Mechanical formulas sheet, Cheat Sheet of Mechanical Engineering

Download Mechanical formulas sheet and more Cheat Sheet Mechanical Engineering in PDF only on Docsity! 17109) DSN= NNN 94 vv, ony) pin yon O'NNNN 7197 YAW ‘oO? WN] O'NANN Alw'n F (Tension/Compression) ax'n2/an'nn ynxn A ayinv/annn Wy ONAN TI otjm K, F, 12 Ems nna now Am 6° Ymax b . Ky = K, (Bending Stress) n5'9> ynxn % N9'99 VAY OANA TI OTN Kw) aS'9> vInIN M,. ) 7n'y Way A'99 7ITIN OID VAAN "M!077 FPN Yona) gio! VY 220 AMIR INN Tin] n9'997 JNA TIN Z nn’) F (Shear Stress) N7'TA NIN ANNIND ANTA yNRN . A OON NIN N'WOIN NNW M'7a yANN nown T3yn1 nnon “mn'o7n mira yarn a'7a NN AXIND '7Ta yaXN Tra aya yay OANA TD OTN Kis n> Fiyy nna now Am] M,:R (Torsion Stress) N'!9N ANYIND 21'7Ta ynRN T= Ky (ania aa ort) NANA j9IT2 NN|NN "M07 ATA YANN P f I" Tin'9 ANXIND AVTA yaNNA Tira Tin'9 WY ONAN TI OT Ky.) ‘ins vanin M, wm] nna orm R, as AAR oI Typ oT jI9 9"y Ann JPW ynAn nm ipw yarn ©.,..[MPa] ay'nY/an'nnn ARXXIND "WAIN yaXnA Smee n'99N ANYIND "WAIN yaNN Smee] VTA NDA ARLINI DVTA YARD Typ] Tin'9n AXXIND AI'Ta YANN Tura] q pTin ‘aan nan Vipw yarn ©.,..[ MPa] lA, max = Janina Ww ay yarn Supa} woTi nin'02 aT 2 F, = force at solid length, L,: the maximum force that the spring ever sees [, = force at operating length, [.,: the maximum force the spring secs in normal operation force at installed length, L;: the force varies between F, and F, for a reciprocating spring, force at free length, L¢: this force is zero a y ‘op-max | Yop-max —t— Yetash + =D L Lop-max (c) Same spring (d) Same spring (e) Same spring with inital imum at solid height, L, preload, F; operating load. (to be avoided). 297n NR? PUR TAY 1Y¥N1 PUR ‘vom ‘nnn nid Wao ayna AIR "WOIN PUN oni PR ry'Dy#a NN9NnN "n'o7Nn ynxXn T F Lo Tt =—+- “Mogan "Ta yuNXn max = 7 Vy SWRI A= ae “na nn now Zo= a Tena Ww 719 ANNI vInIN T= = “na yw wnton onin 8FD + 4F 8FD + d T. = — = —— — max" ad? nd? wd? 2D 8F.D 8FC Ss, Tmax = Ks* 3. NS” z= nud nud Ns n'0vv0 NONYN T'n}'T AONYA 8FD Tox = Ky Cag = Ky AT Kx a20r! x40 +2 © 2C 4C-3 yon 7Y 01D Wwlj7: D; yon 7 yn WWI? : D, yon 7w yxinn rW1j7:D yon qin nna ?NA wij id -p'977 NY'09 :P (WOIN Y'97 WN NDING NI9ID 'NW f'2 j7nqaN D, = D—d 1979 y'9777 TUX IL, D,=D+d D;+D, 2 D= D . . c= = Spring index y'9j77 Oj7TX D a | ny yopn nine a oF “* Gd* Gd ~~ 8DIN, 8C3N, k = AHIAL _h-F RTL, By k= Ly - Lo FE. k i F< FSF, r= Fimat Fo 2 F ok, ma m(t) f A K,=1+4q(K,-1) Orin” ony) (Fatigue) Ma» yNn an rm n> Fey TAN Nd JINI WARD YYINN Nd Alw'n an'nn WAY yxymn ynaxn niryNA Vay ONANN TI OTN K, yxinn n> Fn ) nna now Am] NI9"YNA WAY DYNAN THN OTN DiovyNA Way o'NANN 119 OT K, jan povw — nwa oT g qnan oovIw — oan 1199 OTN K, N9'9) WAY yyinn ynan niryNA Vay ONANN TI OTN K, AS'9> vInIN M,, ) Mon VAN "MOF PNIN MIX] gio! V¥ 220 AMIR ONIN a inn Nd