ࡱ> 9;8o` Objbj ^8%ottt,.,.,.8d.|.d2P/(1"J1J1J1OOOOOO $hR-utOOJxOOOOOO-J1J1WWWOOJ1tJ1WOOWWX tJ1D/ 0O,.PZ(0ԉ3RԉPԉtlOOOOWOOOOOOOOOO--GWjOOOOOOOOOOOOOO,.,. Disk Brakes and Clutches     Torque capacity under Uniform Wear condition per friction surface  EMBED Equation.3  Where f: Coefficient of friction pa: Maximum pressure on brake pad d,D: Inner and outer pad diameters Torque capacity under uniform pressure conditions per friction surface  EMBED Equation.3  Maximum clamping forces to develop full torque For Uniform Wear  EMBED Equation.3  For Uniform Pressure  EMBED Equation.3  Problem #M8 Given: A multi-plate disk clutch d=0.5 D=6 Pmax=100 psi Coefficient of friction=0.1 Power transmitted= 15 hp at 1500 rpm Find: Number of friction surfaces Answer: N=2 (uniform pressure) N=9 (uniform wear) Energy Dissipation in Clutches and Brakes The time it takes for two rotational inertia to reach the same speed after engagement through a clutch is:       EMBED Equation.3  where T: Common transmitted torque w: angular speed in rad/sec The total energy dissipated during clutching (braking) is:  EMBED Equation.3  If the answer is needed in BTU, divide the energy in in-lb by 9336. Problem #M9: A brake with braking torque capacity of 230 ft-lb brings a rotational inertia I1 to rest from 1800 rpm in 8 seconds. Determine the rotational inertia. Also, determine the energy dissipated by the brake.    Solution hints: Convert rpm to rad/sec: w1 = 188 rad/sec Note that w2=0 Find the ratio (I1I2/I1+I2) using time and torque=>9.79 Note that I2 is infinitely large => I1=9.79 slugs-ft Find energy from equation=>173000 ft-lb Springs Coverage: Helical compression springs in static loading Terminology: d: Wire diameter D: Mean coil diameter C: Spring index (D/d) Nt: Total # of coils N: Number of active coils p: Coil pitch Lf: Free length = N*p Ls: Solid length La: Assembled length Lm: Minimum working length Spring Rate of Helical Springs (compression/extension)  EMBED Equation.3  where : N is the number of active coils Plain ends: N=Nt Plain and ground ends: N=Nt-1 Square ends: N=Nt-2 Square and ground ends: N=Nt-2 G: shear modulus = E/2(1+n) G=11.5*106 psi for steels Shear stress in helical springs for static loading  EMBED Equation.3  where  EMBED Equation.3  and C is the spring index. Shear strength in springs  EMBED Equation.3  Ferrous without presetting  EMBED Equation.3  Ferrous with presetting Solid Lengths Ls=(Nt+1)d with plain