratesthe load up to speed (to check speed usea tachometer or stroboscope). Record thestarting voltage at all possible startinglocations of the device. This is proportion-al to the T
BREAKAWAY
. Next, back off slowlyuntil the motor stalls. Read the voltage.This is proportional to the T
FRICTION
.
“Test” With A DC Drive
The DC method requires that both voltageand amperage readings be taken from thearmature circuit (See Figure C). Speed ofthe DC motor is proportional to the voltagewhile T
FRICTION
is proportional to the arma-ture amperage.
METHODS FOR MEASURING THE BREAKAWAY ANDFRICTION TORQUE OF A MACHINE.
r
machine shaft
V
voltmeterACmotororgearmotor
l i n e
DCmotororgearmotor
DCVA
N SARMVoltmeterAmpmeter
Figure C—PM DC motor or gearmotor with voltmeter and ampmeter connected for loadmeasurement.Figure B—AC motor or gearmotor withadjustable autotransformer, and voltmeter connected for load measurement.Figure A—Simple “string and pulley” method oftorque measurement (Torque = Force readingon spring scale x radius of the pulley)
For maximum accuracy, the actual test motor should be sent to the manufacturerwith the voltage, amperage and speed information for bench (or dynamometer)testing. The minimum starting torque should also be supplied.
FIGURE 1
MECHANISMEFFICIENCIES %
Acme Screw (Brass Nut)35 - 65Acme Screw (Plastic Nut)5 - 85Ball-Screw85 - 95Preloaded Ball-Screw75 - 85Spur or Bevel Gears92
per stage
Timing Belt96 - 98Chain and Sprocket95 - 98Worm Gears80 - .6G(G=gear ratio)
FRICTIONCOEFFICIENTS (SLIDING) µ
Steel on Steel.58Steel on Steel(Greased).15Aluminum on Steel.45Copper on Steel.36Brass on Steel.44Plastic on Steel.2Liner Bearings.001
MATERIAL oz lb gmDENSITIES in
3
in
3
cm
3
Aluminum1.57.0982.72Brass4.96.318.6Copper5.15.3228.91Plastic.64.041.11Steel4.48.287.75
conversion tablestable 1table 3table 2

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