Tire Vibration Explanation

At what speed should you balance your tires? Here's a little primer on tire vibration. First, it is necessary to understand that all solid bodies act as "spring/mass/damper" entities; that is, they have "natural frequencies" at which they will vibrate. To illustrate, imagine a 2X4 clamped horizontally by its end to a bench. Deflect the board downward a few inches and let it go; it will vibrate up and down at a constant frequency with gradually diminishing amplitude until it comes to a rest. The frequency at which it vibrates is its "natural frequency." The amount of movement at the end of the board is described as the "amplitude" of the vibration and is a function of the displacement used to deflect the board. The number of oscillations which the board goes through before coming to rest is an indication of the "natural damping" characteristics of the board. If the board is made of a dense wood which exhibits heavy damping, it will come to rest after just a few oscillations. If, however, the board is lightly damped, it will bounce up and down for quite a few oscillations before stopping.

If, next, we make a series of small, equal force inputs at regular intervals to the board, it will begin to oscillate at the frequency equivalent to the input force (termed the "forcing function"). If the wood is reasonably damped, it is able to dissipate the energy of the forcing function input at the same rate as the energy is input and will cause the oscillations to achieve and stabilize at a given amplitude, dependent on the amplitude of the forcing input. (Some materials, however, have very light damping, and it is possible for the amplitude to actually increase for a given sinusoidal input at the body's natural frequency; this will cause the amplitude of the body to keep increasing until structural failure.) All solid bodies, including your tires, exhibit these vibratory characteristics in both linear and rotational motion. In the case of your tires, the mass is essentially the weight of the wheel/tire/brake disk assembly, with lighter masses leading to higher natural frequencies. The spring constant of the assembly is a function of the tire pressure and suspension spring stiffness, with higher spring constant (stiffer springs or tires) also leading to higher natural frequency. The damping constant is primarily a function of the tire sidewall construction and the shock absorber damping factor; heavier damping tends to dissipate the vibration quicker but damping that is too heavy causes the vibratory loads to be transmitted back into the supporting structure (the car frame) rather than being dissipated as heat.

Many folks have a mistaken impression that if the wheel is out of balance, the amplitude of the vibration will get progressively worse as wheel rotational speed (the "sinusoidal frequency or period") is increased. I've heard tire shop gurus tell unsuspecting customers: "I spun it up to 120 mph and it balanced perfectly." The problem is that the vibrational amplitude does NOT increase linearly with an increase in frequency. The amplitude rather will increase as the tire/wheel approaches its natural frequency, then the amplitude will begin to decrease at a logarithmic rate as the rotational frequency increases further. Translated into English, that means that the amplitude of the vibration is zero at rest, increases to a maximum amplitude at its natural frequency (rpm), and then falls off rapidly as the frequency of rotation (rpm) increases. The amplitude of the vibration depends on several characteristics of the wheel/tire assembly; namely, the mass, the tire pressure (which affects the tire's "spring constant"), and the tire structure (which affects the tire's "natural damping"). Unfortunately, for 15 inch radial ply tires, the natural frequency most commonly falls at an wheel rotational frequency which equates to roughly 60 to 65 mph. This is why many folks seem to complain that their steering wheels start to shimmy at 60 mph and the shimmy seems to disappear at about 70. The vibratory amplitude decreases logararithmically with increasing rpm at a rate approaching 10 dB per 10 mph of speed increase, so that the vibratory amplitude at 80 may only be 1% of the amplitude at 60. That low level of vibration is not apparent to the average driver and explains why the guru was so successful at balancing the tire at 120 mph without really solving the initial problem of vibration at 60. The moral here is that the tire guru should be instructed to balance the tire for the speed at which the vibration is the worst (which for most cars usually happens around 65 mph) rather than at some elevated speed. If you find that your tires bounce the worst at 75, then this tire rpm is the natural frequency of your tires/wheels and the place where the vibation feedback will be greatest, so it makes sense to balance them at this speed. Hope this makes sense and helps.