ends Ls=(Nt)d with ground ends Spring Surge Frequency  EMBED Equation.3  Where g is the gravitational acceleration and Wa is the weight of the active coils:  EMBED Equation.3  with g being the specific gravity of spring material. For steel springs when d and D are in inches:  EMBED Equation.3  Example #M10: Consider a helical compression spring with the following information (not all are necessarily needed): Ends: Squared and ground Spring is not preset Material: Music wire (steel) with Sut=283 ksi d=.055 inches and D=0.48 inches Lf=1.36 inches and Nt=10 Find the following. Answers are given in parentheses. Spring constant, K (14.87 lb/in) Length at minimum working load of 5 lbs (1.02) Length at maximum load of 10 lbs (0.69) Solid length (0.55) Load corresponding to solid length (12.04 lbs) Clash allowance (0.137) Shear stress at solid length (77676 psi) Surge frequency of the spring (415 Hz) Design of Welds Welds in parallel loading and transverse loading  SHAPE \* MERGEFORMAT  Weld Geometry      Analysis Convention Critical stresses are due to shear stresses in throat area of the weld in both parallel and transverse loading. For convex welds, t=0.707w is used. Yield strength of weld rods used in analysis is 12 ksi smaller than their nominal minimum yield strength. Analysis Methodology Under combined loading, different stresses per unit leg length are calculated and combined as vectors. Stresses based on weld leg (w) Direct tension/compression:  EMBED Equation.3  Direct shear:  EMBED Equation.3  Bending:  EMBED Equation.3  Torsion:  EMBED Equation.3  Formulas for Aw, Sw, and Jw are attached for different weld shapes. Problem M11a -Welds subject to direct shear: Two steel plates welded and are under a direct shear load P. The weld length is 3 inches on each side of the plate and the weld leg is 0.375 inches. What maximum load can be applied if the factor of safety is 2 against yielding? The weld material is E60 with a yield strength of 60 ksi nominal.  SHAPE \* MERGEFORMAT  Solution (of M11a): From Table: Aw = 2d = 6  EMBED Equation.3  The design strength of the weld material in shear is: Sys=.58 Sy = .58(60-12) = 48*.58 = 27.84 ksi Using a factor of safety of 2, the allowable shear stress is: Sys,a = 27.84/2 = 13.92 ksi Equating stress and strength .6284F = 13920 ( F=22150 lbs Problem #M11b Welds subject to torsion:  "%&*nop; < = P Q R S U ֥r`#jV@ hhhC"RCJUVaJjhhhC"RCJUaJhC"R5CJ$\j~hC"RCJ$EHUjU@ hC"RCJUVaJhhhC"RCJH*aJjhC"RCJ$EHUjT@ hC"RCJUVaJjhC"RCJ$UhhhC"RCJaJjhC"RCJUmHnHu hC"RCJ$hrhC"R5" #$%'()*no; < T `gd2x^$^a$NOO  ! [ \ \ ] ^ _ ` c d e f h m n ±ԩԩԝԝԒԒԊtttttjjhC"RCJ$UjhC"RCJUmHnHu hC"RCJ$hKhC"R5hhhVsCJaJhhhC"RCJH*aJhhCJaJ!j\hhhC"RCJEHUaJ#jW@ hhhC"RCJUVaJhhhC"RCJaJjhhhC"RCJUaJ!jhhhC"RCJEHUaJ$    * G m n \ ^ ` d f i j k  ^`k l m 8 : h j $(2468\T|}^gd/w^gdh`gd2x  : h j z | ~ "$&(06Կ԰ԖykbRRRjhC"RCJUmHnHuh/w5CJ$\h/wh/w5CJ\aJh/whC"R5CJH*\aJh/whh5CJ\aJh/whC"R5CJ\aJja hC"RCJ$EHUjs@ hC"RCJUVaJhC"RCJ$OJQJhhhC"RCJaJ hC"RCJ$jhC"RCJ$Uj hC"RCJ$EHUj\s@ hC"RCJUVaJ68RT|}  HI^_opNPǼǵퟖ}qjhC"RCJ$EHUj@ hC"RCJUVaJjhC"RCJ$UhC"R5CJ$\hh5CJ$\ hC"RCJ$ hC"R5\ h/w5\h/wh/wCJaJh/whC"RCJaJhhhC"RCJH*aJhhhC"RCJOJQJaJhhhC"RCJaJh/wCJaJ, 9G]n.^ Dz|``gd/w & F  & F >@XZz| #$%&BC^_rsǧziW#jaY@ hhhC"RCJUVaJ!jhhhC"RCJEHUaJ#ja@ hhhC"RCJUVaJjhhhC"RCJUaJjjhC"RCJ$EHUjʉ@ hC"RCJUVaJjhC"RCJ$U hC"R5\ hC"RCJ$hhhC"RCJH*aJhhhC"RCJOJQJaJhhhC"RCJaJhhhC"RCJH*aJ| BC^  8 NogdVpD`gdh`gdVpD``gd/wstu  !45678gh±ԫԍԍԍԍԅ|o|`Qo|ԍjmhC"R5CJ$EHU\j@ hC"RCJUVaJjhC"R5CJ$U\hC"R5CJ$\h/wCJaJhhhC"RCJH*aJhhhC"R5CJ\aJhC"R hC"RCJ$!jBhhhC"RCJEHUaJ#jY@ hhhC"RCJUVaJhhhC"RCJaJjhhhC"RCJUaJ!jhhhC"RCJEHUaJh CEqrzlz]lVJJhhhC"RCJH*aJ hhhC"RhVpDhC"R5CJH*\aJhVpDhVpD5CJ\aJhVpDhC"R5CJ\aJhVpD5CJ$\!jQhhhC"RCJEHUaJ#jI@ hhhC"RCJUVaJhhhC"RCJOJQJaJ!jhhhC"RCJEHUaJ#j@ hhhC"RCJUVaJjhhhC"RCJUaJhhhC"RCJaJ45LMNOPQ_`aghijloptv'FGZμ֤֞~~ojhhhC"RCJUaJhC"R5CJ$\h/w5CJ$\hhhC"R6CJ]aJ hC"RCJ$jhC"RCJUmHnHuj!hVsUjhVsUmHnHuhVsjhVsUhC"R hC"R5\ hh5\hhhC"RCJaJhhhC"RCJH*aJ%o?U4Q_ahiklpuv & F `&'E_no 6gdVpD` & F  & F Z[\]op°|jYKhhhC"R5CJ\aJ!j;)hhhC"RCJEHUaJ#j"@ hhhC"RCJUVaJ!j&hhhC"RCJEHUaJ#jK@ hhhC"RCJUVaJ!j$hhhC"RCJEHUaJ#j@ hhhC"RCJUVaJhhhC"RCJaJjhhhC"RCJUaJ!j5"hhhC"RCJEHUaJ#j@ hhhC"RCJUVaJ!%CDE]0LopѴn_QhhhC"R5CJ\aJj+hhhI1CJUaJ(jhhhZCJUaJmHnHuhhhZCJaJjhhhZCJUaJ hhhZ hhhC"RhVpD5CJ$\hVpDhVpD5CJ\aJhVpDhC"R5CJH*\aJhVpDhC"R5CJ\aJhC"R5CJ$\hhhC"RCJaJhhhC"RCJH*aJ  vẕ̟̀zlalRFhVpDhC"R5CJaJhVpDhC"R5CJH*\aJhVpD5CJ\aJhVpDhC"R5CJ\aJ hCJ$ jhhhC"RCJaJ!j#,hhhC"RCJEHUaJ#j(@ hhhC"RCJUVaJjhhhC"RCJUaJhhhC"RCJH*aJhhhC"RCJaJhq)5CJ\aJhhhC"R5CJ\aJhhhC"R5CJH*\aJ6tLLLMMMMMNNNNNNNNNNNNO &`#$gdk~`gdq)gdhLLLWLZLLLLLLLLLLLMMMMMMMMM"M:M=MM|q|bVMhVpD5CJaJhVpDhC"R5CJaJhVpDhC"R5CJH*\aJhVpD5CJ\aJhVpDhC"R5CJ\aJj1hC"REHUj"@ hC"RCJUVaJj.hC"REHUjf"@ hC"RCJUVaJhC"RjhC"RUhhh38CJaJhhh> CJaJhhhC"RCJaJUhVpDCJaJhVpDhVpD5CJaJA round steel bar is welded to a rigid surface with a fillet weld all around. The bars outer diameter is 4.5. Determine the critical shear stresses in the weld when the bar is subjected to a 20,000 lb-in pure torque.  