Appendix C Appxc
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SELECTING THE
SureStep™
STEPPING SYSTEM
APPENDIX
C
In This Appendix...
Selecting the SureStep™ Stepping System . . . . . . . . . . . . .C–2
The Selection Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .C–2
How many pulses from the PLC to make the move? . . . . . . . . .C–2
What is the positioning resolution of the load? . . . . . . . . . . . . .C–3
What is the indexing speed to accomplish the move time? . . . .C–3
Calculating the Required Torque . . . . . . . . . . . . . . . . . . . . . . . .C–4
Leadscrew - Example Calculations . . . . . . . . . . . . . . . . . . . .C–8
Step
Step
Step
Step
Step
1
2
3
4
5
-
Define the Actuator and Motion Requirements . . . . . .C–8
Determine the Positioning Resolution of the Load . . . .C–8
Determine the Motion Profile . . . . . . . . . . . . . . . . . . . .C–9
Determine the Required Motor Torque . . . . . . . . . . . .C–9
Select & Confirm Stepping Motor & Driver System . .C–10
Belt Drive - Example Calculations . . . . . . . . . . . . . . . . . . .C–11
Step
Step
Step
Step
Step
1
2
3
4
5
-
Define the Actuator and Motion Requirements . . . . .C–11
Determine the Positioning Resolution of the Load . . .C–11
Determine the Motion Profile . . . . . . . . . . . . . . . . . . .C–12
Determine the Required Motor Torque . . . . . . . . . . .C–12
Select & Confirm Stepping Motor & Driver System . .C–13
Index Table - Example Calculations . . . . . . . . . . . . . . . . . .C–14
Step
Step
Step
Step
Step
1
2
3
4
5
-
Define the Actuator and Motion Requirements . . . . .C–14
Determine the Positioning Resolution of the Load . . .C–14
Determine the Motion Profile . . . . . . . . . . . . . . . . . . .C–15
Determine the Required Motor Torque . . . . . . . . . . .C–15
Select & Confirm Stepping Motor & Driver System . .C–16
Engineering Unit Conversion Tables, Formulae, & Definitions: C–17
Appendix C: Selecting the SureStep™ Stepping System
Selecting the SureStep™ Stepping System
The selection of your SureStep™ stepping system follows a defined process. Let's
go through the process and define some useful relationships and equations. We will
use this information to work some typical examples along the way.
The Selection Procedure
The motor provides for the
required motion of the load
through the actuator (mechanics
that are between the motor shaft
and the load or workpiece). Key
information to accomplish the
required motion is:
Indexing
Speed
Acceleration
• total number of pulses from
the PLC
Deceleration
Move Time
• positioning resolution of the
load
• indexing speed (or PLC pulse
frequency) to achieve the
move time
• required
motor
torque
(including the 100% safety
factor)
• load to motor inertia ratio
In the final analysis, we need to achieve the required motion with acceptable
positioning accuracy.
How many pulses from the PLC to make the move?
The total number of pulses to make the entire move is expressed with the equation:
Equation 햲: Ptotal = total pulses = (Dtotal ÷ (dload ÷ i)) x step
Dtotal = total move distance
dload = lead or distance the load moves per revolution of the actuator's drive shaft
(P = pitch = 1/dload)
step = driver step resolution (steps/revmotor)
i = gear reduction ratio (revmotor/revgearshaft)
Example 1: The motor is directly attached to a disk, the stepping driver is set at 400
steps per revolution and we need to move the disk 5.5 revolutions. How many
pulses does the PLC need to send the driver?
Ptotal = (5.5 revdisk ÷ (1 revdisk/revdriveshaft ÷ 1 revmotor/revdriveshaft))
x 400 steps/revmotor
= 2200 pulses
C–2
SureStep™ Stepping Systems User Manual
Fourth Edition
12/2012
Appendix C: Selecting the SureStep™ Stepping System
Example 2: The motor is directly attached to a ballscrew where one turn of the
ballscrew results in 10 mm of linear motion, the stepping driver is set for 1000 steps
per revolution, and we need to move 45 mm. How many pulses do we need to send
the driver?
