Probabilistic analysis of failed heavy duty hydraulic cylinders
 In properly designed hydraulic cylinders the contact between piston and bore is avoided by wear rings sometimes called guide rings. The load at which metallic contact occurs depends on the stiffness of the wear rings and the deformation to contact. The deformation to contact depends on the groove and ring dimensions according rclearance = dgroove/2 + wring - Dpiston/2.Deterministic approach: The worst case combination of dimensions at which metallic contact at design load can be expected is a safe method, but results in a nominal large radial clearance required. Since a small nominal value of the radial clearance is profitable a probabilistic approach is assumed. Probabilistic approach: With all dimensions assumed to be normally distributed within the µ±3σ tolerance interval, the nominal radial clearance can be based on a probability of contact less than for instance 1%.
The 1% percentile of the radial clearance is calculated
 Diameter piston min  10-3 m max  10-3 m Diameter groove min  10-3 m max  10-3 m Ring thickness min  10-3 m max  10-3 m Diameter piston µ 10-3 m σ  10-3 m Diameter groove µ 10-3 m σ  10-3 m Ring thickness µ 10-3 m σ  10-3 m Radial clearance µ 10-3 m σ  10-3 m Radial clearance 1% percentile min 10-3 m max  10-3 m Radial clearance worst case min 10-3 m max  10-3 m Conclusion: The elastic deformation of the wear ring to contact is much larger than   could be expected on the basis of the worst case deterministic approach. www.tribology-abc.com