Solution olutions s Manual Manual to accompany
MACHIN MACHINE E ELEMEN ELEMENTS TS IN MECH ME CHA A NICAL NICAL DESI DESIGN GN
Fourth Edition
Rob Robert L. Mott
Copy Copyri righ ghtt
© 2004 2004 hy Pear Pearso son n Educ Educat atio ion, n,
Inc. Inc.,, Uppe Upperr Sadd Saddle le Rive River, r, New New Jers Jersey ey
0745 07458. 8.
Pearso Pearson n Prentic Prenticee Hall. Hall. All righ rights ts reserve reserved. d. Printe Printed d in the the Unite United d States States of Ameri America. ca. This This public publicati ation on is prot protect ected ed by Copyri Copyright ght and permis permissio sion n should should be obtai obtained ned from from the publis publisher her prior prior to any prohibi prohibited ted reprod reproduct uction ion,, storag storagee m a retrie retrieval val system system,, or transm transmiss issiou iou in any any form form or or by any any means means,, electr electroni onic, c, mechan mechanica ical, l, photoc photocopy opying ing,, record recordmg, mg, or likewise. likewise. For For inform information ation regarding regarding permissio permission(s), n(s), write write to: Rights Rights and Permission Permissionss Department Department.. Pearso Pearson n Prenti Prentice ce HalJTM HalJTM is a tradem trademark ark of Pear Pearson son Educat Education ion,, Inc. Inc. Pearson® Pearson® is a registe registered red trademark trademark of Pearson Pearson pic Prenti Prentice ce Hall® Hall® is a regis register tered ed tradem trademark ark of Pearso Pearson n Educat Education ion,, Inc. Inc.
Instructor Instructorss of classes classes using Mott, Machin Machinee Elemen Elements ts in Mechan Mechanica icall Design Design,, Fourth Fourth Editio Edition, n, from the the solutio solutions ns manual manual for classroom classroom use.
PEARSON
may reproduce reproduce material material
10 9 8 7 6 5 4 3 2 1
--1'11'111 jl'P
Hall
ISBN ISBN 0-13-140 0-13-140873 873-9 -9
CONTENTS S olut olutions ions Manual Manual for
Copy Copyri righ ghtt
© 2004 2004 hy Pear Pearso son n Educ Educat atio ion, n,
Inc. Inc.,, Uppe Upperr Sadd Saddle le Rive River, r, New New Jers Jersey ey
0745 07458. 8.
Pearso Pearson n Prentic Prenticee Hall. Hall. All righ rights ts reserve reserved. d. Printe Printed d in the the Unite United d States States of Ameri America. ca. This This public publicati ation on is prot protect ected ed by Copyri Copyright ght and permis permissio sion n should should be obtai obtained ned from from the publis publisher her prior prior to any prohibi prohibited ted reprod reproduct uction ion,, storag storagee m a retrie retrieval val system system,, or transm transmiss issiou iou in any any form form or or by any any means means,, electr electroni onic, c, mechan mechanica ical, l, photoc photocopy opying ing,, record recordmg, mg, or likewise. likewise. For For inform information ation regarding regarding permissio permission(s), n(s), write write to: Rights Rights and Permission Permissionss Department Department.. Pearso Pearson n Prenti Prentice ce HalJTM HalJTM is a tradem trademark ark of Pear Pearson son Educat Education ion,, Inc. Inc. Pearson® Pearson® is a registe registered red trademark trademark of Pearson Pearson pic Prenti Prentice ce Hall® Hall® is a regis register tered ed tradem trademark ark of Pearso Pearson n Educat Education ion,, Inc. Inc.
Instructor Instructorss of classes classes using Mott, Machin Machinee Elemen Elements ts in Mechan Mechanica icall Design Design,, Fourth Fourth Editio Edition, n, from the the solutio solutions ns manual manual for classroom classroom use.
PEARSON
may reproduce reproduce material material
10 9 8 7 6 5 4 3 2 1
--1'11'111 jl'P
Hall
ISBN ISBN 0-13-140 0-13-140873 873-9 -9
CONTENTS S olut olutions ions Manual Manual for
CONTENTS S olut olutions ions Manual Manual for Machin Machine e Elemen Elementts in Mechan Mechanica icall Design Design,, 4th ed. ed. Robert L. Mott Mott B y: Robert Tab Table of Cont Content ents... s..... ....
ii
MDESIGN software Included on the CD in the book Spr Spreadsheets
,
iii
included on the CD in the Sol Solutions Ma Manual
,
x
Solution Solutions s to end-of-ch end-of-chapt apter er probl problem ems s Chapter 1: Th T he Nature of Mechanical Design
1
Chapter 2: Materials in Mechanical Design......
3
Cha Chapter 3: Str Stress and Def Deform ormation Ana Analysis. sis... .. ...... ... ... .... ..... .. ... ... ... ...... ... ... ........ ... ..... 9 Chapter 4: Combined Stresses and Mohr's Circle
31
Chapter 5: Design for Different Types of Loading Chapter 6: Columns
,
,
64
Chapter 7: Belt Drives and Chain Drives Cha Chapter 8: Kinematics of Gears .,. ... ... ...
42
, 77 ........ ........
Chapter 9: Spur Gear Design
... ...
....... ........ ..
_.
87 108
Cha Chapter 10 10: Helical Gea Gears, Bev Bevel Gea Gears, and Wormgearing
151
Chapter 11: Keys, Couplings, and Seals
180
Chapter 12: Shaft Design
.. . ..
.. .. .. .. .. ... .. ..
Chapter 13: Tolerances and Fits
.. .. .. ..
,
184 206
cted
Chapter 14: Rolling Contact Bearings
211
ng, ng, or
Chapter 16: P lain Surface Bearings
217
Chapter 17: Linear Motion Elements
224
Chapter 18: Fasteners,
226
Chapter 19: Springs
228
Chapt Chapter er 20: 20: Machi Machine ne Fra Fram mes, es, Bolt Bolted Conne Connect ctio ions ns,, and and Weld Welded ed J oin oints
243 243
Chapter 21: Electric Motors and Controls
254
by e ma
naterial
Cha Chapter 22: Motion Co Con ntrol: Clu Clutches and Brakes 1
iii
,
257
TH
MACHINE ELEMENTS IN MECHANICAL DESIGN, 4 By: Robert
EDITION
L. Mott
Published by Prentice-Hall, Inc.
MDES/GN - Mechanical Design Software
Comments On Its Use For Problem Solutions Introduction
Th.e.design of machine elements jnherently .involves extensive procedures, complex calculations, and many design decisions. Data must be found from numerous charts and tables. Furthermore, design is typically iterative, requiring the designer to try several options for any given element, leading to the repetition·ofdesign calculations with new data or new design decisions. This is especially true·for complete mechanical devices containing several components as the interfaces between components are considered. Changes to one component often require changes to mating elements. Use of computer aided mechanical design software can facilitate the design process by perfonning many of the tasks while leaving the major design decisions to the creativity and judgment of the designer or engineer. We emphasize that users of computer software must have a solid understanding
of the principles of design and stress analysis to
ensure that design decisions are based advlsetbat·thesoftware
on
reliable foundations.
We
be used only after mastering a given design
methodology by careful study and practicing manual techniques. Then, data with known results can be applied to the software as a check on the understanding
of the program's Input and output.
Included in this book is the MDES/GN mechanical design software created by the TEDATA Company. Derived from the very successful MDESIGN mec software produced for the European market, the U.S. version of MDESIGN employs standards and design methods that are in typical use in North America. Manyof the textual aids and design procedures come directly from this book, Machine Elements in Mechanical Design.
Topics for which the MDESIGN software can be used as a supplement to this book include: Beam stress analysis
Beam deflections
Mohr's circle
Columns
Belt drives
Chain drives
Spur gears
Helical gears
Shafts
Keys
Power screws
Springs
Rolling contact bearings
Plain surface bearings
Bolted connections
Fasteners
Clutches
Brakes
Special icons are placed in the book at places where use of one of the 28 modules in the software is pertinent.
v
Basic Features of MOES IGN MOE SIG N soflware is a useful tool for problem solving and design. Users must first ensure that the software is appropriatetothe
nature of the problemlo be solved. While the 28 modules cover a wide
range of applications within the field of machine design, not every problem can be solved. The soflware is very user friendly and each module contains several textual and graphic aids that explain the technical
Basic Features of MOES IGN MOE SIG N soflware is a useful tool for problem solving and design. Users must first ensure that the software is appropriatetothe
nature of the problemlo be solved. While the 28 modules cover a wide
range of applications within the field of machine design, not every problem can be solved. The soflware is very user friendly and each module contains several textual and graphic aids that explain the technical "bases on which the module is constructed .and.the data that must be entered by the user. Input screens prompt the user to define the problem and to make basic design decisions. Several modules contain extensive data bases that allow the user to consider multiple optional designs and compare them to select the more optimum choice. Some modules also provide a parametric analysis feature. After all necessary data are entered, the user applies the
Calculate
feature to cause the module
to perform the required analyses and produce the output in an easy to read format. The
Calculate
feature
is represented on the tooioaras an image of a blue calculator with a yellow gear. Altematively, the user can use the function key, F10. Input and output can be reported in several different units selected by the user. Conversions, if needed, are automatically accomplished by the software. The output always contains lists of pertinent input values and computed results. Many modules augment the basic output with graphical displays of the results and pictorial views of the element being designed. Some modules include cautionary comments when results do not meet design requirements, advising the user to redesign the element. DeKfiptions
of the Modules
The following sections list the 28 modules organized into 13 groups and provide brief discussions about each module. Included are the chapter where each module can be used, a basic description of the type
of problems
that can be solved, the type of input data required, and the type of output results that are
produced. NOTE: The computed results from MOE SIGN may not match exactly those reported in the book for example problems or end of chapter problems. Values for some parameters may be selected by a user from charts and graphs In the book, whereas the program may compute those giving slightly different results. For some modules, particularly Ball and Roller Bearings, databases in the program are different from those in the book. Columns Group:
P ertinent to Chapter 6 in the book.
C olumn Analysis Module:
S ections 6-6, 6.7, 6·11 and 6.12
Centrally loaded straight or crooked columns and eccentrically loaded straight columns are analyzed.lnput data required are: column length, end fIXity, material, cross section shape and dimensions, amount of crookedness if any and amo t f . . . . ,un 0 eccentncity of the hne of action of the load if any. Output for straight, ce~tratty loaded columns includes critical buckling load and allowable load. Output for crooked and eccentncally loaded columns includes maximum stresses. For eccentrically loaded columns, the rnaxmum lateral deflection of the column is also computed.
_
_ Column Design Module: Section 6-10 Given the required load on a column of a given length with specified end fixity, the program computes the minimum acceptable diameter of'acolumn with a solid circular cross section. Pertinent to Chapters 3 and 5 in the book.
Seams Group:
Statically Detenninate Beams Module: This is a very extensive beam analysis program that allows the application of loads in virtually any direction including concentrated forces, distributed loads, concentrated moments, and torques. It offers visualization of the beam, its supports, and its loading pattem. Careful data entry is advised. Statically Indeterminate Beams Module: This program analyzes beams on more than two supports with a large variety of loading types. Combined Stress and Mohr's Circle:
Pertinent to C hapters 4 and 5
Given the stress condition on an element, the program completes Mohr's circle, presents maximum principal stresses, maximum shear stress, and the orientation of those elements. The Mohr's circle is drawn automatically. V-Selt Drives:
Pertinent to Chapter 7, Section 7-4
This tool for designing V-belt drives is based on an extensive data base of ratings for three sizes of V.belts. The input data screen allows the specification of power to be transmitted, speeds, approximate center distance, and service factor. The program presents a list of suitable belttypes, sizes, and standard lengths, and sheave sizes from which the user selects one combination. The performance of that design is then displayed. Numerous subsequent altemative designs can be easily created. Pertinent to Chapter 7, Section 7-6
Chain Drives:
An aid for designing roller chain drives, this program includes an extensive data base of the latest power ratings for roller chain drives from the American Chain Association. The input data screen allows the specification of power to be transmitted, speeds, approximate center distance, number of chains, and service factor. The program presents a list of suitable chain sizes and sprockets from which the user can select one combination. Single or multiple strands of chain can be used. Gearing Group:
Pertinent to Chapters 8, 9, and 10
Separate modules are provided for Spur Gearing, Helical Gearing, Bevel Gearing, and wormgearing.
