Abstract: A new concept of the differential shear theory is presented, based on the study of process and result of the high pressure double roller cracker for brittleness material crushing. The existing of the differential shear force is proved through mathematical method, and the occurrence of shear force is proved to be related to the differential of compression speed of material passing the roller cracker at any moment. Further, it was explained what lumpy brittleness material passing the double roller cracker is crushed into caky powder, and the inherent law is revealed, of which high pressure double rolls cracker shears brittleness material continuously and densely. The nonlinear functions E(θ) and G(θ) related to the thickness, density and compactness of materials are obtained by experiment. The calculating formulas of the total force of running rollers acted on the layers of material and the power consumption are calculated by integration in the valid scope. The computer simulation of the mathematic model and experimental test of the physical prototype are applied to verify the calculation with the differential shear theory. The differential shear theory is practical and informative for product experiments and design, and with reference value for the mechanical study of rolling metal material and similar rolling process.

Key words: Mathematical model, Brittleness material, Crush, Differential shear, Double roller, High pressure, Flaw, Remanufactured motor rotor, Ultrasonic testing, Wavelet packet shannon entropy