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Theoretical Relationships The greatest stressing of the ring occurs during assembly, as the ring must be stretched open sufficiently to enable the inner contour to slip over the outer diameter of the piston.
σ = the stress in the outermost element ρ_{1} = radius of curvature of the unstressed ring ρ_{2} = radius of curvature of the stressed ring, measured at the same point a more convenient expression for the opening stress was derived, since the solution to the mathematically exact relationship would be too complicated. The constants in equations (12) to (15) were determined by means of computed tables and assure a high degree of conformity between the equations in the stated form and the exact solution: The following applies to rings of rectangular cross section: 1. Opening the piston ring solely under tangential force: (12)
and k = piston ring parameter (equation 10) 2. Opening the piston ring by means of a sleeve:
k = piston ring parameter (equation 10) d_{H }= diameter of sleeve The following applies to slotted oil control rings: 1. Opening the piston ring solely under tangential force:
2. Opening the piston ring by means of a sleeve:
l_{u} = moment of inertia of the unslotted cross section l_{s} = moment of inertia of the slotted cross section l_{m} = x_{2} = twice the distance between centre of gravity and inside diameter k = piston ring parameter (equation 10) d_{H} = diameter of sleeve 



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