Shigleys Mechanical Engineering Design 9th edition Richard G. Budynas, J. Keith Nisbett - Solutions

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When a motor armature inertia, a pinion inertia, and a motor torque reside on a motor shaft, and a gear inertia, a load inertia, and a load torque exist on a second shaft, it is useful to reflect all the torques and inertias to one shaft, say, the armature shaft. We need some rules to make such
Apply the rules of Prob. 16–26 to the three-shaft system shown in the figure to create a motor shaft shish kebab. (a) Show that the equivalent inertia Ie is given by (b) If the overall gear reduction R is a constant nm, show that the equivalent inertia becomes (c) If the problem is to
For the conditions of Prob. 16–27, make a plot of the equivalent inertia Ie as ordinate and the stepdown ratio n as abscissa in the range 1 ≤ n ≤ 10. How does the minimum inertia compare to the single-step inertia?
A punch-press geared 10:1 is to make six punches per minute under circumstances where the torque on the crankshaft is 1300 lbf ?ft for ½ s. The motor’s nameplate reads 3 bhp at 1125 rev/min for continuous duty. Design a satisfactory flywheel for use on the motor shaft to the extent of
The punch-press of Prob. 16–29 needs a flywheel for service on the crankshaft of the punch press. Design a satisfactory flywheel to the extent of specifying material, rim inside and outside diameters, and width. Note ωmax , ωmin ,Cs , energy transfer, and peak power the flywheel
Compare the designs resulting from the tasks assigned in Probs. 16–29 and 16–30. What have you learned? What recommendations do you have?
A 6-in-wide polyamide F-1 flat belt is used to connect a 2-in-diameter pulley to drive a larger pulley with an angular velocity ratio of 0.5. The center-to-center distance is 9 ft. The angular speed of the small pulley is 1750 rev/min as it delivers 2 hp. The service is such that a service factor
Perspective and insight can be gained by doubling all geometric dimensions and observing the effect on problem parameters. Take the drive of Prob. 17–1, double the dimensions, and compare.
A flat-belt drive is to consist of two 4-ft-diameter cast-iron pulleys spaced 16 ft apart. Select a belt type to transmit 60 hp at a pulley speed of 380 rev/min. Use a service factor of 1.1 and a design factor of 1.0.
In solving problems and examining examples, you probably have noticed some recurring forms
Return to Ex. 17–1 and complete the following. (a) Find the torque capacity that would put the drive as built at the point of slip, as well as the initial tension Fi . (b) Find the belt width b that exhibits nf s = nd = 1.1. (c) For part b find the corresponding F1a , Fc , Fi , F2 , power, and
Take the drive of Prob. 17–5 and double the belt width. Compare Fc, Fi , F1a, F2, Ha, nf s , and dip.
Belted pulleys place loads on shafts, inducing bending and loading bearings. Examine Fig. 17–7 and develop an expression for the load the belt places on the pulley, and then apply it to Ex. 17–2.
Example 17–2 resulted in selection of a 10-in-wide A-3 polyamide flat belt. Show that the value of F1 restoring f to 0.80 is
Two shafts 20 ft apart, with axes in the same horizontal plane, are to be connected with a flat belt in which the driving pulley, powered by a six-pole squirrel-cage induction motor with a 100 brake hp rating at 1140 rev/min, drives the second shaft at half its angular speed. The driven shaft
The mechanical efficiency of a flat-belt drive is approximately 98 percent. Because of its high value, the efficiency is often neglected. If a designer should choose to include it, where would he or she insert it in the flat-belt protocol?
