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Theoretical Relationships Contact Pressure The ring is pressed against the cylinder wall under a contact pressure p which is governed by the dimensions and total free gap of the ring and by the modulus of elasticity of the material used. The total free gap is defined as the distance, measured along the neutral axis, between the ends of a piston ring in its uncompressed state (Fig. 2).
A ring can be given a constant or a variable contact pressure [2, 3], the latter being a function of the angle (φ) (Fig. 3).
Measurement of the contact pressure is extremely difficult. Therefore, in practice it is calculated from the tangential force. This is the force which, when applied tangentially to the ends of the ring, is sufficient to compress the ring to the specified closed gap. By comparing the bending moment of the tangential force against that of the constant contact pressure, the following relationships are established (Fig. 4):
For the case when p is constant, e.g. the ring is compressed inside a flexible tensioning tape, the following expression can be derived for the bending moment M:

(1) 
The bending moment M can also be expressed in terms of the tangential force F_{t}:

(2) 
From (1) and (2)

(3) 


Fig. 2: Piston Ring Nomenclature
Fig. 3: Constant and Variable Contact Pressure of a Piston Ring
Fig. 4: Relationship between Constant Contact Pressure and Tangential Force 