Machine Design Databook 2010 Part 7 pdf

FIGURE 16-18 Power absorption and starting torque for balanced and unbalanced seals. (M. J. Neale, Tribology Handbook, Butterworths, London, 1973.) PACKINGS AND SEALS 16.33 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. PACKINGS AND SEALS REFERENCES 1. Lingaiah, K., and B. R. Narayana Iyengar, Machine Design Data Handbook,Vol. I(SI and Customary Units), Suma Publishers, Bangalore, India, 1986. 2. Lingaiah, K., Machine Design Data Handbook, Vol. II (SI and Customary Metric Units), Suma Publishers, Bangalore, India, 1986. 3. Maleev, V. L., and J. B. Hartman, Machine Design, International Textbook Company, Scranton, Pennsylvania, 1954. 4. The American Society of Mechanical Engineers, ASME Boilers and Pressure Vessel Code, Section VIII, Division I, 1986. 5. Whalen, J. J., ‘‘How to Select the Right Gasket Material,’’ Product Engineering, Oct. 1860. 6. Shigley, J. E., and C. R. Mischke, Standard Handbook of Machine Design, McGraw-Hill Book Company, 1986. 7. Neale, M. J., Tribology Handbook, Butterworths, London, 1975. 8. Ratelle, W. J., ‘‘Seal Selection, Beyond Standard Practice,’’ Machine Design, Jan. 20, 1977. 9. ‘‘Packings and Seals’’ Issue, Machine Design, Jan. 1977. 10. Faires, V. M., Design of Machine Elements, Macmillan Book Company, 1955. 11. Bureau of Indian Standards. 12. Rothbart, H. A., Mechanical Design and Systems Handbook, McGraw-Hill Book Company, New York, 1985. 13. Lingaiah, K., Machine Design Data Handbook, McGraw-Hill Book Company, New York, 1994. 16.34 CHAPTER SIXTEEN Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. PACKINGS AND SEALS CHAPTER 17 KEYS, PINS, COTTERS, AND JOINTS SYMBOLS 4;5;6 a addendum for a flat root involute spline profile, m (in) A area, m 2 (in 2 ) b breadth of key, m (in) effective length of knuckle pin, m (in) dedendum for a flat root involute spline profile, m (in) d diameter, m (in) d 1 major diameter of internal spline, m (in) d 2 minor diameter of internal spline, m (in) d 3 major diameter of external spline, m (in) d 4 minor diameter of external spline, m (in) d c core diameter of threaded portion of the taper rod, m (in) d pl large diameter of taper pin, m (in) d m (or d pm ) mean diameter of taper pin, m (in) d nom nominal diameter of thread portion, m (in) D diameter of shaft, m (in) pitch diameter, m (in) F force, kN (lbf) force on the cotter joint, kN (lbf) pressure between hub and key, kN (lbf) F 0 , F 00 force applied in the center of plane of a feather keyed shaft which do not change the existing equilibrium but give a couple, kN (lbf) F 0 2 , F 00 2 two opposite forces applied on the center plane of a double feather keyed shaft which give two couples, but tending to rotate the hub clockwise, kN (lbf) F t tangential force, kN (lbf) F  frictional force, kN (lbf) h thickness of key, m (in) minimum height of contact in one tooth, m (in) l length of key (also with suffixes), m (in) length of couple (also with suffixes), m (in) length of sleeve, m (in) L length of spline, m (in) l o , s o space width and tooth thickness of spline, m (in) m module, mm, m (in) M b bending moment, N m (lbf in) M t twisting moment, N m (lbf in) 17.1 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. 