Yamaha YK180X, YK120X owner manual When the objects center line is offset from the rotation center

CHAPTER 3 Installation

5)When the object's center line is offset from the rotation center.

The equation for the moment of inertia, when the center of the cylinder is offset by the distance "x" from the rotation center as shown in Fig. 3-16, is given as follows.

I=

J=

=

ρπD 4h			+	ρπD2 hx2		=	mD	2	+ mx2 (kgm2)
32					4		8
ρπD4 h		+		ρπD2 hx2
32g					4g
WD2	+		Wx 2		(kgfcmsec2)
8g			g						h
						... (Eq. 3.5)

ρ: Density (kg/m3, kg/cm3)

g: Gravitational acceleration (cm/sec2) m : Mass of cylinder (kg)

W : Weight of cylinder (kgf)

Center line

Rotation center

D

x

Fig. 3-16

In the same manner, the moment of inertia of a cylinder as shown in Fig. 3-17 is given by

ρπ D 2h

(

D 2

h2

) +

ρπ D 2 h x 2

m

D 2

h

2

) + mx2 (kgm2)

I=

+

=

(

+

16

4

3

4

4

3

4

J=

ρπ D2 h

(

D 2

+

h 2

) +

ρπ D 2h x 2

16g

4

3

4g

Cneter line

D 2

h 2

Wx 2

W

=

(

+

) +

(kgfcmsec2)

4g

4

3

g

... (Eq. 3.6)

D

x

h

Fig. 3-17

In the same manner, the moment of inertia of a prism as shown in Fig. 3-18 is

given by

I=	ρabc(a2 + b2 )		+ ρabcx2=					m(a2 +b 2)	+ mx2 (kgm2)
	12						12
									Center line
	ρabc(a2 + b2 )				ρabcx2
J=			+
	12g				g
=	W(a2 + b2 )	+		Wx2		(kgfcmsec2)
	12g				g				c
							... (Eq. 3.7)		b

x

a

m: Mass of prism (kg)

W : Weight of prism (kgf)

Fig. 3-18

3-26