EMBED Equation.3   EMBED Equation.3  Problem #M11c Welds subject to bending: Solve the previous problem with a bending moment of 35000 lb-in acting on the welds instead of the torsion load.  EMBED Equation.3   EMBED Equation.3  Problem #M11d Welds subject to combined loads: If the design shear strength (Sys) in the weld is 27800 psi, what is the factor of safety against yielding when both stresses in previous two problems are acting on the bar.  EMBED Equation.3  FS = 27800/12948=2.15     PAGE  PAGE 9 D d I1 I2 Throat: t Leg : w P 3 3 P P OR MMMMMMMMMMMMMMMMMMNNNNNNNNNNNNNNȻ󲪢vg]UQhjrjhjrUj9hC"REHUjl'@ hC"RCJUVaJhhh38CJaJhhhC"RCJaJhq)hq)hq)5hq)hC"R5H*hq)hVpD5hq)hC"R5hC"R5CJ$\j7hq)hq)EHUj+%@ hC"RCJUVaJj4hq)hq)EHUj$@ hC"RCJUVaJhC"RjhC"RUNNNNNNNNOOOOOO O O OOOOOO!O#O$O&O'O(O)O*O+O,O.O:O@OAOBONOOOROSOTOWOXOYOZO\O_OaObOƹƩߥ}hZeh/h h]Yh=hbLh2h FhRWhFh OhC"R6CJ$] hC"RCJ H* hC"RCJ$H* hC"RCJ hC"RCJ$hC"Rh2x0JmHnHuhk~h h0Jjh0JUhjrjhjrU1OOOOOOOOOOOOOOOOOOOO O!O#O$O&O'O*O+O &`#$gdk~h]hgd+O.O/O9O:OBOCODOEOFOGOHOIOJOKOLOMONOOOPOQOROSOTOUOVOWOXOYOZOZO[O\O]O^O_O`OaObOcOdOfOgOjOkOnOoOqOrOtOuOxOyOzO{O|O}O~OOgdVsbOdOfOgOiOjOkOmOnOoOqOrOtOuOxOyO}O~OOOøøíhC"RhSpwhE(h0hWYhWYhWYCJ(aJ(hI1hVsCJ$aJ$hVshI1hVsCJ aJ hVsCJ aJ hI1hI1CJ aJ hI1CJ aJ hI1hI1hI1CJ$aJ$hi`OOOO5 01h:p/ =!"#$% za$E2fY_,I!)( >|~Dd (AJ  C A? "2bѶQD`!bѶQ @2xcdd``>$d@9`,&FF(`T A?d-< Kzjx|K2B* Rj8 :@u!f0)0`D6;35V ZZ|0@deѬ粁Pfߢbc^al08 |t1/=LprTg@ӘAљVS)@?#ExX dnpenR~CPXrTvmpŰg" W7qod<RQPM\KLLJ% 4u3CdbxDd 0l(AJ  C A? "2~02 `!~02 Վ H|xcdd``>$d@9`,&FF(`Ts A?dbn@=P5< %!@5 @_L ĺE60X@V+ȝATN`gbM-VK-WMcZ>  f22J`:ѬgP~3{Fgw ^c#?G# 'HEo@`@!eȿgױT$`7&I9 @bR wإXsĹ?q HEA4rS7D.v0o8?021)Wx\]\~bcR6fDd J  C A? "2Yb%q0r?!R:`!Yb%q0r?!R6 8>@2jxcdd``$d@9`,&FF(`TE[RcgbR .@=P5< %!@5 @_L ĺE~0X@*ȝATN`gbM-VK-WMcZ>  f22j`hVl ل7D$${9A*R~72"72c @|7.Fz8J,2727)?(XsTݿ R[la7 Wqod '.h B.] `pedbR ,.I񸠩?17jrDd lJ  C A? "2#<~^J&VD-`!#<~^J&VD-@ pvxcdd``>$d@9`,&FF(`T A?df33(ĒʂT/&`b]F"L L7@,a KL *'031d++&1{~-` P3vq%0qd4+a|V_g TBSO}L`-9A**a|>v_$ b8@*R{ ͸_F{1"K1 Ma(w a@M`b G {YlƫLp₦\.p%F&&\ O`q+7ړDd J  C A? "2 #q1a|#< `! #q1a|#< `PxڝS=KA0D CPI4""F0Igc( R\+`! HFs$!wΛ{{ސ?`p "D!a( )cxyE2$9~=mƫ|I~~Z/<;bDH=K.fxtDT( rūyV+sh[>e(ccYxElEJ O3}$##]|"=;IIƯ(.Kݢe ^0nRcΓDrR=._xt5.Y3[MI'vCm p[c9 33y+TDO!bս@Lޔ~fKwDd 0J  C A? "29y`؈rYZ `!9y`؈rYZ HxڝK@߽$I )*(PDJTE[c -l .A-7D( Րhj{/ht8 GdVΙ.cN(;aL i4dTFjR]kV 0$}G=T">"hn>?)]jݱ[51_\+rOk̒78ʸ('I#ɢԋ~2A}ջdn^N0^[|[x'G7~ˡ7Z} |xU%:Q׌+܏|Xw?