The motor is supplied by the rated voltage. The motor is suddenly disconnected and the evolution of the speed is plotted during the free stop (Figure 11).

Figure 11

From now, we will consider the time origin at the instant t₀, respectively t₀ = 0.

Moment of inertia J. From the general equation of the speed in the instant of the disconnection

,

it results

.

The static torque in the instant of the disconnection T_s0 is due to only mechanical looses,

,

and the ratio dt/dW can be determined by tracing the tangent to the speed curve in the disconnection instant. It results

.

Finally it is obtained

,

because

.

The viscous frictions coefficientk_v. In the instant of the disconnection

,

so, it could be written

,

respectively

.

(1)

The general equation of the speed during the free stop

,

has the solution

,

with

,

(2)

the mechanical time constant.

By writing the general solution for the instant t = t_s, W = 0, it results

, respectively .

By expressing the dry frictions torque T_f from (1),

,

(3)

the previous equation becomes

.

For the left side of the previous equation, we take into account (1) and we obtain:

.

It results:

.

Taking also into account the expression (2) of the mechanical time constant, it results the equation:

,

(4)

In this equation, the unknown variable is k_v.

The equation (4) is non linear one, the form of the solution being

,

where W(a) is the W Lambert function. This is the inverse of the function . Its value for

,

results as solution of the equation

,

that could be solved by numerical iterations.

Finally, for the experimental values, is obtained

k_v = 0,003262 Nms.

Dry frictions torque T_f. It can be computed directly using (3). It results

T_f = 0,1 Nm.