St_Mod12_F10

St_Mod12_F10 - Module 12: Fric=on Fundamentals November 1, 2010 Module Content 1. Fric=on is the force of interac=on between two

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Unformatted text preview: Module 12: Fric=on Fundamentals November 1, 2010 Module Content: 1. Fric=on is the force of interac=on between two bodies in rela=ve (sliding) mo=on. 2. The impending mo=on condi=on and equa=ons are cri=cal to iden=fy for solu=on of typical fric=on problems. Possible impending mo=on condi=ons include: (i) slip at 1 point, (ii) slip at many points, and (iii) =p. 3. Fric=on is o[en coupled to the analysis of mechanisms (like machines and frames). 4. Wedges and flat belts experience fric=on in the same way as flat sliding contacts; the analysis tools are very similar (even though the details are slightly different). Module Reading, Problems, and Demo: Reading: Chapter 8 Problems: Fundamental Problem 8.5, Prob. 8.6, 8.56, 8.62, 8.75, 8.97 Demo: none Homework PlaRorm: hSp://www.masteringengineering.com Course Blog: hSp://pages.shan=.virginia.edu/sta=cs2010 MAE 2300 Sta=cs © E. J. Berger, 2010 12 ­ 1 Introducing Chapter 8 ­ ­Fric=on • “fric=on” is a general term we use to describe the sta=onary/sliding interac=on of two surfaces • a “smooth” surface is fric=onless • fric=on arises on “rough” surfaces MAE 2300 Sta=cs © E. J. Berger, 2010 12 ­ 2 Introducing Chapter 8 ­ ­Fric=on • “fric=on” is a general term we use to describe the sta=onary/sliding interac=on of two surfaces • a “smooth” surface is fric=onless • fric=on arises on “rough” surfaces MAE 2300 Sta=cs © E. J. Berger, 2010 12 ­ 2 Introducing Chapter 8 ­ ­Fric=on • “fric=on” is a general term we use to describe the sta=onary/sliding interac=on of two surfaces • a “smooth” surface is fric=onless • fric=on arises on “rough” surfaces MAE 2300 Sta=cs © E. J. Berger, 2010 12 ­ 2 Introducing Chapter 8 ­ ­Fric=on • “fric=on” is a general term we use to describe the sta=onary/sliding interac=on of two surfaces • a “smooth” surface is fric=onless • fric=on arises on “rough” surfaces MAE 2300 Sta=cs © E. J. Berger, 2010 12 ­ 2 Concept: Sta=c vs. Sliding Fric=on • slowly increase the applied force P from 0... MAE 2300 Sta=cs © E. J. Berger, 2010 12 ­ 3 Concept: Sta=c vs. Sliding Fric=on • slowly increase the applied force P from 0... MAE 2300 Sta=cs © E. J. Berger, 2010 12 ­ 3 Concept: Sta=c vs. Sliding Fric=on • slowly increase the applied force P from 0... MAE 2300 Sta=cs © E. J. Berger, 2010 12 ­ 3 Concept: Sta=c vs. Sliding Fric=on • slowly increase the applied force P from 0... “impending motion” MAE 2300 Sta=cs © E. J. Berger, 2010 12 ­ 3 Concept: Sta=c vs. Sliding Fric=on • slowly increase the applied force P from 0... “impending motion” MAE 2300 Sta=cs © E. J. Berger, 2010 12 ­ 3 Concept: Sta=c vs. Sliding Fric=on • slowly increase the applied force P from 0... MAE 2300 Sta=cs © E. J. Berger, 2010 12 ­ 3 Concept: Sta=c vs. Sliding Fric=on • slowly increase the applied force P from 0... MAE 2300 Sta=cs © E. J. Berger, 2010 12 ­ 3 Concept: Sta=c vs. Sliding Fric=on • slowly increase the applied force P from 0... Fs and Fk typically tell the story of fric3on... MAE 2300 Sta=cs © E. J. Berger, 2010 12 ­ 3 Theory: Fric=on Angle and Loca=on • the loca=on and angle of the resultant contact interface force (normal force + fric=on force) gives us some useful informa=on about