THK ET20 Series, Manual

Page: 19 / 28

Technical Materials
Moment of Inertia for a Cylinder
Moment of Inertia for a Rectangular Solid
Calculating Torque in Horizontal Applications (Installed from the Bottom Surface)
Moment of Inertia for a Hollow Cylinder
Moment of Inertia for an Object with Different Centers of Rotation and Gravity
Outer diameter:
D
(m)
Length:
L
(m)
Mass:
m
(k g )
Density:
ρ
(k g /m
3
)
Outer diameter:
D
1
(m)
Inner diameter:
D
2
Length:
L
(m)
Mass:
m
(k
g
)
Density:
ρ
(k
g
/m
3
)
Depth:
A
(m) Width:
B
(m)
Height:
C
(m) Mass:
m
(k
g
)
Density:
ρ
(k
g
/m
3
)
If
I
is less than the permissible moment of inertia, the product can
be used.
If I
is greater than or equal to the permissible moment of inertia, the
product cannot be used. Please select a different model or reduce
the mass or rotational radius.
For the permissible moment of inertia for each model, please consult
the "Angular Velocity versus Permissible Moment of Inertia" graph.
I
: Moment of inertia (k g ·m 2 )
ω′
: Angular acceleration (rad/s 2 )
Please ensure a safety margin of 1.5 or greater.
Example) External torque (friction torque)
External torque =
μ
・
m
・ g ・
r
m
:
Workpiece mass (k
g
) g : Gravitational acceleration (m/s
2
)
μ
: Friction coefficient ET20: 0.020
r
: Rotary table radius ET20: 29 (mm)
ET35: 0.017 ET25: 34 (mm)
Confirm whether or not the calculated torque satisfies the requirements for the maximum
output torque for the model.
If
T
1
is less than the maximum output torque, the product can be used.
If T
1
is greater than or equal to the maximum output torque, the product cannot be used.
Please select a different model or reduce the mass or rotational radius.
For the maximum output torque for each model, please consult the "Angular Velocity
versus Output Torque" graph.
Calculating Torque in Horizontal Applications (Installed from a Side Surface)
m
: Workpiece mass (k g ) g : Gravitational acceleration (m/s
2
)
r
: Radius (m)
I
: Moment of inertia (k g ·m 2 )
ω′
: Angular acceleration (rad/s
2
)
Please ensure a safety margin of 1.5 or greater.
Confirm whether or not the calculated torque satisfies the requirements for the
maximum output torque for the model.
If T
2
is less than the maximum output torque, the product can be used.
If T
2
is greater than or equal to the maximum output torque, the product cannot be
used.
Please select a different model or reduce the mass or rotational radius.
For the maximum output torque for each model, please consult the "Angular
Velocity versus Output Torque" graph.
T
2
= (
m
·
g
·
r
+
I ω
' +
external torque
)
× safety margin
(Rotational radius)
r
m (Workpiece mass)
g (Gravitational
direction)
Ix
Iy
1
–
8
m ( + )
π
–
32
= =
ρ · L · D 4 m · D 2
=
1
–
4
D 2
–
4
L 2
–
3
=
[k
g
·m 2 ]
[k
g
·m 2 ]
Ix
Iy
1
–
8
m ( + )
π
–
32
=
ρ · L · (D
1
4 − D
2
4 ) m ( D
1
2 + D
2
2 )
=
1
–
4
D
1
2
+
D
2
2
–
4
L 2
–
3
=
=
[k
g
·m 2 ]
[k
g
·m
2
]
Iy
Ix
1
–
12
m ( A 2 + B 2 )
=
1
–
12
m ( B 2 + C 2 )
=
1
–
12
=
ρ · A · B · C ·( A 2 + B 2 )
1
–
12
=
ρ · A · B · C ·( B 2 + C 2 )
[k
g
·m 2 ]
[k
g
·m 2 ]
Ix
1
–
12
=
:
: ρ · A · B · C m
l Distance between X and X
0
(center of rotation X
0
)
(m)
[k
g
·m
2
]
m
(
A
2 +
B
2 + 12·
l
2 )
T
1
= ( I × ω ' + external torque ) × safety margin
Rectangular solid:
Depth
A
(m), height
B
(m), width
C
(m), mass
m
(k
g
)
Cube:
Depth
A
(m), height
A
(m), width
A
(m), mass
m
(k g )
Density:
ρ
(k g /m 3 )
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