Yamaha YK-X Series, User Manual

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3-20
CHAPTER 3 Installation
6-2 Equation for moment of inertia calculation
Usually the R axis load is not a simple form, and the calculation of the moment of
inertia is not easy. As a method, the load is replaced with several factors that
resemble a simple form for which the moment of inertia can be calculated. The
total of the moment of inertia for these factors is then obtained.
The objects and equations often used for the calculation of the moment of inertia
are shown below. Incidentally, there is the following relation:
J (kgfcmsec
2
) = I (kgm
2
)
×
10.2.
1) Moment of inertia for material particle
The equation for the moment of inertia for a material particle that has a rota-
tion center such as shown in Fig. 3-14 is as follows:
This is used as an approximate equation when x is larger than the object size.
x
J=
Wx
g
2
(kgfcmsec
2
)
g : Gravitational acceleration (cm/sec
2
)
m : Mass of material particle (kg)
... (Eq. 3.1)
I= mx
2
(kgm
2
)
W : Weight of material particle (kgf)
Fig. 3-14
2) Moment of inertia for cylinder (part 1)
The equation for the moment of inertia for a cylinder that has a rotation center
such as shown in Fig. 3-15 is given below.
D
h
J=
ρπ
D h
32g
WD
8g
=
4 2
(kgfcmsec
2
)
... (Eq. 3.2)
I=
ρπ
D h
32
mD
8
=
4 2
(kgm
2
)
ρ
: Density (kg/m
3
, kg/cm
3
)
g : Gravitational acceleration (cm/sec
2
)
m : Mass of cylinder (kg)
W : Weight of cylinder (kgf)
Fig. 3-15