Mathematical modelling and parametric evaluation of a detachable vibration-damping ergonomic handrail cover for railway shunters

Railway shunters ride on wagon footsteps and hold steel handrails amid coupling impacts, jerks and track-induced vibration. This study develops a two-degree-of-freedom model of a detachable cover clamped to a standard handrail without drilling or welding. Retaining cover-shell inertia gives coupled equations and closed-form transfer functions for the shell and an effective hand mass. Four 60-80 Shore A variants are evaluated under three idealized spectra. With adopted parameters, the hand-dominated mode is 22.6-25.1 Hz, compared with 25.2 Hz for the bare handrail, whereas the shell mode is 158-814 Hz. Two comparisons are required. The model-based biodynamic response ratio compares T 2 with the bare-hand response T b a s e and remains 1.00-1.07. The contact-surface ratio compares T 1 with bare-rail motion and, over the common 8-200 Hz validity band, is 1.00-1.06 after W h weighting and 1.00-1.48 without weighting. Thus, internal hand response, shell motion and an ISO 10819 palm-adapter output must not be treated as the same observable. A necessary stiffness condition, k c ≲ k s , is combined with the anti-rotation pressure constraint. For the assumed 2-3 MPa admissible pressure, the four variants would require approximately 12-78 MPa to reach that stiffness condition; this is a parameter-dependent feasibility result, not a universal impossibility proof. A minimax screen favours V4 within this band, but no full-band optimum is claimed. Engineering benefits remain anti-rotation retention, ergonomics and retrofit installation. A verification programme using paired rail/cover measurements, a separate standard glove test and a slip-torque test is proposed.