Concept explainers
In Ex. 14-5 use nitrided grade 1 steel (4140) which produces Brinell hardnesses of 250 core and 500 at the surface (case). Use the upper fatigue curves on Figs. 14-14 and 14-15. Estimate the power capacity of the mesh with factors of safety of SF = SH = 1.
EXAMPLE 14-5 A 17-tooth 20° normal pitch-angle helical pinion with a right-hand helix angle of 30° rotates at 1800 rev/min when transmitting 4 lip to a 52-tooth helical gear. The normal diametral pitch is 10 teeth/in. the face width is 1.5 in, and the set has a quality number of 6. The gears are straddle-mounted with bearings immediately adjacent. The pinion and gear are made from a through-hardened steel with surface and core hardnesses of 240 Brinell on the pinion and surface and core hardnesses of 200 Brinell on the gear. The transmission is smooth, connecting an electric motor and a centrifugal pump. Assume a pinion life of 108 cycles and a reliability of 0.9 and use the upper curves in Figs. 14-14 and 14-15.
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Shigley's Mechanical Engineering Design (McGraw-Hill Series in Mechanical Engineering)
- Use the general shaft layout given and determine critical diameters of the shaft based on infinite fatigue life with a design factor of 1.5. Check for yielding. Check the slopes at the bearings for satisfaction of the recommended limits in Table 7-2. Assume that the deflections for the pulleys are not likely to be critical. 10 in 500 lbf 75 lbf 8-in dia. Bearing at O 10.0" 500 lb d 75 lb Material 1040 Q and T 18 in Use the following shaft layout assuming a pulley transmits torque through a key and keyseat at location A to another pulley at location B. Assume the tensions in the belt at pulley Bare T₁ and T2, where T₁ is 15% of T2. NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. 10-in dia. 12 in T₂ 8.0⁰ T₁ 18.0" 10.0" I B pulley diameter = 8.0" Sut 113 kpsi T2 T1 pulley diameter = 10.0" Sy 86 kpsi 12.0" Bearing at C Using the DE-Goodman criteria and a design factor of 1.5, calculate the diameter based on the shaft's loadings…arrow_forward2. At a machined shaft shoulder the small diameter d is 25mm the large diameter D is 40mm, and the fillet radius is 2.5 The bending moment is 2300N mm and the steady torsion moment is 1800 N mm The heat-treated steel shaft has an ultimate strength of Sut- 850Mpa The reliability goal is 099 (ka- 0.786, kb 0.870, ke 0.814) Determine the fatigue factor of safety of the design described in this sectionarrow_forwardFigure below shows a portion of a pump that is gear-driven at uniform load and speed. The 25 mm diameter solod shaft supported by the bearings is to be made of machined AISI 1045 CD steel. The helical gear is subjected to the axial force F-498 y a radial load F- 750 N and a tangential load of F-1.995 N. Assume the component is g at room temperature of 70F and the material has s0s reliability factor. Hint: Be careful when you calculate the bending moment at the fillet, as all the three forces on the helical gear cause bending moment at the fillet. Calculate resultant bedina moment from all the three forces. Bending moment is completely reversed loading.) 25-mm solid round shaft Fillet Bending K, = 2.0 Torsional k, = 1.5 Axial K,18 F. F, F Pump Helical spur gear -50 mm -250-mm dia FIGURE 1. Identify the critical locations) of stress and show it clearly in a diagram. 2 Identity cleary, all the components of stresses (at the critical point) that will be calcurated (by drawing and clearty…arrow_forward
- The rotating shaft shown in the figure is machined from AISI 1040 CD steel (sy = 490 MPa, Sut = 590 MPa). It is subjected to a transverse force of F = 8 kN between the supports. The system designed to be operated at a temperature of 120°C with a reliability of 99%. Estimate the number of cycles to failure. All dimensions are in mm. Assume all fillets are 3mm in radius. 25 D. 20 20 -35 D. 180- 3 R. 500 F 280 -175- -50 D. 25 D. | ª -20 20arrow_forwardUse the general shaft layout given and determine critical diameters of the shaft based on infinite fatigue life with a design factor of 1.5. Check for yielding. Check the slopes at the bearings for satisfaction of the recommended limits in Table 7-2. Assume that the deflections for the pulleys are not likely to be critical. 