Machine Design
Questions & Answers
1- Consider the shaft below. This shaft is rotating with a rotational rate of 500 rpm. All the dimensions shown are in millimeters. All the shoulders have fillets with a 2 mm radius. Assume the material used to make the shaft is cold-drawn AISI 1020. Assume the keyseats have dimensions of r/d = 0.02 at points A and B. The loads applied to the shaft from the gears are shown in the 3D image. Points O and C are supported by bearings. (50 points) a. Calculate the radial support forces on the bearings, assuming a simply supported beam. b. Plot the shear force and moment diagrams for this shaft. c. Determine the critical points on this shaft. d. Determine the midrange and alternating components of the bending moment and torque on critical points. e. Determine the endurance limit for this shaft. Assume 0.99 reliability. (Make reasonable assumptions for other correction factors) f. Focusing on the critical points calculate the minimum factor of safety using goodman's. criteria for infinite life. Does this shaft break?
2- We need to select a ball bearing for a shaft. Based on our designed shaft the bore diameter is 30 mm, and the shaft is rotating at 600 rpm. A life of 5000 hours for the bearing is ideal as we have other maintenance to perform on other parts of the machine. The bearing will have to endure around 10 kN of radial load and 1 kN of axial load. We are aiming for a reliability of 0.99. Assume the ratings are done for 1 million revolutions. (20 points) b. a. Calculate the load rating of the bearing that can be used for such a condition. Referring to the catalog provided, choose a bearing that we can purchase from SKF, if any.
3- We need to analyze a journal bearing that has a shaft diameter of 70.00 mm with a unilateral tolerance of -0.02 mm. The bushing bore has a diameter of 70.10 mm with a unilateral tolerance of 0.06 mm. The bushing is 35 mm long and supports a load of 2.5 kN. The journal speed is 960 rev/min. For the minimum clearance assembly, and for two different lubricants "SAE 20" and "SAE 40" operating at an average film temperature of 60°C find (30 points): a. The minimum film thickness, b. The power loss, c. The lubricant flow rate, d. The lubricant side flow rate, e. Which of these two lubricants would you choose? Why?
4. Two identical steel plates are each 1 in thick, and are compressed with one bolt (1/4-20 UNC grade 8) and nut. Washers are used under the head of the bolt and under the nut. a) Determine a suitable length of the bolt, rounded up to the nearest 1/4" b) Determine the bolt stiffness, assuming E = 30x10^6. c) Determine the stress on the bolt if the preload is 3 kip, and service load is 15 kip, and material stiffness is 12.69 Mlbf/in.
3. A½-13 UNC bolt is used to hold a steel plate using a tapped hole. Calculate the minimum number of threaded needed to hold the plate. Round up to the nearest thread.
The spur gear train given in HW5.4 is to be designed (4 gears in total) for a factor of safety of 2 for bending and 2.5 for surface stresses. Material to be used is Grade 2 through-hardened steel. Assume quality standard of 5, uncrowned tooth, enclosed and accurately mounted. All gears in the system must be designed to survive 10^8 cycles with a reliability of 0.99. Find the required surface hardness for individual gears. Make any additional assumptions as your see fit.
Fastener Homework Assignment 1. A 3/4 in - 16 UNF SAE grade 5 bolt is subjected to a load P of 6 kip in a tension joint. The initial bolt tension = 25 kip. The bolt and joint stiffnesses are kb = 6.50 and km = 13.8 Mlbf/in, respectively. Determine the preload and service load stresses in the bolt. Compare these to the SAE minimum proof strength of the bolt.
A 1-in-diameter solid round bar is made of AISI 1040 CD steel (sy= 71 kpsi, su = 85 kpsi ). It is operating at a temperature of 300°F, and is subjected to a purely reversing torque of 2000 lbf.in. Estimate the number of cycles to failure if the expected reliability is 99%. Redo the solution for a reversing torque of 8500 lbf.in. Note: The Von Mises stress for pure torsion would be o' = √37²
A solid square rod is cantilevered at one end. The rod is 0.8 m long and supports a completely reversing transverse load at the other end of 50 kN. The material is AISI 1060 hot-rolled steel (s = 370 MPa, Su = 680 MPa). Use a design factor of 2 and determine the dimensions of the square cross section for the following cases. Neglect any stress concentration. a. The rod must support this load for 100 cycles. b. The rod must support this load for 104 cycles. c. The rod must have infinite life.