Each module basically follows the procedures described in the book. Input data include
the diametral pitch, number of pinion teeth, input speed, output speed, certain material factors, overload factor, reliability factor, and others depending on the module. The program provides guidance for the quality number and the specification of the number of teeth in the gear and its face width. The geometry factors for bending and pitting resistance are computed by the program for some modules, while others require the user to input those usingtables and charts from the book or from charts reproduced in the
vii
hel screens. Outputs include actual output spee d , sizes of pertinent geometric features, '. forces on gear
hel screens. Outputs include actual output spee d , sizes of pertinent geometric features, '. forces on gear teeth, and tooth stresses. T he acceptability of stresses is evaluated by the ~rogram with suggestions for the types of materials to be specified. Multiple designs can be tried very quickly to work toward an optimum final result. Keys Group:
P ertinent to Chapter 11
separate modules are provided for Parallel Keys and Woodruff
Keys, using design pro~dures
similar to those presented in the book. Input can be either the torque to be transmitted of power and shaft speed. The shaft diameter isspecified,likely
or the .combination
based on prior stress analysts, Matenals
for the key, the shaft, and the hUb of the power transmitting element are selected from a list taken from Appendix 3 in the book. The yield strengths are then automatically inserted. The usespeclnss a design factor and the length of the hub. The program determines the appropriate size forthe 'key according to the shaft s ize and the stress analyses using procedures similar to those outlined in the book. Bearings Ball
Group:
and Roller Bearings:
Pertinent to Chapters 14 (Rolling contact)
and 16 (Plain surface)
Chapter 14
This program aids in the specification of itcommercially available bali or roller bearing from extensive databases for t6 different types of bearings from two widely known manufacturers,
FA G and
SK F. The user selects the preferred type, and provides detafor redial and thrust loads, speeds, desired hours
of 'life, and size limitations. N e w factorsihat are not discussed in the book are also specified:
Viscosity Grade for the lubricant to be applied (typical choice is 66); Operating Temperature
(typical
choice is 40"C); and Contamination Factor (tYP ical choice is 1.0). The program then produces a list of possible'bearings, organized in oroer of the bore size. The User selects oneandtl1e
program completes
the calculation of performance, giVing the projected life of the bearing in hours that is compared with the desired life. SU bsequent trials may be done qulte quickly to work toward an optimum design. NOTE: The basicdynarnic /()~ data .repodedfr1r any [Jivenbearing
wiN not match those given in
the book because the bearings come from different Sources and because an additional
tector, a23. called
the Material and Lubrication Factor, is applied. T h e value of this factor is prOprietary to a given manufacturer andfypically yields a higher value for basic dynamic load, C, than is reported in the book. Plain Surface Bearings:
.Chapter 16, Section 16-6
This program assists in the deSign of boundary lubricated plain Surface bearings using the methOd presented in Section 16-5 of the book. The user enters data for radial/oad, diameter, and the desired ratio of bearing length
to
speed, minimum shaft
diameter. The program then computes the required
pVvalue and recommends a material from Table 16-1 in the book that has an acceptable
rating for pv,
NOTE: Data for the wear factor, K, and the coefficient of dynamic friction are not available in the book version of the software and are repOrted in the output W!'th I -v a ues of 0.000.
Vl1l
Power Screws:
Pertinent
to Chapter
17 Linear
Motion Elements;
Section
17-2
Power Screws:
to Chapter
Pertinent
17 Linear
Motion Elements;
The procedures described in'Section 17-2 of the book are implemented a power screw with Acme threads having a 14
1/2'
Section
17-2
by this program to design
thread angle. The user enters data for the load to be
moved, the distance traveled, and the time to move the load. The material for the screw isseleeled
from
lists of steels, aluminums, cast irons, copper alloys, bronzes, and zinc alloys. The strength data are automatically entered by the program. The design value for the coefficient of frielion is entered. The output includes the dimensions
of the standard Acme screw threads from Table 17-1 in the book. The
program checks the tensile stress in the screw and the shear stress 'in the threads. The minimum length of MQagement'of
the threads with a nut is reported. The program also computes the torque required \0
raise and lower the load, the efficiency, the linear speed of the nut, the rotational speed of the screw, and the power required to drive the screw. !fthe screw is loaded in compression,it
should be analyzed for
column buckling using the Column Analysis module.
Joints Group:
Pertinent
Fasteners:
Chapter
to Chapters 18, section
18 18-4
This module completes the procedure outlined in Section 18-4 in the book for designing and analyzing bolted joints that provide clamping loads. Input data include the total load applied to the joint and the number of bolts. A Demand Factor, k, is specified that gives the allowable percent of the proof load of the screw material, often taken to be 75%. The factor, k1, is based on the lubrication present and is
setteo.tsfor
typical conditions urness the threads are thoroughly
process.awmoowasks
fortheSAEmaterial
cleaned. After starting the Calculate
grade forthe bolt as listed ln Table 18-1 in the book. The
output includes the required size of bolt, taken from the list in Table 16-4 in the book, and the tightening torque.
Springs Group:
Chapter
19
This group contains three modules for Helical Compression Springs,
and Helical Torsion
Springs.
Springs,
Helicat Extension
Each module implements the design procedures developed in
the book and uses data from the book for spring wire sizes and material properties. Helical Compression
Springs:
Section
19..0
Method 1 for the design of helical compression
springs illustrated in Example Problem 19-2 is
used in this module. The user supplies values for forces and lengths, end type, wire type, type of service {Iight,average,severe),and stress (typicaltyinthe
an inilialestimateofthe
range from 60 to 140ksi).
mean diameter of the spring and the design shear The program determines
an appropriate wire diameter,
computes the actual stresses, and outputs the geometry of the spring. Helical Extension
Springs:
Section
19-7
The method for designing helical extension springs illustrated in Example Problem 19-4 is used in this module. The user supplies values for forces and lengths, end type, wire type, type of service (light, average, severe), and an initial estimate of the mean diameter of the spring and the design shear stress
(tYPically
h
(tYPically . In the range f rom 80 ta 140 kSI·)The .. program determines an appropriate wire diameter, computes the actual stresses, and outputs the geometry of the spring. Helical Torsion S prings:
S ect jon 19-8
The method for designing helical torsion springs illustrated in Example Problem 19-5 is used in this module. The user supplies values for moments and angles of rotation, end type, wire type, type of service (light, average, severe), and an initial estimate of the mean diameter of the spring and the design bending stress (typically in the range from 11010 190ksi). The program determines an appropriate wire diameter, computes the actual stresses, and outputs the geometry of the spring. Joints Group:
Bolted C onnections:
C hapter 20, S ection 20-3
This module determines the minimum required diameter of the bolts in a connection subjected to direct s hear and shear due to a moment applied to the member similar to that shown in Figure 20-5 in the book. The bolted connection may be comprised of any array of bolls for which the distance from the centroid of the array 10 any.individual bolt is th.esame. E xamples area rectangular alTay .of four.bolts or a circular array of any number of bolts. The analysis considers only a single force to be applied to the connection. If more than one force is applied, the resultant
of all
applied forces must be determined by the
user for input to the program. Both the magnitude and the Orientation of the line o r action .of the force must be known. The program assumes that the bolls are subjected to single shear. If they are in double shear, the applied force should be divided by 2.0. Inputs required are the shear lead, the ·number of bolts, the perpendicular distance from the line of action oflhe load to the centroid of the boll pattem, the radial distance from the centroid to any boll, the x and y distances from the centroid to the bolt, and the angle of inclination of the applied load. The angle, Cl,
is zero for a vertically downward load. Graphic and textual helps are provided.
The output consists of the forces on Ihe bott, the required diameter and the nearest standard boll diameter as S hown in Table 18-4 in the book. Welded J oints: The method
Chapter 20, Section 20-4 O f Section
20-4
of the
:book is used in this module to compute the required size of
weld to carry .a specified force using a weld geometry selected from those shown in F igure 20-8 in the book. This figure is included on help screens in the program. Inputs required are the type of jOint, key dimensions of the joint, the location of the load, and the allowable force per inch of weld length taken from Table 2Q,3 that 'ISshe hi. th wn ona e p screen In e program. The term, bending console length, ab, is the distance, a, shown under the Bending column of Figure 20-8. Similarly, Ihe term, twistirrg console length at, is the d'istan·ce a f th I n ., . , ,rom e J orslon co um . OUtputs inclUde geometry factors ·of the weld pattern, bending momenl, twisting moment, forces on the weld, and Ihe required weld leg size. T .
x
Clutches and Brakes Group:
Chapter 22
Clutches and Brakes Group:
Chapter 22
This group contains five modules for Cone or Plate-Type Clutches or Brakes and Short Shoe, Long Shoe, and Band Brakes. Each module implements the design procedures developed in the book. Plate-Type Clutch or Brake:
Section 22-11
The procedure illustrated in Example Problem 22-6 is used in this module for the analysis of a plate-type clutch or brake. The user inputs the desired friction torque, the nonmalactuation force available, the coefficient of friction, the rotational speed, and a reasonable value for the ratio of the outside radius to the inside radius (say 1.50). The program computes the required mean radius, the outside radius, the inside radius, the frictional power absorbed and the wear ratio (hplin\ Cone Clutch or Brake
Section 22-13
The procedure illustrated in Example Problem 22-7 is used in this module for the analysis of a cone clutch or brake. The user inputs the desired friction torque, the mean radius of the drum, the cone angle, and the coefficient offriction. The program computes the required axial actuation force. Short Shoe Drum Brake:
Section 22-14
The procedure illustrated in Example Problem 22-8 is used in this module for the analysis of short shoe drum brakes. The user inputs the friction torque desired and proposes the drum diameter, coefficient of friction, and basic dimensions of the actuation system. The program computes the required actuation force. Long Shoe Drum Brake:
Section 22-14
The procedure illustrated in Example Problem 22-9 is used in this module for the analysis of long shoe drum brakes. The user inputs the drum speed, friction torque desired, drum radius, coefficient of friction, design value for maximum pressure, and the basic dimensions of the actuation system. The program computes the required width of the brake pad, the actuation force, the frictional power, and the wear ratio (hp/in\ Band Brake
Section 22-15
The procedure illustrated in Example Problem 22-10 is used in this module for the analysis of band brakes. The user inputs the drum speed, braking torque desired, design value for maximum pressure, drum radius and width, coefficient of friction, the angle of wrap of the band on the drum, and the basic dimensions of the actuation system. The program computes the friction torque, the actuation force, 2
the friction power, and the average wear ratio (hp/in ). Subsequent iterations are quickly done to work toward an optimum design.
MACHIN MACHINE E ELEMENTS IN MECHANICA MECHANICAL L DESIGN DESIGN
MACHIN MACHINE E ELEMENTS IN MECHANICA MECHANICAL L DESIGN DESIGN Fourth Fourth Edition Edition Robert L. Mott P rent rentice ice-Hall -Hall P ublish ublishin ing g Compa Company ny Descr Descrip ipttion ion of Sprea Spreads dsh heet eets Inclu Includ ded on CD in Solut Solution ions
Manua Manuall
Introduction The The Solut Solutio ions ns Manu Manual al for for this his book book inciu inciude des s a com comput puter disk disk that cont contai ains ns 26 com comput putatio ationa nall aids aids that hat are are keyed keyed to the the book. book. The files are writ writtten as Microsoft Microsoft Excei spreadsh spreadsheet eets s uSing Version Version 2002 2002 on WindowsXP. Many of the the spread spreadshee sheetts appea appearr in the tex textt. Other Others s were were prepar prepared ed to P rodu rodu~ ~ solut solutions ions for the .Solution .Solutions s Manual. Manual. The given given spread spreadshe sheet ets s includ include e data data and and result results s from from cert certain figur figures es Inthe the text text.. from from cert certain exam example ple probl problem ems, s, or for cert certain ain problem problems from the end of chapt chapters ers cont containing aining the analy analyst sts s and design procedu procedures res feature featured d in the the program programs. s. The The foll follow owin ing g sect sectio ions ns giv give brie brieff descr escrip ipttions ions of each each spr spreads eadshe heet et.. Many Many are are discu discusse ssed d in the the text ext in more ore ext extensive ensive det detail. It is expec expectted that hat you you will will verify verify all of the the element elements s of each spread spreadshee sheett before before using them for solut solutions ions to specific specific problem problems.
