CHAPTER 17 FLEXIBLE MECHANICAL ELEMENTS LECTURE NOTES DR. HAFTIRMAN

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1 CHAPTER 17 LEXIBLE MECHANICAL ELEMENTS LECTURE NOTES DR. HATIRMAN

2 lexible Mechanical Elements Belts Roller chains Wire rope lexible shafts

3 lexible Mechanical Elements Belts, ropes, chains, and other similar elastic, or flexible machine elements are used in conveying systems and in the transmission of power over comparatively long distance.

4 Belt Type Type of belts igure Joint Size Range Center Distance lat Yes t mm No upper limit Round Yes d 3 0mm No upper limit V None Limited b 8 19mm Timing None Limited p mm

5 Crowned pulleys are used for flat belts. Grooved pulleys or sheaves are used for round or V belts. Toothed wheels or sprockets are used for timing belts.

6 Crowned pulley

7 Type of pulley Solid round stock pulleys Cap tube pulleys

8 Narrow body pulleys

9 Timing Belt

10 Timing Belt

11 lat-belts geometry Open Belt Closed Belt

12 Nonreversing and reversing belt drives a. Nonreversing belt b. Reversing crossed belt c. Reversing open-belt drive

13 Reversing crossed belt

14 Quarter-twist belt drive

15 Variable-speed belt drives

16 lat and round-belt drives The efficiency of a V-belt drive ranges from about 70 to 96 percent. lat-belt drives produce very little noise and absorb more torsional vibration from the system than either V-belt or gear drives. When an open-belt drive is used, the contact angles are found to be θ θ d D π sin π + sin 1 1 D d C D d C Where D diameter of large pulley d diameter of small pulley C center distance θ angle of contact

17 The Length of the belt L [4C The angle of wrap is the same for both pulleys and is θ π + The belt length for crossed belts is ( D d) D + d sin 1 C ] 1/ + 1/ ( Dθ + 1/ θ L [4C ( D + d) ] + ( D + D d) dθ d )

18 Where i initial tension c hoop tension due to centrifugal force tension due to the transmitted torque T D diameter of the pulley ) exp( 1 ) exp( ) ( ) exp( φ φ ω φ ω ω f f mr f mr mr c c c c D T D T N v V g c bt s r n mm d m dn V c i c i c i c i / ' / ' 9.81 ) (, 10 /, sec, / Δ Δ + ω ω γ ω π Δ '

19 orces and torques on a pulley 1 ) exp( 1 ) exp( ) exp( 1 ) exp( 1 ) exp( / φ φ φ φ φ f f f f f D T D T D T i c i c i c i

20 Plot of initial tension i against belt tension 1 and The transmitted power is H ( ) V kw

21 ( 1 ) b a Velocity correction factor C v for leather belts ( i ) a allowable largest tension, N a C b belt width, mm a manufacturer allowed tension N/mm C p pulley correction factor C v velocity correction factor p C v

22 The flat-belt drive

23 Example 17-1 A polyamide A-3 flat belt 150mm wide is used to transmit 11. kw under light shock condition where K s 1.5 and a factor of safety equal to or greater than 1.1 is appropriate. The pulley rotational axes are parallel and in the horizontal plane. The shafts are 440 mm apart. The 150 mm driving pulley rotates at 9.17 r/s in such a way that the loose side is on top. The driven pulley is 450 mm in diameter. See ig The factor of safety is for unquantifiable exigencies. a) Estimate the centrifugal tension c and the torque T b) Estimate the allowable 1, and allowable power H a c) Estimate the factor of safety. Is it satisfactory.

24 Solution Nm n n K H T N g V c m N bt s m V f rad C d D d s nom d d (11.)(1.5)(1.1) (13.74) / (150)7 10 / (150)(9.7) exp[0.8(3.0186)] ) exp( (440) sin sin ω γ ω π φ π θ π θ

25 ( 1 ) a - to transmit the torque T is ( ( i 1 1 ) ) a a T d b C C ( 1 ) a a p [( v 1 (76.3) 1017N (17.8)0.70(1) ) a ] N N

26 The combination ( 1 ) a, and i will transmit the design power of 11.(1.5)(1.1)15.4kW and protect the belt. We check the friction development by solving for f : f ' f ' < 1 ( 1 ) a ln φ f,0.31 < c 0.80 c ln fos H H nom K s (1.5) 1.1 The belts is satisfactory and the maximum allowable belt tension exist. If the initial tension is maintained, the capacity is the design power of 15.4 kw

27 a) Weighted idler pulley Belt-tensioning schemes b) Pivoted motor mount c) Catenary-induced tension

28 lat-belt tensions

29 Metal-belt tensions and torques

30 V-belt tensions

31 Chain

32 Chain

33 Chain

34 Timing-belt drive showing portions of the pulley and belt

35 Engagement of a chain and sprocket

36 Chordal speed variation

37 Wire Rope

38 Wire Rope

39 Wire Rope

40 Wire Rope

41

42 Section of wire rope

43 Wire Rope

44

45 Percent strength loss due to different D/d ratio

46 The fatigue life of wire rope and the sheave pressure

47 Service life curve based on bending and tensile stresses.

48 lexible Shaft

49 lexible Shaft

50 lexible Shaft

51 lexible Shaft

52 lexible Shaft

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