jN] WALD aATIO"ONR Nd aw'n ann AWAY ATIO"7ONN yarn DiovyNA Way o'NANN 119 OT K, ATION Nd Fam qnna now 4,7] n9'99 Wy ATIO"ONN ynan DiovyNA Wy o'NANN 719 OT K, aS'9>) vIn M,, , oma van "mon NIN y, M2) gion V8 220 ANN VININ Tin] o,, =(4, )+3(z,,)° (Von Mises) o7'n |ID 9"y ,717w YN ynan Tw yxin yaxn On {ura "m7 VAIN YONA Opp 447] ANITA yNIA YONA Tp yp] (Von Mises) 07 j19 O"y ,717Y NTIO"7ONR yNXN Viww ATIONONN YANN C,,, [pa] "MN ATION YANN Ftura| AV'1a ATION YANN Tp 7 AY INND N99 FW NVI MIN imnro | mn yI9'0 (>2PAN [pH 92) [ area | \ -—————— ner Ou onna 71a Oy ayydn 71a / 1 Lana / 3 r Temperature Strength El oC] PC) So ol) MPa (kpsi) MPa (kpsi) co i 1030 aT 205 (400} 848 (123) 648 (94) 17 47 495 aan 315 (600) 800 (114) @ 621 (90) 19 53 401 Qar 425 (800) 73) (108) [| 579 (84) 23 60 302 ast 540 (1000) 669 (97) 517 (75) 28 65 255 aar 850 (1200) 586 (85) 441 (64) 32 70 207 Normalized 925 (1700) 521 (75) 345 (50) 32 61 149 Anneoled __- 870 (1600) 430 (62) 317 (46) 35 64 137 Toad G&T 205 (400) 1113) 93 (86) T 2B 57 at 425 (800) 758 (110) 552 (80) 21 54 241 at 650 (1200) 634 (92) 434 (63) 29 65 192 Normalized 900 (1650) 590 (86) 374 (54) 28 55 170 Annealed 790 (1450) 519 (75] 353 (51) 30 57 149 1050 Qa 205 (400) 1120(163) 807 (117) 9 27 514 oar 425 (800) 1090 (158) 793(115) 13 36 Add oar 650 (1200) 717 (104) 538 (78) 28 65 235 Normalized 900 (1650) 748 (108) 427 (62) 20 39 217 Annealed 790 (1450) 636 (92) 365 (53) 24 40 187 1060 Q&T 425 (800) 1080 (156) 765 (111) 14 4] 3N] QB 540 (1000) 965(140) 669 (97) 17 45 27 Q8T 650 (1200) 800(116) 524 (76} 23 54 229 Normalized 900 (1650) 776 (112) 421 (61) 18 37 229 Annealed 790 (1450) 26 (91) 372 (5A) 2 38 18179 (Soderberg) ANTIO 9"y — Nis"yNnny Nin'or aTPN n= 1 Vann 'n nnn 797 o'NNN ;= oO, + On mona nin'vr oT S, S, ATIO'VONR YANN Down "Wa PIN yxinn yaxn (Yield strength ) ay1> yoxn 1 (Goodman) jntia 9"y — nis'yna? nin'wr oTFN ny oc oc Or ni2x? 09 Nay Ninn? o'xNn S, S,, monyna’? nin'va oT ATIO'ONN YANN mown "Waa PIN yxinn yoxn (Ultimate Tensile strength ) oyna 71a / 72” ynXN Suir 1 (Gerber) ana 9"y — nis'yna? Nin'va ATM NIT791 ANI NIN? O'NNN monyna’? nin'va oT ATIO'ONN YANN mown "Waa PIN yxinn yoxn (Ultimate Tensile strength ) ovAn Yaa /7aw ynxn Stu ) (Elliptic) noD"2X O"Y — Nis'yNA? nin'vr oOTFN o>'yn D NIN VANS NiT77 o-NNN MiorynAy Nin'va oT" ATIO'ONN YANN mown "Waa PIN yxinn yoxn (Yield strength ) ny ynxn ss »sAANS ISO YPN (665 >”) ISO 795 D?72IwN D7 PITIN 22°93 11799 pay Dara Det» Daman wp Ayo TAn now wy wy Tv Tan now wp wp oon nme w039 >>>OPON amne roe | sm0poN P % 1 2 P A 1 a tmm] | [mm] | fmm) {| fmm) | fmm] | fmm) | [mm4 [mm] [mm] 2 0.40 1.79) 1.509 1.740 7 238 0.45 2.98 1.948 2.200 3 0.5 4.47 2.387 2.675 a0 0.6 6.00 2.764 3.110 4 07 175 3.141 3.545 5 08 12.7 4.079 4.420 6 1 17.9 4.773 5.350 8 1.25 32.8 6.466 7.188 