It is is recom recommen mended ded that that you you mainta maintain in the given given Using the Spreadsh Spreadsheet eets: s: spreadshee spreadsheets ts as they initially initially appear appear on the disk, disk, consi consider dering ing them them to be be master master copies copies.. To use a program program for SOlving other proble problems, ms, call it up in in Excel Excel and use the the ·Save Save as. comman command d to name name it something something different. different. For instance, instance, the Origin Original al program program cal/ed cal/ed Column Analy should ld be Analysis sis shou considered consi dered the ma Use problem "Save as" and call it, Column Analy Analysis sis _ Worki Working ng.. Then use that version versi onmaster. forster. general proble m Solving. Solving. it , for example, Colum You shou should ld stud study y the con concept cepts s and and the solut solution ion techn echniq ique ues s for for each each type of prob proble lem m befo beforre usin using g the spread spreadshee sheetts. You should should work work sam sample probl problem ems s by hand hand first. first. Then enter the appr approp opria riatte data into into the spread spreadshee sheet tded to verify ver ify the solu ion . tIn most most spread spreadshe sheet ets, s, the data data that need need to be enter entered ed are are ident identifi ified ed by gray gray-sha -shaded areas areas andsolut by titali ition. alic c ype. ype. Descrip Descripttions ions
of Spreadsh Spreadsheet eets s
The descr escript iptions ions are are giv given here here in the orde orderr that hat the Sub S ubje ject cts s for the spr spreads eadshe heet ets s are are cov covered ered in the the text ext. The files files are list listed ed on the disk in alph alphabe abettical order order..
Co~umnAnalysis: Chapt Chapter 6. Analyze Analyzes s strai straigh ghtt colum columns ns of unifor uniform m cross cross section section to detem detemnin nine e the cntlca cntlca~buck ~bucklin ling g load load and the the allow allowab able le load. load. The spread spreadshe sheet et shows shows result results s for Exa E xam mple P roble roblem m 6-1 as given In Figure Figure 6-9 on page page 242. 242. U.S. Custom Customary ary unit units s are are used. used. A descrip descripttion is given given in Section Section 6-8. 6-8. The proc proces ess s IS esse esse~ ~tlall lally y the same same as th that show shown in the the flow flow char chartt of Figu Figure 6-4. -4. Not Note that a shor shortt macro program program In Visual Visual BaSICIS BaSIC IS used to to decide decide w~ether ether the colum column is iong (EUler) (EUler) or short (J . B. J ohn ohnson) son) and and to com complet lete the calc calcul ulat atio ion n of the cnt cntlcal lcal bUCk bUCkli ling ng load load Be th t Excel Excel prog progra ram m enables macros. . sure a your Column Column Analysis Analysis SI: .Chapt COlumn AnalYSis: AnalYSis: exce t SI't Chapter er 6. Same Same as COlumn d Th The solution to Exam Example ple Probl Problem em 6-2 6-21S show shown as giv given en in Figu Figure 6-1 6-10 0 on pag page e 243 243. p UOis are are use use . CirCUlar CirCUlar Column Column Analysis: Analysis: Chapt A I '. Chapter 6. Special Special versio version n of Col t .c prope propert rties ies of a COlumnwit COlumnwith h a solid cirCUlar cirCUlar cross cross Section Section are c umn na ysls In which which th~ g.eo g.eom me n spr spreadshe sheet can be used sed as an iterative des' des' t I omputed Whe When the diameter IS input. The The to a circula circularr cross cross section section to carry carry a give given n load load Ig~ oOF deter determ mine the requir required ed diam diameter eter of a colum column n wit with . ee Igur Igure e 6-14 -14 on on page age 249 249.
xii
;
Crooked Crooked Column Column Analysis: Analysis:
Chapt Chapter er 6. Sectio Section n 6-11 6-11.. Anal Analyz yzes es the allo allow wable able load load on a colum column of const constan antt cross cross sect section ion with ith a give given n amou amount nt of croo crooke kedn dness ess.. Dat Data from from Exam Example ple Proble Problem m 6-4 are are used used
;
Crooked Crooked Column Column Analysis: Analysis:
Chapt Chapter er 6. Sectio Section n 6-11 6-11.. Anal Analyz yzes es the allo allow wable able load load on a colum column of const constan antt cross cross sect section ion with ith a give given n amou amount nt of croo crooke kedn dness ess.. Dat Data from from Exam Example ple Proble Problem m 6-4 are are used used
as show shown n in Figur Figure e 6-16 6-16 on page page 252. 252.
Eccentric Eccentric Column Column Analysis: Analysis:
Chapt Chapter 6. Section Section 6-12. 6-12. Compu Computtes the require required d yield yield streng strengtth of the the mater aterial ial and and the the resul resultting maxim aximum um defle deflect ction ion of the the middle iddle of a colum column that hat is loaded loaded eccent eccentri ricall cally. y. Dat Data from from Exam Example ple Proble Problem m 6-6 6-6 are are used used as show shown n in Figur Figure e 6-18 6-18 on page page 256. 256.
Chain Chain Drive Design: Design: Chapt Chapter er 7. Desig Design n of roll roller er chain chain driv drives es as desc descri ribe bed d in Sectio Section n 7-6. 7-6. User must ust obt obtain ain rat rated pow power dat data from from Table Tables s 7-5, 7-5, 7-6, 7-6, or 7-7 7-7 to specif specify y a suit suitable able chai chain n num number ber and and num number ber of teet teeth h in the the smaller smaller sprocket sprocket..
Contact Contact Ratio-Spu Ratio-Spur r GeatS: GeatS: Chapt Chapter 8. Compu Computtes the contact contact rat ratio for spur spur gears gears using using the proce procedu dure re show shown n on page page 317 317 in Sec S ecttion ion 8-4. 8-4.
Bevel Gear Geometly: Geometly:
Chapt Chapter 8. Compu Computtes the geom geometric etric feat featur ures es of stra straigh ightt beve bevell gear gears s using using the form formulas ulas list listed ed in Tabl Table e 8-7 8-7 in Sectio Section n 8-8 8-8 and illust illustra ratted in Exam Exampl ple e Proble Problem m 8-6 on page page 337. 337. Two Two iden identtical ical prog progra ram ms are are show shown n side-b side-byy-sid side. e. One shows shows the result results s of Exam Example ple Proble Problem m 8-6 8-6 and and the the othe otherr can be used used to solve any any give given n probl problem em.. Chapter er 8. Compu Computtes essen essenttial ial geom geomet etri ric c feat featur ures es of a worm orm and and Wormge Wormgeari aring ng Geomet Geometry, ry, CD, VR: Chapt worm wormge gear ar,, the cent center er dist distance ance bet between ween their heir shaft shafts, s, and and the the velocit velocity y rat ratio. Uses proce procedu dure re from from Section Section 8-10 8-10 as ill illus usttrat rated in Exam Example ple Proble Problem m 8-7. 8-7. The spre spread adshe sheet et was used used to to compl complet ete e Proble Problem ms 52-5 52-57 7 at the the .end of the chapte chapter. r. Chapter er 8. Compu Computtes the geom geomet etri ric c feat featur ures es of spur spur and and helic helical al gear gears s using using the the Gear Geometry: Chapt rela relattions ionshi hips ps in Sectio Sections ns 8-4 8-4 and and 8-7. 8-7. Can be used used for P robl roblem ems s
1-9 1-9 and and 41-44 41-44..
GeatS VR Design: Chapt Chapter er 8. Aid Aids s in the spec specif ifica icattion ion of the the num number ber of tee teetth in a pini pinion on and and gear gear to prod produc uce e a spe specif cifie ied d velo veloci citty rat ratio. io. Uses a proc proced edur ure e similar ilar to that that shown shown in Sectio Section n 8-13 8-13 on pag pages es 350350357 357 and illust illustra ratted in Tabl Table e 8-9. 8-9. An int integer eger is ent enter ered ed for for the the num number ber of tee teetth in the pini pinion on.. The prog progra ram m compu computtes the requ requir ired ed appro approxi xim mate ate num number ber of teet teeth h in the the gear gear to produce produce the given given veloci velocitty rat ratio. io. The user user the then n ent enters ers an int integ eger er for for the act actual ual num number ber of gea gearr teet eeth. The prog progra ram m iden identtifie ifies s the combi combina nattion of num numbe bers rs of teeth eeth that hat prod produce uces s the minim minimum differ differen enttial between ween the desired desired rat ratio and and the actua actuall rat ratio. io. The spre spread adsh shee eett was used used to complet plete e Proble Problem ms 62-65 62-65 at the end end of the the chap chaptter. er.
Spur Gear Forces: Forces:
Chapt Chapter 9. Compu Computtes the tan tange gent ntial ial,, radi radial, al, and norm normal force forces s on spur spur gear teet teeth of a giv given desig design n trans ransm mitt itting ing a giv given en pow power at a giv given en pini pinion on speed speed.. It uses uses the the metho ethod d of Sect Section ion 9-3. 9-3. The The spre spread adsh shee eett was used sed to com complet plete e Prob Problem lems 1-6 1-6 at the end end of Chapt Chapter 9. The The resu result lts s for for Probl Problem ems 1 and and 2 are shown shown in the the master aster..
Spur GeatS-Design-U.S.:
Chapt Chapter er 9. Perfor Perform ms a com complet plete e desig design n anal analys ysis is for for a pai pairr of spu spurr gear gears, s, inclu includi ding ng the essent essential geom geomet etry ry,, tange angent ntial ial force force,, requ require ired d bend bendin ing g stre stress ss num number, ber, and and require required d cont contact stre stress ss num number. ber. All modif odifyi ying ng fact factor ors s for for stre stress ss calcu calcula lattions ions as desc descri ribe bed d in Sect Sections ions 9-8 9-8 to 9-1 9-12 2 are are inclu include ded. d. The data data from from Exam Example ple Proble Problem m 9-5 9-5 are are shown shown in the given given spre spread ad sheet sheet as illu illust stra ratted in Figure Figure 9-28 9-28 on pag pages es 416416-41 417. 7. An ext extensiv ensive e discu discussi ssion on of the sprea spreadsh dshee eett is give given n in Sect Section ion 9-14 9-14 on page pages s 415-4 415-419 19.. An added added feat featur ure e of the spreadsh spreadsheet eet on the the CD C D is the compu computtation ation of the requ requir ired ed hard hardne ness ss (HB) for for thr throu ough gh-h -har arde dene ned d Grade Grade 1 stee steell usin using g the equa equattions ions in Figur Figures es 9-10 9-10 and and 9-11. 9-11. The user user can then hen specif specify y suit suitable able mater aterial ials s and and list them at the bot bottom of the the spread spreadshe sheet et..
