Conversion between Hz and Belt Tension in other Engineering Units

The relationship between Tension and Frequency is given by the following expression

T = 4 M L² F²

T = Tension in Newtons

L = Span Length in metres

F = Frequency in Hz (as measured on the CLAVIS meter)

M = Mass per unit length of the belt, in kg/metre

For a 4 rib alternator belt as fitted to CE-14 diesel, the weight of the belt is 0.103kg. The length of the belt is 1.038m, therefore

M = 0.103/1.038

M = 0.1

For a 5 rib alternator belt as fitted to BE146, the weight of the belt is 0.096kg. The length of the belt is 0.868m, therefore

M = 0.096/0.868

M = 0.11

Example 1 - BE146

Setting frequency is 220Hz. What is the tension in lbs?

Top span length is 0.17m (where the frequency measurement was taken).

Mass per unit length is 0.11 for a 5 rib belt

T = 4 x 0.11 x (0.17 x 0.17) x (220 x 220)

T = 610N

To produce results in kg force divide by 9.81

T = 610/9.81 = 62 Kgf

To produce results in pound force, convert the kgf reading by multiplying by 2.2

T = (610/9.81) x 2.2 = 136.4 lbs

Example 2 - BE146

Setting tension is 140lbs. What should the frequency be?

140 lbs = 140/2.2kg = 63.6kg

63.6kg = 63.6 x 9.81N = 624N

T = 4 M L² F²

We know that the span length (ie. the distance between the point of contact on one pulley, to the point of contact on the second pulley) is 0.17m, that the mass per unit length of a 5 rib belt is 0.11kg/m, and the setting tension is 624N. Therefore:

624 = 4 x 0.11 x (0.17 x 0.17) x F²

F² = 624/ (4 x 0.11 x 0.17 x 0.17)

F² = 49,072