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Source: MACHINE DESIGN DATABOOK p pressure, MPa (psi) tangential pressure per unit length, MPa (psi) p 1 maximum pressure where the shaft enters the hub, MPa (psi) p 2 pressure at the end of key, MPa (psi) p d (or P) diametral pitch Q external load, kN (lbf) R resistance on the key and on the shaft to be overcome when the hub is shifted lengthwise, kN (lbf) t thickness of cotter, m (in) xm profile displacement, m (in) z number of teeth, number of splines  stress tensile or compressive (also with suffixes), MPa (psi)  b1 nominal bearing stress at dangerous point, MPa (psi)  shear stress, MPa (psi)  angle of cotter slope, deg  angle of friction, deg  coefficient of friction (also with suffixes) SUFFIXES b bearing c compressive d design m mean p pin s small end t tensile, tangential ROUND OR PIN KEYS The large diameter of the pin key STRENGTH OF KEYS Rectangular fitted key (Fig. 17-1, Table 17-1) Pressure between key and keyseat FIGURE 17-1 d ¼ 3:035 ffiffiffiffi D p to 3:45 ffiffiffiffi D p SI ð17-1aÞ where d and D are in mm d ¼ 0:6 ffiffiffiffi D p to 0:7 ffiffiffiffi D p USCS ð17-1bÞ where d and D are in in d ¼ 0:096 ffiffiffiffi D p to 0:11 ffiffiffiffi D p SI ð17-1cÞ where d and D are in m Particular Formula 17.2 CHAPTER SEVENTEEN Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. 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KEYS, PINS, COTTERS, AND JOINTS TABLE 17-1 Dimensions (in mm) of parallel keys and keyways For shaft Above 6 8 10 12 17 22 30 38 44 50 58 65 75 85 95 110 130 150 170 200 230 260 290 330 380 440 diameters Up to 8 10 12 17 22 30 38 44 50 58 65 75 85 110 110 130 150 170 200 230 260 290 330 380 440 500 Key cross Width b 2 3 4 5 6 8 10 12 14 16 18 20 22 25 28 32 36 40 45 50 56 63 70 80 90 100 section Height h 2 3 4 5 6 7 8 8 9 10 11 12 14 14 16 18 20 22 25 28 32 32 36 40 45 50 Keyway depth In shaft t 1 1.2 1.8 2.5 3.0 3.5 4.0 5 5 5.5 6 7 7.5 8.5 9.0 10 11 12 13 15 17 19 20 22 25 28 31 (nominal) In hub t 2 1 1.4 1.8 2.3 2.8 3.3 3.3 3.8 3.8 4.3 4.4 4.9 5.4 5.9 6.4 7.4 8.4 9.4 10.4 11.4 12.4 13.4 14.4 15.4 17.4 19.5 t 1 þ0.05 þ0.1 þ0.15 Tolerance on À0.00 À0.0 À0.00 keyway depth t 2 þ0.05 þ0.1 þ0.15 À0.00 À0.0 À0.00 Chamfer or r max 0.25 0.35 0.55 0.80 1.30 2.00 2.95 radius of key r min 0.16 0.25 0.40 0.60 1.00 1.60 2.50 Keyway radius r 2 max 0.16 0.25 0.40 0.60 1.00 1.60 2.50 Length of key L min 6 6 8 10 14 18 22 28 36 45 50 56 63 71 80 90 100 110 125 140 160 180 200 220 250 280 L max 20 36 45 50 71 90 110 140 160 180 200 220 250 280 320 360 400 400 400 400 400 400 400 400 400 400 Source: IS 2048, 1962. 