Geometry Factor-I-Pitting:
Chapt Chapter 9. Compu Computtes the value value of the the geomet geometry ry fact factor or,, I, used used in the the calcu calcula lattion ion of cont contact act stre stress ss for for spur spur gear gears s in Equat Equatio ion n 9-25 9-25 on page page 401 401 of the the tex textt. Progra Program m uses uses the algor algorit ithm hm from from Appendi Appendix x A20. A20. Chapter er 9. Same Same as Spur Gears-Des exceptt the geom geomet etry ry fact factor, or, I, Spur Gears-Des Gears-Design-U ign-U.S .S .•With I: Chapt Gears-Design ign excep is comput puted wit within hin the progr program am instead instead of being being inpu inputt by the user. user. The progr program am Geometry Geometry Factor· Factor·llintegrated ed within within $pur GeatS-Des addittional ional inpu inputt value value is neede needed d for for the the pressu pressure re Pitting is integrat GeatS-Design. ign. One addi angle. Chapter er 9. Simil Similar ar to Spur GeatS-Desl exceptt SI metri etric c dat data are are used used as Spur GeatS-Design-SI: Chapt GeatS-Deslgn: gn: excep descr describ ibed ed in Sectio Section n 9-13 9-13 and and illus illusttrat rated in Exam Example ple Proble Problem m 9-6. 9-6. Dat Data from from Exam Example ple Proble Problem m 9-6 9-6 are used in the the given given spreadshe spreadsheet et.. XIII
Chapter Chapter 9. Section 9-16. 9-16. Determ Determi.n i.nes es the ~ower transmi transmittting capaclt capaclty of a Spur Gears-Capacity-U.S.: Gears-Capacity-U.S.: given given set of spur spur gears gears considering considering both bending bending stren strengt gth h and pitt pitting resistance. resistance. The user must must Input the allowab allowable le bending bending stress stress and allowab allowable le contact stress stress based on the the materi material al specified specified for the pinion pinion and the gear using Figures Figures 9-10 to 9-15 and Tables Tables 9-3 and 9-4. 9-4. The spreadsheet spreadsheet includes includes the the comput computat ation ion of the the required required bending stress number, number, Sat, and contact contact stress number, number, sac, based on user-ent user-entered ered hardne hardness ss (HB) for for thr throug ough-h h-har arden dened ed Grade Grade 1 steel steel usin using g the the equat equation ionss in Figure Figuress 9-10 9-10 and 9-11. 9-11. The user must transcri transcribe be these values values into into the the spreadsheet spreadsheet if, if, in fact fact,, this kind kind of materi material al is specified. specified. Chapter 9. Completes Completes the design of plastic plastic gears gears using the procedur procedure e from from Plastic Gears· Design: Chapter pages 440-1. Data Data are shown for for E xample xample P roblem roblem 9-6. Chapter Chapter 10. Comput Computes es the for forces ces on heli helical cal gear gear teeth eeth as describ described ed in Section Section 10-2 10-2 and illust illustra ratted in Exampl Example e P robl roblem em 10-1. Complet Completes es the design design analy analysis sis for for a pair pair of helical helical gears gears as descri described bed in Section Sectionss 10-3 10-3 to 10-5 and ill illust ustra ratted in Examp Example le P robl roblem em 10-2. 10-2. Used for for the solut solutions ions to P roblem roblemss 1-11 at the end of C hapter hapter 10. Helical Gears-Design: Gears-Design:
Chapter Chapter 10. Similar Similar to Spur Gears-Capacity: with with modifi modificat cations ions for the Gears-Capacity: special special geome geomettry of heli helical cal gear teeth. eeth. Used for for the the solut solution ionss to P robl roblem emss 12 and and 13 at the end of Chapter Chapter 10. The user must must input input the allow allowable able bending bending stress stress and allowab allowable le contact contact stress stress based on the the materi material al specified specified for the pinion pinion and the gear gear using using Figures Figures 9-10 to to 9-15 and Tables 9-3 and 9-4. The spreadsheet includes the computati computation on of the the required bending s tress tress number, number, s a " and cont contact stre stress ss num~r, s~,based on user-ent user-entered ered hardn hardness ess (HB) for for thro through-h ugh-hard ardened ened Grade 1 steel steel using the equat equation ionss In Figur Figures es 9-10 9-10 and 9-11 9-11.. The user must must transcr ranscrib ibe e these valu values es int into the spread spreadshee sheett if in fact, this kind of material is s pecified. ' Helical Gears-capacity: Gears-capacity:
Gears - Design: Bevel Gears Wormg Wormgear earing ing
- Desig Design: n:
Chapter Chapter 10. Comput Computes es forces forces and stresses stresses on bevel gears. gears. Computes Computes some geome geomettry values, forces, forces, and stresses for wormgear wormgearing ing..
Chapter Chapter 12. Computes Computes the the minim minimum um acceptabl acceptable e diamet diameter er for shaft shaftss using Equation Equation 122~~ 2~~n ':th :th bendi bending ng and and torsion orsion are are presen presentt and Equation Equation 12-16 12-16 when when only only vert vertical ical sheari shearing ng stre stress ss is ~odifyi~ odifyi~9 9 f:~~so~~ so~~~~~~r~~ r~~s :or torques, forces, forces, bending moments, moments, pertinent pertinent material material strengt strengths, hs, at several several selected selected sections sections of t~en~~ en~~'fta 'ftand nd .~t .~tress concent concentration ration factor. factor. The progra program m is typi typicall callyy applied applied given given spreadsheet spreadsheet uses data data from from one Ias ;. ustra ustratted in Desig Design n Ex~mp Ex~mple le 12-1 12-1 on pages pages 548-5 548-552. 52. The lon Figure Figure 12-19 12-19 on page 561. 561. A discussio discussio ocath on the shaft shaft .In .In.Desl .Deslgn gn Exampl Example e 12-1 12-1 as illu illust stra ratted in no f e sprea spreadsh dsheet eet IS In Sectio Section n 12.1 12.10. 0. f . Foree Foree Fits: C hapter 13, S ection 13-8 S tr betwee between n mat mating ing memb member erss assembl assembled ed ~it ~ith h e~es e~es or Force Fits. Fits. Comput Computes es the pressur pressure e at the the int interfa erface ce result resulting stresses stresses and deform deformat ations ions for the ~ I~t I~terferen erference ce fit (See S ection ection 13-6.) 13-6.) Also comput computes es the from from Exampl Example e P robl roblem em 13-2 13-2 are are Shown in th a Ing Ing memb member erss usmq usmq the the proced procedur ure e on pages pages 587-8 587-8.. Data Data e example. . 1: C hapter 19 S ection Spring Spring Design-M Design-Metho ethod d met method from from Exampl Example e P robl roblem em 19-2 19-2 to d ' 19-6. 19-6. The give given n spread spreadshee sheett uses data data and the the to fit given geomet geometric rical al limit limitat ations. ions. S ee ~~J ~rn~ rn~~f~ helical helical compression compression spring spring for a given given loading loading and fit given . e on page 753 and the accompanying dis cus sion. Spring Spring Design-M Design-Metho ethod d 2' C h . . . apter 19. S imilar to S rI D deSign deSignin ing g to a set of geom geomet etri rical calli lim mital italio ions ns S Ex P ng eslg 1 wit without hout the rest restri rict ction ion of eslgn· n·Me Meth thod od and and the aCCOmp aCCOmpany anyingdiSCUSSio gdiSCUSSion. n. . ee amp ample Prob Probllem 19 19-3, -3, Fig Figure 19-17 -17 on on page age 753 753, Shaft Shaft Design: Design:
xi v
CHAPTER 1 THE NATURE OF MECHANICAL DESIGN
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CHAPTER 2
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CHAPTER 2 MATERIALS IN MECHANICAL DESIGN
1.
Ul t i mat e t ensi l e st r engt h i s t he appar ent st r ess at t he peak of t he st r ess- st r ai n cur ve.
2.
Yi el d p oi nt i s t he val ue of t he appar ent s t r es s f r om t he st r ess- st r ai n cur ve at whi ch t her e i s a l ar ge i ncr ease i n st r ai n wi t h no i ncr ease i n st r ess. I t i s t he poi nt wher e t he st r ess- st r ai n cur ve exhi bi t s a hor i zont al sl ope.
3.
Yi el d s t r engt h i s t he appar ent s t r es s f r om t he s t r es s st r ai n cur ve at whi ch t her e i s a l ar ge i ncr ease i n st r ai n wi t h l i t t l e i ncr ease i n st r ess f or mat er i al s t hat do not exhi bi t a yi el d poi nt . The of f set met hod i s used by dr awi ng a l i ne par al l el t o t he st r ai ght par t of t he st r essst r ai n cur ve t hr ough a val ue of 0. 2\ on t he st r ai n axi s.
4.
Many l ow al l oy st eel s exhi bi t a yi el d poi nt .
5.
The pr opor t i onal l i mi t i s t he appar ent st r ess on t he st r essst r ai n cur ve at whi ch t he cur ve devi at es f r om a st r ai ght l i ne. At t hi s val ue, t he mat er i al i s usual l y st i l l el ast i c. The el ast i c l i mi t i s t he appar ent st r ess at whi ch t he mat er i al i s def or med pl ast i cal l y and wi l l not r et ur n t o i t s or i gi nal si ze and shape.
6.
Hooke' s l aw appl i es t o t hat por t i on of t he st r ess- st r ai n cur ve t hat i s a st r ai ght l i ne f or whi ch st r ess i s pr opor t i onal t o st r ai n.
7.
The modul us of el ast i ci t y i s a measur e of t he st i f f ness of a mat er i al .
8. .
The per cent el ongat i on i s a measur e of t he duct i l i t y of a mat er i al .
9.
The mat er i al i s not duc t i l e. Mat er i al s havi ng a per c ent el ongat i on gr eat er t han 5\ ar e consi der ed t o be duct i l e.
10.
poi s s on' s r at i o i s t he r at i o of t he l at er al s t r ai n i n a mat er i al t o t he axi al st r ai n when subj ect ed t o a t ensi l e l oad.
11.
Fr om
~Q .
2- 5
G E/ [ 2( 1+Vl ] G = 42. 9 GPa =
=
( 114 GPal / [ 2( l +O. 33l ]
12.
Har dness - 52. 8 HRC ( Appr oxi mat e; Appendi x
13.
Tensi l e st r engt h ~ 235 ksi 14. - 17.
J~)
( Appr oxi mat e; Appendi x
19)
Errors in given stat_ents:
14.
A har dness of HB 750 i s ext r emel y har d, char act er i st i c of t he har dest st eel s i n t he as- quenched or sur f ace har dened condi t i on. Appendi x 3 shows anneal ed st eel s t o have har dness val ues i n t he appr oxi mat e r ange of HB 120 t o 230.
15.
Har dness on t he HRB sc al e i s nor mal l y l i mi t ed t o HRB 100.
16.
Har dness on t he HRC scal e i s nor mal l y no l ower t han HRC 20.
17.
The r el at i onshi p bet ween har dness and t ensi l e st r engt h i s onl y val i d f or st eel s.
16.
Char py and I zod t est s measur e i mpact st r engt h.
19.
I r on and car bon.
20.
I n a ddi t i o n t o i r o n a nd c a r bo n, AI SI 4340 s t e el ni ck el , chr omi um, and mol ybdenum. ( Tabl e 2- 3)
21.
Appr oxi mat el y 0. 40% car bon i n AI SI 4340 st eel .
22.
L ow- c ar bon: Medi um- c ar bon: Hi gh- c ar bon:
23.
Typi c al l y a be ar i ng s t eel c ont ai ns 1. 0% c ar bon.
24. 25.
Ot her el ement s ar e of t en pr esent . c o nt a i ns
Less t han 0. 3% 0. 30% t o 0. 50% 0. 50% t o 0. 95%
Lead i s added t o AI SI 12L13 s t eel t o i mpr ove machi nabi l i t y. Shaf t s ar e of t en made f r om AI SI 1045 4140, 6150, and 8650 s t eel s. ( Tabl e 2- 1/ ) ,
4640,
5150,
26.
Gear s ar e of t en made f 5150, 6150, and 8650 r om AI SI 1045, 4140, 4340, st eel s. ( Tabl e 2- l f )
27.
The bl ades of a pos t ho l e di r esi st ance, hi gh st r engt h gger shoul d have good wear s t e el i s a r e as o na bl e c h ~ a nd go od duc t i l i t y . AI SI 1060
4640,
Ol.ce.
26.
AI SI 5160 OQT 1000 i s hi cont ai ni ng appr oXi mat e~ gh- car bon, chr omi um s t eel , I t was heat t r eat ed by ~ O' f O% car bon and 0. 60% chr omi um. t emper at ur e, quenched i ne~i ng above i t s upper cr i t i cal de gr e es F ahr e nhe i t I t h 1, a nd t he n t e mpe r e d a t 1000 k s i o r 1040 MP a) a~d a s f a i r l y hi gh s t r e ngt h (Sy ~ 151 good duct i l i t y ( 14% el ongat i on) .
4
29.
