With rapid development in electronics and microelectromechanical systems (MEMS) technology, it becomes possible and attractive to monitor rotor dynamics by directly installing MEMS accelerometers on rotors. This paper studies the mathematical modelling of the orthogonal outputs from an on-rotor MEMS accelerometer and proposes a method to eliminate the gravitational acceleration projected on the measurement axes. This is achieved by shifting the output in the normal direction by π/2 using a Hilbert transform and then combining it with the output of the tangential direction. With further compensation of the combined signal in the frequency domain, the tangential acceleration of the rotor is reconstructed to a high degree of accuracy. Experimental results show that the crankshaft tangential acceleration of a reciprocating compressor, obtained by the proposed method, can discriminate clearly between different discharge pressures and hence can allow common leakage faults to be detected, located and diagnosed for online condition monitoring purposes.