ֽ'_ǏaO7]D4$8{E*^m; y+hS,˙>w(pDd X J   C A? "2q 'B6 6t]>`!q 'B6 6t]"  7dtxcdd``  !"#$%&'()*+,-./1234567p:=d>?A@BCDFEGHIKJLMNPOQSRTUVXWYZ[]\^`_abcefhgijklmnqrstuvwxyz{|}~Root Entry} F/O<@,Data 0<WordDocument|^ObjectPool'pnO/O_1075270890FpnOpnOOle CompObjfObjInfo  #&'(+./258;>ADGJMPSVYZ]`cfiloruxyz} FMicrosoft Equation 3.0 DS Equation Equation.39qxl. T=fp a d8(D 2 "d 2 )Equation Native _1075271063 FpnOpnOOle CompObj f FMicrosoft Equation 3.0 DS Equation Equation.39qxl&  T=fp a 12(D 3 "d 3 ) FMicrosoft Equation 3.0 DS EqObjInfo Equation Native  _1075271353FpnOpOOle CompObjfObjInfoEquation Native h_1075271450 FpOpOuation Equation.39qxL'. F=p a d2(D"d) FMicrosoft Equation 3.0 DS Equation Equation.39qOle CompObjfObjInfoEquation Native xd8T F=p a 4(D 2 "d 2 ) FMicrosoft Equation 3.0 DS Equation Equation.39qx'. t=I 1 I 2 ( 1 " 2 _1075278684FpOpOOle CompObjfObjInfoEquation Native _1075278797"FpPOpPOOle !CompObj "f)T(I 1 +I 2 ) FMicrosoft Equation 3.0 DS Equation Equation.39qxH*D E=I 1 I 2 ( 1 " 2 ) 2 2(I 1 +I 2ObjInfo!$Equation Native %_1075283967$FpPOpPOOle ) ) FMicrosoft Equation 3.0 DS Equation Equation.39qxx'. k=d 4 G8D 3 N=dG8NC 3CompObj#%*fObjInfo&,Equation Native -_1075284426;)FpPOpPOOle 0CompObj(*1fObjInfo+3Equation Native 4 FMicrosoft Equation 3.0 DS Equation Equation.39qxc'  max =K s 8FDd 3 FMicrosoft Equation 3.0 DS Eq_1075284577.FpPO`OOle 6CompObj-/7fObjInfo09uation Equation.39qx<oT K s =1+12C FMicrosoft Equation 3.0 DS Equation Equation.39qEquation Native :X_1075534177,63F`O`OOle <CompObj24=fObjInfo5?Equation Native @N_10755342658F`O`OOle B2. d"0.45S u FMicrosoft Equation 3.0 DS Equation Equation.39q2 l d"0.65S uCompObj79CfObjInfo:EEquation Native FN_10755456301J=F`O`OOle HCompObj<>IfObjInfo?KEquation Native Lv FMicrosoft Equation 3.0 DS Equation Equation.39qZ)D f n =12 kgW a FMicrosoft Equation 3.0 DS Eq_1075545752BF`O` OOle NCompObjACOfObjInfoDQuation Equation.39q`- W a =14 2 d 2 DN FMicrosoft Equation 3.0 DS Equation Equation.39qEquation Native R|_1075546185@OGF` O` OOle TCompObjFHUfObjInfoIWEquation Native X_1075715359EYLF` O` OOle [f'. f n =13900dND 2 HZ FMicrosoft Equation 3.0 DS Equation Equation.39qG& =1.41CompObjKM\fObjInfoN^Equation Native _c_1075715345QF` O` O4FwA w FMicrosoft Equation 3.0 DS Equation Equation.39qG& =1.414VwA wOle aCompObjPRbfObjInfoSdEquation Native ec_1075715403cVF` OPUOOle gCompObjUWhfObjInfoXj FMicrosoft Equation 3.0 DS Equation