Formulae
and Conversion
Factors for
Motion Transfer
P-7293-HD-A4
3/17.... Huco Dynatork 888-829-6637 | +44 (0) 1992 501900
59
Formulae and Conversion Factors
International System(SI)
SI BASE UNITS
Name
Imperial System (FPS)
TORQUE
Quantity
Unit Symbol
length
mmetre
mass
kgkilogram
time
ssecond
electric current
A
ampere
M - Torque in Nm
Thermodynamic temperature
K
kelvin
M- Torque in lbf . ft
F - Force in N
luminous intensity
cdcandela
F - Force in lbf
r - Radius of lever in m
r - Radius of lever in ft
P - Power in kW
P - Power in hp
n - Rotational speed in
n - Rotational speed in rpm
LETTER SYMBOLS & SI UNITS IN
POWER TRANSMISSION ENGINEERING
Symbol
Quantity
M- F . r
P=
modulus of elasticity
(Young’s modulus)
SI Unit Name
Symbol
Pa
W-F.s=m.g.s
pascal
N Newton
G (W)
weight
N
Newton
J
moment of inertia
kgm2
kilogram
metre squared
M (T)
Newton metre
Nm
mmass
kg kilogram
Ppower
W watt
ppressure
Pa pascal
ρ
density (mas density)
kg/m3-
σ
stress
Papascal
W (E)
work (energy)
J
η
efficiency
1-
μ
coefficient of friction
1
s - Length of path in ft
m - Mass in kg
g - Acceleration of free fall
(9.81) in m/s2
WK2-Flywheel effect lb . ft2
n - Rotational speed in rpm
9.55 Ma
braking time in s
J - Moment of inertia in kgm2
WK2-Flywheel effect in kgm2
n - Rotational speed in
n - Rotational speed in
1/min or r/min
rpm
Ma- Acceleration
1 . Wor. r2
2
braking torque
in lb . ft
ext
braking torque in Nm
Linear motion
P = Fr . v
1000
Fr = μ . m . g
Linear motion
P = Fr . v
33000
Fr = μ . W
Rotary motion
M.n
P=
9550
Rotary motion
P=
P-Power in kW
P - Power in hp
Fr - Frictional resistance in N
Fr - Frictional resistance in lbf
m - Mass in kg
W- Weight in lb
g - Acceleration of free fall
v - Velocity in ft/min
W.v
η . 33000
MOMENT OF INERTIA
M.n
5250
μ - Coefficient of friction
η - Efficiency in decimals
M- Torque in lbf . ft
μ - Coefficient of friction
n - Rotational speed in rpm
Solid Cylinder
Solid Cylinder
J = 1 . m . r2ext
2
WK2 = 1 . W . r2ext
2
= 1 . 1000 . π . ρ . l . d4ext
32
= π . ρ . l . d4ext
32
= 98 ρ . l . d4ext
= 0.1 ρ . l . d4ext
Hollow Cylinder
Hollow Cylinder
J = 1 . m . (r2 ext +r2 int)
WK2 = 1 . W . (r2 ext + r2 int)
2
2
η - Efficiency in decimals
v - Velocity in m/s
308 Ma
ta - Acceleration or
Ma- Acceleration or
P=
WK2 . n
ta =
braking time in s
Imperial System (FPS)
Lifting motion
= 1 . 1000 . π . ρ . l (d4ext-d4int)
32
= π . ρ . l (d4ext - d4int)
32
= 98 . ρ . l (d4ext - d4int)
= 0.1 . ρ . l (d4ext - d4int)
torsional stiffness and resonant frequency
M- Torque in Nm
n-Rotational speed in 1/min or
r/min
60
F - Force in lbf
ta - Acceleration or
-
m.g.v
P=
η . 1000
5880
W- Work (energy) in lb . ft
j.n
ta =
joule
Lifting motion
WK2 . n2
W=
182.5
ACCELERATION OR BRAKING TIME
POWER
(9.81) in m/s2
W- F . s
