PEARSON ETEXT ENGINEERING MECH & STATS
15th Edition
ISBN: 9780137514724
Author: HIBBELER
Publisher: PEARSON
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Chapter 20, Problem 23P
To determine
The angular velocity of the axle
The angular velocity of the axle
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2. A shaft is supported on bearings A and B, 800 mm between centres. A 20 degrees straight tooth spur gear having 600 mm pitch diameter, is located 200 mm to the right of the left hand bearing A, and a 700 mm diameter pulley is mounted 250 mm towards the left of bearing B. The gear is driven by a pinion with a downward tangential force while the pulley drives a horizontal belt having 180 degrees angle of wrap. The pulley also serves as a flywheel and weighs 2000 N. The maximum belt tension is 3000 N and the tension ratio is 3: 1. Determine the maximum bending moment and the necessary shaft diameter if the allowable shear stress of the material is 40 MPa.
Two involute gear wheels work with an angle of pressure of 20⁰
and rotate in opposite directions. The smaller wheel has 20 teeth of 5
mm module and rotates at 2000 rev/min. The larger wheel has 80 teeth
and is the driven member.
If the contact ratio is 1:4, and if the are of recess is 1-2 times as large as
the are of approach, determine: (a) the addenda of the teeth on both
wheels, (b) the greatest speed of sliding between the teeth, (c) the center
distance of the gears, and (d) the working depth.
5. For the engine-transmission-propeller problem shown below, The engine generates a torque of
219lb-ft, and it is bolted to a frame at locations A and B. The transmission reverses the rotation
direction. The transmission ratio is 1.5 (i.e. the propeller speed is -1/1.5 the engine speed, the
minus sign indicates the change in direction).
d. Sketch the free body diagram. Be sure to show the torques at the input and outputs to
the different components. Note the change in the rotation direction between the engine
and shaft.
e. Solve for the reaction forces at the bolt supports of the engine, if the distance between
them is 1 ft.
Propeller
Engine
Reduction
ratio 1.5
Engine is attached
B
Chapter 20 Solutions
PEARSON ETEXT ENGINEERING MECH & STATS
Ch. 20 - The propeller of an airplane is rotating at a...Ch. 20 - The disk rotates about the z axis at a constant...Ch. 20 - The ladder of the fire truck rotates around the z...Ch. 20 - The ladder of the fire truck rotates around the z...Ch. 20 - At a given instant, the antenna has an angular...Ch. 20 - The disk rotates about the shaft S, while the...Ch. 20 - The electric fan is mounted on a swivel support...Ch. 20 - The electric fan is mounted on a swivel support...Ch. 20 - The truncated double cone rotates about the z axis...Ch. 20 - Prob. 20P
Ch. 20 - Gear B is driven by a motor mounted on turntable...Ch. 20 - Prob. 22PCh. 20 - Prob. 23PCh. 20 - Prob. 26PCh. 20 - Prob. 27PCh. 20 - Prob. 30PCh. 20 - So1ve Example 20.5 such that the x, y, z axes move...Ch. 20 - Prob. 38PCh. 20 - At the instant = 60, the telescopic boom AB of...Ch. 20 - Prob. 40PCh. 20 - Prob. 42PCh. 20 - Prob. 43PCh. 20 - Prob. 44PCh. 20 - Prob. 46PCh. 20 - Prob. 47PCh. 20 - Prob. 48PCh. 20 - Prob. 49PCh. 20 - Prob. 50PCh. 20 - Prob. 51P
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- For the epicyclic gear train shown, wheels B and C are rigidly attached to the input shaft (p) and they rotate at the same speed as the input shaft. The teeth numbers of the wheels are as given. D=90, B=30, C=20, E=100 Determine the output shaft speed (q) and its direction with respect to the input shaft, when: a. Only wheel D is fixed b. Only wheel E is fixed b. C B The input shaft rotates at 1200 rpm. You are required to forum two tablesarrow_forwardA gear system shown in Figure 1 consists of gear B and C with radii of 80 mmand 200 mm, respectively. Gear B with a mass of 0.9 kg is free to rotate at pointA of the arm AO. The arm is free to rotate on the fixed axis O. Whereas, gear Cis fixed on the axles O in a way that it will never rotate. The arm has a mass of0.8 kg and a radius of gyration about O of 140 mm. Moreover, the arm AO hasa center of gravity located at point G.1.1. If the uniform torque of 4 Nm is applied to the arm OA, initially at rest in thehorizontal position, calculate the velocity of point A as it reaches the top point A’.1.2. Use the table method to calculate the angular speed of gear B, provided that thearm rotates at 5,118 rad/s.arrow_forwardDraw free-body diagrams of the two gears, assuming an input couple M on theOUT X shaft of the larger gear in the direction shown. Include forces at bearings A, B, D and E. M isthe reaction couple at the output shaft - i.e. the resistance to turning of the object being driven.The gears have 48 and 24 teeth respectively. If the input gear (large gear) turns at 100 rpm(= revolutions per minute), the output speed (small gear) is _______rpm.Wil OUT X IN Xl M be larger or smaller than M ?arrow_forward
- The pinion (gear 2 on shaft a) rotates at 695 rev/min clockwise and transmits 1497 W through the idler pair (gears 3 and 4 on shaft b) to the output gear (gear 5 on shaft c). Gears 2 and 3 have a module of 3 mm, and gears 4 and 5 have a module of 2 mm. Pressure angles are all 20 degrees. Solve for the magnitude of the force that shaft b must apply to gears 3 and 4 to maintain static equilibrium in the figure shown here. Co 18T- 327 X 18T 5 -48Tarrow_forwardA steel shaft 800 mm long transmitting 15 kW at 400 r.p.m. is supported at two bearings at the twoends. A gear wheel having 80 teeth and 500 mm pitch circle diameter is mounted at 200 mm from theleft hand side bearing and receives power from a pinion meshing with it. The axis of pinion and gearlie in the horizontal plane. A pulley of 300 mm diameter is mounted at 200 mm from right hand sidebearing and is used for transmitting power by a belt. The belt drive is inclined at 30° to the vertical inthe forward direction. The belt lap angle is 180 degrees. The coefficient of friction between belt andpulley is 0.3. Design and sketch the arrangement of the shaft assuming the values of safe stresses as :τ = 55 MPa; σt= 80 MPa. Take torsion and bending factor 1.5 and 2 respectively.arrow_forwardIn the gear system shown, the motor applies a 190 lb-ft torque to the gear at A. A torque of Tc = 392 lb-ft is removed from the shaft at gear C, and the remaining torque is removed at gear D. Assume that DA-4-in.-diameter, Dg=12-in.-diameter, L₁=56 in., and L₂-30 in. Segments (1) and (2) are solid 1.5-in.-diameter steel [G = 12200 ksi] shafts, and the bearings shown allow free rotation of the shaft. Determine: (a) the maximum shear stresses T₁, T₂ in segments (1) and (2) of the shaft. (b) the rotation angle D/B of gear D relative to gear B. Answers: (a) T₁ (b) D/B = = i ᎠᏴ ; A DA i B L₁ Tc amala ksi, T₂ = L2 i Tp D ksi.arrow_forward
- A pair of gears, having 40 and 30 teeth respectively, are of 25° involute form. Theaddendum length is 5 mm and the module is 5.5 mm. If smaller wheel is the driver androtates at 1500 r.p.m. find the velocity of sliding at the point of engagement and at thepoint of disengagement.arrow_forwardA synchronous belt drive system is used as a speed reducer. The input shaft rotates at 1000 rpm and has a 36-tooth sprocket with a pitch diameter of 3.609 in. The output shaft has a 72- tooth sprocket with a pitch diameter of 7.218 in. the center distance between the two shafts is 15.01 in. Determine the following for the belt drive: a. The belt wrap on the input and output sprocketsb. The belt perimeter lengthc. Draw the schematic of the belt drive systemarrow_forwardA rack and pinion is a pair of gears that converts rotational motion into translation. As shown in the figure, a torque τ is applied to the shaft. The pinion rotates and causes the rack to translate. The mass moment of inertia of the pinion is I and the mass of the rack is m. Draw the free-body diagram and derive the differential equation of motionarrow_forward
- The two 1-kg gears A and B are attached to the ends of al 3-kg slender bar. The gears roll within the fixed ring gear C, which lies in the horizontal plane. (Figure 1) Figure 150 mm 400 mm- 150 mm Part A If a 10-N m torque is applied to the center of the bar as shown, determine the number of revolutions the bar must rotate starting from rest in order for it to have an angular velocity of WAB = 22 rad/s. For the calculation, assume the gears can be approximated by thin disks. Express your answer using three significant figures. ►View Available Hint(s) the number of revolutions = Submit Provide Feedback VAE vec ? Next >arrow_forwardA gear engine automobile is traveling along a curved track of 120m radius. Each of the four wheels has a moment of inertia of 2.3 kg m2 and an effective diameter of 600 mm. The rotating parts of the engine have a moment of inertia of1.25kg m2 the gear ratio of the engine to back wheel is 3:2.The engine axis is parallel to the gear axle and the crank shaft rotates in the same sense as the road wheels. The mass of the vehicle is 2050 kg and the center of mass is 520 mm above the road level. The width by the track is 1.6m, what will be the limiting speed of the vehicle if all the four wheels maintain contact with the road surface (b) Explain the function of a flywheel from a crank effort diagram.arrow_forwardAs shown in the figure a planetary gear train consist of the arm C coupled to two gears A and B with 40 and 60 teeth respectively. If the arm rotates at 150 rpm in the anticlockwise direction about the center of the fixed gear A. Calculate the speed of gear B. How fast will gear B move if the gear A makes 300 rpm in the clockwise direction instead of being fixed. (must use Tabular method) B Arm C C A B Nber of teeth Total rotationsarrow_forward
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