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# CES Mechanics I Lecture 12

RWTH Aachen University, Bachelor program in Computational Engineering Science

Topics:

• Dry friction. 9.2

The Coulomb model of dry friction (as opposed to fluid friction) considers three cases:

• Static friction, or Haftung, with friction force F taking a value necessary for an equilibrium, and being between zero and the maximum F_\mathrm{max} = \mu_s N, where \mu_s is the static friction coefficient, or Haftungskoeffizient and N the normal force.
• Impending sliding, with friction force F reaching the maximum F_\mathrm{max}.
• Kinetic friction, or Reibung, with friction force F constant and equal \mu_k N, where \mu_k is the kinetic friction coefficient, or Reibungskoeffizient.
• Impending sliding is considered very often, leading to a common but incorrect assumption that F = \mu_s N always.
• Equilibrium analysis in the presence of friction.
• Impending tipping.
• Equilibrium analysis (tipping and friction).

Equilibrium analysis when sliding and tipping is possible:

1. no information about motion is given

(1a) assume equilibrium, solve for unknowns including friction reactions and normal reaction offsets

(1b) check friction reactions against maximum static friction; check normal reaction offsets against minimum or maximum.

2. given information about impending sliding (or tipping) and the surface where it occurs

(2a) set friction reaction to maximum static friction (or set normal reaction offset to minimum or maximum)

(2b) solve equilibrium equations for unknowns

3. given information about impending motion and the surface where it occurs

(3a) assume impending sliding, proceed to 2, check normal reaction offset against minimum or maximum

(3b) if not OK, assume impending sliding, proceed to 2

4. given information about impending motion but not the surface where it occurs

(4a) assume impending motion at one of the surfaces

(4b) proceed to 3, then proceed to 1b for all remaining surfaces

(4c) if not OK, assume impending motion for another surface, go back to 4b

Corresponding Gross et al. Statik chapters are shown in red.

Key techniques:

• Deciding whether the object is stationary under the applied loads.
• Finding maximum or minimum FBD parameters that will keep the object or objects from sliding.
• Sliding and tipping analysis.
• Using moment balance to find position of normal reaction.
• Finding maximum or minimum FBD parameters that will keep the object or objects from sliding and tipping.

Three easy questions in a final self-scoring test concerning statics from Loughborough University. Compare answers to 1:a, 2:b, 3:a. Where on earth is Loughborough? The red dot on the right...

ConcepTests (accessible from RWTH domains only):

Thinking of abandoning engineering for a lucrative computer game business? Who isn't. But they sometimes have to consider friction as well.

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