Equation.39qG=L =1.414MwS w FMicrosoft Equation 3.0 DS Equation Equation.39qEquation Native kc_1075716799Tm[FPUOPUOOle mCompObjZ\nfObjInfo]pEquation Native qg_1075718399`FPUOPUOOle sK&+ =1.414TcwJ w FMicrosoft Equation 3.0 DS Equation Equation.39qp =1.41CompObj_atfObjInfobvEquation Native w_1075716710eFPUOPUO4VwA w =1.414F.375(6)=0.6284Fpsi FMicrosoft Equation 3.0 DS Equation Equation.39q& J w =(Ole {CompObjdf|fObjInfog~Equation Native d 3 /4)=(4.5 3 /4)=71.57in 3 FMicrosoft Equation 3.0 DS Equation Equation.39qD =1.41_1075716845jFPUOPOOle CompObjikfObjInfolEquation Native _1075717271hwoFPOPOOle CompObjnpf4TcwJ w =1.414(20000)(2.25).25(71.57)=3556.2psi FMicrosoft Equation 3.0 DS Equation Equation.39qObjInfoqEquation Native _1075717419tFPOPOOle +T S w =d 2 /4=(4.5 2 )/4=15.9in 2 FMicrosoft Equation 3.0 DS Equation Equation.39qg  =1.41CompObjsufObjInfovEquation Native _1075717996r^yFPOP7O4MwS w =1.414(35000).25(15.9)=12450psi FMicrosoft Equation 3.0 DS Equation Equation.39q+ =  1Ole CompObjxzfObjInfo{Equation Native 2 + 22 = 3556 2 +12450 2 =12948psiOh+'0  4 @ L Xdlt|Machine Designfar Normal.dotfar$d@9`,&FF(`TI A?d-n@=P5< %!@5 @_L ĺEZ@,a ˁ &v& ro&f01d++&1{~-` P{q0W5,|6F10ߤb_?c`RaQ 0A0/=Lp{VqĸOqɳL#A|wN|E  f22z10}CnbE*Ć?mc bHD7DCe;9"%f;(B\ P z1RLu .X2727)?(z+Xԃé~K|`سqO`duႦE.pz%pF&&\ >'f8WADd lJ   C A ? "2Tq?kC3`!wTq?kC34 Excdd``g 2 ĜL0##0KQ* W A?d 3zjx|K2B* Rj8 :@u!f010uX@V ;ȝATNA $37X/\!(?71k f3ˈ9 $\ '01ޕg>S؄Jtw3nLp/f0?Q C!|,2 Ma(w .?3;xkZ+Dd 8hijJ   C A ? " 2IH,^Sgmi[`!aIH,^Sgm@v |/xcdd``ed``baV d,FYzP1n:&lB@?b  ㆪaM,,He`HI? 01d++&1{~-Č`u ,@RF\dJ+!5# f22J`rG?ُsA:S\`@4 ɳ L ؄< sH\&ϙ@*\ËLrA Ɩ Xf\PX587'00TsAS 8%AtA``#RpeqIj.M9@Gp,]nwDd! D  3 @@"?WDd J  C A? "2g']"y"`!g']"@@0= [xcdd``a 2 ĜL0##0KQ* W.d3H1)fY;AL`r!0׌=!`(1䂦.p:%JF@+KRsA<.h:$`q4GvWDd J  C A? "2Amʓw$`!Amʓw@@0= [xcdd``a 2 ĜL0##0KQ* W.d3H1)fY;@c"o)Sk%)uG=P4AAWwO31l 'u-LȰaR3;9a P8V{JBW\\݆pΡsw4'_?Λb[[1{^kq+bW"![)^}ӣ!⯥1Dd |J  C A? "2M ZefX'2/`!M ZefX'2`&0xcdd``db``baV d,FYzP1n:B@?b 5sC0&dT20$ͤ KXB2sSRs=b pi#/  J*/* ‡< E@AajЃ@0H^ΏM| >)l>U,{s͎.},Hb@‰N@ᐙst> Wzz`(~&aw&I9 @x6$bps |,ao4bӛ'HEܞlf 9b nv0o8221)Wx ], 0`q_:Dd hFJ  C A? "2f͞w޴gUVqB1`!:͞w޴gUVq@,xcdd``vf 2 ĜL0##0KQ* W@FRcgbR v񿙁zjx|K2B* R>0pE1At 2Bab`*f,ov*35v5 @Hfnj_jBP~nbC@Vg F\ LNd((L3/gy f $ClTOL`PE >a 's&0uJT%`^2ǚb Ʀf0 ThA>65&yA0~1/H^ N&FpfrBTBپlyBPׁ݇/҅0d ųLE'C oȟCUG2Dd`penR~CP + RakcG2BXl\M9 %\]=rI)$5b#@r8 ?Dd |J  C A? "2tTKJ R14`!tTKJ R1`!0xڥOK0d]gʤӃ!®" Ă 7(7?'/~ IM@焩4/y'yb0X"DϣR13,U0 >`am`铁&;qkXA>)(rͶ]g[]U.