To prove: The system given can be represented as, [ x ˙ 1 ⋯ x ˙ 2 ] = [ A 1 ⋮ − B 1 C 2 ⋯ ⋯ ⋯ B 2 C 1 ⋮ A 2 ] [ x 1 ⋯ x 2 ] + [ B 1 ⋯ 0 ] r ; y = [ C 1 ⋮ 0 ] [ x 1 ⋯ x 2 ] .

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Answer 1

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Chapter 5, Problem 42P

To determine

To prove: The system given can be represented as,

[ x ˙ 1⋯ x ˙ 2]=[ A 1⋮− B 1 C 2⋯⋯⋯ B 2 C 1⋮ A 2][ x 1⋯ x 2]+[ B 1⋯0]r; y=[ C 1⋮0][ x 1⋯ x 2] .

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The gears shown in the figure have a diametral pitch of 2 teeth per inch and a 20° pressure angle. The pinion rotates at 1800 rev/min clockwise and transmits 200 hp through the idler pair to gear 5 on shaft c. What forces do gears 3 and 4 transmit to the idler shaft? TS I y 18T 32T This a 12 x 18T C 48T 5

Question 1. Draw 3 teeth for the following pinion and gear respectively. The teeth should be drawn near the pressure line so that the teeth from the pinion should mesh those of the gear. Drawing scale (1:1). Either a precise hand drawing or CAD drawing is acceptable. Draw all the trajectories of the involute lines and the circles. Specification: 18tooth pinion and 30tooth gear. Diameter pitch=P=6 teeth /inch. Pressure angle:20°, 1/P for addendum (a) and 1.25/P for dedendum (b). For fillet, c=b-a.

5. The figure shows a gear train. There is no friction at the bearings except for the gear tooth forces. The material of the milled gears is steel having a Brinell hardness of 170. The input shaft speed (n2) is 800 rpm. The face width and the contact angle for all gears are 1 in and 20° respectively. In this gear set, the endurance limit (Se) is 15 kpsi and nd (design factor) is 2. (a) Find the revolution speed of gear 5. (b) Determine whether each gear satisfies the design factor of 2.0 for bending fatigue. (c) Determine whether each gear satisfies the design factor of 2.0 for surface fatigue (contact stress). (d) According to the computation results of the questions (b) and (c), explain the possible failure mechanisms for each gear. N4=28 800rpm N₁=43 N5=34 N₂=14 P(diameteral pitch)=8 for all gears Coupled to 2.5hp motor

Answer 2

Question

Chapter 5, Problem 42P

To determine

To prove: The system given can be represented as,

[ x ˙ 1⋯ x ˙ 2]=[ A 1⋮− B 1 C 2⋯⋯⋯ B 2 C 1⋮ A 2][ x 1⋯ x 2]+[ B 1⋯0]r; y=[ C 1⋮0][ x 1⋯ x 2] .

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Answer 3

Question

Chapter 5, Problem 42P

To determine

To prove: The system given can be represented as,

[ x ˙ 1⋯ x ˙ 2]=[ A 1⋮− B 1 C 2⋯⋯⋯ B 2 C 1⋮ A 2][ x 1⋯ x 2]+[ B 1⋯0]r; y=[ C 1⋮0][ x 1⋯ x 2] .

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Answer 4

Question

Chapter 5, Problem 42P

To determine

To prove: The system given can be represented as,

[ x ˙ 1⋯ x ˙ 2]=[ A 1⋮− B 1 C 2⋯⋯⋯ B 2 C 1⋮ A 2][ x 1⋯ x 2]+[ B 1⋯0]r; y=[ C 1⋮0][ x 1⋯ x 2] .

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Answer 5

Chapter 5, Problem 42P

To determine

To prove: The system given can be represented as,

[ x ˙ 1⋯ x ˙ 2]=[ A 1⋮− B 1 C 2⋯⋯⋯ B 2 C 1⋮ A 2][ x 1⋯ x 2]+[ B 1⋯0]r; y=[ C 1⋮0][ x 1⋯ x 2] .

Answer 6

Chapter 5, Problem 42P

To determine

To prove: The system given can be represented as,

[ x ˙ 1⋯ x ˙ 2]=[ A 1⋮− B 1 C 2⋯⋯⋯ B 2 C 1⋮ A 2][ x 1⋯ x 2]+[ B 1⋯0]r; y=[ C 1⋮0][ x 1⋯ x 2] .

Answer 7

Chapter 5, Problem 42P

To determine

To prove: The system given can be represented as,

[ x ˙ 1⋯ x ˙ 2]=[ A 1⋮− B 1 C 2⋯⋯⋯ B 2 C 1⋮ A 2][ x 1⋯ x 2]+[ B 1⋯0]r; y=[ C 1⋮0][ x 1⋯ x 2] .

Answer 8

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Answer 9

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Answer 10

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Answer 11

Ch. 5 - Prob. 1RQ Ch. 5 - Name three basic forms for interconnecting...Ch. 5 - For each of the forms in Question 2, state...Ch. 5 - Besides knowing the basic forms as discussed in...Ch. 5 - For a simple, second-order feedback control system...Ch. 5 - Prob. 6RQ Ch. 5 - Prob. 7RQ Ch. 5 - How are summing junctions shown on a signal-flow...Ch. 5 - If a forward path touched all closed loops, what...Ch. 5 - Name five representations of systems in state...

To prove: The system given can be represented as, [ x ˙ 1 ⋯ x ˙ 2 ] = [ A 1 ⋮ − B 1 C 2 ⋯ ⋯ ⋯ B 2 C 1 ⋮ A 2 ] [ x 1 ⋯ x 2 ] + [ B 1 ⋯ 0 ] r ; y = [ C 1 ⋮ 0 ] [ x 1 ⋯ x 2 ] .

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To prove: The system given can be represented as,

[ x ˙ 1⋯ x ˙ 2]=[ A 1⋮− B 1 C 2⋯⋯⋯ B 2 C 1⋮ A 2][ x 1⋯ x 2]+[ B 1⋯0]r; y=[ C 1⋮0][ x 1⋯ x 2] .

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Chapter 5 Solutions

To prove: The system given can be represented as, [ x ˙ 1 ⋯ x ˙ 2 ] = [ A 1 ⋮ − B 1 C 2 ⋯ ⋯ ⋯ B 2 C 1 ⋮ A 2 ] [ x 1 ⋯ x 2 ] + [ B 1 ⋯ 0 ] r ; y = [ C 1 ⋮ 0 ] [ x 1 ⋯ x 2 ] .

Concept explainers

Videos

To prove: The system given can be represented as, [ x ˙ 1⋯ x ˙ 2]=[ A 1⋮− B 1 C 2⋯⋯⋯ B 2 C 1⋮ A 2][ x 1⋯ x 2]+[ B 1⋯0]r; y=[ C 1⋮0][ x 1⋯ x 2] .

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Chapter 5 Solutions

To prove: The system given can be represented as,

[ x ˙ 1⋯ x ˙ 2]=[ A 1⋮− B 1 C 2⋯⋯⋯ B 2 C 1⋮ A 2][ x 1⋯ x 2]+[ B 1⋯0]r; y=[ C 1⋮0][ x 1⋯ x 2] .