1 36.0 6.773 7.350 10 1s 52.3 8.160 9.026] 1.25 56.3 8.466 9.188| 12 1.75 76.3 9.853 10.863} 1.25 86.0 10.466 10.647 14 2 104 11.546 12.701 1S 116 12.160 13.026 16 2 144 13.546 14.701 1S 157 14.160 15.026| 20 25 225 16.933 18.376 1.5 259 18.760 | 19.026 24 3 324 20.319] 22.051 2 365 21.546 | 22.701 30 3.5 519 25.706] 27.727 2 596 27.546 | 28.701 36 4 759 31.092] 33.402 2 884 33.546 | 34.701 42 4 1050 36.779 39.077 2 1230 39.546 | 40.701 48 5 1380 | 41.866] 44.752 2 1630 45.456 | 46.701 56 5.5 1910 | 49.252] 52.428 2 2250 53.516 | 54.70 64 6 2520 56.639] _ 60.639 2 2980 61.546 | 62.701 Nominal! Mechanical Properties Head Marking aterial, range | P9of Min. Yield | renin (mm) | (MPa) (Mpa) Strength Met bolts All Sizes Class 8.8 below 580 640 800 \ A ) Medium Carbon Steel, |_16mm 7 eee” an 600 660 830 Class 10.9 smm - 940 1040 Alloy Steel, Quenched | j99mm 830 Wes and Tempered 10.9 Glass 12-9 Lemm - 1100 1220 Alloy Steel, Quenched | 499mm 970 and Tempered 12.9 magnetic. Steel alloy with 17- thru 450 Typeat | _ 702 19% Chromium and 8- | 20mm Typical Usually stamped 4-2 13% Nickel 11 ~ | ROX ,DVUN'N 7a "YANN? OMY NN’? WAX N'7AI Dyn [AN'ON' NTITN NR YAINw O'NNN /it'n n'01n7 A438 Noon 9819) 9499 minor wan P SK Q 9 ,a ~) P/2 Er Pre oo: | p + 12 ;bAA VY? FAMA WIN P nd-1 AN q'na Ww C Tapa Dw PT AAI aaa wy wisw n> On) nna oan sen i "yn (n>) onw Fry AIA ITN? NW! PRAT AIA WAY Danan Vy? awa Wis P nd>—-2 FN q'na Fw TapA DAW PT aw - nar aman ['2. ninn BY WA'N .X anmaan 2ITa an ny nt (yigan najanv) ana ww wisw Vy nd Qn (An onw O77) DINTH x OT f; "yn (n>) onw Fry nna oan 790Nn i yan 'nows0n n yann ‘now J D'nA aT Ly penan Vx? avm Vis P nd-2 an Aina Vw Tapa WM WTI NTP? aaa f'a Ninn NV7AWN a (ylfa nino ja) aqiaa wy wisw Vy n> On) (Qn ony oF) natn x OTN f; "yin (n>) onw Fry nanan rs0n i yan 'now 190n 7 yan ‘now 2 D'nA OTM Ly i-n-fy-R Qrox fy “DR, fi *M Ros mnian Dewan 13 Wana AwWMNa VID 7IN's VINM —3 myn PDN yilaz FNM? RYN DAA LN C 1w'na ana YW wisw Vy nd Qn (An onw oT) nINTH x OTP f; win'9 oN Mw. mi oman qs0n i orn R yana ‘now 2 D'NA OTN Ly yan ‘now r90n 1 Wana AwWMNa VID 7IN's VINM —3 myn ay PNA ORYNI DAA A C 121'na ann nNA omMyA AID W Ww VN Oya] (Qn! onw oT) NINTH 'X OT f, vommnm M [N-mm] (anna omya aqaa) “m'o7n orth Rivax ora r90n i yan 'nowr90n n yann ‘now J D'nA aT Ly yinna porn Ww ape IR? Danan Vy? avin Wis P ndn-4az7MN (C Tapa DAM PT raw N27) aqiaa wy awisw Vy n> Qn) (an ony oF) NINTH NOT f, vim M, =P-L N-mm] marin q90n i C atm vn pina aaa FMn orn R,ax DIN WwW Yann ‘now |! qD'!NA OTN Ly yan 'now ron 1 ynna oan yn apo IR, (7 nopna pnw. awa 7719) 17109) DSN= NNN 94 vv, ony) pin yon O'NNNN 7197 YAW ‘oO? WN] O'NANN Alw'n F (Tension/Compression) ax'n2/an'nn ynxn A ayinv/annn Wy ONAN TI otjm K, F, 12 Ems nna now Am 6° Ymax b . Ky = K, (Bending Stress) n5'9> ynxn % N9'99 VAY OANA TI OTN Kw) aS'9> vInIN M,. ) 7n'y Way A'99 7ITIN OID VAAN "M!077 FPN Yona) gio! VY 220 AMIR INN Tin] n9'997 JNA TIN Z nn’) F (Shear Stress) N7'TA NIN ANNIND ANTA yNRN . A OON NIN N'WOIN NNW M'7a yANN nown T3yn1 nnon “mn'o7n mira yarn a'7a NN AXIND '7Ta yaXN Tra aya yay OANA TD OTN Kis n> Fiyy nna now Am] M,:R (Torsion Stress) N'!9N ANYIND 21'7Ta ynRN T= Ky (ania aa ort) NANA j9IT2 NN|NN "M07 ATA YANN P f I" Tin'9 ANXIND AVTA yaNNA Tira Tin'9 WY ONAN TI OT Ky.) ‘ins vanin M, wm] nna orm R, as AAR oI Typ oT jI9 9"y Ann JPW ynAn nm ipw yarn ©.,..[MPa] ay'nY/an'nnn ARXXIND "WAIN yaXnA Smee n'99N ANYIND "WAIN yaNN Smee] VTA NDA ARLINI DVTA YARD Typ] Tin'9n AXXIND AI'Ta YANN Tura] q pTin ‘aan nan Vipw yarn ©.,..[ MPa] lA, max = Janina Ww ay yarn Supa} woTi nin'02 aT 2 F, = force at solid length, L,: the maximum force that the spring ever sees [, = force at operating length, [.,: the maximum force the spring secs in normal operation force at installed length, L;: the force varies between F, and F, for a reciprocating spring, force at free length, L¢: this force is zero a y ‘op-max | Yop-max —t— Yetash + =D L Lop-max (c) Same spring (d) Same spring (e) Same spring with inital imum at solid height, L, preload, F; operating load. (to be avoided). 297n NR? PUR TAY 1Y¥N1 PUR ‘vom ‘nnn nid Wao ayna AIR "WOIN PUN oni PR ry'Dy#a NN9NnN "n'o7Nn ynxXn T F Lo Tt =—+- “Mogan "Ta yuNXn max = 7 Vy SWRI A= ae “na nn now Zo= a Tena Ww 719 ANNI vInIN T= = “na yw wnton onin 8FD + 4F 8FD + d T. = — = —— — max" ad? nd? wd? 2D 8F.D 8FC Ss, Tmax = Ks* 3. NS” z= nud nud Ns n'0vv0 NONYN T'n}'T AONYA 8FD Tox = Ky Cag = Ky AT Kx a20r! x40 +2 © 2C 4C-3 yon 7Y 01D Wwlj7: D; yon 7 yn WWI? : D, yon 7w yxinn rW1j7:D yon qin nna ?NA wij id -p'977 NY'09 :P (WOIN Y'97 WN NDING NI9ID 'NW f'2 j7nqaN D, = D—d 1979 y'9777 TUX IL, D,=D+d D;+D, 2 D= D . . c= = Spring index y'9j77 Oj7TX D a | ny yopn nine a oF “* Gd* Gd ~~ 8DIN, 8C3N, k = AHIAL _h-F RTL, By k= Ly - Lo FE. k i F< FSF, r= Fimat Fo 2 F ok, ma m(t) f A K,=1+4q(K,-1) Orin” ony) (Fatigue) Ma» yNn an rm n> Fey TAN Nd JINI WARD YYINN Nd Alw'n an'nn WAY yxymn ynaxn niryNA Vay ONANN TI OTN K, yxinn n> Fn ) nna now Am] NI9"YNA WAY DYNAN THN OTN DiovyNA Way o'NANN 119 OT K, jan povw — nwa oT g qnan oovIw — oan 1199 OTN K, N9'9) WAY yyinn ynan niryNA Vay ONANN TI OTN K, AS'9> vInIN M,, ) Mon VAN "MOF PNIN MIX] gio! V¥ 220 AMIR ONIN a inn Nd jN] WALD aATIO"ONR Nd aw'n ann AWAY ATIO"7ONN yarn DiovyNA Way o'NANN 119 OT K, ATION Nd Fam qnna now 4,7] n9'99 Wy ATIO"ONN ynan DiovyNA Wy o'NANN 719 OT K, aS'9>) vIn M,, , oma van "mon NIN y, M2) gion V8 220 ANN VININ Tin] o,, =(4, )+3(z,,)° (Von Mises) o7'n |ID 9"y ,717w YN ynan Tw yxin yaxn On {ura "m7 VAIN YONA Opp 447] ANITA yNIA YONA Tp yp] (Von Mises) 07 j19 O"y ,717Y NTIO"7ONR yNXN Viww ATIONONN YANN C,,, [pa] "MN ATION YANN Ftura| AV'1a ATION YANN Tp 7 AY INND N99 FW NVI MIN imnro | mn yI9'0 (>2PAN [pH 92) [ area | \ -—————— ner Ou onna 71a Oy ayydn 71a / 1 Lana / 3 r Temperature Strength El oC] PC) So ol) MPa (kpsi) MPa (kpsi) co i 1030 aT 205 (400} 848 (123) 648 (94) 17 47 495 aan 315 (600) 800 (114) @ 621 (90) 19 53 401 Qar 425 (800) 73) (108) [| 579 (84) 23 60 302 ast 540 (1000) 669 (97) 517 (75) 28 65 255 aar 850 (1200) 586 (85) 441 (64) 32 70 207 Normalized 925 (1700) 521 (75) 345 (50) 32 61 149 Anneoled __- 870 (1600) 430 (62) 317 (46) 35 64 137 Toad G&T 205 (400) 1113) 93 (86) T 2B 57 at 425 (800) 758 (110) 552 (80) 21 54 241 at 650 (1200) 634 (92) 434 (63) 29 65 192 Normalized 900 (1650) 590 (86) 374 (54) 28 55 170 Annealed 790 (1450) 519 (75] 353 (51) 30 57 149 1050 Qa 205 (400) 1120(163) 807 (117) 9 27 514 oar 425 (800) 1090 (158) 793(115) 13 36 Add oar 650 (1200) 717 (104) 538 (78) 28 65 235 Normalized 900 (1650) 748 (108) 427 (62) 20 39 217 Annealed 790 (1450) 636 (92) 365 (53) 24 40 187 1060 Q&T 425 (800) 1080 (156) 765 (111) 14 4] 3N] QB 540 (1000) 965(140) 669 (97) 17 45 27 Q8T 650 (1200) 800(116) 524 (76} 23 54 229 Normalized 900 (1650) 776 (112) 421 (61) 18 37 229 Annealed 790 (1450) 26 (91) 372 (5A) 2 38 18179 (Soderberg) ANTIO 9"y — Nis"yNnny Nin'or aTPN n= 1 Vann 'n nnn 797 o'NNN ;= oO, + On mona nin'vr oT S, S, ATIO'VONR YANN Down "Wa PIN yxinn yaxn (Yield strength ) ay1> yoxn 1 (Goodman) jntia 9"y — nis'yna? nin'wr oTFN ny oc oc Or ni2x? 09 Nay Ninn? o'xNn S, S,, monyna’? nin'va oT ATIO'ONN YANN mown "Waa PIN yxinn yoxn (Ultimate Tensile strength ) oyna 71a / 72” ynXN Suir 1 (Gerber) ana 9"y — nis'yna? Nin'va ATM NIT791 ANI NIN? O'NNN monyna’? nin'va oT ATIO'ONN YANN mown "Waa PIN yxinn yoxn (Ultimate Tensile strength ) ovAn Yaa /7aw ynxn Stu ) (Elliptic) noD"2X O"Y — Nis'yNA? nin'vr oOTFN o>'yn D NIN VANS NiT77 o-NNN MiorynAy Nin'va oT" ATIO'ONN YANN mown "Waa PIN yxinn yoxn (Yield strength ) ny ynxn ss »sAANS ISO YPN (665 >”) ISO 795 D?72IwN D7 PITIN 22°93 11799 pay Dara Det» Daman wp Ayo TAn now wy wy Tv Tan now wp wp oon nme w039 >>>OPON amne roe | sm0poN P % 1 2 P A 1 a tmm] | [mm] | fmm) {| fmm) | fmm] | fmm) | [mm4 [mm] [mm] 2 0.40 1.79) 1.509 1.740 7 238 0.45 2.98 1.948 2.200 3 0.5 4.47 2.387 2.675 a0 0.6 6.00 2.764 3.110 4 07 175 3.141 3.545 5 08 12.7 4.079 4.420 6 1 17.9 4.773 5.350 8 1.25 32.8 6.466 7.188 1 36.0 6.773 7.350 10 1s 52.3 8.160 9.026] 1.25 56.3 8.466 9.188| 12 1.75 76.3 9.853 10.863} 1.25 86.0 10.466 10.647 14 2 104 11.546 12.701 1S 116 12.160 13.026 16 2 144 13.546 14.701 1S 157 14.160 15.026| 20 25 225 16.933 18.376 1.5 259 18.760 | 19.026 24 3 324 20.319] 22.051 2 365 21.546 | 22.701 30 3.5 519 25.706] 27.727 2 596 27.546 | 28.701 36 4 759 31.092] 33.402 2 884 33.546 | 34.701 42 4 1050 36.779 39.077 2 1230 39.546 | 40.701 48 5 1380 | 41.866] 44.752 2 1630 45.456 | 46.701 56 5.5 1910 | 49.252] 52.428 2 2250 53.516 | 54.70 64 6 2520 56.639] _ 60.639 2 2980 61.546 | 62.701 Nominal! Mechanical Properties Head Marking aterial, range | P9of Min. Yield | renin (mm) | (MPa) (Mpa) Strength Met bolts All Sizes Class 8.8 below 580 640 800 \ A ) Medium Carbon Steel, |_16mm 7 eee” an 600 660 830 Class 10.9 smm - 940 1040 Alloy Steel, Quenched | j99mm 830 Wes and Tempered 10.9 Glass 12-9 Lemm - 1100 1220 Alloy Steel, Quenched | 499mm 970 and Tempered 12.9 magnetic. Steel alloy with 17- thru 450 Typeat | _ 702 19% Chromium and 8- | 20mm Typical Usually stamped 4-2 13% Nickel 11 ~ | ROX ,DVUN'N 7a "YANN? OMY NN’? WAX N'7AI Dyn [AN'ON' NTITN NR YAINw O'NNN /it'n n'01n7 A438 Noon 9819) 9499 minor wan P SK Q 9 ,a ~) P/2 Er Pre oo: | p + 12 ;bAA VY? FAMA WIN P nd-1 AN q'na Ww C Tapa Dw PT AAI aaa wy wisw n> On) nna oan sen i "yn (n>) onw Fry AIA ITN? NW! PRAT AIA WAY Danan Vy? awa Wis P nd>—-2 FN q'na Fw TapA DAW PT aw - nar aman ['2. ninn BY WA'N .X anmaan 2ITa an ny nt (yigan najanv) ana ww wisw Vy nd Qn (An onw O77) DINTH x OT f; "yn (n>) onw Fry nna oan 790Nn i yan 'nows0n n yann ‘now J D'nA aT Ly penan Vx? avm Vis P nd-2 an Aina Vw Tapa WM WTI NTP? aaa f'a Ninn NV7AWN a (ylfa nino ja) aqiaa wy wisw Vy n> On) (Qn ony oF) natn x OTN f; "yin (n>) onw Fry nanan rs0n i yan 'now 190n 7 yan ‘now 2 D'nA OTM Ly i-n-fy-R Qrox fy “DR, fi *M Ros mnian Dewan 13 Wana AwWMNa VID 7IN's VINM —3 myn PDN yilaz FNM? RYN DAA LN C 1w'na ana YW wisw Vy nd Qn (An onw oT) nINTH x OTP f; win'9 oN Mw. mi oman qs0n i orn R yana ‘now 2 D'NA OTN Ly yan ‘now r90n 1 Wana AwWMNa VID 7IN's VINM —3 myn ay PNA ORYNI DAA A C 121'na ann nNA omMyA AID W Ww VN Oya] (Qn! onw oT) NINTH 'X OT f, vommnm M [N-mm] (anna omya aqaa) “m'o7n orth Rivax ora r90n i yan 'nowr90n n yann ‘now J D'nA aT Ly yinna porn Ww ape IR? Danan Vy? avin Wis P ndn-4az7MN (C Tapa DAM PT raw N27) aqiaa wy awisw Vy n> Qn) (an ony oF) NINTH NOT f, vim M, =P-L N-mm] marin q90n i C atm vn pina aaa FMn orn R,ax DIN WwW Yann ‘now |! qD'!NA OTN Ly yan 'now ron 1 ynna oan yn apo IR, (7 nopna pnw. awa 7719) IniX DA pon? on pa {077200 NX? Nin AINA AYIA 1422 H2p-n Hw2d own |'1n YiTan Alan Dx | ANID DINA AAA nyAP oman A, mm] AMANAAV'OD Phun) BIND ANANA N42 190n 71 ana wiz d BINA ANANA WNT ND) 190n own jan Tan ywa nx on nora anana nid W0n aaa wy wisw n> On jw qwarra now A, DiNa VINA ANIM ATA yAND [z] ‘nyav 70'n now A, ADyNY yan yn? [P] aaa nya? wT] yan poon yin 70n Fv] ania Mwy, mj yin T"70 Neeu] ara ny'nan A,=7-d,-h Nyape: = 9-65 P arya onan |) 4, =0.25e(d?-d;) P= M,-n 9550 ch tan(y 72k tint) ~M,-20 tan(v+@) 16 aa nin ayaa nizya 77 (qian Pw Tnx ano May AYpIEN ATIAYY 7NY APA ATID) aaa wy wisw n> On TNX 212'03 ya AAAW 77MIN I mm] In'5 vInmM Mirnn AAA yiow /AAAAA Fw AIAN DIT any anana on nur Face] TVNYY VAY PRA Nj?!'T1 y<@ WR OPNN Dy AVY VAN mony : maya on'/ M10nn on! oinin A?'TAN ,2IW'0 ANNAN n1'o77n - i<l nnannnnoa Monn Nousput mionn on' i Ninput vinin AORN ,1I'0 NMAN A?"Tan - 7<1 NNAN Maan Monn RATIO Napa 0191 T"70 Dinu Nouipur Zinput v"2a'a Monn — Ayn on'/ nionn on Ny, Z mionn ont i iput ‘output ('9) ym aaa o'wr90N Z, input yan ‘ava onnwrson Z, ‘output Turn w"aza ayonN — Aya on'/ Mionn on! (yn jir7'nna Aw ayn aay) mionn on: i {i'n nynnnvr rD0n Z, ory Yavaa ow rs0n Z, mww nionn — maya on'/ Monn on: muionn on' i input ‘output yim Yavaa ovrw son Z, input yan ‘ava. ow >90n Z, ‘output _ Disna AYN Monn — Maya on'/ Monn on! mionn on: i ‘output yim ‘a'a viz D. input yam ‘ata roig D, ‘output n Mionn on"? omm ya qwypa Finput Foutput i Mionnan xxv omimM M ne mionna ni7'y1 77 Mionnan 019) vin M, input muionn on' i 17 v-60,000 n=———— aD aDn 60,000 — ‘ouput Non input ‘aia T'70 0 "remy niwa anand i 5 ‘ata ‘Nn Wl? Dinu aa Den nNaN nywn nn'nn " 7 Yala ‘y'n Vol? Donn 0 "re ynn json yin 720n Fav] oman Mwy. n) yin T"70 Neew] ym jo0n yin poon P. input Pra WUT 790A Pin, ; nvu> m7" 7) P_1000P _ 9550P M,=—= @o 227 on 60 y= na input Mota = ThA niizya 792 — Nwna ‘D WwW N71 NTI 18 comm vii Mw. wi] ppon Fav] nner nanan me see 0 "re nionn ny) miionn nix 77 nxt on P ‘output 0101 7200 P. input _nou padojacer ‘V-belt sheave ‘Spur gear 6.00in PD ‘Chain sprocket 10,00 in PD (a) Side view of shaft Belt drive to conveyor Gear E drives Input from gear swater turbine to generator (6) Orientation of elements A, C, and £ as viewed from right end of shaft far (@) Pictorial view Ay showing forces 4 ——_ Fax Fox (8) Forces on shaft 40" Hotel —, {6 Forces on shaft at sprocket C (d) Forces on gear E. EDrives Q Fag = 28 Fy = S24 Fey = 180 Rpy = 164 Fey = 624 Rp, = 188 |enetonet setotbobor A c E B c D tay = $89 Rpg = 398 I 482 os 482) Shearing 311 go Seeing p Las force, V Cy force, (lb) ib) gy {_J.. 23 sas 4800 2882 2964 Bending Bending moment, Mf c moment, Mf e {being A B c & 1080 Mg = 16682 + 28927 = 3339 bein — 1668 Mg = V1982 + 48002, = 4804 Ib-in Mp = Vi0s0% + 29687 = 3155 Ibein (@} Horizontal plane >) Vertical plane W,on gear B pushes gear B away Radial force, W, (a) Action forces—gear A (b) Reaction forces. drives gear B. Forces exerted on Forces exerted on gear A by gear B. gear B by gear A. ‘Dr. His | ib 1223 Ib {2109 Ib c & A Win 15 in Win D A Iin in C iin 458 Ib 1529 Ib 4620 Ib 1680 Ibs Be Hic ‘By ‘Dy 2520 1223 ‘Shearing O Shearing force, V Loe 06 force, ¥ Cb) (lb) —2100 = 1680 16 800 A B c D A B JAN Bending Bending © ec DB moment, Af moment, Mf (Ib+in) 7640 4 ax39 _(ibsind — 21 000 (a) Horizontal plane, x-direction () Vertical plane, y- Rotation Driving sheave sheave Rotation " T, = Torque exerted Tg = Reaction torque ‘e Rotation ‘on sprocket A exerted on sprocket B by the shaft by the shaft Rotation Net torque on A Net torque on B Rotation Ty = Fi- F) (D4) Ty = (Fi ~ Fz) (Dp/2) Fg = Fy + Fy Fg = Bending force ‘on shaft FIGURE 12-6 Forces on belt sheaves or pulleys IN] Opyn)rspAM. - fF [kW] Jon) povn - =P [kW] *pvpeN pov - Pg mya .12 [m/s] AST IWMNpNYAD - Vv jo-m De ny Dy [N] Dyan pyannmno nd —- Ss; 1000 P [IN] Dapa pylAMMO Md - Sz Bow AMMO MIO - k [m] yn ranwip - d S,=k.-F, [m] monn 29a wip - Dj, D2, Ds S=S,-F, [Nm] Jon vw - M, may - 4 _ D [rpm] DaAIWIMDPDNVAN - n,n M, =(S;- 82) AIST pamnoanna on - i Pesky Pon AMANO -— ky [m] ayy - OL a L=157(Do +d ja29 4 Domdo) [m] Jopn DIM MYN WIP - do = 0 * Lo 4A [m] Da plpnmw - A [m] JN AIA MYN WIP - Do nD, ny 10 Twya Jwna 60x 1000 _m-d-n, 60,000 Pky P= ky M-= 9550P n T, = 4508 =E._?, G Nv M-v? Q=2T, -N -cos(B) aAyRnA AMAN AYIA ANAN 1] Joza tatan roiz 4, Joj vata T"'70 Nees] AY Ww wT) 'MOPOR j790n Alw'n AVIA WW WTI '2'079N PON Paw] (onwal AYINA alo? ANNA ,A7I0N O'D7IW) DN'w OTN k, oinin Mwy, wn] ‘a'a T'0 Nreu] 23 ‘aia Tw omm awn oon Frwy oinin Mwy, wi) ‘a'a T'0 Nreu] WNT) Niyvixd 10n Alw'n wom nwa rs0n N AVIA WW WTI '2'079N PON Paw] TNX AYA WaVAY Nialony 7a0n P! B AMIN nT aT G AYA PR oF C, WOTIn AYN Nin'nn aw'n AYINT? D000 Tin'‘nnn Ty nin'nn ot R AMIN nT aT G “Amn poon Fay] nw s0n N Avena DNA Y,,9 AYIA ANN TTA oT? M Dyn 7y 'vvO Only alw'n ova Wy Vy on Qn AYINT? D000 Tin'‘nnn Ty nw s0n N Ayr Ww yIow nut B dd (AMPN AVY) PTIN nINAN 7a 2wW "MIN JI? AWN Yan Fw "nN wl? 4 si nn) Vayn ‘any j70n Fav] ‘an T'70 Neeu] (naa AVY) Nis"ynA nInan 1a Ww "MIN wl? AWN Yan Ww Nn Vl? fn] “pw vmin May a (anim) nio"y na? ANIM ynxn [oh say nin > (130160). n nin 2 9 2M M,= (2in'5 vINM Dy AS'DD VINM PW AIT) TIP!W OMIM “pw vmin May a Ad'99 WAY OANA TI OT Ky, Ap'9> om Myy. oi K, uin's van My. on (ani awn) nis"ynad ANIM ynan (anim) nio"y na? ANIM ynxn [hay otra] monn WwW yA Aw'n WAY Nin'oa aT Ss (aznm avy) "Mn Jol? Alw'n Yan ww "nn viz d, min] wot) nin'e2 oT [n] d>3 16-[n] 4 kK, Mw) 43 KM any 44 kK, My 43 Kea Minny a S, S, S, S, [Nm] a vw [Nm] 7999 vy [Nm] Dymo vy [Nm] 39 YON mina vw Zy [mm? noe) (TNA IT) 24 10 n9'927 DANA TD aT k, Ag'997 ATION ONIN Mw) Diwnay “waa prin S, Yinio/AvTa? ONAN TI OT70 ky, wine? ATIOY7ONX vIn M air) Mownay "aa prin S, ns'9>7 yxin vin Myo) yaina Ww ayDA Ta S, ‘in'97 yxinn vin Miu) 1099 1 C=P-L'- fy fi < Catalogue lom Ww WIT) NIT WI Alwin 1om WwW NTI IT AWD Guy 2om Yy on Fin} lon Ww ON VIR Lote] qa Mw oT7 a mrt on ot f, Muoronv on f, Nya alzo7 97 m1 TAwWID C catalogue -T1A N'TA ND OMY IO"! — TH 10m AY AANA TN VP TVA OWN YTD NI NN ‘an wy Ty9N NNW Ayqy = 3 10 ostinder!Cone L=L,-n-60-10° -VN onmya Dal “7N'T N22 OlAVY 10! — Nn") 10! 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