the nature of the contact interac=ons • angle of sta=c fric=on (shown) • angle of kine=c fric=on (Fig. 8 ­2a) • the loca=on of the resultant normal force is important for maintaining moment equilibrium MAE 2300 Sta=cs © E. J. Berger, 2010 12 ­ 4 Theory: Fric=on Angle and Loca=on • the loca=on and angle of the resultant contact interface force (normal force + fric=on force) gives us some useful informa=on about the nature of the contact interac=ons • angle of sta=c fric=on (shown) • angle of kine=c fric=on (Fig. 8 ­2a) • the loca=on of the resultant normal force is important for maintaining moment equilibrium MAE 2300 Sta=cs © E. J. Berger, 2010 12 ­ 4 Theory: Impending Mo=on, Three Types slip at 1 point 3p slip at 2 or more points MAE 2300 Sta=cs © E. J. Berger, 2010 12 ­ 5 Theory: Impending Mo=on, Three Types slip at 1 point our goal is to write the “impending mo3on equa3on” consistent with these different cases 3p slip at 2 or more points MAE 2300 Sta=cs © E. J. Berger, 2010 12 ­ 5 Game: What’s the Impending Mo=on Equa=on? ➀ ➁ MAE 2300 Sta=cs © E. J. Berger, 2010 12 ­ 6 Example: Tip or Slip? • The crate has a mass of 350 kg and is subjected to a towing force P ac=ng at a 20o angle with the horizontal. If the coefficient of sta=c fric=on is μs = 0.5, determine the magnitude of P to just start the crate moving down the plane. ans.: P = 981 N MAE 2300 Sta=cs © E. J. Berger, 2010 12 ­ 7 Example: Tipping and Slipping • The crate has a weight of 200 lb., and a center of gravity at G. Determine the height h of the tow rope so that the crate slips and =ps at the same =me. What horizontal force P is required to do this? Use μs = 0.4. ans.: P = 80 lb., h = 5 I. MAE 2300 Sta=cs © E. J. Berger, 2010 12 ­ 8 Theory: Wedges MAE 2300 Sta=cs © E. J. Berger, 2010 12 ­ 9 Theory: Wedges MAE 2300 Sta=cs © E. J. Berger, 2010 12 ­ 9 Theory: Wedges • • the FBDs are generally straight ­ forward: idealize all contacts as point forces, then apply the relevant impending mo=on equa=ons • © E. J. Berger, 2010 wedge problems are inherently problems in which two or more interfaces slip simultaneously • MAE 2300 Sta=cs wedges are used to do useful work, o[en by securing or li[ing loads if the system is sta=onary under the load P = 0, then it is called “self ­locking” 12 ­ 9 Theory: Flat Belts with Fric=on • consider a flat belt (not a V ­belt or other geometry) wrapped around a sta=onary surface (NOT a pulley) MAE 2300 Sta=cs © E. J. Berger, 2010 12 ­ 10 Theory: Flat Belts with Fric=on • consider a flat belt (not a V ­belt or other geometry) wrapped around a sta=onary surface (NOT a pulley) MAE 2300 Sta=cs © E. J. Berger, 2010 12 ­ 10 Theory: Flat Belts with Fric=on • consider a flat belt (not a V ­belt or other geometry) wrapped around a sta=onary surface (NOT a pulley) MAE 2300 Sta=cs © E. J. Berger, 2010 12 ­ 10 Theory: Flat Belt Fric=on Deriva=on MAE 2300 Sta=cs © E. J. Berger, 2010 12 ­ 11 Theory: Flat Belt Fric=on Deriva=on MAE 2300 Sta=cs © E. J. Berger, 2010 12 ­ 11 Theory: Flat Belt Fric=on Deriva=on MAE 2300 Sta=cs © E. J. Berger, 2010 12 ­ 11 Theory: Flat Belt Fric=on Deriva=on MAE 2300 Sta=cs © E. J. Berger, 2010 12 ­ 11 ...
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This note was uploaded on 02/09/2012 for the course MAE 2300 taught by Professor Staff during the Fall '10 term at UVA.

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