Laboratory
4
High-Speed Camera: Spring
Surge | MECH324
Dynamics of Machines |
OBJECTIVES:
- Gain experience taking measurements with a high-speed camera.
-
Investigate spring surge and a spring's natural frequency.
BACKGROUND:
Often, when we model spring-mass systems, we focus on the natural frequency
of the system as a whole but ignore the natural frequencies of the individual
components (i.e. assume the spring is massless). This assumption is fine for simple
analyses, but there are cases when the natural frequency of the spring itself
can affect the behavior of the entire system. For example, an engine's valve spring
used to help a valve better follow a cam can (adversely) influence the behavior
of the cam-follower system at high RPMs. At certain RPM ranges (typically very
high -- past the red line), the opening and closing of the valves can cause the
spring to "surge".
When
a helical spring is compressed and then released with nothing attached to its
ends, it will vibrate at its natural frequency laterally
(like a guitar string - see video)
and/or longitudinally (along the length of the spring). If the spring is fixed
at one end and driven at its free end by a pulsed or oscillatory force, the
spring may being to "surge." Surge refers to an elastic wave that travels
longitudinally through the spring. Surge can cause undesirable changes in spring
force as well as increased stresses in the spring material as the spring goes through a motion cycle. Spring surge can also result in "clash" between the coils if the surge has large enough amplitude and/or if significant compression occurs during a surge. Clash can cause noise, vibration, and surface damage (with accelerated fatigue).
Surge can often
be induced by harmonics of the natural frequency (whole number multiples or fractions
of fn). It has been found that harmonics up the thirteenth can
be significant in causing surge. Therefore, a rule of thumb is to have the spring's
natural frequency at least 13 times greater than the main driving frequency of
the system.
Typically, the natural frequency of a system (e.g., a spring
by itself) is given by:
For
a helical spring, the spring rate, k, is proportional to of the spring
wire diameter, d, spring coil diameter (to center of wire), D, the
number of active, non-supported coils, Na, and the gravitational
constant, G:
Similarly,
the mass of the spring is proportional to d, D, NA, and the density of
the material, ρ:
After
substituting: For
steel springs:
Hz (d and D in inches)
Hz (d and D in millimeters)
The
above frequency equations are for springs fixed at both ends. If only one
end of the spring is fixed, it behaves like a fixed-fixed spring of twice its
length. Thus, for a spring with only one end fixed, the frequency is 1/2
the value given by the above equations.
MATERIAL AND METHODS:
Because most springs that are commonly used in industrial/mechanical applications
are steel, are relatively short and have small diameters, it is usually difficult
or impossible to measure a spring's natural frequency with the naked eye.
As can be seen from the above equations, the natural frequency can be reduced
by increasing the number of coils involved (e.g., a longer spring), increasing
the diameter of the spring, decreasing the size of the wire, or using a material
with a low density. What fits these criteria? A Slinky,
of course!
- Holding the Slinky at both ends (fixed-fixed), pull back
a coil (in the longitudinal direction) and let her rip.
- Use a stop watch
to measure how long it takes for the wave to travel down the spring and back again.
- Now
hold only one end of the Slinky (free-fixed), pull back the other end, and let
go.
- Measure this frequency and compare it to the fixed-fixed situation.
- Holding
both ends again, drive one end back and forth at varying frequencies until the
Slinky begins to surge (the coils start to clash).
- Marvel at this phenomenon.
See
the slinky
video demo to see other slinky vibration effects.
Now, we will try to
visually measure natural frequency using a smaller, industrial/mechanical
spring (like those that are used in the cart
setup). However, springs of this size have such a longitudinally high
natural frequency that it can only be measured with a high speed camera.
We will be using a Kodak camera capable of taking 10,000 frames per second (normal
video cameras take 30 fps). The camera should already be set
up for you.
To get familiar using the camera, first measure the vertical scan
rate of a computer monitor. - Point the camera at a CRT monitor and adjust
the aperture and zoom.
- Assuming the scan rate is somewhere around 60 Hz
(depends on monitor and graphics card), choose a suitable frames per second.
- Measure
and record the amount of time it takes for a scan to go from the top to bottom
of the monitor.
Now that you're an experienced high-speed cinematographer,
measure the natural frequency of the spring. - Using calipers, measure
and record the wire diameter and coil diameter of the spring.
- Count the
number of active coils of the spring.
- Calculate the natural frequency
of the spring. Assume that both ends of the spring will be fixed.
- Adjust
the camera (aperture, focus) and light to capture the spring's vibration.
- Using
your kung-fu grip, hold both ends of the spring (or use a jig to attach both ends).
- Using
you fingernail, pencil, or the like, pull one of the spring's coils back (along
the axis of the spring) and release it.
- Get some footage.
- The
video should display the time as the frames advance. Measure how long it
takes for the wave to travel along the full length (there and back again) of the
spring.
- Use this period to calculate the frequency. Compare this frequency
to the predicted value.
- Now, hold/fix only one end of the spring.
- Pull
the other end back and release it. Here are some sample clips (shock
pulse, longitudinal
vibration)
- How does this frequency compare to the fixed-fixed case?
Unfortunately,
the natural frequency of this spring is too high to drive into surging with the
cart setup (since the carts can only be driven at a few hundred RPM before it
goes crazy). If you could use a different spring, how could you use the
cart setup to get a spring to surge? To see spring surge in IC engine valve springs,
see the clips online.
PLEASE
NOTE:
There is "homework" due for next week's lab, so
be sure to read next week's lab
to see what to turn in. This "homework" will form the basis for your
quiz and Lab scores next week. You can start this work with your group with the
extra time available this week in Lab. Use the time to brainstorm ideas with your
group. Clear your final ideas with the TAs first (before you leave) because
not all ideas will be suitable (or interesting) for filming with the equipment
we have. In general, the best things to film have large amplitude motion or effects
that happen too fast to see with the naked eye. Check out Dr. Dave's gallery
of high speed video clips if you're having trouble coming up with viable ideas.
ADDITIONAL
RESOURCES:
