Problem The intermediate shaft in the two-stage gearbox shown below is to be designed. The transmitted power is 100 kW through this shaft which is rotating at 2,500 rev/min. The dimensions are summarized in the table with variables corresponding to the figure. The gears have diameters d3 and d4, thicknesses tg3 and tg4, and both have a 20° pressure angle. The distance between bearings and gears are a, b and c. Input tos K = 2 g3 Input Shaft FE4 # ‒‒‒‒ → Intermediate Shaft Output Shaft k-tpt #10 Output Z d. d₂ a= b = C = d3 = tg3 = d₁ = tg4 = 350 200 250 300 50 200 50 mm mm mm mm mm mm mm Design the shaft with a minimum design factor of n = 4 for static yield and n = 1.5 for infinite life based on the Modified- Goodman criteria. Due to cost constraints, the mass of the shaft cannot exceed 25 kg (based on volume and density of the material you choose). The bearings and gears must be set against shoulders with steps of 1.2-1.5 D/d ratio, be fitted with appropriately size keyways (see Table 7-6), and all dimensions must be preferred sizes as listed in Table A-17 (you may use increments of 5 mm for sizes above 50 mm as well). Use the same bearing on both shaft ends, and reference Table 11-2 for basic bearing dimensions (diameter and width), ensuring that 3 times the "Cio" load rating for Deep Groove ball bearings is satisfied for the size you select Calculations showing the shaft passes both static failure and fatigue failure criteria for the specified design factor at multiple locations of potential high stress. Include a summary of the shaft mass. Be neat and clear in your methodology and results. Please provide some sample calculations and a results summary if you are submitting printed spreadsheet stress calculations. Make sure the spreadsheets are well labeled and easy to follow.