Variational and energy principles

Bauchau, Olivier A.

doi:10.1007/978-90-481-2516-6_12

Cited by 1 publication

(2 citation statements)

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“…The principle of minimum complementary energy [19,20] is utilized to develop the static model so that it can deal with an arbitrarily configured fixture-workpiece system without suffering from static indeterminacy of problems. The static model is then essentially a constrained nonlinear optimization model.…”

Section: Static Modelmentioning

confidence: 99%

“…The constraint (17) represents the static equilibrium condition; (18) results from the fact that constant clamping forces are used; (19) represents the Coulomb friction law; (20) comes from the unilateral nature of a fixture-workpiece contact; (21) represents the non-yielding constraint on the contact stress where S y is the yield strength of the workpiece material while a i is the radius of the ith contact region and is a function of the normal force P i . The forces are then substituted into the contact force-displacement relationship to calculate the contact elastic deformation due to clamping.…”

Section: Static Modelmentioning

confidence: 99%

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Mathematical methodology for optimization of the clamping forces accounting for workpiece vibratory behaviour

Chaari

Abennadher

Louati

et al. 2014

Int. J. Simul. Multidisci. Des. Optim.

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-This paper addresses the problem of determining the minimum clamping forces that ensure the dynamic fixturing stability. The clamping force optimization problem is formulated as a bi-level nonlinear programming problem and solved using a computational intelligence technique called particle swarm optimization (PSO). Indeed, we present an innovative simulation methodology that is able to study the effects of fixture-workpiece system dynamics and the continuously change due to material removal on fixturing stability and the minimum required clamping forces during machining. The dynamic behaviour of the fixtured workpiece subjected to time-and space-varying machining loads is simulated using a forced vibration model based on the regenerative vibrations of the cutter and workpiece excited by the dynamic cutting forces. Indeed, Material removal significantly affects the fixture-workpiece system dynamics and subsequently the minimum clamping forces required for achieving fixturing dynamic stability.

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Section: Static Modelmentioning

confidence: 99%