CHAPTER 17 LEXIBLE MECHANICAL ELEMENTS LECTURE NOTES DR. HATIRMAN
lexible Mechanical Elements Belts Roller chains Wire rope lexible shafts
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.
Belt Type Type of belts igure Joint Size Range Center Distance lat Yes t 0.75 5mm No upper limit Round Yes d 3 0mm No upper limit V None Limited b 8 19mm Timing None Limited p mm
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.
Crowned pulley
Type of pulley Solid round stock pulleys Cap tube pulleys
Narrow body pulleys
Timing Belt
Timing Belt
lat-belts geometry Open Belt Closed Belt
Nonreversing and reversing belt drives a. Nonreversing belt b. Reversing crossed belt c. Reversing open-belt drive
Reversing crossed belt
Quarter-twist belt drive
Variable-speed belt drives
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
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 )
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( 1 1 1 1 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, / 1000 1 6 + Δ + + + + Δ + ω ω γ ω π Δ '
orces and torques on a pulley 1 ) exp( 1 ) exp( ) exp( 1 ) exp( 1 ) exp( / 1 1 1 + + + + + + φ φ φ φ φ f f f f f D T D T D T i c i c i c i
Plot of initial tension i against belt tension 1 and The transmitted power is H ( ) V 1 1000 kw
( 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
The flat-belt drive
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 17-10. 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.
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 76.3 9.17 159(11.)(1.5)(1.1) 159 191 9.81 9.9(13.74) / 9.9 10 9450(150)7 10 / 13.74 1000 (150)(9.7) 11.19 exp[0.8(3.0186)] ) exp( 3.0186 (440) 150 450 sin sin 6 6 1 1 ω γ ω π φ π θ π θ
( 1 ) a - to transmit the torque T is ( ( i 1 1 ) ) a a T d b C C ( 1 ) a a p [( 1869 + 85 v 1 (76.3) 1017N 0.150 150(17.8)0.70(1) ) a ] 1869 1017 191 1169.5N 1869 85N
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 1 3.0186 1869 191 ln 85 191 0.31 fos H H nom K s 15.4 11.(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
a) Weighted idler pulley Belt-tensioning schemes b) Pivoted motor mount c) Catenary-induced tension
lat-belt tensions
Metal-belt tensions and torques
V-belt tensions
Chain
Chain
Chain
Timing-belt drive showing portions of the pulley and belt
Engagement of a chain and sprocket
Chordal speed variation
Wire Rope
Wire Rope
Wire Rope
Wire Rope
Section of wire rope
Wire Rope
Percent strength loss due to different D/d ratio
The fatigue life of wire rope and the sheave pressure
Service life curve based on bending and tensile stresses.
lexible Shaft
lexible Shaft
lexible Shaft
lexible Shaft
lexible Shaft