In metal belts, the centrifugal tension Fc is ignored as negligible. Convince yourself that this is a reasonable problem simplification
A designer has to select a metal-belt drive to transmit a power of Hnom under circumstances where a service factor of Ks and a design factor of nd are appropriate. The design goal becomes Hd = Hnom Ksnd . Use Eq. (17–8) to show that the minimum belt width is given by
Design a friction metal flat-belt drive to connect a 1-hp, four-pole squirrel-cage motor turning at 1750 rev/min to a shaft 15 in away, running at half speed. The circumstances are such that a service factor of 1.2 and a design factor of 1.05 are appropriate. The life goal is 106 belt passes, f =
A beryllium-copper metal flat belt with Sf = 56.67 kpsi is to transmit 5 hp at 1125 rev/min with a life goal of 106 belt passes between two shafts 20 in apart whose centerlines are in a horizontal plane. The coefficient of friction between belt and pulley is 0.32. The conditions are such that a
For the conditions of Prob. 17–15 use a 1095 plain carbon-steel heat-treated belt. Conditions at the driving pulley hub require a pulley outside diameter of 3 in or more. Specify your belt, pulley sizes, and initial tension at installation.
A single V belt is to be selected to deliver engine power to the wheel-drive transmission of a riding tractor. A 5-hp single-cylinder engine is used. At most, 60 percent of this power is transmitted to the belt. The driving sheave has a diameter of 6.2 in, the driven, 12.0 in. The belt selected
Two B85 V belts are used in a drive composed of a 5.4-in driving sheave, rotating at 1200 rev/min, and a 16-in driven sheave. Find the power capacity of the drive based on a service factor of 1.25, and find the center-to-center distance
A 60-hp four-cylinder internal combustion engine is used to drive a brick-making machine under a schedule of two shifts per day. The drive consists of two 26-in sheaves spaced about 12 ft apart, with a sheave speed of 400 rev/min. Select a V-belt arrangement. Find the factor of safety, and estimate
A reciprocating air compressor has a 5-ft-diameter flywheel 14 in wide, and it operates at 170 rev/min. An eight-pole squirrel-cage induction motor has nameplate data 50 bhp at 875 rev/min. (a) Design a V-belt drive. (b) Can cutting the V-belt grooves in the flywheel be avoided by using a V-flat
The geometric implications of a V-flat drive are interesting. (a) If the earth’s equator was an inextensible string, snug to the spherical earth, and you spliced 6 ft of string into the equatorial cord and arranged it to be concentric to the equator, how far off the ground is the string? (b)
A 2-hp electric motor running at 1720 rev/min is to drive a blower at a speed of 240 rev/min. Select a V-belt drive for this application and specify standard V belts, sheave sizes, and the resulting center-to-center distance. The motor size limits the center distance to at least 22 in.
The standard roller-chain number indicates the chain pitch in inches, construction proportions, series, and number of strands as follows
Equate Eqs. (17–32) and (17–33) to find the rotating speed n1 at which the power equates and marks the division between the pre-maximum and the post maximum power domains.
A double-strand no. 60 roller chain is used to transmit power between a 13-tooth driving sprocket rotating at 300 rev/min and a 52-tooth driven sprocket. (a) What is the allowable horsepower of this drive? (b) Estimate the center-to-center distance if the chain length is 82 pitches. (c) Estimate
A four-strand no. 40 roller chain transmits power from a 21-tooth driving sprocket to an 84-tooth driven sprocket. The angular speed of the driving sprocket is 2000 rev/min. (a) Estimate the chain length if the center-to-center distance has to be about 20 in. (b) Estimate the tabulated horsepower
A 700 rev/min 25-hp squirrel-cage induction motor is to drive a two-cylinder reciprocating pump, out-of-doors under a shed. A service factor Ks of 1.5 and a design factor of 1.1 are appropriate. The pump speed is 140 rev/min. Select a suitable chain and sprocket sizes.
