Planetary gearboxes have parallel paths formed by planets sharing the input torque loads. Unequal load sharing among planets can lead to inefficiency and accelerated fatigue. To thoroughly reveal the fault signatures，this paper establishes a vibration signal model of the planets under different load distribution conditions. The derived Fourier spectrum illustrates the uneven distribution of the planet load can cause additional signal components and the shift of the natural frequency of the system. The spectral structure impacted by input torques and the severity of the planet position error is summarized. Numerical simulation and experimental results agree well with the proposed theoretical model.