Development of a Process for Optimising the Number of Springs in Modular Elastic Gears of Rack Rail Pinion Systems for Vibration Data-Based Railway System Safety

Rack railway systems operating on steep-gradient routes rely on rack-and-pinion propulsion mechanisms that generate substantial vibrational excitation through cyclic gear mesh contact, adversely affecting passenger comfort and long-term mechanical reliability. Conventional integrated steel gears transmit propulsive forces without inherent vibration attenuation, and a systematic design methodology for optimising the internal rubber spring configuration of elastic gears for such applications has not been established. This study develops a kinematic spring-mass model for both conventional steel and elastic rubber gear configurations in a Korean rack railway propulsion system and validates it through controlled experimental testing. A high-speed rail–wheel contact simulator was employed to measure vertical vibrational accelerations under rigid–rigid (steel–steel) and rigid–resilient (steel–rubber elastic gear) contact conditions, with a load simulating steep-gradient operational forces applied to the gear assembly. The elastic gear achieved a 25.1-fold reduction in vertical vibrational acceleration relative to the steel gear baseline (6.4 m/s2 vs. 160.7 m/s2). Time-domain statistics (mean, RMS, standard deviation and peak envelope) are reported for both configurations from repeated runs. Analysis of the normalised effective stiffness as a function of the number of rubber springs predicts that four springs represent a practical optimum, beyond which the incremental stiffness change falls below 0.5%; experimental validation of intermediate spring counts is identified as future work. A spring-number optimisation framework is proposed that returns both a spring count and a rubber compound specification, balancing vibration attenuation against load distribution, torque-transmission capacity and component fatigue life.