A centrifugal pump is driven by a 50-hp synchronous motor at a speed of 1800 rev/min. The pump is to operate at 900 rev/min. Despite the speed, the load is smooth (Ks = 1.2). For a design factor of 1.1 specify a chain and sprockets that will realize a 50 000-h life goal. Let the sprockets be 19T
A mine hoist uses a 2-in 6 x 19 monitor-steel wire rope. The rope is used to haul loads of 4 tons from the shaft 480 ft deep. The drum has a diameter of 6 ft, the sheaves are of good-quality cast steel, and the smallest is 3 ft in diameter. (a) Using a maximum hoisting speed of 1200 ft/min and a
A temporary construction elevator is to be designed to carry workers and materials to a height of 90 ft. The maximum estimated load to be hoisted is 5000 lbf at a velocity not to exceed 2 ft/s. For minimum sheave diameters and acceleration of 4 ft/s2, specify the number of ropes required if the
A 2000-ft mine hoist operates with a 72-in drum using 6 x 19 monitor-steel wire rope. The cage and load weigh 8000 lbf, and the cage is subjected to an acceleration of 2 ft/s2 when starting. (a) For a single-strand hoist how does the factor of safety n = Ff /Ft vary with the choice of rope
Generalize the results of Prob. 17–31 by representing the factor of safety n as
From your results in Prob. 17–32, show that to meet a fatigue factor of safety n1 the optimal solution is
For Prob. 17–29 estimate the elongation of the rope if a 9000-lbf loaded mine cart is placed on the cage. The results of Prob. 4–6 may be useful.
A full journal bearing has a journal diameter of 1.000 in, with a unilateral tolerance of −0.0015 in. The bushing bore has a diameter of 1.0015 in and a unilateral tolerance of 0.003 in. The l / d ratio is unity. The load is 250 lbf and the journal runs at 1100 rev/min. If the average
A full journal bearing has a journal diameter of 1.250 in, with a unilateral tolerance of −0.001 in. The bushing bore has a diameter of 1.252 in and a unilateral tolerance of 0.003 in. The bearing is 2.5 in long. The journal load is 400 lbf and it runs at a speed of 1150 rev/min. Using an
A journal bearing has a journal diameter of 3.000 in, with a unilateral tolerance of −0.001 in. The bushing bore has a diameter of 3.005 in and a unilateral tolerance of 0.004 in. The bushing is 1.5 in long. The journal speed is 600 rev/min and the load is 800 lbf. For both SAE 10 and SAE 40,
A journal bearing has a journal diameter of 3.000 in with a unilateral tolerance of −0.003 in. The bushing bore has a diameter of 3.006 in and a unilateral tolerance of 0.004 in. The bushing is 3 in long and supports a 600-lbf load. The journal speed is 750 rev/min. Find the minimum oil film
A full journal bearing has a journal with a diameter of 2.000 in and a unilateral tolerance of −0.0012 in. The bushing has a bore with a diameter of 2.0024 and a unilateral tolerance of 0.002 in. The bushing is 1 in long and supports a load of 600 lbf at a speed of 800 rev/min. Find the
A full journal bearing has a shaft journal diameter of 25 mm with a unilateral tolerance of −0.01 mm. The bushing bore has a diameter of 25.04 mm with a unilateral tolerance of 0.03 mm. The l/d ratio is unity. The bushing load is 1.25 kN, and the journal rotates at 1200 rev/min. Analyze the
A full journal bearing has a shaft journal with a diameter of 30.00 mm and a unilateral tolerance of −0.015 mm. The bushing bore has a diameter of 30.05 mm with a unilateral tolerance of 0.035 mm. The bushing bore is 50 mm in length. The bearing load is 2.75 kN and the journal rotates at 1120
A journal bearing has a shaft diameter of 75.00 mm with a unilateral tolerance of −0.02 mm. The bushing bore has a diameter of 75.10 mm with a unilateral tolerance of 0.06 mm. The bushing is 36 mm long and supports a load of 2 kN. The journal speed is 720 rev/min. For the minimum clearance
A full journal bearing is 25 mm long. The shaft journal has a diameter of 50 mm with a unilateral tolerance of −0.01 mm. The bushing bore has a diameter of 50.05 mm with a unilateral tolerance of 0.01 mm. The load is 2000 N and the journal speed is 840 rev/min. For the minimum clearance