I n gener al , a hi gh har dness wi t h good duct i l i t y ar e desi r abl e f or machi ne par t s and t ool s subj ect ed t o i mpact l oads as s een by a s hov el . A har dnes s of HRC 40 cor r esponds t o appr oxi mat el y HE 375 and i s consi der ed moder at el y har d. Whi l e t hi s i s a good l evel , even a hi gher val ue up t o HRC 50 ( HB 475) woul d be bet t er , pr ovi ded duct i l i t y i s f ai r l y hi gh, say about 15% el ongat i on. Appendi x 3 shows s ome f or ms of oi l - quenched AI SI 1040 and none l i st ed have suf f i ci ent l y hi gh har dness. Appendi x 4- 1 s hows t he s ame mat er i al quenched i n wat er and t emper ed. AI SI 1040 WQT 700 has a har dness of HB 401 ( HRC 43) wi t h appr oxi mat el y 20% el ongat i on and a yi el d poi nt of 92 ksi .
30.
Thr ough har deni ng i nvol ves heat i ng t he ent i r e par t f ol l owed by quenchi ng t o achi eve t he har dened condi t i on. Except f or some var i at i on i n t hi ck sect i ons, t he par t i s har dened t hr oughout . But no chemi cal composi t i on changes occur . In car bur i zi ng, t he chemi cal composi t i on of t he sur f ace i s changed by t he i nf usi on of car bon. Thus, car bur i zi ng r esul t s i n a har d sur f ace whi l e t he cor e i s sof t er .
31.
I nduct i on har deni ng i s a heat t r eat i ng pr ocess i n whi ch t he ar ea t o be har dened i s subj ect ed t o a hi gh- f r equency el ect r i c cur r ent cr eat ed by a coi l , i nduci ng cur r ent f l ow near t he sur f ace of t he par t and causi ng l ocal heat i ng. Af t er suf f i ci ent t i me t o br i ng t he sur f ace t o a t emper at ur e above t he upper cr i t i cal t emper at ur e of t he mat er i al , t he par t i s quenched t o har den t he sur f ace.
32.
Some car bur i zi ng gr ades of st eel s ar e AI SI 1015, 1020, 1022, 1117, l 11S, 411S, 4320, 4620, 4820, 8620 and 9310. The car bon cont ent r anges f r om 0. 10% t o 0. 20%.
33.
The AI SI 200 and 300, s er i es of s t ai nl es s s t eel s ar e nonmagnet i c.
34.
Chr omi um gi ves st ai nl ess st eel s good cor r osi on r esi st ance.
35.
ASTM f \ qq: st t r uct ur al st eel i s used f or most wi de- f l ange beams .
36.
HSLA st r uct ur al st eel s ar e hi gh- st r engt h, l ow- al l oy st eel s havi ng yi el d st r engt hs i n t he r ange of 42 - 100 ksi ( 290 700 MPa.
37.
Thr ee t ypes of c as t i r on a r e gr ay i r on, duc t i l e i r on, and mal l eabl e i r on.
3S.
ASTM A4S- S3, Gr ade 30 i s a gr ay i r on wi t h a t ensi l e st r engt h of 30 ksi ( 207 MPa) ; no yi el d st r engt h; l ess t han 1% el ongat i on ( br i t t l e) ; modul us of el ast i ci t y ( st i f f ness) of 15x106 psi ( 103 GPa) .
Pr obl em 38.
( cont i nued)
ASTM A536- 84, Gr ade 100- 70- 03 i s a duct i l e, i r on wi t h a t ensi l e st r engt h of 100 ksi ( 689 MFa) ; a y~el d st r engt h of 70 ks i ( 483 MFa) ; 3% el ongat i on ( br i t t l e) ; modul us o~ el ast i ci t y ( st i f f ness ) of 22xl 0 6 psi ( 152 GPa) . ASTM A47- 84, Gr ade 35018 i s a mal l eabl e i r on wi t h a t ensi l e st r engt h of 53 ksi ( 365 MFa) ; a yi el d st r engt h of 35 ksi ( 241 MFa) ; 18% el ongat i on ( duct i l e) ; modul us of el as t i ci t y ( st i f f ness ) of 25xl 0 6 psi ( 172 GPa) . ASTM A220, Gr ade 70003 i s a mal l eabl e i r on wi t h a t ensi l e st r engt h of 85 ksi ( 586 MFa) ; a yi el d st r engt h of 70 ksi ( 483 MFa) ; 3% el ongat i on ( br i t t l e) ; modul us of el ast i ci t y ( st i f f ness ) of 26xl 0 6 psi ( 179 GPa) . 39.
Powder ed met al s ar e pr ef or med i n a di e under hi gh pr es s ur e and s i nt er ed at a hi gh t emper at ur e t o f use t he par t i cl es . Re- pr ess i ng af t er s i nt er i ng i s s omet i mes used.
40.
Par t s made f r om Zamak 3 zi nc cast i ng al l oy t ypi cal l y have good di mensi onal accur acy and smoot h sur f aces, a t ensi l e st r engt h of appr oxi mat el y 41 Ksi ( 283 MPa) , a yi el d st r engt h of 32 Ksi ( 221 MFa) , 10% el ongat i on, and a modul us of el ast i ci t y of 12. 4xl O' psi ( 85 GPa) . ( Appendi x 10)
41.
t ool st eel s ar e t ypi cal l y used f or st ampi ng di es, punches, and gages. ( Tabl e 2- 5) Type D
42.
The s uf f i x condi t i on.
43.
The s uf f i x H on al umi num 3003- H14 i ndi c at es h ' s t r ai n har dened. t at ~t was
44.
The s uf f i x T on al umi num 6061- T6 ' t r eat ed. ~ndi cat es t hat i t was heat
45.
Al umi num 7001- T6 has t he h' h ~ 98 ks i ( 676 MFa) ' y' l d ~g est st r engt h; t ensi l e st r engt h 91 k s i , ~e s t r engt h ( 627 MF a) . Al umi num al l oy 6061 i s one of t h e most ver s at i l e. Thr ee t ypi cal us es of t ' t ' s t r uct ur es, chemi cal pr ~can~~m al l oys ar e aer os pace har dwar e , es s~ng equi pment , and mar i ne
0 on
al umi num 6061- 0 i ndi c at es
t he anneal ed
=
46. 47.
48.
Br onze i s an al l oy of phosphor us, ni ckel z, Co pper wi t h t i n, al umi num l ead, , ~nc, mangan ' es e , o r s i l i c on.
49.
Br onz e C86200 i s a manganese br onze cast i ng al l oy wi t h a t ensi l e st r engt h of 95 ksi ( 655MPa) ; yi el d st r engt h of 48 ks i ( 331 MFa) ; 20% el ongat i on ( duct i l e) ; modul us of el ast i ci t y of 15x10 6 psi ( 103 GPa) .
50.
Br onz e
51.
Ther moset t i ng pl ast i cs under go a chemi cal change dur i ng f or mi ng r esul t i ng i n a st r uct ur e of cr oss- l i nked mol ecul es. The pr oc es s cannot be r ever s ed or r epeat ed. Ther mopl as t i c mat er i al s can be f or med r epeat edl y by r eheat i ng because t he mol ecul ar st r uct ur e i s ess ent i al l y unchanged dur i ng pr ocess i ng.
is
used f or gear s and bear i ngs.
PEr;
52.
a) Gear s: Nyl on, pol ycar bonat e, el ast omer , phel ol i c. b) Hel met s: c ) Tr ans par ent s hi el d: Ac r yl i c . ABS, pol ycar bonat e, acr yl i c, PVC, composi t e. e) Pi pe: ABS, PVC. el ast omer . g) Swi t ch par t s: pol
53.
Desi gner s of par t s t o be made f r om composi t e mat er i al s can cont r ol 1) base r esi n, 2) r ei nf or ci ng f i ber s, 3) amount of f i ber s, 4) or i ent at i on of f i ber s, 5) number of l ayer s, 6) over al l t hi ckness, 7) or i ent at i on of l ayer s, 8) combi nat i ons of t ypes of mat er i al s .
54.
Composi t e mat er i al s ar e compr i sed of t wo or mor e di f f er ent mat er i al s, t ypi cal l y a r esi n r ei nf or ced by f i ber s.
55.
Resi ns used f or composi t es i ncl ude pol yest er s, epoxi es, pol yi mi des .
56.
Rei nf or ci ng f i ber s used f or composi t es ar e gl ass, bor on, ar ami d, and car bon/ gr aphi t e.
57.
Spor t i ng equi pment i s made f r om gl ass / epoxy, bor on/ epoxy, and gr aphi t e/ epoxy composi t es.
58.
Aer ospace st r uct ur es ar e made f r om gl ass/ epoxy, bor on/ epoxy, gr aphi t e/ epoxy, and ar ami d/ epoxy composi t es.
59.
Sheet mol di ng compound i s t ypi cal l y a gl ass/ pol yest er compos i t e.
60.
SMC' s ar e used f or aut o and t r uck body panel s and l ar ge hous i ngs.
61.
Rei nf or ci ng f i ber s ar e pr oduced as cont i nuous f i l ament s, chopped f i ber s, r ovi ng, f abr i c, yar n, and mat s.
1
.,...
acet al , ~pol yur et hane ABS and pol ycar bonat es. d) St r uc t ur al hous i ng: p e r , phenol i c, pol yest er / gl ass f ) Wheel s: Pol yur et hane yi mi de, phenol i c, P I T .
.,... 62.
Wet pr ocessi ng of composi t es i nvol ves, t he l ayup of f abr i c r ei nf or ci ng sheet s on a f or m, sat ur at ~on of t he sheet s wi t h t h e r e s i n , a nd c u r i n g u nd er h ea t a nd p r e s s u r e .
63 .
pr ei mpr egnat ed co mpos i t e mat ~r i al s ar e ~r oduce d wi t h t he r esi n al r eady on t he f i ber s ~n a conven~ent f or m, cal l ed a p r e pr e g. T he p r e pr e g i s l a ye r e d o nt o t h e f o r m a nd cur ed.
64 .
SMC' s ar e pr ei mpr egnat ed f abr i c s heet s f or med i n a mol d and cur ed si mul t aneousl y under heat and pr essur e.
65 .
P ul t r u s i o n i s a p r o c es s o f c o a t i n g t h e f i b er r ei nf or cement as i t i s pul l ed t hr ough a heat ed di e t o pr oduce a cont i nuous f or m s uch as t ubi ng, st r uct ur al s h a pe s , r o d, a nd h at s e c t i o ns u s e d t o s t i f f e n a i r c r a f t s t r uct ur es .
66.
I n t he f i l ament wi ndi ng pr ocess , cont i nuous f i l ament s ar e pl aced ar ound a mandr el i n a cont r ol l ed pat t er n and t hen c u r e d. T he pr o c es s i s u s ed f o r p i p e, p r e s s ur e v es s e l s , r ocket mot or cases, cont ai ner s and encl osur es.
67 .
S pe c i f i c s t r e ng t h i s t h e r a t i o o f t h e s t r e ng t h mat er i al t o i t s s peci f i c wei ght .
68 .
speci ~i c st i f f ness i s t he r at i o of t he modul us of el ast ~ci t y of a mat er i al t o i t s speci f i c wei ght .
69 .
Ma nY , c ~o s i t e s h av e s i g ni f i c a nt l y h i g he r v a l u es o f spec~f ~c st r engt h and speci f i c st i f f ness t han met al s. 70 • 73 r ef er t o P1gur e 2- l Z and Tabl e
of a
2- ~.
Ge ne r a l c o nc l u s i o ns f r o m Qu es t i o ns 70 - 73 : T he s p e c i f i c st r engt hs, of t he met al s l i st ed r ange f r om 0. l 94xl 06 t o 1. 00xI 0 6 ~n appr oxi mat 1 f ' s t i f f nes s es ' ar e v er y e y a ac t or of 5. 0. The s pec i f ~c appr oxi mat 1 near l y equal f or al l met al s l i s t ed, e y 1. 0xI 0 S i n The 'f ' h c ompos i t es I' d . s pec ~ ~c s t r engt hs of t e ~s t er ange 1 87 t ' , 04. 86xI 0 6 t han a ny o f t he met al . ~n, much h~gher s t i f f n es s a bo ut 2 / 3 t ~t G~a s s / e po x y h as a s p e c i f i c composi t es l i st ed r an T he o t h er 0 t h e me t a l s . t he met al s . ge f r om 2. 2 t o 8. .3 t i me s a s s t i f f a s See
Sect i on 2- 18 f or
answer s
t o Quest i ons
74 t o 78.
