A
Calculating loads, forces and moments of
inertia, avoiding risks and damage
It is not only the weight which counts; shape and position are also often decisive factors
EA
+ M
Overview
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Calculation of the torque
acting on the tilting axis
B mass and moment of inertia
Calculation of the
B
D
D
TF
A
A
D
R
R
LL
JA
T2
/ T3
MOT / KAB
WMS / CNC
R
L
R
LL
R
R
D
D
RJJ
L
B
D
rr
A
A
B
B
J JA
JA
r
A
JA
RFX/LFX
B
B
A
A
B
A
D
Workpiece
clamping
JA
L
Rotar y table
TF...T1-507510
TF-510510
TF...T1-510520
TF...T1-520520
B
R
D
J
DJA
J
JBA
D
JA
B
R
D
JA
L
d
vario(X)(1)
0
3.5
0
0
d
R
r
b JA
R
76
a
A
A
r
JA
b
L
JA
a
Calculation of the torque in the tilting direction
(without intrinsic torque of the dividing axis):
Rs = R + L/2
M = m x Rs x g
r
A
fix(X)
65
68.5
86.5
114
B
R
d
A
Calculation of the total torque in the tilting
direction (with intrinsic torque of the dividing
axis):
M tot = M + Me (Me is the gear unit loading
without load; see appropriate T-type rotary
table pp. 13–29)
JJAA B
dD
d
R JA
LL b R
a L
Distance R
R
L
L
L
JA
L
General
accessories
R
B
R
D
L
L
D
D
L
m=
JA =
D:
Outside diameter of the round
bar [m]
L: Length of the round bar [m]
r: Turning radius [m]
p: Density [kg/m2]
m: Mass of the round bar [kg]
Moment of inertia of the round
JA:
bar at center A [kgm2]
J: Moment of inertia [kgm2]
m=
J=
Side length [m]
Side length [m]
Side length [m]
Density [kg/m2]
Turning radius [m]
Moment of inertia [kgm2]
a:
b:
L:
p:
JA:
Side length [m]
Side length [m]
Side length [m]
Density [kg/m2]
Moment of inertia [kgm2]
b
A
Legend
JA
A = Dividing axis
a
B = Tilting axis
R = Radius between tilting axis and spindle nose of dividing
axis [m]
Rs = Distance to the centre of mass [m]
m = Mass [kg]
M = Torque calculated from m x g x Rs [Nm]
Me = Torque acting on the tilting axis caused by the dead
weight of the tilting axis [Nm]
g = Acceleration due to gravity 9.81 [m/s2]
πD2
x Lp
4
mD2
πD2
2
8
LL
A
aaL
r
JA =
1
m (D2 + d2)
8
πD2
b
b
b
)(
x Lp -
πd2
4
1
m (a2 + b2 + 12r2)
m = abLp
JA =
1
12
)
x Lp
m = abLp
12
JJAA
JA
a
(
JA =
JJAA
JA
A
A
m=
4
a
rr
x Lp
4
mD
b
aaL
A
A
A
8
JA = J + m x r2
D:
Outside diameter of the
cylinders [m]
d: Bore diameter of the cylinder [m]
L: Length of the round bar [m]
p: Density [kg/m2]
m: Mass of the cylinder [kg]
Moment of inertia [kgm2]
JA:
a:
b:
L:
p:
r:
JA:
b
b
LL
D:
Outside diameter of the round
bar [m]
L: Length of the round bar [m]
p: Density [kg/m2]
m: Mass of the round bar [kg]
Moment of inertia [kgm2]
JA:
JJAA B
T1
A
Technology /
engineering
A
Calculation of loads and forces
M (a2 + b2)
Densities of different materials
x dynamic speed (p)
Iron
7.85 x 103kg/m3
Cast iron 7.85 x 103kg/m3
Aluminum 2.7 x 103kg/m3
Copper
8.94 x 103kg/m3
Brass
8.5 x 103kg/m3