17.3 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. KEYS, PINS, COTTERS, AND JOINTS Crushing strength The tangential pressure per unit length of the key at any intermediate distance L from the hub edge (Fig. 17-1, Table 17-2) The torque transmitted by the key (Fig. 17-1) The general expression for torque transmitted accord- ing to practical experience For dimensions of tangential keys given here. Shearing strength The torque transmitted by the key (Fig. 17-1) The shear stress at the dangerous point (Fig. 17-1) TAPER KEY (Fig. 17-2, Table 17-3) The relation between the circumferential force F t and the pressure F between the shaft and the hub The pressure or compressive stress between the shaft and the hub The torque p ¼ p 1 À L tan  ð17-2Þ where tan  ¼ p 1 À p 2 L 2 ¼ p 1 L 0 M t ¼ 1 2 p 1 DL 2 À DL 2 2 tan  ð17-3Þ M t ¼ 1 4  b1 hDL 2 À 1 18  b1 bL 2 2 ð17-4Þ where p 2 ¼ 0, when L 2 ¼ L o ¼ 2:25D; tan  ¼ p 1 L o ¼  b1 h 4:5D Refer to Table 17-2. M t ¼ 1 2  1 bDL 2 À 1 9  1 bL 2 2 ð17-5Þ where tan  ¼ p 1 L o ¼  1 b 2:25D  1 ¼ M t L 2 bð0:5D À0:11L 2 Þ ð17-6Þ F t ¼  1 F ð17-7Þ F ¼ blp ð17-8Þ M t ¼ 1 2  1 blpD ð17-9Þ where  1 ¼ coefficient of friction between the shaft and the hub ¼ 0:25 Particular Formula FIGURE 17-2 17.4 CHAPTER SEVENTEEN Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. KEYS, PINS, COTTERS, AND JOINTS TABLE 17-2 Dimensions (in mm) of tangential keys and keyways Keyway Keyway Shaft Key Shaft Key diameter, D Height, h Width, b Radius, r chamfer, a diameter, D Height, h Width, b Radius, r chamfer, a 100 10 30 2 3 460 46 138 4 5 110 11 30 2 3 480 48 144 5 6 120 12 36 2 3 500 50 150 5 6 130 13 39 2 3 520 52 156 5 6 140 14 42 2 3 540 54 162 5 6 150 15 45 2 3 560 56 168 5 6 160 16 48 2 3 580 58 174 5 6 170 17 51 2 3 600 60 180 6 7 180 18 54 2 3 620 62 186 6 7 190 19 57 2 3 640 64 192 6 7 200 20 60 2 3 660 66 198 6 7 210 21 63 2 3 680 68 204 6 7 220 22 66 2 4 700 70 210 6 7 230 23 69 3 4 720 72 216 6 7 240 24 72 3 4 740 74 222 6 7 250 25 75 3 4 760 76 228 6 7 260 26 78 3 4 780 78 234 6 7 270 27 81 3 4 800 80 240 6 7 280 28 84 3 4 820 82 246 6 7 290 29 87 3 4 840 84 252 6 7 300 30 90 3 4 860 86 258 6 7 320 32 95 3 4 880 88 264 8 9 340 34 102 3 4 900 90 270 8 9 360 36 108 3 4 920 92 276 8 9 380 38 114 4 5 940 94 282 8 9 400 40 129 4 5 960 96 288 8 9 420 42 126 4 5 980 98 294 8 9 440 44 132 4 5 1000 100 300 8 9 Notes: (1) The dimensions of the keys are based on the formula: width 0.3 shaft diameter, and thickness ¼0.1 shaft diameter; (2) if it is not possible to fix the keys at 1208, they may be fixed at 1808; (3) it is recommended that for an intermediate diameter of shaft, the key section shall be the same as that for the next larger size of the shaft in this table. Source: IS 2291, 1963. KEYS, PINS, COTTERS, AND JOINTS 17.5 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. KEYS, PINS, COTTERS, AND