How do you avoid Vibrations?

Vibrations are ubiquitous in our life. Their importance
cannot be ignored even if we want to. e.g we do not want the vibrations from
tire movement of a moving car, travel to steering wheel. (Not that our road
conditions make it easy to ride…) The washer dryer in the house, are usually
kept in the basement to transmit all the vibrations to the floor.  Have you ever tried using the blender on a
plastic mount?   

 The general adage
is: Sensitive objects need to be protected from Vibrations. Isolators are used
in machine tools, photolithographic equipment, metrology equipment like
coordinate measuring machines. All external vibrations generate internal
vibrations in the working zone, for instance, between cutting tool and
workpiece, or CMM’s measuring stylus and part being measured.

One can open any design book and get a standard equation
for vibration.

f_n = ω_n / 2 π = (1 / 2 π) * √(k/m)

where k is system stiffness, m is the mass, and f is
natural frequency.

The above equation leads to the conclusion

(a)  Softer
isolaters transmit less vibration from support to object. Which means isolators
should be made of metal springs or lightly filled rubber.

(b)  The
object becomes sensitive to minor excitations. The practical aspect being,
machine tool tables reversing directions or repositioning of photolithography
tools.

Hence, it becomes important to make the isolating system
dynamic. One approach is to simply attach a stiff block onto isolator. But this
is an expensive approach, requiring floor space and lot of effort to move.

This leads to need for a dynamic damper, such that
damping offered is relative to applied frequency and stiffness of the
structure. E.g:  door dampers, or dampers
used in race cars.

Vibrations in these two cases are unidirectional (axial).
For more complex systems,(CMM machine, machine tools, photolithographic
equipment ) designers need to consider multi-directional vibrations.

SolidWorks Simulations can help design dampers. Users can
also uses standard built in functions to simulate the effect of a damper. SolidWorks
Simulation has the following damping models.

Modal
Damping : Modal
damping is defined as a ratio of the critical damping C_cr for each
mode. Critical damping C_cr is the least amount of damping that
causes a system to return to its equilibrium position without oscillating.

The modal damping ratio can
be determined accurately with proper field tests. The ratio varies from 0.01
for lightly damped systems to 0.15 or more for highly damped systems.

When experimental data is not
available, use data from a similar class of systems to determine the damping
properties. Smaller ratios are more conservative since higher ratios reduce vibration
amplitudes. In general, neglecting damping leads to a conservative estimate of
the system's response. The software has damping ratios for standard systems.

If designer knows the
stiffness of damping material. He can use a more realistic model (Rayleigh Damping) to compute effective
damping using combination of the mass and stiffness matrices.

Rajat Trehan

Product Manager - Design Validation

Computer Aided Technology Inc.