The crank is much heavier than stock. More than 10 lbs. There is no perceptible loss of response and the motor is extremely smooth. In my experience, lightweight cranks are of little benefit at the RPM levels of a Norton. Particularly with a streetbike where a lightweight crank just increases the vibration and stress on the cases and anything else bolted to the motor.
Thanks Jim.
Considered independently, a crankshaft has at least 4 different dynamic modes which needs to be considered: Bending dynamics in two axes and torsional dynamics are the most important ones. First order bending mode eigenfrequency is governed by sqrt(c/m) were m is the crankshaft mass and c the spring stiffness of the shaft. Now, you have increased both.
c = 48*E*I/L^3.
I ~ pi*d^4/64, assuming I is governed by journal size only (a very coarse simplification).
Since your d increased from 1.75" to 2", d_new = 1.143*d_old
I_new = 1.493 * I_old
Since E and L are as before,
c_new = 1.493 * c_old.
m_new ~ 1.417 * m_old (an approximation, comparing with a standard crankshaft)
Therefore,
f_new = sqrt(1.493 / 1.417) * f_old = 1.026 * f_old
However, if c_old was to be kept and the mass reduced from 24 lb to say 19.2 lb (-20%), then
f_light = sqrt(1/0.8) * f_old = 1.118 * f_old
Which supports your statement that bending mode vibrations will increase, the increase is not dramatic however. I have assumed you referred to vibrations in the vertical plane.
The crankshaft noes not vibrate on its own. Supported by the crankcase, we may model the system as a two-mass vibrating system (keeping the isolastic supports out of the discussion for now). Combustion exerts harmonic forces onto the crankshaft, which is thought as being supported on very stiff springs at another mass located in the center of the bearing. This mass condenses weight of the crancase between the bearing and the nearest engine support. The latter mass is then supported by weaker springs towards the reference "ground", i.e., the the nearest engine support, considered to be non-moving.
We are now looking at the excitation of the crankshaft itself, i.e., the first mass of the two.
The eigenfrequency or the nearest higher order frequencies (n=2,3,4) is a problem only if it's getting close to the combustion force excitation frequency. The lowest exitation fequency f_exc is at 900 rpm = 15 Hz.
Assuming the crankshaft is homogeneous, which it isn't of course, the bending mode eigenfrequency calculates to f_old ~ 400 Hz. The real frequency may be half that figure.
Stress amplitude in the crancase is a function of the frequency ratio f/fc, where fc is the lowest eigenfrequency of the crankcase.
We have a case of base excitation, where the crankshaft is the "base".
http://www.brown.edu/Departments/En...Notes/vibrations_forced/vibrations_forced.htm
A calculation estimate showed that fc = 1500 Hz approx.
Since f_old / fc = ~0.25, the amplitude diagram shows that amplitude amplification is about 1.0 (see left part of the diagram), hence there will be no larger displacement and therefore np additinal stress in the crankcase as crankshaftmass is varied. Inclusion of c/shaft bolt weakness and structural damping will not alter these considerations.
In plain english, we find that for the bending spring associated with the first mass, the excitation force fails to excert the crankshaft within the domain of allowable revs. The harmonic force passes through the bending action spring (there might be a phase change) onto the second mass which is supported by a stiffer spring governed by the tensile stiffness of aluminum.
We find that the crancase will not be affected by resonance. If fc=1500 Hz is accurate, the highest ratio f_exc/fc = ~ 0.1 at maximum rpm which means the crankcase will act as a solid lump. This does not mean that certain less stiff parts like cooling fins can't enter into a resonant mode.
Thus we find that neither excitatin by harmonic combustion forces nor dynamic coupling will induce crancase vibrations.
In reality the estimated frequencies will be lower due to structural damping within the material itself, and (for the crankshaft additionally) due to friction in case a bolt-up crankshaft is examined. The analysis above neglects the effect of the clamped barrel and cylinder head.
In a second post I will look at the static balance forces of the crankshaft and the crankshaft weight dependency.
-Knut
. I'm too busy trying to get the race bike ready for El Mirage on the 21st. Maybe next year.