JOINTS TABLE 17-3 Dimensions (in mm) of taper keys and keyways Shaft Key Keyway in shaft and hub Chamfer Keyway Up to and Width, b or radius width, b Depth in Tolerance Depth in Tolerance Radius, r 2 , Above including (h9) Height, hr 1 , min (D10) shaft, t 1 on t 1 hub, t 2 on t 2 max 6 8 2 2 0.16 2 1.2 þ0.05 0.5 0.16 8 10 3 3 — 3 1.8 — 0.9 10 12 4 4 4 2.5 1.2 12 17 5 5 5 3.0 1.7 þ0.1 0.25 17 22 6 6 0.25 6 3.5 2.1 22 30 8 7 — 8 4.0 þ0.10 2.5 — 30 38 10 8 10 5.0 2.5 38 44 12 8 12 5.0 2.5 — 44 50 14 9 0.40 14 5.5 2.9 0.40 50 58 16 10 — 16 6.0 — 3.4 58 65 18 11 18 7.0 3.3 — 65 75 20 12 20 7.5 3.8 75 85 22 14 0.60 22 8.5 4.8 85 95 25 14 — 25 9.0 4.3 þ0.2 0.60 95 110 28 18 28 10.0 5.3 — 110 130 32 10 32 11.0 6.2 130 150 36 25 36 12.0 7.2 150 170 40 22 1.00 40 13.0 þ0.15 8.2 1.00 170 200 45 25 — 45 15.0 9.2 — — 200 230 50 28 50 17.0 10.1 230 260 56 32 56 19.0 12.1 260 290 63 32 1.60 63 20.0 11.1 1.60 290 330 70 36 — 70 22.0 13.1 þ0.3 — 330 380 80 40 80 25.0 14.1 380 440 90 45 2.50 90 28.0 16,1 2.50 440 500 100 50 100 31.0 18.1 Source: IS 2292, 1963. 17.6 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. 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KEYS, PINS, COTTERS, AND JOINTS The necessary length of the key The axial force necessary to drive the key home (Fig. 17-2) The axial force is also given by the equation FRICTION OF FEATHER KEYS (Fig. 17-3) The circumferential force (Fig. 17-3) The resistance to be overcome when a hub connected to a shaft by a feather, Fig. 17-3a and subjected to torque M t , is moved along the shaft The equation for resistance R,if and  2 are equal The equation for torque if two feather keys are used, Fig. 17-3b The force F 2 applied at key when two feather keys are used, Fig. 17-3b The resistance to be overcome when the hub con- nected to the shaft by two feather keys Fig. 17-3b and subjected to torque M t is moved along the shaft For Gib-headed and Woodruff keys and keyways l ¼ 2M t  1 bpD ð17-10Þ F a ¼ F  þ F  ¼ 2 2 F þF tan  ð17-11Þ where  2 ¼ 0:10, tan  ¼ 0:0104 if the taper is 1 in 100 F a ¼ 0:21pbl ð17-12Þ F t ¼ M t a ð17-13Þ R ¼ F t þ  2 F 0 ð17-14Þ ¼ð þ  2 ÞF t ð17-15Þ and F 0 ¼ F 00 ¼ F t ¼force assumed to be acting at the shaft axis without changing the equilibrium Fig. 17-3a R ¼ 2F t ð17-16Þ M t ¼ 2F 2 a ð17-17Þ F 2 ¼ M t 2a þ F t 2 ð17-18Þ R 2 ¼ 2F 2 ¼ R 2 ð17-19Þ Refer to Tables 17-4 and 17-5. Particular Formula FIGURE 17-3 Feather key. KEYS, PINS, COTTERS, AND JOINTS 17.7 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. KEYS, PINS, COTTERS, AND JOINTS TABLE 17-4 Gib-head keys and keyways (all dimensions in mm) Shaft diameter, d Key Key in shaft and hub Chamber or Width of Radius at Up to and Width, Height Tolerance Height of radius, keyway Depth in Tolerance Depth in Tolerance bottom of Above including b (h9) (nominal) h on h gib-head, h 1 r 1 (min) (D10) shaft, t 1 on t 1 hub, t 