Engineering Mechanics of Static Assistant Professor Dr Ahmed

Engineering Mechanics of Static Assistant Professor Dr Ahmed Majhool Chapter six: Friction Section C Applications of Friction in Machines

• Normal reaction on bearing Engineering Mechanics of Static Assistant Professor Dr Ahmed Majhool – Point of application – Friction tends to oppose the motion – Friction angle Φ for the resultant force

• Lateral/Vertical load on shaft is L Engineering Mechanics of Static Assistant Professor Dr Ahmed Majhool • Partially lubricated bearing – Direct contact along a line • Fully lubricated bearing – Clearance, speed, lubricant viscosity

-R will be tangent to a small circle of radius rf called the friction circle ∑M A =0 � M = Lr f = Lr sin φ For a small coefficient of friction, φ is small sinφ ≈ tanφ M = μ Lr Engineering Mechanics of Static Assistant Professor Dr Ahmed Majhool **(since μ= tanφ) Use equilibrium equations to solve a problem ** Moment that must be applied to the shaft to overcome friction for a dry or partially lubricated journal bearing

Engineering Mechanics of Static Assistant Professor Dr Ahmed Majhool Disc Friction Thrust Bearings Sanding Machine

Consider two flat circular discs whose shafts are mounted in bearings: they can be brought under contact under P Max torque that the clutch can transmit = M required to slip one disc against the other Engineering Mechanics of Static Assistant Professor Dr Ahmed Majhool p is the normal pressure at any location between the plates � Frictional force acting on an elemental area = μpd. A; d. A = r dr dӨ

Engineering Mechanics of Static Assistant Professor Dr Ahmed Majhool Moment of this elemental frictional force about the shaft axis = μprd. A Total M = ∫μprd. A over the area of disc

Engineering Mechanics of Static Assistant Professor Dr Ahmed Majhool *Assuming that μ and p are uniform over the entire surface P = πR 2 p (axial force) * Substituting the constant p in M = ∫μprd. A Magnitude of moment required for impending rotation of shaft≈ moment due to frictional force μP acting a distance 2⁄3 R from shaft center Frictional moment for worn-in plates is only about 3⁄4 of that for the new surfaces � M for worn-in plates = 1⁄2(μPR)

If the friction discs are rings (Ex: Collar bearings) with outside and inside radius as Ro and Ri , respectively (limits of integration Ro and Ri ) P = π(Ro 2 -Ri 2 )p Engineering Mechanics of Static Assistant Professor Dr Ahmed Majhool The frictional torque: Frictional moment for worn-in plates � M= 1⁄2 μP(Ro+Ri )