A 1 ¼ - ×1 ¼ - in sleeve bearing supports a load of 700 lbf and has a journal speed of 3600 rev/min. An SAE 10 oil is used having an average temperature of 160◦F. Using Fig. 12–16, estimate the radial clearance for minimum coefficient of friction f and for maximum load-carrying capacity
A full journal bearing has a shaft diameter of 80.00 mm with a unilateral tolerance of −0.01 mm. The l/d ratio is unity. The bushing has a bore diameter of 80.08 mm with a unilateral tolerance of 0.03 mm. The SAE 30 oil supply is in an axial-groove sump with a steady-state temperature of
A 2 ½ ×2 ½ - in sleeve bearing uses grade 20 lubricant. The axial-groove sump has a steady-state temperature of 110◦F. The shaft journal has a diameter of 2.500 in with a unilateral tolerance of −0.001 in. The bushing bore has a diameter of 2.504 in with a unilateral tolerance of
A set of sleeve bearings has a specification of shaft journal diameter of 1.250 in with a unilateral tolerance of −0.001 in. The bushing bore has a diameter of 1.252 in with a unilateral tolerance of 0.003 in. The bushing is 1 ¼ in long. The radial load is 250 lbf and the shaft rotational
A natural-circulation pillow-block bearing has a journal diameter D of 2.500 in with a unilateral tolerance of −0.001 in. The bushing bore diameter B is 2.504 in with a unilateral tolerance of 0.004 in. The shaft runs at an angular speed of 1120 rev/min; the bearing uses SAE grade 20 oil and
An eight-cylinder diesel engine has a front main bearing with a journal diameter of 3.500 in and a unilateral tolerance of −0.003 in. The bushing bore diameter is 3.505 in with a unilateral tolerance of +0.005 in. The bushing length is 2 in. The pressure-fed bearing has a central annular
A pressure-fed bearing has a journal diameter of 50.00 mm with a unilateral tolerance of −0.05 mm. The bushing bore diameter is 50.084 mm with a unilateral tolerance of 0.10 mm. The length of the bushing is 55 mm. Its central annular groove is 5 mm wide and is fed by SAE 30 oil is 55◦C
Design a central annular-groove pressure-fed bearing with an l′/d ratio of 0.5, using SAE grade 20 oil, the lubricant supplied at 30 psig. The exterior oil cooler can maintain the sump temperature at 120◦F for heat dissipation rates up to 1500 Btu/h. The load to be carried is 900 lbf at
Repeat design problem Prob. 12–18 using the nominal bushing bore B as one decision variable and the radial clearance c as the other. Again, Trumpler’s criteria to be used.
Table 12–1 gives the Seireg and Dandage curve fit for the absolute viscosity in customary U.S. engineering units. Show that in SI units of mPa . s and a temperature of C degrees Celsius, the viscosity can be expressed as μ = 6.89(106) μ0 exp [(b/ (1.8C + 17))] Where μ0 and b
For Prob. 12–18 a satisfactory design is d = 2.000+0 in b = 2.005+0.003 in −0.001 -0 Double the size of the bearing dimensions and quadruple the load to 3600 lbf. (a) Analyze the scaled-up bearing for median assembly. (b) Compare the results of a similar
An Oiles SP 500 alloy brass bushing is 1 in long with a 1-in bore and operates in a clean environment at 70◦F. The allowable wear without loss of function is 0.005 in. The radial load is 500 lbf. The shaft speed is 200 rev/min. Estimate the number of revolutions for radial wear to be 0.005 in.
Choose an Oiles SP 500 alloy brass bushing to give a maximum wear of 0.002 in for 1000 h of use with a 400 rev/min journal and 100 lbf radial load. Use hCR = 2.7 Btu/ (h. ft2. ◦F), Tmax = 300◦F, fs = 0.03, and a design factor nd = 2. Table 12–13 lists the bushing sizes available from
Make a two-view drawing or a good freehand sketch of a helical compression spring closed to its solid height and having a wire diameter of 1/2 in, outside diameter of 4 in, and one active coil. The spring is to have plain ends. Make another drawing of the same spring with ends plain and ground.
It is instructive to examine the question of the units of the parameter A of Eq. (10–14). Show that for U.S. customary units the units for Auscu are kpsi . inm and for SI units are MPa . mmm for ASI which make the dimensions of both Auscu and ASI different for every material to which Eq.
