Question

1. Consider the lathe machine tool shown in the figure below. For a simplified vibration analysis, the lathe bed can be considered as a rigid body having mass and inertia, and the headstock and tailstock can each be replaced by lumped masses. In addition, the bed can be assumed to be supported on springs at the ends as shown in the figure below. Derive the equation of motion in matrix form using the deflection $x(t)$ of the C.G. and rotation $\theta(t)$ using Newton's second law of motion. (20 points) Headstock Live center Dead center Tailstock Bed C.G. m, $J_0$ A B k1 $l_1$ $l_2$ k2

          1. Consider the lathe machine tool shown in the figure below. For a simplified vibration
analysis, the lathe bed can be considered as a rigid body having mass and inertia, and the
headstock and tailstock can each be replaced by lumped masses. In addition, the bed can
be assumed to be supported on springs at the ends as shown in the figure below. Derive
the equation of motion in matrix form using the deflection $x(t)$ of the C.G. and rotation
$\theta(t)$ using Newton's second law of motion. (20 points)
Headstock Live center Dead center Tailstock
Bed
C.G.
m, $J_0$
A
B
k1
$l_1$
$l_2$
k2

1. Consider the lathe machine tool shown in the figure below. For a simplified vibration
analysis, the lathe bed can be considered as a rigid body having mass and inertia, and the
headstock and tailstock can each be replaced by lumped masses. In addition, the bed can
be assumed to be supported on springs at the ends as shown in the figure below. Derive
the equation of motion in matrix form using the deflection x(t) of the C.G. and rotation
θ(t) using Newton's second law of motion. (20 points)
Headstock Live center Dead center Tailstock
Bed
C.G.
m, J0
A
B
k1
l1
l2
k2

Added by Dennis L.

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