j . n2
W- Work (energy) in Nm = Ws = J
F - Force in N
s - Length of path in m
m - Mass in kg
g - Acceleration of free fall
(9.81) in m/s2
J - Moment of inertia in kgm2
n - Rotational speed in
1/min or r/min
FORMULAE
International System(SI)
n
WORK
W=
Fforce
torque
5250 . P
P=
n
1/min or r/min
Mechanics
E
M- F . r
9550 . P
Huco Dynatork 888-829-6637 | +44 (0) 1992 501900
CT ≤ (FR x 2 π)2
1 + 1
JM + JL
(
)
FR ≤ 1 x
2π
(
1 + 1
JM + JL
)
x CT
Where
CT =torsional stiffness
(Nm/rad);
JM =motor inertia (kgm2)
FR =resonant frequency (Hz)
JL =load inertia (kgm2)
..... P-7293-HD-A4
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Formulae and Conversion Factors
FORCE
1N
1kp
1p
1tonf (UK)
1lbf
1ozf
N
1
9.807
9.81 x 10-3
9964
4.448
-
=
=
=
=
=
=
kp
0.1020
1
1 x 10-3
1016
0.4536
28.4 x 10-3
p
102.0
1000
1
1.02 x 106
453.6
28.35
tonf (UK)
100.4 x 10-6
0.984 x 10-3
0.984 x 10-6
1
0.5 x 10-6
27.9 x 10-6
lbf
0.2248
2.205
2.2 x 10-3
2240
1
62.5 x 10-3
ozf
3.597
35.27
35.3 x 10-3
35.8 x 103
16
1
VELOCITY
1km/h
m/min
1m/s
1mile/h
1ft/min
1ft/s
1in/s
km/h
1
0.06
3.6
1.609
18.3 x 10-3
1.097
91 x 10-3
=
=
=
=
=
=
=
m/min
16.667
1
60
26.82
0.3048
18.288
1.524
m/s
0.2778
16.7 x 10-3
1
0.4470
5.08 x 10-3
0.3048
25.4 x 10-3
mile/h
0.6214
37.3 x 10-3
2.237
1
11.4 x 10-3
0.6818
56.8 x 10-3
ft/min
54.68
3.281
196.85
88
1
60
5
ft/s
0.9113
54.7 x 10-3
3.281
1.467
16.7 x 10-3
1
83.3 x 10-3
in/s
10.936
0.656
39.37
17.6
0.2
12
1
TORQUE
1Nm
Ncm
1kgfm
1lbf.ft
1lbf.in
1ozf.in
Nm
1
0.01
9.8067
1.356
0.1129
7.062 x 10-3
=
=
=
=
=
=
Ncm
100
1
980.67
135.6
11.29
0.7062
kgfm
0.10197
1.02 x 10-3
1
0.1383
11.5 x 10-3
0.72 x 10-3
lbf.ft
0.73756
7.376 x 10-3
7.233
1
83.3 x 10-3
5.21 x 10-3
lbf.in
8.8507
88.5 x 10-3
86.796
12
1
62.5 x 10-3
ozf.in
141.61
1.4161
1389
192
16
1
POWER
1kW
1PS
1hp
1kgfm/s
1ft.lbf/s
=
=
=
=
=
kW
1
0.7355
0.7457
9.81 x 10-3
1.36 x 10-3
PS
1.360
1
1.014
13.33 x 10-3
1.84 x 10-3
hp
1.341
0.9863
1
13.15 x 10-3
1.82 x 10-3
kgfm/s
102.0
75
76.04
1
0.1383
ft.lbf/s
737.6
542.5
550
7.233
1
kgfm2 (GD2)
4
1
0.1686
39.23
5.423
lb.ft2(WK2)
23.73
5.933
1
232.7
32.17
kpms2
0.102
25 x 10-3
4.30 x 10-3
1
0.1383
ft lbf s2
0.7376
0.1844
31.1 x 10-3
7.233
1
MOMENT OF INERTIA AND OTHER FLYWHEEL EFFECTS
1kgm2 (mr 2)
1kgfm2 (GD 2)
1lb.ft2(WK 2)
1kpms2
1ft lbf s2
=
=
=
=
=
kgm2 (mr2)
1
0.25
42.1 x 10-3
9.807
1.356
LENGTH
1mm
1m
1in
1ft
1yd
1km
1mile
P-7293-HD-A4
mm
1
1000
25.4
304.8
914.4
-
m
0.001
1
0.0254
0.3048
0.9144
1000
1,609
3/17.... in
0.3937
39.370
1
12
36
39,370.07
63,346.45
ft
0.0033
3.2808
0.0833
1
3
3,280.83
5,278.87
yds
0.00109
1.0936
0.0277
0.3333
1
1,093.613
1,759.623
km
0.001
0.0000254
0.000304
0.000914
1
1.609
miles
0.0006215
0.0000158
0.0001894
0.000568
0.6215
1
Huco Dynatork 888-829-6637 | +44 (0) 1992 501900
61