Motorcycle Vibrations and Natural Frequencies

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Kevin Cameron (Robert Martin/)

For late-model motorcycles vibration is no longer an issue, for in so many designs, vibration is canceled at its source: the rapid up-and-down motions of the piston(s) in their bores. Balance shafts are a fine thing because in addition to removing a major source of discomfort and fatigue from motorcycling, they actually save weight by making unnecessary the heavy chassis members that were once necessary to survive the fatigue resulting from engine shaking forces. Back in the day experienced mechanics knew just where to look for each model’s “signature” fatigue cracks; a coil bracket here, a license plate holder there.

Complaints of vibration most often took the form of “It’s not so bad around town, but when you get to 55 or so it’s really shaking. Then above 60-65 or so, it smooths out.”

Smooths out? How can that be? Do the pistons somehow move back and forth more softly above 65 mph? Of course not, and one day at MTS (Minneapolis Testing Service) motorcycle innovator and (later) career F1 engineer Robin Tuluie showed me how such come-and-go vibration works.

In one of the many MTS labs, Robin had a 750 Yamaha set up on a two-post shaker. That means that each wheel was resting on a pad backed by a vertical hydraulic piston that could be driven up and down at various frequencies and amplitudes. Such shaker rigs, often with many more posts, have greatly simplified, made more accurate, and shortened the testing of all kinds of vehicles (F1 cars included).

All structures are flexible to some degree. The combination of flexibility, essentially a spring, plus a mass produces an oscillator which vibrates at an inherent natural frequency. The obvious example is a tuning fork. A common motorcycle example of such a spring-and-mass system is the 7/8-inch-diameter steel tube handlebar. For mass, it has the hand levers, throttle, mirrors (if any), and switches or other controls at each end. The spring is the bar itself and its mounting.

On Kawasaki’s 1972-75 H2 750 triple, crankshaft vibratory motion is like that of a double-bladed kayak paddle, each end sweeping out a circle but with the center hardly moving at all. Transmitted to the handlebars through the chassis, this would become very noticeable and unpleasant when engine rpm came into step with the natural frequency of the flexible bars. The solution was to place substantial weights inside the handlebar ends, reducing the natural frequency of that system enough that the normal range of engine speeds no longer excited it. Now the hands no longer become numb in minutes.

Yet it is systems like this that produce “vibration periods”—vibrations that at some engine rpm intensify, then peak, and at higher revs yet, die away as the engine’s exciting frequency rises above the natural frequency of whatever is vibrating.

The MTS two-post shaker showcased the front wheel whip that was so pronounced on classic British parallel twins and on Harley’s Sportster. Back when fork tube diameter was around 35mm (1-3/8 inches) fork tubes were more flexible than today, and the mass in that system was the front wheel plus the brake and fender. Both of those engine types were “overbalanced” to take most of their vibration out of the easily perceived up-and-down direction (numb bum) and redirect it to fore-and-aft shaking, which is less felt by the rider. At an idle speed of around a thousand rpm, that fore-and-aft engine shaking force came into step with the fork tubes and wheel system’s natural frequency, causing the front wheel to visibly shake forward and back. As you accelerated away from rest, engine rpm rose too high to excite this shaking and it died out.

When I rode one of BMW’s large flat twins a number of years ago, I noticed a buzz as I rolled along a country lane. Wondering whether this was a basic engine vibration or just a sympathetic vibration of some part of the bike, I rode to a place where I could accelerate to higher speeds. The buzz I felt did not go away, but increased steadily in severity with engine rpm, telling me this was not going to “smooth out” at some speed. It was inherent to the engine itself.

I was therefore not surprised a year of two later when BMW added a balance shaft to its growing flat twins. What was the source of the vibration in such a naturally smooth engine? It’s naturally smooth because its pistons always move opposite one another, canceling their primary shaking force. The source of the buzz I’d felt was that the engine’s two connecting rods, being phased at 180 degrees to each other, must be offset one ahead of the other by just under 2 inches so they don’t hit each other. Because of that offset, each time the pistons decelerated to BDC they slightly rotated the engine one way around a vertical axis through its center of mass. When they decelerated to TDC 180 degrees later, they yanked it the other way.

This had not been a problem at the lower piston weight and rpm of earlier 500cc flat twins. But as displacement and higher rpm were added to lift performance, piston weight and inertia loading had risen to the point where the oscillation I had felt had to be canceled by a balancer.

Major manufacturers have their own vibration test equipment and keep up to date on the level of vibration that riders regard as reassurance that their motorcycle is still a real machine, versus the level that would be rejected as unacceptable. Classic British twins had no balance shafts because more vibration was tolerated in their time. But the similar middleweight parallel twins now being built by many makers are well-smoothed by balancers.

Put your prototype bike on the shaker and make a frequency sweep. Its various flexible parts become blurred as they come into resonance, reappearing as the rising frequency goes out of step with their motions. Many engineers now refer to certain parts by their natural frequencies. All this work adds up to more comfortable riding, fasteners that stay tight, and less fatigue after a day’s ride.

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