Ptotal = (45 mm ÷ (10 mm/revscrew ÷ 1 revmotor/revscrew)) x 1000 steps/revmotor
= 4500 pulses
Example 3: Let's add a 2:1 belt reduction between the motor and ballscrew in
example 2. Now how many pulses do we need to make the 45 mm move?
Ptotal = (45 mm ÷ (10mm/revscrew ÷ 2 revmotor/revscrew)) x 1000 steps/revmotor
= 9000 pulses
What is the positioning resolution of the load?
We want to know how far the load will move for one pulse or step of the motor
shaft. The equation to determine the positioning resolution is:
Equation 햳: L = load positioning resolution = (dload ÷ i) ÷ step
Example 4: What is the positioning resolution for the system in example 3?
L = (dload ÷ i) ÷ step
= (10 mm/revscrew ÷ 2 revmotor/revscrew) ÷ 1000 steps/revmotor
= 0.005mm/step
0.0002"/step
What is the indexing speed to accomplish the move time?
The most basic type of motion profile is a
"start-stop" profile where there is no
acceleration or deceleration period. This
type of motion profile is only used for
low speed applications because the load
is "jerked" from one speed to another and
the stepping motor will stall or drop
pulses if excessive speed changes are
attempted. The equation to find indexing
speed for "start-stop" motion is:
Start - Stop Profile
Indexing
Speed
Move Time
Equation 햴: fSS = indexing speed for start-stop profiles = Ptotal ÷ ttotal
ttotal = move time
Fourth Edition
12/2012
SureStep™ Stepping Systems User Manual
C–3
Appendix C: Selecting the SureStep™ Stepping System
Example 5: What is the indexing speed to make a "start-stop" move with 10,000
pulses in 800 ms?
fSS = indexing speed = Ptotal ÷ ttotal = 10,000 pulses ÷ 0.8 seconds
= 12,500 Hz.
For higher speed operation, the
"trapezoidal" motion profile includes
controlled
acceleration
&
deceleration and an initial non-zero
starting speed. With the acceleration
and deceleration periods equally set,
the indexing speed can be found
using the equation:
Trapezoidal Profile
Indexing
Speed
Start
Speed
Acceleration
Deceleration
Move Time
Equation 햵: fTRAP = (Ptotal - (fstart x tramp)) ÷ (ttotal - tramp)
for trapezoidal motion profiles
fstart = starting speed
tramp = acceleration or deceleration time
Example 6: What is the required indexing speed to make a "trapezoidal" move in
800ms, accel/decel time of 200 ms each, 10,000 total pulses, and a starting speed
of 40 Hz?
fTRAP = (10,000 pulses - (40 pulses/sec x 0.2 sec)) ÷ (0.8 sec - 0.2 sec)
16,653 Hz.
Calculating the Required Torque
The required torque from the
stepping system is the sum of
acceleration torque and the running
torque. The equation for required
motor torque is:
Torque
Pullout torque is the maximum torque that the
stepping system can provide at any speed. The
typical safety factor is to keep the required torque
under 50% of the ideal available torque to avoid
pullout or stalling.
Equation 햶: Tmotor = Taccel + Trun
Taccel = motor torque required to
Required Motor Torque
Versus Speed
accelerate and decelerate
the total system inertia
(including motor inertia)
Trun = constant motor torque requirement to run the mechanism
due to friction, external load forces, etc.
Speed
In Table 1 we show how to calculate torque required to accelerate or decelerate an
inertia from one speed to another and the calculation of running torque for common
mechanical actuators.
C–4
SureStep™ Stepping Systems User Manual
Fourth Edition
12/2012
Appendix C: Selecting the SureStep™ Stepping System
Table 1 - Calculate the Torque for "Acceleration" and "Running"
The torque required to accelerate or decelerate an inertia with a linear change in
velocity is:
Equation 햷: Taccel = Jtotal x (speed ÷ time) x (2 ÷ 60)
Jtotal is the motor inertia plus load
inertia ("reflected" to the motor
shaft). The (2 ÷ 60) is a factor used
to convert "change in speed"
expressed in RPM into angular
speed (radians/second). Refer to
information in this table to
calculate "reflected" load inertia for
several common shapes and
mechanical mechanisms.
