Load Determination:
[Given]:
(1) geometry of the object or device is given
(2) location of the mass center of each link is given
(3) Given input force or moment
Solving the Problem:
(1) Free-body diagram for each member
(2) Setup equations for each member
For 2D problems:
--- 2 force equations
--- 1 moment equation
For 3D problems:
--- 3 force equations
--- 3 moment equations
For static problems:
--- Sum of forces = 0
--- Sum of moment = 0
For dynamic problems:
--- Sum of forces = m*a
--- Sum of moment = I*a
Vibration Loading:
--- Finite Element Analysis (FEA)
--- Boundary Element Analysis (BEA)
Undamped Natural Frequency:
Period of the natural frequency:
Tn = 1/ fn
Spring Constant (k):
Fs = k * d (for linear spring)
\ k = Fs ¤ d
Where
Fs º spring force
d º deflection of the spring
Damping Coefficient (d, or C):
where
Damped Natural Frequency:
(For 1 DOF free or forced vibration)
(Free Vibration)
rad/s
Hz
Dynamic forces:
(Avoid Resonance)
Impact Loading:
--- the time of load application is less than half of the period of the natural frequency of the system.
(Apply load slowly --- static load)
(Apply load rapidly --- impact load)
(1) Striking Impact --- actual collision of two bodies. (hammering)
(2) Force Impact --- suddenly applied load with no velocity of collision. (friction clutches and brakes)
Energy Method:
Elastic energy:
Treat the struck body as spring effect.
\
The impact kinetic energy: (for horizontal impact)
where
h º correction factor for energy dissipation
vi º impact velocity
Therefore,
Þ (dynamic force)
Static force: W = k * dst
\
For vertical impact from a height of h:
The impact energy: E = mg (hh + di )
= W (hh + di )
Therefore, the dynamic force ratio becomes
Correction Factor for axial impact of a rod is:
where
mb º mass of the struck object
m º mass of the striking object