Quasi-2D Unsteady Flow Procedure for Real Fluids (PREPRINT)

Campbell, Bryan T.; Davis, Roger L.

doi:10.21236/ada450906

Cited by 1 publication

(1 citation statement)

References 5 publications

(5 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For vibration directions that correspond to a drill extending as it unwinds, (an axial-torsional mode) the chatter response frequency is found to be lower than the natural frequency of the oscillation, a result confirmed in experiment [3]. We have not considered nonlinear stability results in this paper, it is a calculation that would require projection on a center manifold for the infinite-dimensional delay differential equation [6], we take up this question in another paper [7]. Suffice to say that we expect it to be different for the two models, as the nonlinear results were different for the non-regenerative case, due to the difference in the coefficient on theη 2 terms.…”

Section: Discussionmentioning

confidence: 82%

Investigations of Nonlinear Forces in Metal Cutting

Stone¹,

Askari²,

Tat³

2006

Computing Letters

View full text Add to dashboard Cite

During chatter in metal cutting the tool vibration would cause a variation in "effective" rake angle of the cutter, generating a force variation that depends on penetration rate: a kind of process damping. This effect is examined for forces computed both from a theoretical Merchant-type model, and from a numerical database of forces for metal cutting constructed from a suite of AdvantEdge simulations. Since the tool can potential vibrate at any angle relative to the workpiece, the forces for varying angle of vibration were computed, and the dynamic stability consequences considered. It is found that the two models lead to similar forces for varying vibration angle, at least through first order. Depending on the vibration angle the force will either increase or decrease with both chip load and penetration rate, reflecting the difference in the effect on the chipload and cutting speed with varying vibration direction. Second order terms in penetration rate were different in the two formulations, possibly a result of approximations used in the calculations involved in the Merchant formulation. Dynamically this means that the linear stability of each vibration angle is the similar for the two models, while the differences in nonlinear terms results in differences in the type Hopf bifurcation observed upon loss of stability.

show abstract

Section: Discussionmentioning

confidence: 82%