Analysis of minimum zone sphericity error using minimum potential energy theory

Theoretical derivation of the minimum zone criteria of sphericity error based on the principle of minimum potential energy is proposed. All the measured data points are enclosed by two concentric spherical surfaces between which a fictitious spring is assumed to be placed. These two concentric spherical surfaces can be mathematically determined by five active data points. When the spring contracts, the potential energy of the simulated mechanical system tends to reduce which yields two new concentric spheres with smaller radial separation and new active data points. Finally, a stable state will be reached to the condition of minimum potential energy. The criteria conforming to such a state can be derived. A direct search scheme to the global minimum solution is also proposed. The clearance between such two concentric spherical surfaces is the minimum zone of spherical form error.