CHAPTER 3 STRESS AND DEFORMATION ANALYSIS
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l ~J'T.G
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=
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(J.
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:
c. ... f[ftooo oYloS,II4J +-{I+ Q
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COLIIMN: L~'IZm.jS=J,2SIJI.;C.~·I),&2S/N.
0 -
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COLIIMN: L~'IZm.jS=J,2SIJI.;C.~·I),&2S/N.
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8.J6IIN.;
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P s I'
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t=
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o
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5
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1/- 3•.s9.1Ni
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2,Z8/IIJ~= %.~Z.dO'N. h. ....
I 'f ,-
5'y::SlJolJIP.r/; e=.]oXIO('S;
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JH ~ " COLlu.AI-
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e=2BIC/6'1Si:
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~ztz1,Y,j
868
r:o r , = 207A111?d.. J TdstI.r71lirJ.lf
1 ! t A ¥ - PS6 )[Sec!
1281
L'
/.".19
,1 .
~
A= 1~"=1,Z8;
c;/='nJer/
ArT,., 113'.JSjl:36d
sc, (J.sl(l1zt
A
.1oH,,/SIJAIFblZ_1.4.
h ~
LEr
" )~ _ Pc.~: f5.~'I){J, 0 8'60/l6){//1.7)"'1 = - 37sbb L6 AI .J b'o 11/")
[.-n"
£9
J
A/
19. 7
=3
•
CENT"lf!ALLO~D: 51'«./1"{
TLla,:
5'"~ I t
Sy=J'ocoPslj
~/'I=S
Y Lo 7U-'Z. LtJAO: '-=S:SOOOU¥.,l. -2:lSl1JLB C,::.IJo ASSu""G C(JLII""JIIf LOAl~ : ~Q. 6-8: .I.or HPa-t'KLJ L.
A~rll"'tr
C&l..lJI't" S'fJPPu:a
1i,ulliOl, 3
I
)(
2~SllO /n.6) H (3DlIO')
x-
1 3 '1
(
F 1Xt;t)-P, JI~6D C(JL~"'IJJ K.::
V~Y"YL".r=/Z,ll1/"
rv81!!' "~fJ/-lv,Z:y=II,71"'_L/~Hrrt
LOAD: C-5,-J(f sren.clMt.'IV6l.: A -a. (,Y/N'; 12,=t1,Y91/11;# = -3 K,-/JJ. .. 1.(J{hJ!p,'I") "'2.Z,: AJ'r... IfJ' -s,=.s~0C0('S;J C e o/:JD -LoN'8t'1L.
F a.
=
P<:Jt/Ai = rr~eA
/I' ~(JOX/t')U.N) _ '1U;UJ 1(2UJ&. - - : . . . . : . .: = = -
=
)/(J:V ...)"
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CC"NTRALLoArJ: P.
A ·
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, .. T I I_ "
• 8.7"IIN'1'USES
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SIf,f(E"
k~tJ.
'S
IT"!lox,,') 1..)./'1)
U'f~"J
~
L
/I?SlJL8
=
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I9ND
~ <
tti .. .r Y 4- ~J60~=120oo~i
J r - - U ~ I ':! " " A ) ~ - ll OJ'' .&. r/+ @'Y)8lo.'I)8)S'~ 1.//2. .;J,6fI L : tl,6'1YJ.,(Ii'J/J <:(.2(0.'1") f o R . PIL2 W OO L, • O d ~ II 1z.o~" /3'( IfFR.+rJOl!:
/J .",.,)....
70
ECCENTRIC COLUMN ANALYSIS
Data
111.),
~ 4~ 4
CeHTVtL
-
~
~
lT~F
s.e: KL.~(iJ.IJX/8'..s7''rJ 'F':'" I?U,
from:RI5.~ii;;;,l;
from:RI5.~ii;;;,l;
ECCENTRIC COLUMN ANALYSIS
Data Solves Equation 6-13 for design stress and Equation 6-14 for maximum deflection
.-~'dBt!iifQi\.'V4i:!l!QI!i!l":!i1'~~"Qi..::: _ -.:i~ _ $ !'
Use consistent U.S. Customary units. Computed Values:
Eq. Length, L. =KL =
Column const., C c =
126.0 in
113.5
Argument of sec 0.769 for strength Value of secant = 1.3913 =
Argument of sec = 0.444 for deflection Value of secant 1.1073 =
Slender. ratio, KLJ r
=
90.6
Column is: short FINAL RESULTS Req'd yield strength Must
be
46,929 psi
less than actual yield strength: s = 46,000 psi
Max Deflection, y....
'It
=
=
0.322 In
ECCENTRIC COLUMN ANALYSIS
~ ~'Data from: F
Solves Equation 6-13 for design stress and E quation 6-14 for maximum deflection , .--d .T ~ jL ] jjll~ ln r ·,_.~ ~ ! , Use consistent U.S. Customary u n its Com utlld Values: NOTE: This solution considers the eccentric load with bending about the horizontal axis. Eq. Length, L.
=
KL =
Column const., C c = Argument of sec Value of secant = Argument of sec Value of secant
40.0 In
70.2
=
0.855 for strength 1.5236
=
0.494 for deflection 1.1355
=
Slender. ratio, KUr =
92.4
Column is: long FINAL RESULTS Req'd yield strength = 39,964 psi Must be less than actual yield strvngtl/:
40,000 psi Max Deflection, y.... 0.237 In See also Solution 38B for buckling about the thinner vertical axis. 5
= =
COLUMN ANALYSIS PROGRAM Refer to Figure 6-4 for analysis logic
\":j! !lQ !!i fQ l1t'!!m,,:J lJ i'$:m' c
It$',
E
Use consistent
U.S. Customary units.
Computed Values:
Eq . Length, L~
=
KL
Column const., C c
=
40.0 in
=
70.2
NOTE: Cross section properties taken with respect to the vertical axis because the load is central to that axis. But buckling is expected about the axis through the thin (0.40 in) section.
Slender. ratio, KLJ r
=
347.8
Column is: long Critical Buckling Load
=
4I91b
Allowable Load 183 Ib This value governs the design, not soIutlon 3BA =
AIYl1L.YJ/J"
7?tA'T
As
F~n
S'rli;q-II,
m IJv~ LII
reHOT h.:::
A
L ~ ~,"'III
vn
t:iUtGlt-
rrr:
C£lVritAl.L Y Lo/ht:laJ
AriJlIl $
1'rtnv
CUt..V,AfN
.4XI.r I t:= a,vaIII
i/J.//o/N
rtr l''''ol.l'1t1LA Wl1I11V:>:!
73
P.. " /6.1".
Data from: Pfti6renf.~ Solves Equation6-13 for designstress and Equation 6-14 for maximum deflection Use consistent ,. i'it8r,d~ iI!!I?Silil""'''~ ''!''r".".•"J.....,..'... ,'''''Xes", I 51Metne . u n .i t [ tV . . .. . ". '~'" ".... •
E C C E N T R IC C O L U M N A N AL Y S I S
A ..
Com
Eq. Length,
L.
uted Values:
= KL
Column const.,
=
Cc =
Argument of sec Value of secant
=
=
Argument of sec = Value of secant =
Slender. ratio, KUr =
750.0 m m
63.9
0.811 for s tre n g lb 1.4512 0.468 for defledj~ 1.1205
102.9
Column is; long F I N A L RESULTS Req'd yield strength ..
389 M PI
Must be less than actual yield strength:
.. M ax Deflection,
y......
Piston rod Is safe for
9"
M PI
2.41 mm
p•.. 6 2 0 0 N .
COLUMN ANALYSIS PROGRAM Refer to Figure 6-4 for analysis logic
.l!i!4.~:,",i!!¥I!,r!fI*~ !ii~ inj·_-':~ ";:~ .$'~
Use consistent
U.S. Customary units.
Com u18dValues: NOTE: Analysis of straight pipe. See also Solution 40B for crooked pipe. Eq. Length,
L.
=
KL =
Column const., C
c
Slender. ratio, KUr
156.0 In
=
128.3
=
198.2
Column is: long =
Critical Buckling Load 8,101 Ib Straight Pipe Allowable Load 2,700 Ib See also Solution 40B for crooked pi =
75"
C R O O K E D C O L U MN A N AL Y S I S Solves Equation6-11for AllowableLoad Us e consistent
u.s. Customaryun~:
Com uted Values:
Eq. Length,
L.
=
KL
Column const., C
c
=
=
156.0In
128.3
Euler buckling load = C, in Eqn. 6-11 = C2
8101 Ib ·22074
in Eqn. 6-11 = 3.483E+07
Slender. ratio. KUr =
198.2
Column is: 1000g StnJlght Column Critical Bucklin Load = 8,101 Ib
Crooked Column Allowable Load. 1,711 Ib This value governs the use of the I • See solution for slrel ht pipe; Problem 4OA.
CHAPTER 7 BELT DRIVES AND CHAIN DRIVES
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= /£0./ 4;
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11
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78
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P roblems 38-42 are design problems for chain drives for which there are no unique solutions. The general procedure is illustrated above for one possible solution for P roblem 38. This and the other design problems are shown on the following pages using the spreadsheet from the C D-ROM that is included with this Solutions Manual. Data for design power from Tables 7-5,7~, or 7-7 must be used to ensure that the selected chain has sufficient capacity,
8/
_
C H A I N D R IV E D E S IG N I n it ia l' n
u t D a ta :
Actual chain length: center distance: A ct ua l center distance: Angle of wrap-Driver sprocket: Angle of wrap-Driven sprocket:
Computed
actual
102.00 in
39.938 pitches 39.938 in 173.8 degrees 188.4 degrees
_ ~
r S I l . @ I d , b e ' ifl'lt~teNlfaifj20!m~.
CHAIN DRIVE DESIGN Initial In ut Data:
Co m
Actual output speed: P itch diameter-Driver sprocket: P itch diameter-Driven s rocket:
------------
..
CHAIN DRIVE DESIGN
Initial In ut Data:
11.95 hp rating at 2200 rpm from vendor Actual output speed: Pitch diameter-Dnver sprocket: Pilch diameter-Driven s rocket:
8S
C H A I N D R IV E D E S IG N Initial In u t Data:
from vendor
CHAPTER 8
CHAPTER 8 KINEMATICS
OF GEARS
Gear Geometry
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Housing Dimensions
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Gear Trains - Analysis IV
lie 0 Alo Alt: ::.MJ.d -~2 --. _._ _. ,~. _
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Helical Gears
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Helical Gears
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=
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B E V E L G E A R G E O M E T RY
'~~fJ ~:~f.f.~WgllfM~ili~f@~:~!~jMtnf:~I~;fJ H~:; G IV E N D A T A
N .o D 'l lile u i)i' .
f ll t4 1 m f h ' I ii ' D iiinrell:al
ite
e'mt§JiL~~· C O M PU T ED
VALUES
Gear ratio P itch diameter: P inion P itch diameter: Gear Pitch cone angle: Pinion P~ch cone angle: Gear Outer cone distance Nominal face width Maximum face width (a) Maximum face width (b)
C O MP UT ED
3.000 2.500 7.500 18.435 71.565 3.953
V A L UE S
Gear ratio P itch diameter: P inion P itch diameter: Gear Pitch cone angle: Pinion Pitch cone angle: Gear Outer cone distance
in in degrees degrees in
1.186 in 1.318 in 1.667 in
Nominal face width Maximum face width (a) Maximum face width (b) ! l1 I r ? O f F a c e w id tlJ "
2.000 2.500 5.000 26.565 63.435 2.795
in in degrees degrees in
0.839 in 0.932 in 1.000 in
f!ff1 !l'!I E ~~9 ~t~~:~[il{1 J F fW :W !]~~~!!\'!!I 'i]:I \W iijJ !!il1 !f
O . ll O Q
Mean cone distance Ratio Am/Ao
2.345 in
Mean circular pitch mean wor1ling depth Clearance Mean whole depth mean addendum factor Gear mean addendum P inion mean addendum Gear mean dedendum P inion mean dedendum Gear dedendum angle P inion dedendum angle Gear outer addendum P inion outer addendum Gear outside diameter P inion outside diameter
3.328 in
Mean cone distance Ratio Am/Ao
0.842 0.441 in 0.281 in 0.035 in 0.316 in 0.242 0.068 in 0.213 in 0.248 in 0.103 in 4.257 degrees 1. 77 4
0.087 0.259 7.555 2.992
Mean circular pitch mean wor1ling depth Clearance Mean whole depth mean addendum factor Gear mean addendum P inion mean addendum Gear mean dedendum P inion mean dedendum Geardedendum angle P inion dedendum angle Gear outer addendum P inion outer addendum Gear outside diameter P inion outside diameter
degrees in in in in
9 '1
i~ ~ ~
0.839 0.264 0.168 0.021 0.189 0.283 0.047 0.120 0.141 0.068 3.450 1.670 0.061 0.148 5.054 2.764
in in in in in in in in degreeS degrees in in in in
Given:
N» = 18; N G = 72; P d = 12; 20° pressure angle.