Velocity
Accel
Period
Indexing Velocity
Decel
Period
time
T1
Torque
T2
time
T3
Example 7: What is the required torque to accelerate an inertia of 0.002 lb-in-sec2
(motor inertia is 0.0004 lb-in-sec2 and "reflected" load inertia is 0.0016 lb-in-sec2)
from zero to 600 RPM in 50 ms?
Taccel = 0.002 lb-in-sec2 x (600 RPM ÷ 0.05 seconds) x (2 ÷ 60)
2.5 lb-in
Leadscrew Equations
Fgravity
W
JW
Fext
J coupling
J gear
J screw
J motor
Description:
Motor RPM
Torque required to accelerate
and decelerate the load
Motor total inertia
Inertia of the load
Pitch and Efficiency
Running torque
Torque due to preload
on the ballscrew
Force total
Force of gravity and
Force of friction
Incline angle and
Coefficient of friction
Fourth Edition
12/2012
Equations:
nmotor = (vload x P) x i, nmotor (RPM), vload (in/min)
Taccel Jtotal x (speed ÷ time) x 0.1
Jtotal = Jmotor + Jgear + ((Jcoupling + Jscrew + JW) ÷ i2)
JW = (W ÷ (g x e)) x (1 ÷ 2 P)2
P = pitch = revs/inch of travel, e = efficiency
Trun = ((Ftotal ÷ (2 P)) + Tpreload) ÷ i
Tpreload = ballscrew nut preload to minimize backlash
Ftotal = Fext + Ffriction + Fgravity
Fgravity = Wsin, Ffriction = µWcos
= incline angle, µ = coefficient of friction
SureStep™ Stepping Systems User Manual
C–5
Appendix C: Selecting the SureStep™ Stepping System
Table 1 (cont’d)
Typical Leadscrew Data
e=
efficiency
Material:
ball nut
acme with plastic nut
acme with metal nut
µ=
coef. of friction
Material:
steel on steel
steel on steel (lubricated)
teflon on steel
ball bushing
0.90
0.65
0.40
0.580
0.150
0.040
0.003
Belt Drive (or Rack & Pinion) Equations
Fgravity
W
J motor
Fext
JW
J gear
J motor
W1
JW
Fext
J gear
J pinion
Description:
Motor RPM
Torque required to accelerate
and decelerate the load
Inertia of the load
Inertia of the load
Radius of pulleys
Running torque
Force total
Force of gravity and
Force of friction
Fgravity
J pinion
W2
Equations:
nmotor = (vload x 2 r) x i
Taccel Jtotal x (speed ÷ time) x 0.1
Jtotal = Jmotor + Jgear + ((Jpinion + JW) ÷ i2)
JW = (W ÷ (g x e)) x r2 ; JW = ((W1 + W2) ÷ (g x e)) x r2
r = radius of pinion or pulleys (inch)
Trun = (Ftotal x r) ÷ i
Ftotal = Fext + Ffriction + Fgravity
Fgravity = Wsin; Ffriction = µWcos
Belt (or Gear) Reducer Equations
J motorpulley
J motorpulley
J Load
J motor
J motor
J loadpulley
Description:
Motor RPM
Torque required to accelerate
and decelerate the load
Inertia of the load
Motor torque
C–6
J loadpulley
J Load
Equations:
nmotor = nload x i
Taccel Jtotal x (speed÷time) x 0.1
Jtotal = Jmotor + Jmotorpulley + ((Jloadpulley + JLoad) ÷ i2)
Tmotor x i = TLoad
SureStep™ Stepping Systems User Manual
Fourth Edition
12/2012
Appendix C: Selecting the SureStep™ Stepping System
Table 1 (cont’d)
Inertia of Hollow Cylinder Equations
L
Do = 2ro
Di = 2ri
Description:
Inertia
Inertia
Volume
Equations:
J = (W x (ro2 + ri2)) ÷ (2g)
J = ( x L x x (ro4 – ri4)) ÷ (2g)
volume = 4 x (Do2 - Di2) x L
Inertia of Solid Cylinder Equations
L
Description:
Inertia
Inertia
Volume
D = 2r
Equations:
J = (W x r2) ÷ (2g)
J = ( x L x x r4) ÷ (2g)
volume = x r2 x L
Inertia of Rectangular Block Equations
l
h
w
Description:
Inertia
Volume
Equations:
J = (W ÷ 12g) x (h2 + w2)
volume = l x h x w
Symbol Definitions
J = inertia
= density
L = Length
= 0.098 lb/in3 (aluminum)
h = height
= 0.28 lb/in3 (steel)