2 on t 2 r 2ðmaxÞ keyway 10 12 4 4 7 0.16 4 2.5 1.2 0.16 12 17 5 5 þ0.1 8 — 5 3 1.7 17 22 6 6 10 0.25 6 3.5 2.1 0.25 22 30 8 7 11 8 4 2.5 30 38 10 8 12 — 10 5 þ0.1 2.5 þ0.1 38 44 12 8 12 12 5 2.5 — 44 50 14 9 — 14 0.40 14 5.5 2.9 50 58 16 10 16 16 6 — 3.4 0.4 58 65 18 11 18 — 18 7 3.5 65 75 20 12 þ0.2 20 20 7.5 3.8 — 75 85 22 14 22 22 8.5 4.8 85 95 25 14 22 0.60 25 9 4.3 0.60 95 110 28 16 25 — 28 10 5.3 þ0.15 110 130 32 18 28 32 11 6.2 — 130 150 36 20 32 36 12 7.2 150 170 40 22 — 36 1.00 40 13 þ0.15 8.2 1.00 170 200 45 25 40 — 45 15 9.2 200 230 50 28 45 50 17 10.1 — 230 260 56 32 50 56 19 12.1 260 290 63 32 þ0.3 56 1.60 63 20 11.1 1.60 290 330 70 36 63 — 70 22 13.1 þ0.3 330 380 80 40 70 80 25 14.1 — 380 440 90 45 75 2.50 90 28 16.1 440 500 100 50 80 100 31 18.1 2.50 Source: IS 2293, 1963. 17.8 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. 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KEYS, PINS, COTTERS, AND JOINTS [...]... d 7. 629 9.324 10. 379 12 .73 6 14.460 17. 478 20 .73 8 22.484 24 .73 8 27. 711 29. 571 30.566 32 .73 9 34.589 37. 604 39 .72 0 40 .74 0 42.621 44 .74 0 47. 724 50.624 52 .74 0 54.650 57. 648 60 .74 0 62.663 64 .74 0 67. 729 70 . 672 72 .74 0 74 . 676 Measurement between pins, Mi Internal spline 2.42 2.19 1.61 1.66 1.64 1.96 1.68 2.41 1.69 1.88 1.86 2.15 1 .70 2.08 1.84 1.84 1 .70 2.00 1 .71 1.82 1.95 1 .71 1.93 1.80 1 .71 1.90 1 .71 1 .79 ... 47. 6 50.6 53.6 55.6 57. 6 60.6 63.6 65.6 67. 6 70 .6 73 .6 75 .6 77 .6 d4 Note: Values within parentheses are nonpreferred 6 7 7 8 9 11 12 14 14 16 17 18 18 20 21 22 22 24 24 26 28 28 30 31 32 34 34 36 38 38 40 Nominal size d1  d 2 14.68 16.68 17. 68 19.68 21.68 24.68 27. 68 29.69 31.69 34.69 36.69 37. 69 39.69 41.69 44.69 46.69 47. 69 49.69 51.69 54 .70 57. 70 59 .70 61 .70 64 .70 67. 70 69 .70 71 .70 74 .70 77 .70 79 .70 ... 27. 308 28.316 30.552 32.340 35.552 37. 365 38.3 87 40.552 42.384 45.552 48.424 50.552 52.413 55.552 58.448 60.552 62.434 65.552 62.464 70 .552 72 .449 75 .552 78 . 476 80.552 82.461 85.552 88.485 90.552 95.552 Measurement between pins, Mi Internal spline 1 .71 1.85 1 .72 2.30 1 .72 1.81 1 .72 1.80 2.26 1 .72 1 .79 1 .73 1 .78 2. 07 1 .73 1 .78 1 .73 1.99 1 .73 1 .77 1 .73 1.94 1 .73 1 .77 1 .73 1.90 1 .73 1 .76 1 .73 1.88 1 .73 ... 67. 5 70 .0 75 .0 75 .0 77 .5 80.0 85.0 85.0 87. 5 90.0 95.0 95.0 100.0 do d3 12.990 19.5 15.155 21.5 17. 321 24.5 21.651 27. 5 21.651 29.5 23.816 31.5 25.981 34.5 28.146 36.5 30.311 37. 5 30.311 39.5 32. 476 41.5 34.641 44.5 36.806 46.5 38. 971 47. 5 38. 971 49.5 41.136 51.5 43.301 54.5 47. 631 57. 5 47. 631 59.5 49 .79 6 61.5 51.962 64.5 56.292 67. 5 56.292 69.5 58.4 57 71.5 60.622 74 .5 64.952 77 .5 64.952 79 .5 67. 1 17. .. 1.15 1.52 1.46 1. 47 1.43 1.54 1.44 1.50 1.56 1. 47 1. 57 1.53 1.49 1.59 1.50 1.55 1.60 1.52 1.61 2 2 2 2 — — 3 3 3 3 4 3 4 4 4 4 5 4 5 5 5 6 5 6 6 6 7 7 7 7 7 Deviation factor, fa z0 External spline 9.121 9.214 9 .71 4 9.8 07 — — 15.621 14.8 07 15.8 07 15.493 21.028 15. 