Computed values:
= NdNp
Gear ratio
mG
Pitch diameter: Pinion Pitch diameter: Gear
d=
Pitch cone angle: Pinion Pitch cone angle: Gear
r=
Outer cone distance
A o = 0.5D/sin(I)
Face width must be specified:
= 72/18 = 4.000
Np/P d = 18/12 = 1.500 in D = Nc/Pd = 72/12 = 6.000 in tan-1(NplNc) = tan" (18/72) = 14.03° = tan" (72/18) = 75.96° F = tan-1(NdNp)
F
= 0.5(6.00 in)/sin(75.96°) = 3.092 in
= 0.800 in Based on the following guidelines:
Nominal face width: F nom = 0.30 A o = 0.30(3.092 in) = 0.928 in Maximum face width: F max = A.l3 = (3.092 in)/3 = 1.031 in = 10/P d = 10/12 = 0.833in or F_ Mean cone distance
A m = Am(] = A o
-
0.5F = 3.092 in - 0.5(0.80 in) = 2.692 in
Ratio (A",IA,J = (2.692/3.092) = 0.871 [This ratio occurs in several following calculations] Mean circular pitch
pm = (wPd)(A",IA,J = (w12)(0.871)
Mean working depth
h = (2.00/P,J(A",IA,J = (2.00/12)(0.871)
Clearance
c=0.125h=0.125(0.145
Mean whole depth Mean addendum factor Gear mean addendum
Pinion mean addendum Gear mean dedendum
Pinion mean dedendum Gear dedendum angle Pinion dedendum angle Gear outer addendum
Pinion outer addendum
Pinion outside diameter
= 0.145 in
in
h = h + c = 0.145 in +0.018 in = 0.163 in m
CJ
= 0.210 +0.290/(mc)2 =
= 0.210 +0.290/(4.00)2 = 0.228
h
= (0.228)(0.145 in) = 0.033 in ap=h-aG =0.145 in -0.033in=0.1l2in
ao
CJ
=hm-aG =0.163 in-0.033 in=0.130in b» = h« -a p = 0.163 in - 0.112 in = 0.051 in bG
&:;= tan-1(bdAmaJ = tan-1(0.130/2.692) = 2.76° 1 8p = tan-1(bP/AmaJ = tan- (0.05112.692) = 1.09°
aoG ao + 0.5Ftanop aoG = (0.033 in) + (0.5)(0.80 in)tan(1.09°) = 0.0406 in =
aoP = ap + O.5F tan&:; aop
Gear outside diameter
in)=0.018
= 0.228 in
= (0.112 in) +(0.5)(0.80 in)tan(2.76°) = 0.1313 in
Do = D +2aoG cos T Do = 6.000 in + 2(0.0406 in)cos(75.96°) = 6.020 in do=d+2aoPcosr do =
1.500 in +2(0.1313 in)cos(14.04°) = 1. 755 in
9~
--
B E V E L G E A R G E O M ET R Y
~
C O MP U TE D
VALUES
Gear ratio pnch diameter. P inion pnch diameter. Gear pnch cone angle: P inion Pitch cone angle: Gear Outer cone distance Nominal face width Maximum face width (a) Maximum face width (b)
4.000 1.500 in 6.000 in 14.036 degrees 75.964 degrees 3.092 in 0.928 in 1.031 in 0.833 in
C O M PU TE D
Gear pnch P itch pnch pnch Outer
VALUES
ratio diameter: P inion diameter. Gear cone angle: P inion cone angle: Gear cone distance
Nominal face width Maximum face width (a) Maximum face width (b) !!\!~ce width
1191i,g;r;~~~~~~:jj;4l~~g,!~~f1:'II!!mr'H ;,~t,illfiii
t i '
Mean cone distance Ratio Am/Ao Mean circular pitch mean working depth Clearance Mean whole depth mean addendum factor Gear mean addendum P inion mean addendum Gear mean dedendum P inion mean dedendum Gear dedendum angle P inion dedendum angle Gear outer addendum P inion outer addendum Gear outside diameter P inion outside diameter
2.692 in 0.871 0.228 in 0.145 in 0.018 in 0.163 in 0.228 0.033 in 0.112 in 0.130 in 0.051 in 2.767 degrees 1.090 degrees 0.041 in 0.131 in 6.020 in 1.755 in
Mean cone distance Ratio Am/Ao Mean circular pitch mean working depth Clearance Mean whole depth mean addendum factor Gear mean addendum P inion mean addendum Gear mean dedendum P inion mean dedendum Gear dedendum angle P inion dedendum angle Gear outer addendum P inion outer addendum Gear outside diameter P inion outside diameter
4.000 0.500 2.000 14.036 75.964 1.031
in in degrees degrees in
0.309 in 0.344 in 0.313 in
l!l~ jn 0.881 in 0.854 0.084 in 0.053 in 0.007 in 0.060 in 0.228 0.012 in 0.041 in 0.048 in 0.019 in 3.113 degrees 1.227 degrees 0.015 in 0.049 in 2.007 in 0.596 in
BEVEL
GEAR GEOMETRY
'!l~ ;d~'~ ~f0~~ ~g,E"J "l!ilP~ftf!{ 't'6;~i7} ,t,*!F;2 GIVEN
DATA
fiif
&SlI~:~' COMPUTED
VALUES
Gear ratio Pitch diameter. Pinion Pitch diameter: Gear Pitch cone angle: Pinion Pitch cone angle: Gear Outer cone distance Nominal face wid1h Maximum face width (a) Maximum face width (b)
COMPUTED
3.000 0.250 in 0.750 in 18.435 degrees 71.565 degrees 0.395 in 0.119 in 0.132 in 0.208 in
!fl!!f!~ iiffi'@ ~ I M ~ !li:1 l!r , 'i!1 !1 :liii1 9 f;~ ~ ~ lm iil!1 1 1 1 :1 1 1 ', i; Mean cone distance Ratio Am/Ao Mean circular pitch mean working depth Clearance Mean whole depth mean addendum factor Gear mean addendum Pinion mean addendum Gear mean dedendum Pinion mean dedendum Gear dedendum angle Pinion dedendum angle Gear outer addendum Pinion outer addendum Gear outside diameter Pinion outside diameter
0.333 in 0.842 0.055 in 0.035 in 0.004 in 0.039 in 0.242 0.008 in 0.027 in 0.031 in 0.013 in 5.316 degrees 2.217 degrees 0.011 in 0.032 in 0.757 in 0.311 in
VALUES
Gear ratio Pitch diameter: Pinion Pitch diameter: Gear Pitch cone angle: Pinion Pitch cone angle: Gear Outer cone distance
3.000 2.000 in 6.000 in 18.435 degrees 71.565 degrees 3.162 in
Nominal face width Maximum face wid1h(a) Maximum face width (b)
0.949 in 1.054 in 1.250 in
Mean cone distance Ratio Am/Ao Mean circular pitch mean working depth Clearance Mean whole depth mean addendum factor Gear mean addendum Pinion mean addendum Gear mean dedendum Pinion mean dedendum Gear dedendum angle Pinion dedendum angle Gear outer addendum Pinion outer addendum Gear outside diameter Pinion outside diameter
2.662 in 0.842 0.331 in 0.210 in 0.026 in 0.237 in 0.242 0.051 in 0.159 in 0.186 in 0.077 in 3.992 degrees 1.663 degrees 0.065 in 0.194 in 6.041 in 2.369 in
!B ~ lflT 1 !ll~ iilW !i:!!h ~ ) !filr l~ W , ~ j];r ~ :l1 ';Q @ , ~ fiir , ~ r ;1 1 l1 ::1 1 1 ) 1 :
'1 7
Wormgearing
Dw=/.lSo'N,:IAlw"/,
WOlMGFlffi/Jl6:
Nt; .. '10;
F-
o, 62S/K.
C S/N6 LE" 'T1f1?G/fD
LEAl? =ANItl. I'lrc.H~ OeCdJAl.P/nJ+ -
A=
~/1NGtC= ,(IDPe-NO"",
WtJbr
-a ..=
DllrJ'/OE"
rs: k~)=
J / p c J = % .::
lJFDENO""".
Hf7T/t. Ce V e uJ c.l TY
~~S1:a/iS"1/N
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tJ.YY2hv'.
r....L,"~~)-_~_.r_7·
Y t & . Z&=O.lO{)/N.j
fhA •... D,w=
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6I.tJ/8'/N,
DG .. H6k .. YOllo.::-Y.t¥Jd/N.
=C .: ~(f +b",,)h = f!.,Od R A -T 7 o =V,= 1Y4"w1u"" -¥Ofi.:: ~
OU rtf/KeF
rczs»
) /2 .. =2.6ZS'/JI.
NOTE : On the following two pages are the results of P roblems 52-57 giving pertinent geometric properties of worms and wonngears and their velocity ratios. The detailed calculations follow the pattern illustrated above for P roblem 52. The equations come from Section 8-10, Equations 8-33 10 8-38. Compare the results to discern how variations in geometry such as diametral pitch and the number of threads in the worm affect the overall results. This is especially pertinenlla P roblem 53 in Whichthree different designs for wOrm!wonngear sets provide the same velocity ratio. The single threaded worm produces the smallest center distance and overall ~jze of the reducer. But note, also, that it has the smallest lead angle. The lead angle Increases as the number of threads is increased. On the positive side, the small lead angle makes ~e redue:erself-lacking. On the negative side, the small lead angle results in lower mechanical effiCiencyas will be shown in Chapter 10, Section 10-11. The designer musl balance these advantages and disadvantages for each application.
