|MEE Project: Vibration and Shock Isolation
|It is desired to abate the transmitted vibration and shock of a diesel generator installed in the engine room
of a large boat, from the machine to the hull and from the hull to the machine. This should be done without
|making the diesel generator experience excessive motion. The
machine runs at 1500 rpm.
|In a four stroke engine each cylinder fires
every other revolution, therefore the
|the diesel generator as a large, lumped mass|
|lowest frequency of vibration occurs at
1/2 the engine RPM often called the 1/2
|(2000 Kg, resembling a large 6 cylinder Diesel engine and
a 177 KVA generator mated to it) attached to the floor via
four spring-damper combinations resembling elastomeric
(rubber like) mounts. In your one degree of freedom
(dof) approximation, consider only one mount carrying
¼ of the mass of the diesel-generator.
|The higher order|
|harmonics of the1/2 order vibration, 1
order, 1-1/2 order, 2 order, … etc. will
also be present in the vibration
signature. Generator imbalance also
contributes to the 1 order vibration.
|1. Size the mount (find its stiffness) if the resonant|
|frequency of the engine+mount system is not to exceed 50% of the lowest excitation frequency of
the engine; use damping ratio of 5% (typical for natural rubber used in most mounts) to size the
|2. Construct the model of the engine+mount 1 dof approximation.|
|3. Considering the combustion force as the input to the engine, plot the frequency response function
(FRF) of the engine (mass) displacement as well as the transmitted force from the engine to the
|4. Make the FRFs2 of the systems equipped with mounts having damping ratios of 5%, 2.5% (less
than nominal damping of 5%), and 10% (more than nominal damping of 5%) damping. Plot the
magnitude of the FRFs on the same coordinates.
|Contrary to vibration perturbation that is|
|a. Would you use a mount with higher or|
|viewed as a sustained, repetitive forcing
lower damping ratio (same stiffness as
|input that makes the structure to vibrate at
before), if you like to lower the
|the forcing frequency, shock perturbation is
transmitted vibration to the hull?
|classified as a transient, abrupt, occasional|
|b. Would you use a mount with higher or
lower damping ratio (same stiffness as
before), if you like to lower the
transmitted shock from the hull to the
|input that makes the structure to exhibit
transient (decaying) vibration at its natural
frequency. Shock is normally defined by
a pulse, with a half-sine, amongst others,
defining the pulse shape. For example, the
Diesel generator running at a constant rpm
vibrates at the frequencies corresponding to
the harmonics of the running rpm. On the
other hand when the engine is turned on/off
or a wave hits the boat, the isolated
|5. Repeat the experiment of part 4, but this time use
a mount with the stiffness of K/2, K, and K*2
where K is the nominal stiffness calculated in
step 1; use the same damping ratio of 5% for all
|machine vibrates at its natural frequency.|
|6. As discussed in Appendix A, shock isolation
requirement in terms of damping and stiffness conflicts with the vibration isolation requirement.
Propose a feedback control scheme to address the conflict?
|Of force transmissibility, motion response, and relative transmissibility as presented in Appendix A|
|Vibration and Shock Isolation|
|Vibration and Shock isolation systems lower the transmission of vibration and shock between
two interconnected objects. Such systems are commonly realized by placing a set of resilient
elements such as elastomeric (rubber), steel, or air springs between the two objects isolated
from each other (e.g., a piece of equipment and its support structure/base).
|In addition to load-supporting (resilience), an isolation scheme has energy dissipating
attributes. In elastomeric isolators, made of natural or synthetic rubber, the load-supporting
and energy-dissipating tasks are commonly performed by a single element, i.e. the material
|Perturbing force, F|
|If an isolator has the resilience but lacks sufficient
energy-dissipating characteristics, e.g., metal
springs; then separate energy-dissipating means
(e.g., viscous dampers) are paired with the
|The spring-mass-damper system of Figure 1 is
commonly used as the one degree of freedom
representation of an isolated machine/equipment.
The mass M resembles a machine or equipment
being isolated and the pair of spring K and damper
C resemble the isolator.
|Figure 1 Schematic of an isolated
|The goal of a vibration isolation system is to isolate the support structure (base) from the vibration
of the mass caused by the perturbation force F, i.e., lowering the force transmitted to the base Ft,
while avoiding excessive motion of the mass, x. In addition, the vibration isolation system is to
isolate the mass (isolated machine/equipment) from the perturbing motion of the base.
|The effectiveness of a vibration isolation system intended to reduce the transmission of the|
|perturbation force (F) generated by the
machine/equipment to the base (Ft) is evaluated by
transmissibility. The design goal of an isolation
system is to reduce the magnitude of
|Transmissibility, defined by Ft/F, is a measure
of the reduction in a) transmitted force (from
the equipment to the base), provided by an
|transmissibility, over the frequencies of interest,|
|without inducing too much motion into the machine/equipment, itself; in other words, reducing the
magnitudes of transmissibility Ft/F and motion response x/F (or its dimensionless
representation, x/(F/K) ).
|The transmissibility transfer function mapping the perturbation force F to the transmitted force Ft,
i.e., F /F is
|The motion response transfer function mapping the force F perturbing the machine to the motion of
the machine x, i.e., x/F is.
|The effectiveness of a vibration isolation system
used to reduce the vibratory motion transmitted
from a vibrating base (x_base) to the
machine/equipment (x_rel ) is characterized by
Relative transmissibility x_rel/x_base . Note
that x_rel is the motion of the mass/equipment
relative to the perturbing motion of the base.
|Relative transmissibility, defined by|
|x_rel/x_base is the ratio of the relative motion
of the isolated machine/equipment with respect
to the base to the displacement of the base.
Note that the relative motion x_rel is also the
‘deflection’ of the isolator; it is a measure of the
working space required for the isolator.
|Shock perturbations excite all resonances in an isolated system. Therefore a shock isolation
system must be designed to dissipate considerable amounts of energy in a minimal amount of
time which can be done by incorporating a sizeable amount of damping into the isolation system.
That is, to enhance the shock isolation effectiveness, it is desirable for the isolation system to be
|Shock and Vibration Isolation|
|Soft isolators, such as air springs, perform very well as shock isolators; this is despite the
misconception that a good shock isolation system must be mechanically “stiff”. Note that a soft
system behaves as a mechanical low pass filter abating the high frequency components of shock
inputs making a negligible amount of this high frequency energy to get to the isolated mass.
However, the problem with a low frequency device is that shock inputs tend to a) excite the
resonance of the isolator and b) being a low frequency device results in significant deflections
that might be unacceptable due to working space limitations.
|Increasing damping is unfavorable to both the force and displacement transmissibility
under vibration inputs. However, large amounts of damping are required in a shock
isolation system. This is the classic trade-off in shock and vibration isolation system design.
A good compromise is to use a controllable damper that provides light damping in vibration
isolation mode, but can be turned on during a shock event to provide the large amounts of
damping necessary for controlling the effect of the shock input.