%Pwk;dL{!_,ڟ#}65/=9/jH#/J^#~91>5۫dOdBTn#k/H[Xۏy}\ܻCUu _\KVm>j isf#G. [,7⼋sX˟X:OgW۝;qhQW[aBxaT=>+Hŏ*_$ >񸦩(lMxcbu&a#ǮZ|Qef87+wyq']\l eqw}6rw,O[hT{Y:M#qNRFg(?^Dd vJ  C A? "2?u4|d)s38::`!u4|d)s38^ h+@CxڝT=OP>$/HPZC$K$Hn41СK3ti%eME's h,qL¨BBtE0 CY͑ͥc]/љs; %r_꘯>5Xot?vP$gB_/. PTy<##%Z{J)jDUTqQ%8+dR.M{Q"V_y X?ܻSt- :ΛlOp[ _D*Q-p]jwATrg"\]^%Np$}U'P 'yp_MmW\G7a%L EZ5N&8-ŪGNf'?#]7lyGMމLV媲 !Pot@L8̈J':1Table$SummaryInformation(~DocumentSummaryInformation8@CompObjq6Microsoft Office Word@@+@0U@P?jOP՜.+,0 hp  Portland State University( - Machine Design Title  FMicrosoft Office Word Document @@@ NormalCJ_HaJmH sH tH 8@8 Heading 1$@&CJ 8@8 Heading 2$@&CJ$>@> Heading 3$@& 5CJ$\H@H Heading 4$@&^`CJ$B@B Heading 5$@& 5>*CJ$\>@> Heading 6$$@&a$CJ$<@< Heading 7$@&>*CJ$F@F Heading 8$$@&`a$CJ$DA@D Default Paragraph FontViV  Table Normal :V 44 la (k(No List 0>@0 Title$a$CJ 0J@0 SubtitleCJ2B@2 Body TextCJ$<"@< Caption$^a$CJ$4 @24 Footer  !.)@A.  Page Number (123456789:;<=>?@ABCDEFGHIJKLMNOPQRUY]`cghijklmnB%     RS[\xz     ! "#$!&"'#($)%*&+',(-).*/+0,1-2.3/40`fsoyz51<2=3>4?5@6A7 (123456789:;<=>?@ABCDEFGHIJKLMNOPQRUY]`cghijklmnq      !"#$%&'()*+,-./0123456789:;<=>?@AB^ #$%'()*no;<T*Gmn\^`dfijklm^_:<>CDEFX&'/0:hiv-HI/Lgh ; l m { 6 N B \ r  7 h  D E U V NrYZyz %&jk %\ !,DE])* !78:;=>ADMNOZ[\]lnoqruvyz0000000000000*00*0*0*0*0*0*0*00*0*0*0*0*0*0*H0*0000000000000X0000000000000000000000000000000000X0X00+0+ 0+00 0 0m 0m 0m 0m 0m 0m 0m 0m 0 m0000000000000000000(00000000000000000000000000x0x000000000000000 0 0 000 000000000000000000000000000000000000000y00Ay00y00Ay00y00y00y00xAy00y00@0@0y00 yAy00y00)0y00)0y00h*0y00*0y00 40y0 0 40y0 0 4l40y00 ll40y00 40y00 *0y0 0 l40y00m40y00h $$$' 6shZMNbOO !"$()- k |o6O+OZOOO#*+,.Oo<PRm   ; O Q 6 J L   " !#,@BEY[ %' ::::::::::::::_::::_::::::  '!!Or$$E2fY_,I!)i7^r$|ka@O+8kir$5Oc}у%4ir$9C_iyuUi@D(    % h3  s"*?` i c $X99? %4 j  jH k # q jZB l S DnZB mB S D, q &ZB n S DԔ& jk o C :oC"?O :TB p C D& ' %TB q C D4`B r c $D& kl s S 9sC"?j 9H t # A $4 u 8U# Hb v # U#j# Hb wB # j ZB x S DH!PI!8 y C ;yC"?H!# ; z C <zC"?n  <  % Z#  s"*?%` Y c $X99? %4 [ iH \ # WiZB ] S DTZB ^B S DW%ZB _ S DԔ ij ` C 7`C"?Tj!i 7TB a C D  $TB d C D3`B e c $D jj f S 8fC"?j 8N S 3 S N R 3 R <2 N # (2 O TB P c $DTB Q c $DHB T C D< U # ( V < W #  < X #  ( Y  < Z # N [ 3 [  N \ 3 \  x ] S HA*Wide upward diagonal( ^ ( _ < ` # < a # ( b HB k C DHB l C D  m ~BCDEFjJW81*{<@   o xBCDEFjJ @`HB p C D$HB q C D#TB r c $D"HB s@ C DHB t@ C DTB u c $DTB v c $DHB w C DH x # x HB y C D!H z # z B S  ? !