Springs: Design against Fluctuating Load DME- II Module 1: Helical Springs Problem 1 1. A helical compression spring of a cam-mechanism is subjected to an initial preload of 50 N. The maximum operating force during the load cycle is 150 N. The wire diameter is 3 mm, while the mean coil diameter is 18 mm. The spring is made of oil-hardened and tempered valve spring wire of Grade-VW (Sut = 1430 N/mm2). Determine the factor of safety used in the design on the basis of fluctuating stresses Data: πΉπππ₯ = 150 N πΉπππ = 50 N D = 18mm d = 3 mm Material: Oil-hardened and tempered valve spring wire of Grade-VW Sut = 1430 N/mm2 FOS = ? 1. Mean Stress and Stress Amplitude π ππ π« π π π Mean stress: ππ = π²πΊ Torsional stress amplitude: ππ = π² Spring Index πͺ = π« π = ππ π π ππ π« π π π =π Where, stress correction factor K is given by Equation- 11.2(a) Page 169 π²= ππͺ−π ππͺ−π + π.πππ πͺ = 4×6−1 4×6−4 0.615 + 6 π² = π. ππππ Shear stress correction factor: π²πΊ = π + π²πΊ = π + π²πΊ = 1.0833 π.π πͺ π.π π πΉπππ₯ + πΉπππ 150 + 50 π΄πππ πππππ: πΉπ = = = 100 π 2 2 πΉπππ₯ − πΉπππ 150 − 50 πππππ π¨πππππππ π: πΉπ = = = 50 π 2 2 Mean stress: ππ = π²πΊ π ππ π« π π π = π. ππππ π ×πππ ×ππ π ππ ππ = 183.91 N/mm2 Torsional stress amplitude: ππ = π² π ππ π« π π π = π. ππππ π ×ππ ×ππ π ππ ππ = 106.32 N/mm2 2. Factor of Safety For oil-hardened and tempered steel wires (SW and VW grade) πΊ′ ππ = π. ππ πΊππ = π. ππ ππππ = πππ. π π΅/πππ πΊπ = π. ππ πΊππ = π. ππ ππππ = πππ. π π΅/πππ ππ πΊππ − ππ ππΆπΊ π ′ πΊ ππ π = π πΊππ − πΊ′ ππ π π π πππ. π πππ. ππ = π πππ. π πππ. π − πππ. π − πππ. ππ π ππΆπΊ ππΆS = 1.26
