Magnabend Clamping Force:
The graph below was obtained by experimental measurements, but it agrees fairly well with theoretical calculations.
The clamping force can be mathematically calculated from this formula:
F = force in Newtons
B = magnetic flux density in Teslas
A = area of poles in m2
µ0 = magnetic permeability constant, (4π x 10-7)
For an example we will calculate the clamping force for a flux density of 2 Tesla:
Thus F = ½ (2)2 A/µ0
For a force on unit area (pressure) we can drop the “A” in the formula.
Thus Pressure = 2/µ0 = 2/(4π x 10-7) N/m2.
This comes out to 1,590,000 N/m2.
To convert this to kilograms force it can be divided by g (9.81).
Thus: Pressure = 162,080 kg/m2 = 16.2 kg/cm2.
This agrees rather well with the measured force for a zero gap shown on the above graph.
This figure can easily be converted to a total clamping force for a given machine by multiplying it by the pole area of the machine. For the model 1250E the pole area is 125(1.4+3.0+1.5) =735 cm2.
Thus the total, zero-gap, force would be (735 x 16.2) = 11,900 kg or 11.9 tonnes; about 9.5 tonnes per metre of magnet length .
Flux density and Clamping pressure are directly related and are shown graphed below: