Design of Shaft A shaft is a rotating member usually of circular crosssection (soli or hollow), which is use to transmit power an rotational motion. Axles are non rotating member. Elements such as gears, pulleys (sheaves), flywheels, clutches, an sprockets are mounte on the shaft an are use to transmit power from the riving evice (motor or engine) through a machine. The rotational force (torque) is transmitte to these elements on the shaft by press fit, keys, owel, pins an splines. The shaft rotates on rolling contact or bush bearings. Various types of retaining rings, thrust bearings, grooves an steps in the shaft are use to take up axial loas an locate the rotating elements.
Automobile manual transmission
Worm gear box Reuces spee, increases torque output. Power F.v (force x velocity) For rotational power Power P Torque x angular velocity P T.ω (ω in ra/sec) ω π n/60 (n is rpm) T 63,05HP/n (in-lb) T 9,550,000kW/n (N-mm)
Other shaft examples Bevel gear box: changes rotational axis Lawn mower rive: Belt pulley
Bearing mounting consierations an stress concentration
Conventional retaining (or snap) rings fit in grooves an take axial loa, but groves cause stress concentration in shaft Retaining rings are stanarize items, available in various stanar sizes with various axial loa capacities.
Push type retaining rings no grooves require, less stress concentration, but less axial support
Various types of keys for transmitting torque
Other common types of keys
Various types of collar pins
Splines in hubs an shafts allow axial motion an transmits torque All keys, pins an splines give rise to stress concentration in the hub an shaft
Loas on shaft: Shaft loae in only torsion: torsion may have a steay (T av ) an a cyclic (T r ) component.
Loas on shaft ue to gears From power an rpm fin the torque (T), which gives rise to shear stress. From Torque (T) an iameter (), fin F t T/. From F t an pressure angles of gears you can fin F r an F a. F r an F t are orthogonal to each other an are both transverse forces to the shaft axis, which will give rise to normal bening stress in the shaft. When shaft rotates, bening stress changes from tensile to compressive an then compressive to tensile, ie, completely reversing state of stress. F a will give rise to normal axial stress in the shaft.
Loas on shaft ue to pulleys an fly-wheels Pulley torque (T) Difference in belt tensions in the tight (t 1 ) an slack (t ) sies of a pulley times the raius (r), ie T (t 1 -t )xr Left pulley torque T 1 (700-700)x3801,710,000 N-mm Right pulley has exactly equal an opposite torque: T (6750-50)x3801,710,000 N-mm F V Bening forces: Left pulley: F V1 900N; F H1 700+700 9900N Right pulley: F V 900+6750+509900N; F H 0
Bening moment an torque iagrams for the pulley flywheel system 9900N T 1 T F H From Horizontal forces (F H ) an vertical forces (F v ), Bening moments M H & M V are rawn seperately. Then the resultant moments at various points on the shaft can be foun from M M + R H M V 1,710,000 N-mm Torque iag.,7,500 M H 911,50 900N F V M V,7,500 9900N The section containing the left pulley has obviously the highest combination of Torque (1,710,000 N-mm) an Bening moment (,06,685 N-mm) M M + M R H V,7,500,06,685 Resultant bening moment
Design of shaft Axial imensions are often fixe from the layout of the mechanism. Design recommenation is to keep the axial lengths as short as possible to limit bening stress. Simply supporte shaft is better than cantilever or overhang shaft. Shaft esign is to etermine the iameter of the shaft such that it withstan the applie loas, after stress concentrations, with a known factor of safety.
Design of shaft (continue)
Shear (τ) an bening (σ) stresses on the outer surface of a shaft, for a torque (T) an bening moment (M) 3 16 3) / ( T T r J T π π τ For soli circular section: For hollow circular section: 3 3 6) / ( M M r I M π π σ o i o i o i where T T T r J T λ λ π π π τ, ) (1 16 ) ( 16 3) ) / ( ( 3 0 0 0 o i o i o i where M M M r I M λ λ π π π σ, ) (1 3 ) ( 3 6) ) / ( ( 3 0 0 0
Principal Normal Stresses an Max Distortion Energy Failure criterion for non-rotating shafts 1 τ σ σ τ σ σ + + + S an S The stress at a point on the shaft is normal stress (σ) in X irection an shear stress (τ) in XY plane. From Mohr Circle: Max Distortion Energy theory: 1 1 + fs yp N S S S S S Putting values of S 1 & S an simplifying: 3 + fs yp N S τ σ This is the esign equation for non rotating shaft
Design of rotating shafts an fatigue consieration The most frequently encountere stress situation for a rotating shaft is to have completely reverse bening an steay torsional stress. In other situations, a shaft may have a reverse torsional stress along with reverse bening stress. The most generalize situation the rotating shaft may have both steay an cyclic components of bening stress (σ av,σ r ) an torsional stress (τ av,τ r ). From Soerberg s fatigue criterion, the equivalent static bening an torsional stresses are: Using these equivalent static stresses in our static esign equation, the equation for rotating shaft is: