Division 3: DEFINITION OF FREQUENCY AND DAMPING - Council Directive 96/53/EC of 25 July 1996 laying down for certain road vehicles circulating within the Community the maximum authorized dimensions in national and international traffic and the maximum authorized weights in international traffic

In this definition a sprung mass M (kg) above a driving axle or bogie is considered. The axle or bogie has a total vertical stiffness between the road surface and the sprung mass of K Newtons/metre (N/m) and a total damping coefficient of C Newtons per metre per second (N.s/m). The vertical displacement of the sprung mass is Z. The equation of motion for free oscillation of the sprung mass is: $M \frac{d^{2} Z}{{dt}^{2}} + C \frac{d Z}{dt} + kZ = 0$

The frequency of oscillation of the sprung mass F (rad/sec) is: $F = \sqrt{\frac{K}{M} - \frac{C^{2}}{{4M}^{2}}}$

The damping is critical when C = C_o,

where

C_{o} = 2 \sqrt{KM}

The damping ratio as a fraction of critical damping is $\frac{C}{C_{o}}$ .

During free transient oscillation of the sprung mass the vertical motion of the mass will follow a damped sinusoidal path (Figure 2). The frequency can be estimated by measuring the time for as many cycles of oscillation as can be observed. The damping can be estimated by measuring theheights of successive peaks of the oscillation in the same direction. If the peak amplitudes of the first and second cycles of the oscillation are A₁ and A₂, then the damping ratio D is;

D = \frac{C}{C_{o}} = \frac{1}{2π} \times \ln \frac{A_{1}}{A_{2}}

‘ln’ being the natural logarithm of the amplitude ratio.

Division 3 DEFINITION OF FREQUENCY AND DAMPING