179 21.621 20.8 07 21.400 21.493 27. 435 21. 179 27. 621 27. 3 07 26.993 33.435 27. 179 33.214 33.8 07 32.993 39.435 39.121 38.8 07 39.8 07 38.993 Tooth... 24.299 24.249 27. 713 29.445 31. 177 31. 177 34.641 36. 373 38.105 38.105 41.569 41.569 45.033 48.4 97 48.4 97 51.962 53.694 55.426 58.890 58.890 62.354 65.818 65.818 69.283 db 14.6 16.6 17. 6 19.6 21.6 24.6 27. 6 29.6 31.6 34.6 36.6 37. 6 39.6 41.6 44.6 46.6 47. 6 49.6 51.6 54.6 57. 6 59.6 61.6 64.6 67. 6 69.6 71 .6 74 .6 77 .6 79 .6 81.6 d3 10.6 12.6 13.6 15.6 17. 6 20.6 23.6 25.6 27. 6 30.6 32.6 33.6 35.6 37. 6 40.6 42.6... 22  17 25  20 28  23 30  25 32  27 35  30 37  32 38  33 40  35 42  37 45  40 47  42 48  43 50  45 ð52  47 55  50 ð58  53Þ 60  55 ð62  57 65  60 ð68  63Þ 70  65 72  67 75  70 78  73 Þ 80  75 ð82  77 Þ 85  80 ð88  83Þ 90  85 ð92  87 95  90 ð98  93Þ 100  95 105  100 15.0 17. 5 20.0 25.0 25.0 27. 5 30.0 32.5 35.0 35.0 37. 5 40.0 42.5 45.0 43.0 47. 5 50.0 55.0 55.0 57. 5... given at the website 1.4 2.6 2.6 3 .7 3 .7 3 .7 5 6.5 5 6.5 7. 5 6.5 7. 5 9 7. 5 9 (10) 11 9 11 13 11 13 16 3 4 6 6 8 8 8 — 10 10 — 12 12 — 17 17 17 — 22 22 — 30 30 — 4 6 8 8 10 10 10 — 12 12 — 17 17 — 22 22 22 — 30 30 — 38 38 — 6 8 10 10 12 12 12 16 17 17 17 22 22 22 30 30 30 30 38 38 38 38 38 38 8 10 12 12 17 17 17 17 22 22 22 30 30 30 38 38 38 38 — — — — — — 4.0 7. 0 7. 0 10.0 10.0 10.0 13.0 16.0 13.0 16.0... 84.5 73 .612 87. 5 73 .612 89.5 75 .77 7 91.5 77 .942 94.5 82. 272 97. 5 82. 272 99.5 86.603 104.5 db Note: Values within brackets are nonpreferred 6 7 8 10 10 11 12 13 14 14 15 16 17 18 18 19 20 22 22 23 24 26 26 27 28 30 30 31 32 34 34 35 36 38 38 40 Nominal size d1  d 2 14.5 16.5 19.5 22.5 24.5 26.5 29.5 31.5 32.5 34.5 36.5 39.5 41.5 42.5 44.5 46.5 49.5 52.5 54.5 56.5 59.5 62.5 64.5 66.5 69.5 72 .5 74 .5 77 .5... 3.82 6 .76 6 .76 9.66 9.66 9.66 12.65 15 .72 12.65 15 .72 18. 57 15 .72 18. 57 21.63 18. 57 21.63 24.49 27. 35 21.63 27. 35 31.43 27. 35 31.43 43.08 1.0 2.0 1.8 2.9 2.9 2.5 3.8 5.3 3.5 5.0 6.0 4.5 5.5 7. 0 5.1 6.6 7. 6 8.6 6.2 8.2 10.2 7. 8 9.8 12.8 1.0 2.0 1.8 2.9 2.9 2.8 4.1 5.6 4.1 5.6 6.6 5.4 6.4 7. 9 6.0 7. 5 8.5 9.5 7. 5 9.5 11.5 9.1 11.1 14.1 þ0.2 þ0.1 þ0.2 þ0.1 0.6 0.8 1.0 1.0 1.0 1.4 1.4 1.4 1 .7 1 .7 1.8 2.2 . 74 .70 70 .90 þ0.4 3.603 3.5 67. 729 1 .79 4.0 79 .166 1.55 7 39.121 78  74 Þ 38 76 65.818 77 .6 73 .6 77 .70 73 .90 À0.1 3.026 3.5 70 . 672 1.88 4.0 82.263 1.60 7 38.8 07 80  76 38 76 65.818 79 .6 75 .6 79 .70 . 4 72 0 72 216 6 7 240 24 72 3 4 74 0 74 222 6 7 250 25 75 3 4 76 0 76 228 6 7 260 26 78 3 4 78 0 78 234 6 7 270 27 81 3 4 800 80 240 6 7 280 28 84 3 4 820 82 246 6 7 290 29 87 3 4 840 84 252 6 7 300. 69 .70 65.90 À0.1 3.026 3.5 62.663 1.90 4.0 74 .253 1.59 6 32.993 72  68Þ 34 68 58.890 71 .6 67. 6 71 .70 67. 90 þ0.9 4.181 3.5 64 .74 0 1 .71 4.0 76 .036 1.50 7 39.435 75  71 36 72 62.354 74 .6 70 .6 74 .70