500 lbf 75 lbf 8-in dia. Bearing at O 500 lb d 10.0" 75 lb Material 1040 Q and T 18 in Use the following shaft layout assuming a pulley transmits torque through a key and keyseat at location A to another pulley at location B. Assume the tensions in the belt at pulley B are T₁ and T2, where T₁ is 15% of T2. NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. 10-in dia. 12 in T₂ T₁ The mean torque is 0 lb-in. The alternating torque is 2125 lb-in. The mean moment is 0 lb-in. The alternating moment is 5000 lb-in. 18.0" pulley diameter = 8.0" Sut 113 kpsi 10.0 B T2 T1 pulley diameter = 10.0" Sy 86 kpsi 12.0"…arrow_forwardRequired information The shaft shown in the figure is machined from AISI 1040 CD steel. The shaft rotates at 1600 rpm and is supported in rolling bearings at A and B. The applied forces are F₁ = 800 lbf and F2=1200 lbf. Determine the minimum fatigue factor of safety based on achieving infinite life. If infinite life is not predicted, estimate the number of cycles to failure. Also check for yielding -10 in- -10 is -fim All Gillets in R. What are the values of the theoretical stress-concentration factor, the notch sensitivity, and the fatigue stress-concentration factor? The value of the theoretical stress concentration-factor is The value of the notch sensitivity is. The value of the fatigue stress concentration-factor is [arrow_forward
- (4) An electric motor purchased by your employer surprisingly arrived without a keyway in the shaft. The motor has power rating of 7.5kW & 1,800rpm & has a shaft of Ø17mm. It will be used to drive a centrifugal pump using cast iron sheave. Design the square key to be used in the assembly based on maximum bearing & shearing stresses of 580MPa & 370MPa, respectively, and factor of safety of 5.arrow_forwardWhat is the fatigue-strength reduction factor for a shaft with an annealed sled-runner keyway under torsion if the notch sensitivity factor is 0.72?arrow_forwardA gear drive consists of a 16-tooth 20° steel spur pinion and a 48-tooth cast-iron gear having a pitch of 12 teeth/in. For a power input of 1.35 hp at a pinion speed of 700 rev/min, select a face width based on an allowable contact stress of 100 kpsi. Refer to table number 14-8 for elastic coefficient. The face width based on an allowable contact stress of 100 kpsi is in.arrow_forward
- A 76.2 mm diameter shafting of SAE 1040 grade, cold, rolled, having yield point of 50 ksi and with a ¾ x ¾ x 5 inches key. Compute the minimum yield point in the key in order to transmitt he torque of the shaft. The factor of safety to use is 2 and Sys = 0.5 Sy. (Ans: 47.12 ksi)arrow_forwardFigure below shows a portion of a pump that is gear-driven at uniform load and speed. The 25 mm diameter solod shaft supported by the bearings is to be made of machined AISI 1045 CD steel. The helical gear is subjected to the axial force F =499 y a radial load F = 741 N and a tangential load of F=2,006 N. Assume the component is operating at room temperature of 70°F and the material has 50% reliability factor. 25-mm solid Bending K, = 2.0 round shaft Fillet Torsional K = 1.5 F. F, Axial K, = 1.8 F Pump Helical spur gear 50 mm -250-mm dia.- FIGURE 1. Identify the critical location(s) of stress and show it clearly in a diagram. 2. Identify cleary, all the components of stresses (at the critical point) that will be calculated (by drawing and clearly showing the XYZ axes) and show it in a matrix form. Show which components of stresses will have a value zero or non-zero. 3. Calculate the principal stresses and principal directions. Show the principal stresses clearly in a stress element…arrow_forwardDesign a helical compression spring to be used in a cam and follower mechanism made of oil tempered carbon steel, to sustain a load, which varies from 400 N to 980 N. The spring index is 6.8 and the design factor of safety is 1.25. If the yield stress in shear is 770 MPa and endurance stress in shear is 350 MPa, find: 1. Size of the spring wire, 2. Diameters of the spring, 3. Number of turns of the spring, and 4. Free length of the spring. 5. Ks= shear factor 6. whals factor The compression of the spring at the maximum load is 30 mm. The modulus of rigidity for the spring material may be taken as 80 kN/mm:.arrow_forward
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