w = width
= 0.04 lb/in3 (plastic)
W = weight
= 0.31 lb/in3 (brass)
D = diameter
= 0.322 lb/in3 (copper)
r = radius
g = gravity = 386 in/sec2
Fourth Edition
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SureStep™ Stepping Systems User Manual
C–7
Appendix C: Selecting the SureStep™ Stepping System
Leadscrew - Example Calculations
Step 1 - Define the Actuator and Motion Requirements
Fgravity
W
JW
Fext
J coupling
J gear
J screw
J motor
Weight of table and workpiece = 200 lb
Angle of inclination = 0°
Friction coefficient of sliding surfaces = 0.05
External load force = 0
Ball screw shaft diameter = 0.6 inch
Ball screw length = 23.6 inch
Ball screw material = steel
Ball screw lead = 0.6 inch/rev (P 1.67 rev/in)
Desired Resolution = 0.001 inch/step
Gear reducer = 2:1
Stroke = 4.5 inch
Move time = 1.7 seconds
Definitions
dload = lead or distance the load moves per revolution of the actuator’s drive shaft (P = pitch = 1/dload)
Dtotal = total move distance
step = driver step resolution (steps/revmotor)
i = gear reduction ratio (revmotor/revgearshaft)
Taccel = motor torque required to accelerate and decelerate the total system inertia (including motor inertia)
Trun = constant motor torque requirement to run the mechanism due to friction, external load forces, etc.
ttotal = move time
Step 2 - Determine the Positioning Resolution of the Load
Rearranging Equation 햵 to calculate the required stepping drive resolution:
step = (dload ÷ i) ÷ L
= (0.6 ÷ 2) ÷ 0.001
= 300 steps/rev
With the 2:1 gear reduction, the stepping system can be set at 400 steps/rev to
exceed the required load positioning resolution.
A 2:1 timing belt reducer is a good choice for low cost and low backlash. Also, the
motor can be repositioned back under the leadscrew if desired with a timing belt
reducer.
C–8
SureStep™ Stepping Systems User Manual
Fourth Edition
12/2012
Appendix C: Selecting the SureStep™ Stepping System
Step 3 - Determine the Motion Profile
From Equation 햲, the total pulses to make the required move is:
Ptotal = (Dtotal ÷ (dload ÷ i)) x step
= (4.5 ÷ (0.6 ÷ 2)) x 400 = 6,000 pulses
From Equation 햵, the indexing frequency for a trapezoidal move is:
fTRAP = (Ptotal - (fstart x tramp)) ÷ (ttotal - tramp)
= (6,000 - (100 x 0.43)) ÷ (1.7 - 0.43) 4,690 Hz
where accel time is 25% of total move time and starting speed is 100 Hz.
= 4,690 Hz x (60 sec/1 min) ÷ 400 steps/rev
703 RPM motor speed
Step 4 - Determine the Required Motor Torque
Using the equations in Table 1:
Jtotal = Jmotor + Jgear + ((Jcoupling + Jscrew + JW) ÷ i2)
For this example, let's assume the gearbox and coupling inertia are zero.
JW = (W ÷ (g x e)) x (1 ÷ 2P)2
= (200 ÷ (386 x 0.9)) x (1 ÷ 2 x 3.14 x 1.67)2
0.0052 lb-in-sec2
Jscrew ( x L x x r4) ÷ (2g)
(3.14 x 23.6 x 0.28 x 0.34) ÷ (2 x 386)
0.0002 lb-in-sec2
The inertia of the load and screw reflected to the motor is:
J(screw + load) to motor = ((Jscrew + JW) ÷ i2)
((0.0002 + 0.0052) ÷ 22) = 0.00135 lb-in-sec2
The torque required to accelerate the inertia is:
Taccel Jtotal x (speed ÷ time) x 0.1
= 0.00135 x (603 ÷ 0.2) x 0.1 0.4 lb-in
Next, we need to determine running torque. If the machine already exists then it is
sometimes possible to actually measure running torque by turning the actuator
driveshaft with a torque wrench.