%\^`abdfg:<>?@A S/kWtN k tQ ] tTCC//tPWC}tO8tR/tZL tU  t\A!tXCAtWAt[b^NtY6LtV 6t]/" t^: 6 tbC/?taCt`t_ ?th! txCtwCtu ts: tok Ctmk Ctkk 3k tvk mtz} tt: tlk tyCtrk CtqCCktpk k ktZ! to!&)gjy|X[     79?Adf88::;;=>@ACD\]W~   N R & * bn88::;;=>@ACD\]op333333333333333333333*oo<SHnmm^^ghjl::EFXX&':ivvHI  6 6 D E V V z #jj $  )*IK,,E\]]ef&'23Y[  !!788::;;=>@ACD\]llmnnoopqqrrtuuvvxyyzzo88::;;=>@ACD\]*($1( @~V-*Rpo:DF 2>n.t>84fL8:Td2W|d;T]Efkh3R _hX)Nj0]jAV5 k3ZsN~ch ^`OJQJo(h ^`OJQJo(oh pp^p`OJQJo(h @ @ ^@ `OJQJo(h ^`OJQJo(oh ^`OJQJo(h ^`OJQJo(h ^`OJQJo(oh PP^P`OJQJo(h ^`OJQJo(h ^`OJQJo(oh pp^p`OJQJo(h @ @ ^@ `OJQJo(h ^`OJQJo(oh ^`OJQJo(h ^`OJQJo(h ^`OJQJo(oh PP^P`OJQJo(h^`.h^`.hpLp^p`L.h@ @ ^@ `.h^`.hL^`L.h^`.h^`.hPLP^P`L.h^`o()h^`.hpLp^p`L.h@ @ ^@ `.h^`.hL^`L.h^`.h^`.hPLP^P`L.^`OJPJQJ^Jo(-   ^ `OJQJo(o   ^ `OJQJo( xx^x`OJQJo( HH^H`OJQJo(o ^`OJQJo( ^`OJQJo( ^`OJQJo(o ^`OJQJo(h^`o()h^`.hpLp^p`L.h@ @ ^@ `.h^`.hL^`L.h^`.h^`.hPLP^P`L.h ^`OJQJo(h ^`OJQJo(oh pp^p`OJQJo(h @ @ ^@ `OJQJo(h ^`OJQJo(oh ^`OJQJo(h ^`OJQJo(h ^`OJQJo(oh PP^P`OJQJo(h^`)h^`.hpLp^p`L.h@ @ ^@ `.h^`.hL^`L.h^`.h^`.hPLP^P`L.^`OJPJQJ^Jo(- ^`OJQJo(o pp^p`OJQJo( @ @ ^@ `OJQJo( ^`OJQJo(o ^`OJQJo( ^`OJQJo( ^`OJQJo(o PP^P`OJQJo(hh^h`OJPJQJ^Jo(- ^`OJQJo(o ^`OJQJo( ^`OJQJo( pp^p`OJQJo(o @ @ ^@ `OJQJo( ^`OJQJo( ^`OJQJo(o ^`OJQJo(^`OJPJQJ^Jo(- ^`OJQJo(o pp^p`OJQJo( @ @ ^@ `OJQJo( ^`OJQJo(o ^`OJQJo( ^`OJQJo( ^`OJQJo(o PP^P`OJQJo(h ^`OJQJo(h ^`OJQJo(oh pp^p`OJQJo(h @ @ ^@ `OJQJo(h ^`OJQJo(oh ^`OJQJo(h ^`OJQJo(h ^`OJQJo(oh PP^P`OJQJo(h^`.h^`.hpLp^p`L.h@ @ ^@ `.h^`.hL^`L.h^`.h^`.hPLP^P`L.h ^`OJQJo(h ^`OJQJo(oh pp^p`OJQJo(h @ @ ^@ `OJQJo(h ^`OJQJo(oh ^`OJQJo(h ^`OJQJo(h ^`OJQJo(oh PP^P`OJQJo(H H^H` o()^`.pLp^p`L.@ @ ^@ `.^`.L^`L.^`.^`.PLP^P`L.h ^`OJQJo(h ^`OJQJo(oh pp^p`OJQJo(h @ @ ^@ `OJQJo(h ^`OJQJo(oh ^`OJQJo(h ^`OJQJo(h ^`OJQJo(oh PP^P`OJQJo(^`o()^`.pLp^p`L.@ @ ^@ `.^`.L^`L.^`.^`.PLP^P`L. 2>;T]Njhf~V- _h*(5 kfLZs$1(]j~>po:d2W                           \3                \3                                                                             >ȴd                 \3        UTM[/wS 0 0U!/"nj$E(q)w,] -i.7Y0A4\638RS<{LDVpD~TI-L"M OC"RgW]Y A]i`Qj`RcVst1vSpw2x Qzk~gF`reU Fr; jLERWpIKfW`2XWjrMhWYq=?> HbLDZeI1c%Z}"lt?@oodt=oopS S K@@@ @@ @@@(@@@0@@@UnknownGz Times New Roman5Symbol3& z Arial;Wingdings?5 z Courier New"1hƀ‹f&P (P ($4d--2QHX?M[2Machine DesignfarfarP            MSWordDocWord.Document.89q