A helical compression spring is wound using 0.105-in-diameter music wire. The spring has an outside diameter of 1.225 in with plain ground ends, and 12 total coils. (a) What should the free length be to ensure that when the spring is compressed solid the torsional stress does not exceed the yield
The spring in Prob. 10–3 is to be used with a static load of 30 lbf. Perform a design assessment represented by Eqs. (10–13) and (10–18) through (10–21) if the spring is closed to solid height.
A helical compression spring is made of hard-drawn spring steel wire 2 mm in diameter and has an outside diameter of 22 mm. The ends are plain and ground, and there are 8½ 2 total coils. (a) The spring is wound to a free length, which is the largest possible with a solid-safe property. Find
The spring of Prob. 10–5 is to be used with a static load of 75 N. Perform a design assessment represented by Eqs. (10–13) and (10–18) through (10–21) if the spring closed to solid height.
Listed below are six springs described in customary units and five springs described in SI units. Investigate these squared-and-ground-ended helical compression springs to see if they are solid-safe. If not, what is the largest free length to which they can be wound using ns = 1.2?
A static service music wire helical compression spring is needed to support a 20-lbf load after being compressed 2 in. The solid height of the spring cannot exceed 1 ½ in. The free length must not exceed 4 in. The static factor of safety must equal or exceed 1.2. For robust linearity use a
Not all springs are made in a conventional way. Consider the special steel spring in the illustration. (a) Find the pitch, solid height, and number of active turns. (b) Find the spring rate. Assume the material is A227 HD steel. (c) Find the force Fs required to close the spring solid. (d) Find
A holding fixture for a work piece 1 ½ in thick at clamp locations is being designed. The detail of one of the clamps is shown in the figure. A spring is required to drive the clamp upward while removing or inserting a work piece. A clamping force of 10 lbf is satisfactory. The base plate is 5/8
Your instructor will provide you with a stock spring supplier’s catalog, or pages reproduced from it. Accomplish the task of Prob. 10–20 by selecting an available stock spring. (This is design by selection.)
The figure shows a conical compression helical coil spring where R1 and R2 are the initial and final coil radii, respectively, d is the diameter of the wire, and Na is the total number of active coils. The wire cross section primarily transmits a torsional moment, which changes with the coil
A helical coil compression spring is needed for food service machinery. The load varies from a minimum of 4 lbf to a maximum of 18 lbf. The spring rate k is to be 9.5 lbf/in. The outside diameter of the spring cannot exceed 2 ½ in. The spring maker has available suitable dies for drawing 0.080-,
Solve Prob. 10–23 using the Goodman-Zimmerli fatigue-failure criterion.
Solve Prob. 10–23 using the Sines-Zimmerli fatigue-failure criterion
Design the spring of Ex. 10–5 using the Gerber fatigue-failure criterion.
Solve Prob. 10–26 using the Goodman-Zimmerli fatigue-failure criterion.
A hard-drawn spring steel extension spring is to be designed to carry a static load of 18 lbf with an extension of ½ in using a design factor of ny = 1.5 in bending. Use full-coil end hooks with the fullest bend radius of r = D/2 and r2 = 2d. The free length must be less than 3 in, and the body
The extension spring shown in the figure has full-twisted loop ends. The material is AISI 1065 OQ&T wire. The spring has 84 coils and is close-wound with a preload of 16 lbf. (a) Find the closed length of the spring. (b) Find the torsional stress in the spring corresponding to the preload.
Design an infinite-life helical coil extension spring with full end loops and generous loop-bend radii for a minimum load of 9 lbf and a maximum load of 18 lbf, with an accompanying stretch of ¼ in. The spring is for food-service equipment and must be stainless steel. The outside diameter of the
Prove Eq. (10–40). Hint: Using Castigliano’s theorem, determine the deflection due to bending of an end hook alone as if the hook were fixed at the end connecting it to the body of the spring. Consider the wire diameter d small as compared to the mean radius of the hook, R = D/2. Add the
The figure shows a finger exerciser used by law-enforcement officers and athletes to strengthen their grip. It is formed by winding A227 hard-drawn steel wire around a mandrel to obtain 2 ½ turns when the grip is in the closed position. After winding, the wire is cut to leave the two legs as
The rat trap shown in the figure uses two opposite-image torsion springs. The wire has a diameter of 0.081 in, and the outside diameter of the spring in the position shown is ½ in. Each spring has 11 turns. Use of a fish scale revealed a force of about 8 lbf is needed to set the trap. (a) Find
Wire form springs can be made in a variety of shapes. The clip shown operates by applying a force F. The wire diameter is d, the length of the straight section is l, and Young’s modulus is E. Consider the effects of bending only, with d
Using the experience gained with Prob. 10–23, write a computer program that would help in the design of helical coil compression springs.