'18
WORMGEARING
PROBLEM: 52
INPUTDATA
Worm pitch diameter = Diametral pitch
WORMGEARING
PROBLEM: 53A
INPUT DATA
1.250 in 0
Worm pitch diameter = i i h
1.000 in 2
WORMGEARING
PROBLEM: 52
INPUTDATA
Worm pitch diameter = Diametral pitch = No. of worm threads = No. of gear teeth = Face width of gear =
WORMGEARING
1.250 in 10 1 40 0.625 in 0.3142 0.3142 0.3142 4.574 0.100 0.116 1.450 1.019 4.000 2.625 40.00
in in in deg in in in in in in
PROBLEM: 53B
= = = = =
1.000 in 12 1 20 0.500 in
RESULTS
Circular pitch of gear = Axial pitch of worm = Lead of the worm = Lead angle = Addendum = Dedendum = Worm outside diameter = Worm root diameter = Gear pitch diameter = Center distance = Velocity ratio = WORMGEARING
0.2618 in 0.2618 in 0.2618 in 4.764 deg 0.083 in 0.096 in 1.167 in 0.807 in 1.667 in 1.333 in 20.00 PROBLEM: 53C
INPUT DATA
1.000 in 12 2 40 0.500 in
Worm pitch diameter = Diametral pitch = No. of worm threads = No. of gear teeth = Face width of gear = COMPUTED
COMPUTED RESULTS
Circular pitch of gear = Axial pitch of worm = Lead of the worm = Lead angle = Addendum = Dedendum= Worm outside diameter = Worm root diameter = c:oearpitch diameter = Center distance = Velocity ratio =
Worm pitch diameter Diametrat pitch No. of worm threads No. of gear teeth Face width of gear COMPUTED
INPUTDATA
Worm pitch diameter = Dlametral pitch = No. of worm threads = No. of gear teeth = Face width of gear =
PROBLEM: 53A
INPUT DATA
COMPUTED RESULTS
Circular pitch of gear = Axial pitch of worm = Lead of the worm = Lead angle = Addendum = Dedendum = Worm outside diameter = Worm root diameter = Gear pitch diameter = Center distance = Velocity ratio =
WORMGEARING
0.2618 in 0.2618 in 0.5236 in 9.462 deg 0.083 in 0.096 in 1.167 in 0.807 in 3.333 in 2.167 in 20.00
1.000 in 12 4 80 0.500 in
RESULTS
Circular pitch of gear = Axial pitch of worm = Lead of the worm = Lead angle = Addendum = Dedendum = Worm outside diameter = Worm root diameter = Gear pitch diameter = Center distance = Velocity ratio =
0.2618 0.2618 1.0472 18.435 0.083 0.096 1.167 0.807 6.667 3.833 20.00
in in in deg in in in in in in
/00
Gear Trains - Analysis
Gear Trains - Analysis
FOil PI2DItL~'" 58 IlllTltrt.s
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Gear Trains - Kinematic Design VELOCITY RATIO FOR GEARS PROBLEItI63 DESIRED VR = 1.7321 " v'j
P R O B L E M 62 VELOCITY RATIO FOR GEARS 3.1416;: tr DESIREDVR =
NP 16 17 18 19 20 xxi 211 22 23 24
NG 50.27 53.41 56.55 59.69 62.83 65.97 69.12 72.26 75.40
=
=
VELOCITY RATIO FOR GE ARS DESIREDVR= 6.1644 NG
0.01659 0.02395 0.02507 0.01630 0.00841 0.00126 0.00523 0.01116 0.01659
50 3.1250 3.1176 53 3.1667 57 60 3.1579 63 3.1500 166 I 3.1429 69 3.1364 72 3.1304 75 3.1250
Min dill
NP
NP
NGAct VR-Act DIFF Des VR - VR Act
(Wit\. ! .,-",Dl SDL
Min dlff =
XX
XXI221 23 24
27.71 29.44 31.18 32.91 34.64 36.37 38.11 39.84 41.57
NG
VR
Actual
Actual
28 29 31 33 35
1.7500 1.7059 1.7222 1.7368 1.7500 1 714~ 3R 138 I 1.7273 40 1.7391 42 1.7500
0.00126
VELOCITY RATIO FOR GEARS DESIREDVR = 7.42
m
e
NP Act
0.02309 0.01206 0.00225
0.00652 0.01441 0.02156 0.01740 0.00950 0.00225
XX
XX
NG
NG
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Actual
Actual
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Min dlff = 0.00478
P R O B LE M 6 4
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C J.I:
CHAPTER 9 SPUR GEAR DESIGN
Forces on Spur Gear Teeth (iIV£I'I~
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~ove,
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RESULTS:
a b c d e f g h I
Gear speed = VR=mG= pinion PO = gear PO = center distance =C = pilch line speed = torque on pinion shaft = torque on gear shaft = tangential force = radial force = normal force =
486.1 3.600 1.667 6.000 3.833 764
270 972 324 118 345
rpm in in in fIImin Ib in Ib in Ib Ib Ib
Problem 2 Chapter 9
RESULTS:
a b c d e f
Gear speed = VR=mG= pinion PO = gear PO = center distance =C = pitch line speed = torque on pinion shaft torque on gear shaft tangential force radial force nonnal force = = =
g h I
= =
304.4 rpm 3.778 3.600 in 13.600 in 8.600 in 1084 fIImin 2739 Ib in 10348 Ib in 1522 Ib 5541b 1620lb
/0'1
Forces on Spur Gear Teeth Problem 3 " Chapter 9
RESULTS: a
b c
d e f g h I
Gear speed = VR=mG= pinion PO = gear PO = center distance = C = pitch line speed = torque on pinion shaft = torque on gear shaft = tangential force = radial force = normal force =
752.7 4.583 1.000 4.583 2.792 903 13.70 62.77 27.40 9.97 29.16
rpm in in in ftImin Ib in Ibin Ib Ib Ib
Problem 4 Chapter 9
RESULTS:
Gear speed = VR=mG= pinion PO = gear PO = d center distance = C = e pitch line speed = torque on pinion shaft = torque on gear shaft = g tangential force = h radial force = I normal force =
a b c
486.1 rpm 3.600 1.667 in 6.000 in 3.833 in 764 ftImin 270lbin 972 Ib in 3241b 151 Ib 3581b
//0
Forces on Spur Gear Teeth
Forces on Spur Gear Teeth Problem 5 . Chapler9.
RESULTS:
a b c d e f g h I
Gear speed = 304.4 VR= mG= 3.778 pinion P O = 3.600 gear P O = 13.600 center distance = C = 8.600 1084 pitch line speed = torque on pinion shaft = 2739 torque on gear shaft = 10348 1522 tangential force = 710 radial force = 1680 normal force =
rpm in in in ftImin Ibin Ibin Ib
Ib Ib
RESULTS:
a b c d e
g h I
·Gearspeed= VR=mG= pinion PO = gear P O = center distance = C = pitch line speed = torque on pinion shaft = torque on gear shaft = tangential force : radial force = normal force =
752.7 'rpm 4.583 1.000 in 4.583 in 2.792 in 903 ftImin 13.70 Ib in 62.77 Ib in 27.401b 12.781b 30.241b
IL l
Gear Manufacture 7.
and Quality
See S ection 9-4. Fonn milling, shaping, and hobbing.
For P roblems 8 - 16 refer to Table 9-2 for recommended quality numbers. Some judgment is required based on more detailed knowledge of the application. The total composite tolerance (fCT) is estimated from Table 9-1. Rough interpolation has been used. If more precise data are required, refer to AGMA Standard 2000-88 Gear Classification and Inspection Handbook. 8. Grain harvester. Use Q = 5. For P d = 8, Np = 40, No = 100: TCT 9.
p = 0.0130
in; TCT
Printing press: Q = 10. For P d = 20, Np= 40, No = 100: TCT p = 0.0015 in; TCT
G
0
= 0.0150 in.
= 0.0017 in.
10. Auto transmission: Q = 10. For Pd = 8, Np = 40, No = 100: TCT p = 0.0047 in; TC T 0 = 0.0055 in. 11. Gyroscope: Q = 14. For P d = 32, Np = 40, No = 100: TCT p = 0.00031 in; TCT 12. Using Q 10 as compared with Q approximately three times greater. =
=
0
= 0.00035 in.
5, with all other data being equal, requires tooth accuracy
13. Quality number is increasing because of the application. The size of the teeth is also decreasing because of the increasing numerical value of the diametral pitch. This results in a dramatic increase of the accuracy required in the tooth fonn as represented by the TC T values. For the pinion the T eT moves from 0.0130 in to 0.0047 in to 0.00031 in. Similar reductions for the gear. For P roblems 14, 15, and 16, use the lower part of Table 9-2. For precision machine tool, the quality number choice is related to the pitch line speed of the gears, with a higher quality number for faster speeds because the dynamic effects become more pronounced. See solutions for P roblems 1,2, and3 for pitch line speeds. 14. P itch line speed = 764 fIImin (From P rob. 1) Use Q = 8. For Pd = 12, Np = 20, No = 72: TCTp 0.0037 in; TC T 0= 0.0044 in. (Rough interpolation)
=
15. P itch line speed = 1064 fIImin (From P rob. 2) Use Q = 10. For P d = 5, N p = 18, No = 68: TCTp = 0.0037 in; TC T G = 0.0039 in. (Rough interpolation) 16. P itch line speed = 764 fIImin (From P rob. 3) Use Q = 10. For P d = 24, Np = 24, No = 110: TeT p 0.0013 In; TCT 0 = 0.0016 in. (Rough interpolation)
=
Gear Materials Answers for P roblems 17 - 25 are found in Section 9-7. Only brief statements are given here. 17. Bending stre~s are created by the tang~ntial force on the gear teeth acting in a manner similar to th.at on a.cantilever. The maximum bending stress occurs in the root of the tooth where it blends with the mvolute tooth fonn. High levels of contact stress (sometimes called Hertz stress) occur in the face of the t~eth near the pitch line as forces are exerted between the pinion and the gear teeth. The probable failure mode is pitting of the tooth surface. 18. ~e~:t:;t~h=~~drdanrdeS ssglVo' fethallOWatbl~ bending stress numbers and allowable contact stress numbers e ma enal of the teeth. 19. Gear steels are typically medium carbon pi . II hardening using a quenching dt . am or a oy steels that are heat treated by through3140 4140 4340 6150 t an empenng process. Examples are given in Section 9-7. 1040, e c. I
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20. T he AG MA recommends hardnesses from HB 180 to HB 400. 21. Grade 1 steel is typical commercial qualit G d' . quality controls on the alloy content and y. ra es 2 and 3 require progressively more stnngent higher grades. See also AGMA Sta d rdcle2aOnliness of the materials. Costs also increase for the n a 04-B89 Gear Materials and Heat Treatment.
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22. Grades 2 and 3 may be specified for high-speed aerospace applications, turbine engine driven systems, ship propulsion drives, and high-capacity industrial gears such as those in steel rolling mills. 23. Flame or induction hardening, carburizing, and nitriding.
22. Grades 2 and 3 may be specified for high-speed aerospace applications, turbine engine driven systems, ship propulsion drives, and high-capacity industrial gears such as those in steel rolling mills. 23. Flame or induction hardening, carburizing, and nitriding. 24. AGMA Standard 2001-C95 (or latest revision). 25. Gray cast iron, ductile (nodular) iron, and bronze. See Table 9-4. 26. Allowable bending stress numbers are obtained from Figure 9 - 1 0 or by computing values from the equations given in the figure. Use Figure 9 - /1 for allowable contact stress number. a)
Grade 1, 200 HB: S at = 28 200 psi; Sao=93 500 psi
b)
Grade 1, 300 HB: Sat= 26 000 psi; Sac=125 700 psi
c} Grade 1, 400 HB: S at = 23 700 psi; Sac=157 900 psi d)
Grade 1, 450 HB: Using HB > 400 in not recommended.
e)
Grade 2, 200 HB: S at = 36 800 psi; Sac=104 100 psi
f)
Grade 2,300 HB: S at = 47 000 psi; Sac=139 000 psi
g)
Grade 2, 400 HB: Sat= 57 200 psi; Sac=173 900 psi
27. Grade 1, 300 HB; Grade 2,192 HB from Figure 9-/0. 28. 55-64 HRC. See Table 9-3. 29. From Appendix 5: AIS11020, AISI 4118, AISI 8620 as examples. 30. 50-54 HRC with materials having good hardenability.
See Tabte 9-3.
31. AIS14140. AISI 4340, AISI 6150. All must have good hardenability. 32. 83.5 on the HR15N hardness scale used for thin-case materials. 33. Data are found in Tables 9-3, 9-4, and 9 - 1 1 , a} Sat= 45 000 psi; sao=170 000 psi b} Sat= 45 000 psi; Sao=175 000 psi c} S at = 55 000 psi; Sac=180 000 psi d} Sat= 65 000 psi; Sac=225 000 psi e)
S at = 55 000 psi;
f)
Sat= 39 000 psi; sao=155 000 psi
Sao=
180000 psi
g} S at = 51 500 psi; Sac=168000 psi h} S at = 63 500 psi; Sac=216 000 psi
i}
S at = 5 000 psi; sao=50 000 psi
j}
S at = 13 000 psi; Sao=75 000 psi
k} Sat = 27 000 psi; sao=92 000 psi I}
Sat = 5 700 psi; sao=30 000 psi
m} Sat = 23 600 psi; sao=65 000 psi n} Sat = 12000 psi; Notlisted
0)
Sal= 9 000 psi; Not listed
34. Depth = 0.027 in. Figure 9 - '1 : 1 .. 35. Depth = 0.90 mm.
Figure 9- J J ...
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