ASSESSMENT OF THE STRESS-STRAIN STATE OF TORSION BARS OF VEHICLE SUSPENSIONS UNDER VARIABLE LOADS

Abstract

This paper presents a numerical analysis of the stress-strain state of a torsion bar with a diameter of 40 mm and a length of 1200 mm for a light armored vehicle suspension under variable loading conditions using the finite element method in a three-dimensional formulation. The torsion bar is the primary elastic element of the suspension system, providing a spring connection between the wheel and the vehicle frame through elastic torsion of a steel rod. The computational model includes the cylindrical section, spline connections (z = 12, module m = 2.5 mm), and fillet transitions with a radius of 3 mm, discretized using Hex20 isoparametric elements with a total of 284,000 nodes. The element size in stress concentration zones was set to 1.5 mm (d/27), ensuring accurate calculation of maximum stresses. The analysis was performed for steel 45KhN2MFA (σ₀.₂ = 1600 MPa, τ₋₁ = 700 MPa, G = 80 GPa) under a load spectrum of T = 6, 8, 10, 14 kN·m with relative frequencies of 0.55/0.25/0.15/0.05, respectively.

It was established that maximum shear stresses τmax = 1247 MPa occur in the spline connection roots at T = 10 kN·m, corresponding to a stress concentration factor Kτ = 1.57. In fillet transitions, Kτ = 1.37. The torsional stiffness is cφ = 50.3 kN·m/rad and decreases by 5.3% when heated to 150 °C due to a 5% reduction in the shear modulus. Thermal stresses in the temperature gradient zone (∆T = 35 °C) do not exceed 45 MPa, which is less than 6% of mechanical stresses.

Fatigue life assessment using the Palmgren–Miner linear damage accumulation hypothesis for a spectrum with cycle asymmetry coefficient R = 0.15 showed accumulated damage D = 7.37, indicating resource exhaustion under the full load spectrum with a total duration of 4×10⁶ cycles. The greatest contribution to damage accumulation (73%) comes from the fourth load level T₄ = 14 kN·m, which occurs only 5% of operating time. To ensure D ≤ 0.7, limiting the maximum load to T ≤ 10 kN·m or using steel 60S2A with shot peening (τ₋₁,R = 680 MPa), yielding D = 0.68, is recommended. Comparative analysis of five bar sizes (d = 32, 38, 40, 48, 55 mm) showed that adequate fatigue life under the full load spectrum is provided by bars with diameters of 48 mm and above. FEM model verification showed deviation from the analytical solution for the cylindrical section of no more than 1.2%. The results can be used in designing new suspension systems and predicting the residual life of torsion bars in operation.