Trun = ((Ftotal ÷ (2 P)) + Tpreload) ÷ i
Ftotal = Fext + Ffriction + Fgravity
= 0 + µWcos + 0 = 0.05 x 200 = 10 lb
Trun = (10 ÷ (2 x 3.14 x 1.66)) ÷ 2
0.48 lb-in
where we have assumed preload torque to be zero.
From Equation 햶, the required motor torque is:
Tmotor = Taccel + Trun = 0.4 + 0.48 0.88 lb-in
However, this is the required motor torque before we have picked a motor and
included the motor inertia.
Fourth Edition
12/2012
SureStep™ Stepping Systems User Manual
C–9
Appendix C: Selecting the SureStep™ Stepping System
Step 5 - Select and Confirm the Stepping Motor and Driver System
It looks like a reasonable choice for a motor would be the STP-MTR-23055 or
shorter NEMA 23. This motor has an inertia of:
Jmotor = 0.00024 lb-in-sec2
The actual motor torque would be modified:
Taccel = Jtotal x (speed ÷ time) x 0.1
= (0.00135 + 0.00024) x (603 ÷ 0.2) x 0.1
0.48 lb-in
so that:
Tmotor = Taccel + Trun
= 0.48 + 0.48 0.96 lb-in 16 oz-in
160
STP-MTR-23055
140
120
Torque (oz-in)
1/2 Stepping
400 steps/rev
100
1/10 Stepping
2000 steps/rev
80
60
Required
Torque vs. Speed
40
20
0
0
150
300
450
600
750
900
1050
1200
1350
1500
RPM:
It looks like the STP-MTR-23055 stepping motor will work. However, we still need
to check the load to motor inertia ratio:
Ratio = J(screw + load) to motor ÷ Jmotor
= 0.00135 ÷ 0.00024 = 5.625
It is best to keep the load to motor inertia ratio below 10 so 5.625 is within an
acceptable range. For additional comfort, you could move up to the STP-MTR23079 or the larger NEMA 23 motor. In this case, the load to motor inertia ratio
would be lowered to 3.2.
C–10
SureStep™ Stepping Systems User Manual
Fourth Edition
12/2012
Appendix C: Selecting the SureStep™ Stepping System
Belt Drive - Example Calculations
Step 1 - Define the Actuator and Motion Requirements
Fgravity
W
J motor
Fext
JW
J gear
J pinion
Weight of table and workpiece = 3 lb
External force = 0 lb
Friction coefficient of sliding surfaces = 0.05
Angle of table = 0º
Belt and pulley efficiency = 0.8
Pulley diameter = 1.5 inch
Pulley thickness = 0.75 inch
Pulley material = aluminum
Desired Resolution = 0.001 inch/step
Gear Reducer = 5:1
Stroke = 50 inch
Move time = 4.0 seconds
Accel and decel time = 1.0 seconds
Definitions
dload = lead or distance the load moves per revolution of the actuator’s drive shaft (P = pitch = 1/dload)
Dtotal = total move distance
step = driver step resolution (steps/revmotor)
i = gear reduction ratio (revmotor/revgearshaft)
Taccel = motor torque required to accelerate and decelerate the total system inertia (including motor inertia)
Trun = constant motor torque requirement to run the mechanism due to friction, external load forces, etc.
ttotal = move time
Step 2 - Determine the Positioning Resolution of the Load
Rearranging Equation 햵 to calculate the required stepping drive resolution:
step = (dload ÷ i) ÷ L
= ((3.14 x 1.5) ÷ 5) ÷ 0.001
= 942 steps/rev
where dload = x Pulley Diameter.
With the 5:1 gear reduction, the stepping system can be set at 1000 steps/rev to
slightly exceed the required load positioning resolution.
