A norm-coupling method of Tangential Friction Vibration (TFV) and Normal Friction Vibration (NFV) was proposed with the norm theory to solve the difficulty of completely reflecting the wear state feature of tribological pairs by friction vibration in a single direction. The feature of Norm-Coupling Friction Vibration (NCFV) was expressed with matrix 2-norms, and the variation in this feature was analyzed using a running-in process. Result indicates that the matrix 2-norms of friction vibration (M2NFV) can reflect the change in the wear state of tribological pairs in the running-in process. The M2NFV is large at the beginning of the running-in process, followed by a decline as the process continues, and finally, the process produces a stable and smooth fluctuation while reaching the running-in stage. The variation in M2NFV is in close agreement with the change in friction coefficient. Hence, the complete feature extraction of TFV and NFV by the norm-coupling method can reflect the variation in the wear state of the tribological pairs in the running-in process.
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