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Gears 3 and 4 are attached with keys to the shaft shown below. The resultant gear force, PA = 600 lbf., acts at an angle of 20° from the y-axis. The material for the shaft is AISI 1030 steel, Quenched and Tempered (Q&T) at 1200 °F (see Table A- 21 for properties). The shaft is solid and of constant diameter except where the gears attach. At those locations, the shaft has a 1.5 x larger diameter than elsewhere with a ¼” fillet radius. All critical locations have a ground finish. The torque on the shaft (input through the gears) is constant; therefore, the bending stresses are fully reversed. Assume that the geometric stress concentrations of the keyset are K₁ = 2.2 and Kts = 3.0 with a notch radius of 0.05”. The nominal stress would be high at the fillet so when considering the stress concentration factor, consider the fillet rather than the keyset. a) Draw shear and moment diagrams in two planes. b) Using a safety factor of 2.6, determine the safe shaft diameter for static loading. c) Using a safety factor of 2.6 and a reliability of 99%, determine the safe shaft diameter for infinite life. Reflect on the difference in sizes between c) & d). y 20 in 16 in. Pc 10 in. B Gear 3 (24-in. diam) PA 20° Gear 4 (10-in. diam) Figure 2

Gears 3 and 4 are attached with keys to the shaft shown below. The resultant gear force, PA = 600 lbf., acts at an angle of 20° from the y-axis. The material for the shaft is AISI 1030 steel, Quenched and Tempered (Q&T) at 1200 °F (see Table A- 21 for properties). The shaft is solid and of constant diameter except where the gears attach. At those locations, the shaft has a 1.5 x larger diameter than elsewhere with a ¼” fillet radius. All critical locations have a ground finish. The torque on the shaft (input through the gears) is constant; therefore, the bending stresses are fully reversed. Assume that the geometric stress concentrations of the keyset are K₁ = 2.2 and Kts = 3.0 with a notch radius of 0.05”. The nominal stress would be high at the fillet so when considering the stress concentration factor, consider the fillet rather than the keyset. a) Draw shear and moment diagrams in two planes. b) Using a safety factor of 2.6, determine the safe shaft diameter for static loading. c) Using a safety factor of 2.6 and a reliability of 99%, determine the safe shaft diameter for infinite life. Reflect on the difference in sizes between c) & d). y 20 in 16 in. Pc 10 in. B Gear 3 (24-in. diam) PA 20° Gear 4 (10-in. diam) Figure 2

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
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Gears 3 and 4 are attached with keys to the shaft shown below. The resultant gear force, PA = 600 lbf., acts at an angle of 20° from the y-axis. The material for the shaft is AISI 1030 steel, Quenched and Tempered (Q&T) at 1200 °F (see Table A- 21 for properties). The shaft is solid and of constant diameter except where the gears attach. At those locations, the shaft has a 1.5 x larger diameter than elsewhere with a ¼” fillet radius. All critical locations have a ground finish. The torque on the shaft (input through the gears) is constant; therefore, the bending stresses are fully reversed. Assume that the geometric stress concentrations of the keyset are K₁ = 2.2 and Kts = 3.0 with a notch radius of 0.05”. The nominal stress would be high at the fillet so when considering the stress concentration factor, consider the fillet rather than the keyset. a) Draw shear and moment diagrams in two planes. b) Using a safety factor of 2.6, determine the safe shaft diameter for static loading. c) Using a safety factor of 2.6 and a reliability of 99%, determine the safe shaft diameter for infinite life. Reflect on the difference in sizes between c) & d). y 20 in 16 in. Pc 10 in. B Gear 3 (24-in. diam) PA 20° Gear 4 (10-in. diam) Figure 2
Transcribed Image Text:Gears 3 and 4 are attached with keys to the shaft shown below. The resultant gear force, PA = 600 lbf., acts at an angle of 20° from the y-axis. The material for the shaft is AISI 1030 steel, Quenched and Tempered (Q&T) at 1200 °F (see Table A- 21 for properties). The shaft is solid and of constant diameter except where the gears attach. At those locations, the shaft has a 1.5 x larger diameter than elsewhere with a ¼” fillet radius. All critical locations have a ground finish. The torque on the shaft (input through the gears) is constant; therefore, the bending stresses are fully reversed. Assume that the geometric stress concentrations of the keyset are K₁ = 2.2 and Kts = 3.0 with a notch radius of 0.05”. The nominal stress would be high at the fillet so when considering the stress concentration factor, consider the fillet rather than the keyset. a) Draw shear and moment diagrams in two planes. b) Using a safety factor of 2.6, determine the safe shaft diameter for static loading. c) Using a safety factor of 2.6 and a reliability of 99%, determine the safe shaft diameter for infinite life. Reflect on the difference in sizes between c) & d). y 20 in 16 in. Pc 10 in. B Gear 3 (24-in. diam) PA 20° Gear 4 (10-in. diam) Figure 2
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