Reduction is almost always required with a belt drive and a 5:1 planetary
gearhead is common.
Fourth Edition
12/2012
SureStep™ Stepping Systems User Manual
C–11
Appendix C: Selecting the SureStep™ Stepping System
Step 3 - Determine the Motion Profile
From Equation 햲, the total pulses to make the required move is:
Ptotal = (Dtotal ÷ (dload ÷ i)) x step
= 50 ÷ ((3.14 x 1.5) ÷ 5) x 1000
53,079 pulses
From Equation 햵, the running frequency for a trapezoidal move is:
fTRAP = (Ptotal - (fstart x tramp)) ÷ (ttotal - tramp)
= 53,079 ÷ (4 - 1)
17,693 Hz
where accel time is 25% of total move time and starting speed is zero.
= 17,693 Hz x (60 sec/1 min) ÷ 1000 steps/rev
1,062 RPM motor speed
Step 4 - Determine the Required Motor Torque
Using the equations in Table 1:
Jtotal = Jmotor + Jgear + ((Jpulleys + JW) ÷ i2)
For this example, let's assume the gearbox inertia is zero.
JW = (W ÷ (g x e)) x r2
= (3 ÷ (386 x 0.8)) x 0.752
0.0055 lb-in-sec2
Pulley inertia (remember there are two pulleys) can be calculated as:
Jpulleys (( x L x x r4) ÷ (2g)) x 2
((3.14 x 0.75 x 0.098 x 0.754) ÷ (2 x 386)) x 2
0.00019 lb-in-sec2
The inertia of the load and pulleys reflected to the motor is:
J(pulleys + load) to motor = ((Jpulleys + JW) ÷ i2)
((0.0055 + 0.00019) ÷ 52) 0.00023 lb-in-sec2
The torque required to accelerate the inertia is:
Tacc Jtotal x (speed ÷ time) x 0.1
= 0.00023 x (1062 ÷ 1) x 0.1
= 0.025 lb-in
Trun = (Ftotal x r) ÷ i
Ftotal = Fext + Ffriction + Fgravity
= 0 + µWcos + 0 = 0.05 x 3 = 0.15 lb
Trun = (0.15 x 0.75) ÷ 5
0.0225 lb-in
From Equation 햶, the required motor torque is:
Tmotor = Taccel + Trun = 0.025 + 0.0225 0.05 lb-in
However, this is the required motor torque before we have picked a motor and
included the motor inertia.
C–12
SureStep™ Stepping Systems User Manual
Fourth Edition
12/2012
Appendix C: Selecting the SureStep™ Stepping System
Step 5 - Select and Confirm the Stepping Motor and Driver System
It looks like a reasonable choice for a motor would be the STP-MTR-17048 or
NEMA 17 motor. This motor has an inertia of:
Jmotor = 0.00006 lb-in-sec2
The actual motor torque would be modified:
Taccel = Jtotal x (speed ÷ time) x 0.1
= (0.00023 + 0.00006) x (1062 ÷ 1) x 0.1 0.03 lb-in
so that:
Tmotor = Taccel + Trun
= 0.03 + 0.0225 0.0525 lb-in 0.84 oz-in
70
STP-MTR-17048
60
Torque (oz-in)
50
1/2 Stepping
400 steps/rev
40
1/10 Stepping
2000 steps/rev
30
20
Required
Torque vs. Speed
10
0
0
150
300
450
600
750
900
1050
1200
1350
1500
1650
1800
1950
2100
2250
RPM:
It looks like the STP-MTR-17048 stepping motor will work. However, we still need
to check the load to motor inertia ratio:
Ratio = J(pulleys + load) to motor ÷ Jmotor
= 0.00023 ÷ 0.00006 = 3.8
It is best to keep the load to motor inertia ratio below 10 so 3.8 is within an
acceptable range.
