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Engineering Calculator
Rack&Pinion System
Calculation
Straight Teeth
Helical Teeth
Input
Acceleration Time
t
a
=
s
Deceleration Time
t
d
=
s
Constant Speed Time
t
cs
=
s
Dwell Time
t
dw
=
s
System Inclination (degrees)
γ=
°
Traveling Weight
m=
kg
Speed
v=
m/s
Static Friction Coefficient
μ
s
=
Service Factor
1.5
K
A
=
System Efficiency
0.9
η=
Pinion Pitch Diameter
d=
mm
Pinion Inertia
J
P
=
kg·cm
2
Pinion Pressure Angle (degrees)
20
α=
°
Pinion Helix Angle (degrees)
19
β
d
=
°
Pinion Helix Angle (arcmin)
31
β
m
=
'
Pinion Helix Angle (arcsec)
42
β
s
=
"
Machining Force
0
F=
N
Motor Moment of Inertia
J
M
=
kg·cm
2
Max. Motor Speed During Cycle
n
1
=
rpm
Gearbox Moment of Inertia
0
J
g
=
kg·cm
2
Positioning Accuracy
A
p
=
mm
The formulas used for these calculations are available in
this PDF
.
Results
Machine
Cycle Duration
t
cycle
=
s
Cycles per Minute
Z=
Duty Cycle
ED=
%
Friction Force
F
f
=
N
Acceleration Force
F
acc
=
N
Deceleration Force
F
dec
=
N
Force Due to Gravity
F
w
=
N
Max. Tangential Force on Pinion
F
t max
=
N
Max. Radial Force on Pinion
F
r max
=
N
Max. Radial Force on Pinion
F
r max
=
N
Max. Axial Force on Pinion
F
ax max
=
N
Pinion Helix Angle (degrees)
β=
°
Inertias
Total Inertia as Seen by the Motor
J
T1
=
kg·m
2
Load to Motor Inertia Ratio
Λ=
Kinematics
Traversed Distance
L=
m
Linear Acceleration
a=
m/s
2
Linear Deceleration
a=
m/s
2
Pinion Rotational Speed
n
2
=
rpm
Motor
Maximum Required Motor Power
P
1 max
=
kW
Maximum Required Motor Torque
T
1 max
=
N·m
Gearbox
Ideal Gearbox Ratio
i=
Ideal Gearbox Backlash (arcmin)
Δφ=
'
Required Torque on Pinion
T
2 max
=
N·m
Required Torque on Pinion, Adjusted for Service Factor
T
2KA
=
N·m
Buttons
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Diagrams
Straight Teeth
Helical Teeth