Using the experience gained with Prob. 10–30, write a computer program that would help in the design of a helical coil extension spring.
A certain application requires a ball bearing with the inner ring rotating, with a design life of 30 000 h at a speed of 300 rev/min. The radial load is 1.898 kN and an application factor of 1.2 is appropriate. The reliability goal is 0.90. Find the multiple of rating life required, xD , and the
An angular-contact, inner ring rotating, 02-series ball bearing is required for an application in which the life requirement is 50 000 h at 480 rev/min. The design radial load is 610 lbf. The application factor is 1.4. The reliability goal is 0.90. Find the multiple of rating life xD required and
The other bearing on the shaft of Prob. 11–2 is to be a 03-series cylindrical roller bearing with inner ring rotating. For a 1650-lbf radial load, find the catalog rating C10 with which to enter Table 11–3. The reliability goal is 0.90. Choose a bearing and estimate its reliability in use.
Problems 11–2 and 11–3 raise the question of the reliability of the bearing pair on the shaft. Since the combined reliabilities R is R1 R2 , what is the reliability of the two bearings (probability that either or both will not fail) as a result of your decisions in Probs. 11–2 and 11–3?
Combine Probs. 11–2 and 11–3 for an overall reliability of R = 0.90. Reconsider your selections, and meet this overall reliability goal.
An 02-series ball bearing is to be selected to carry a radial load of 8 kN and a thrust load of 4 kN. The desired life LD is to be 5000 h with an inner-ring rotation rate of 900 rev/min. What is the basic load rating that should be used in selecting a bearing for a reliability goal of 0.90?
The bearing of Prob. 11–6 is to be sized to have a reliability of 0.96. What basic load rating should be used in selecting the bearing?
A straight (cylindrical) roller bearing is subjected to a radial load of 12 kN. The life is to be 4000 h at a speed of 750 rev/min and exhibit a reliability of 0.90. What basic load rating should be used in selecting the bearing from a catalog of manufacturer 2?
Shown in the figure is a gear-driven squeeze roll that mates with an idler roll, below. The roll is designed to exert a normal force of 30 lbf/in of roll length and a pull of 24 lbf/in on the material being processed. The roll speed is 300 rev/min, and a design life of 30 000 h is desired. Use an
The figure shown is a geared countershaft with an overhanging pinion at C. Select an angular-contact ball bearing from Table 11–2 for mounting at O and a straight roller bearing for mounting at B. The force on gear A is FA = 600 lbf, and the shaft is to run at a speed of 480 rev/min. Solution of
The figure is a schematic drawing of a countershaft that supports two V-belt pulleys. The countershaft runs at 1200 rev/min and the bearings are to have a life of 60 kh at a combined reliability of 0.999. The belt tension on the loose side of pulley A is 15 percent of the tension on the tight side.
The bearing lubricant (513 SUS at 100◦F) operating point is 135◦F. A countershaft is supported by two tapered roller bearings using an indirect mounting. The radial bearing loads are 560 lbf for the left-hand bearing and 1095 for the right-hand bearing. The shaft rotates at 400 rev/min
A gear-reduction unit uses the countershaft depicted in the figure. Find the two bearing reactions. The bearings are to be angular-contact ball bearings, having a desired life of 40 kh when used at 200 rev/min. Use 1.2 for the application factor and a reliability goal for the bearing pair of 0.95.

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Shigleys Mechanical Engineering Design 9th edition Richard G. Budynas, J. Keith Nisbett - Solutions

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