Fourth Edition
12/2012
SureStep™ Stepping Systems User Manual
C–13
Appendix C: Selecting the SureStep™ Stepping System
Index Table - Example Calculations
Step 1 - Define the Actuator and Motion Requirements
J gear
J motor
Diameter of index table = 12 inch
Thickness of index table = 2 inch
Table material = steel
Number of workpieces = 8
Desired Resolution = 0.036º
Gear Reducer = 25:1
Index angle = 45º
Index time = 0.7 seconds
Definitions
dload = lead or distance the load moves per revolution of the actuator’s drive shaft (P = pitch = 1/dload)
Dtotal = total move distance
step = driver step resolution (steps/revmotor)
i = gear reduction ratio (revmotor/revgearshaft)
Taccel = motor torque required to accelerate and decelerate the total system inertia (including motor inertia)
Trun = constant motor torque requirement to run the mechanism due to friction, external load forces, etc.
ttotal = move time
Step 2 - Determine the Positioning Resolution of the Load
Rearranging Equation 햵 to calculate the required stepping drive resolution:
step = (dload ÷ i) ÷ L
= (360º ÷ 25) ÷ 0.036º
= 400 steps/rev
With the 25:1 gear reduction, the stepping system can be set at 400 steps/rev to
equal the required load positioning resolution.
It is almost always necessary to use significant gear reduction when controlling a
large inertia disk.
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SureStep™ Stepping Systems User Manual
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Appendix C: Selecting the SureStep™ Stepping System
Step 3 - Determine the Motion Profile
From Equation 햲, the total pulses to make the required move is:
Ptotal = (Dtotal ÷ (dload ÷ i)) x step
= (45º ÷ (360º ÷ 25) x 400
= 1250 pulses
From Equation 햵, the running frequency for a trapezoidal move is:
fTRAP = (Ptotal - (fstart x tramp)) ÷ (ttotal - tramp)
= 1,250 ÷ (0.7 - 0.17) 2,360 Hz
where accel time is 25% of total move time and starting speed is zero.
= 2,360 Hz x (60 sec/1 min) ÷ 400 steps/rev
354 RPM
Step 4 - Determine the Required Motor Torque
Using the equations in Table 1:
Jtotal = Jmotor + Jgear + (Jtable ÷ i2)
For this example, let's assume the gearbox inertia is zero.
Jtable ( x L x x r4) ÷ (2g)
(3.14 x 2 x 0.28 x 1296) ÷ (2 x 386)
2.95 lb-in-sec2
The inertia of the indexing table reflected to the motor is:
Jtable to motor = Jtable ÷ i2
0.0047 lb-in-sec2
The torque required to accelerate the inertia is:
Taccel Jtotal x (speed ÷ time) x 0.1
= 0.0047 x (354 ÷ 0.17) x 0.1
1.0 lb-in
From Equation 햶, the required motor torque is:
Tmotor = Taccel + Trun
= 1.0 + 0 = 1.0 lb-in
However, this is the required motor torque before we have picked a motor and
included the motor inertia.
Fourth Edition
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SureStep™ Stepping Systems User Manual
C–15
Appendix C: Selecting the SureStep™ Stepping System
Step 5 - Select and Confirm the Stepping Motor and Driver System
It looks like a reasonable choice for a motor would be the STP-MTR-34066 or
NEMA 34 motor. This motor has an inertia of:
Jmotor = 0.0012 lb-in-sec2
The actual motor torque would be modified:
Taccel = Jtotal x (speed ÷ time) x 0.1
= (0.0047 + 0.0012) x (354 ÷ 0.17) x 0.1
1.22 lb-in
so that:
Tmotor = Taccel + Trun
= 1.22 + 0
= 1.22 lb-in = 19.52 oz-in
350
1/2 Stepping
400 steps/rev
STP-MTR-34066
300
1/10 Stepping
2000 steps/rev
Torque (oz-in)
250
200
150
100
Required
Torque vs. Speed
50
0
0
75
150
225
300
375
450
525
600
RPM:
It looks like the STP-MTR-34066 stepping motor will work. However, we still need
to check the load to motor inertia ratio:
Ratio = Jtable to motor ÷ Jmotor
= 0.0047 ÷ 0.0012 = 3.9
It is best to keep the load to motor inertia ratio below 10 so 3.9 is within an
acceptable range.
