The analysis of vibration characteristics of transient unbalanced rotor response during acceleration is a prerequisite for transient dynamic balancing of rotor systems. Using a three-disk rotor system as the research object, a dynamic model of the multi-disk rotor was established based on the finite element method. Subsequently, 1000 sets of unbalance parameter combinations were uniformly sampled using the Latin hypercube sampling method. The vibration peaks near each critical speed of each disk were calculated, and the sensitivity contribution indices of each parameter were obtained and verified through experiments. The results show that the unbalance magnitude of each disk has a significant effect on the vibration peaks of all orders, with high contribution and mainly positive effects. In contrast, the unbalance azimuth shows low sensitivity to the first two order vibration peaks but has a significant positive contribution to the third-order vibration peaks. Particularly, changes in the azimuth of Disk 1 and Disk 2 cause the third-order peak response to fluctuate by more than 150%. Transient response simulations and experimental validation by varying the unbalance parameters of each disk demonstrate that parameter changes have the most significant effect on the vibration peaks near the critical speeds and the "pseudo-resonance" region. This study provides a theoretical basis for formulating transient dynamic balancing strategies for multi-disk rotor systems.