C–16
SureStep™ Stepping Systems User Manual
Fourth Edition
12/2012
Appendix C: Selecting the SureStep™ Stepping System
Engineering Unit Conversion Tables,
Formulae, & Definitions:
Conversion of Length
To convert A to B,
multiply A by the
entry in the table.
A
µm
mm
m
mil
in
ft
B
µm
mm
m
mil
in
ft
1
1.000E–03
1.000E–06
3.937E–02
3.937E–05
3.281E–06
1.000E+03
1
1.000E–03
3.937E+01
3.937E–02
3.281E–03
1.000E+06
1.000E+03
1
3.937E+04
3.937E+01
3.281E+00
2.540E+01
2.540E–02
2.540E–05
1
1.000E–03
8.330E–05
2.540E+04
2.540E+01
2.540E–02
1.000E+03
1
8.330E–02
3.048E+05
3.048E+02
3.048E–01
1.200E+04
1.200E+01
1
Conversion of Torque
B
To convert A to B,
multiply A by the
entry in the table.
A
Nm
kpm(kg-m)
kg-cm
oz-in
lb-in
lb-ft
Nm
1
1.020E–01
1.020E+01
1.416E+02
8.850E+00
7.380E-01
kpm(kg-m)
9.810E+00
1
1.000E+02
1.390E+03
8.680E+01
7.230E+00
kg-cm
9.810E–02
1.000E–02
1
1.390E+01
8.680E–01
7.230E–02
oz-in
7.060E–03
7.200E–04
7.200E–02
1
6.250E–02
5.200E–03
lb-in
1.130E–01
1.150E–02
1.150E+00
1.600E+01
1
8.330E–02
lb-ft
1.356E+00
1.380E–01
1.383E+01
1.920E+02
1.200E+01
1
Conversion of Moment of Inertia
To convert A to B,
multiply A by the
entry in the table.
A
B
kg-m2
kg-cm-s2
oz-in-s2
lb-in-s2
oz-in2
lb-in2
kg-m2
1
kg-cm-s2
9.800E–02
1
oz-in-s2
7.060E–03
7.190E–02
lb-in-s2
1.130E–01 1.152E+00 1.600E+01
oz-in2
1.830E–05
1.870E–04
2.590E–03
1.620E–04
lb-in2
2.930E–04
2.985E–03
4.140E–02
2.590E–03 1.600E+01
lb-ft2
4.210E–02
4.290E–01 5.968E+00 3.730E–01 2.304E+03 1.440E+02
Fourth Edition
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lb-ft2
1.020E+01 1.416E+02 8.850E+00 5.470E+04 3.420E+03 2.373E+01
1.388E+01 8.680E–01 5.360E+03
1
3.350+02
2.320E+00
6.250E–02 3.861E+02 2.413E+01 1.676E–01
1
6.180E+03 3.861E+02 2.681E+00
1
6.250E–02
4.340E–04
1
6.940E–03
SureStep™ Stepping Systems User Manual
1
C–17
Appendix C: Selecting the SureStep™ Stepping System
Engineering Unit Conversion Tables, Formulae, & Definitions (cont’d):
General Formulae & Definitions
Description:
Equations:
Gravity
Torque
Power (Watts)
Power (Horsepower)
Horsepower
Revolutions
gravity = 9.8 m/s2; 386 in/s2
T = J · ; = rad/s2
P (W) = T (N·m) · (rad/s)
P (hp) = T (lb·in) · (rpm) / 63,024
1 hp = 746W
1 rev = 1,296,000 arc·sec / 21,600 arc·min
Equations for Straight-Line Velocity & Constant Acceleration
Description:
Equations:
v = v + at
f
i
Final velocity final
velocity = (initial velocity) + (acceleration)(time)
x = x + ½(v +v )t
f
i
i
f
Final position final
position = initial position + [(1/2 )(initial velocity + final velocity)(time)]
Final position
xf = xi + vit + ½at2
final position = initial position + (initial velocity)(time) + (1/2)(acceleration)(time squared)
v 2 = v 2 + 2a(x – x )
i
f
i
Final velocity f
final velocity squared = initial velocity squared + [(2)(acceleration)(final position – initial
squared
position)]
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SureStep™ Stepping Systems User Manual
Fourth Edition
12/2012
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