Theory of Torsional Chatter in Twist Drills: Model, Stability Analysis and Composition to Test

Bayly, Philip V.; Metzler, Sandra A.; Schaut, Adam J.; Young, Keith A.

doi:10.1115/1.1381399

Cited by 68 publications

(40 citation statements)

References 29 publications

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“…In each time step, deflections are obtained from solving Eq. (16) and are then used to calculate axial and angular positions of the inserts, q, at the nth time step as follows:…”

Section: Mathematical Modelingmentioning

confidence: 99%

“…Roukema et al [20] proposed a model for torsionalaxial vibration of twist drill which considers the effect of the torsional vibrations in the wave generation on the workpiece surface. While in the study done by Bayly et al [16] that only the effect of the axial flexibility is included in the calculation of the chip thickness, the model proposed by Roukema et al in [20] allows to consider the torsional flexibility in prediction of chip thickness in each time step. It is shown in [20] that when the torsional vibration is included in the model, the amplitude of the vibration reaches a lower limit.…”

Section: Introductionmentioning

confidence: 99%

“…While the variation of the thrust force changes the length of the drill, torque variations also change the length of the drill due to helical geometry of chip flutes [15]. Changes in the length of the drill affect the chip thickness and thus the forces acting on the drill [16,17]. The resulted dynamic forces generate vibrations and can develop to form chatter vibrations.…”

Section: Introductionmentioning

confidence: 99%

“…Considering orthogonality for the structural modes of the drill body and the fact that the dominant frequency in torsional-axial chatter vibration is very close to the first torsional mode, they assumed that the vibrational deflection of the drill is equal to deflection of the drill in its first torsional mode multiplied by a scaling factor. They obtained a delay differential equation with a constant delay while mentioning that the delay term varies slightly due to torsional vibrations [16]. Solving the mentioned delay differential equation determines if the process will be stable or not and hence the limit of radial depth of cut for chatter can be calculated.…”

Section: Introductionmentioning

confidence: 99%

“…Bayly et al [16] have modeled torsional-axial chatter vibrations in drills. Considering orthogonality for the structural modes of the drill body and the fact that the dominant frequency in torsional-axial chatter vibration is very close to the first torsional mode, they assumed that the vibrational deflection of the drill is equal to deflection of the drill in its first torsional mode multiplied by a scaling factor.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Time domain simulation of chatter vibrations in indexable drills

Parsian

Magnevall

Eynian

et al. 2016

Int J Adv Manuf Technol

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Regenerative chatter vibrations are common in drilling processes. These unwanted vibrations lead to considerable noise levels, damage the quality of the workpiece, and reduce tool life. The aim of this study is to simulate torsional and axial chatter vibrations as they play important roles in dynamic behavior of indexable insert drills with helical chip flutes. While asymmetric indexable drills are not the focal points in most of previous researches, this paper proposes a simulation routine which is adapted for indexable drills. Based on the theory of regenerative chatter vibration, a model is developed to include the asymmetric geometries and loadings that are inherent in the design of many indexable insert drills. Most indexable insert drills have two inserts located at different radial distances, namely central and peripheral inserts. Since the positions of the central and peripheral inserts are different, the displacement and thereby the change in chip thickness differs between the inserts. Additionally, the inserts have different geometries and cutting conditions, e.g., rake angle, coating, and cutting speed, which result in different cutting forces. This paper presents a time-domain simulation of torsional and axial vibrations by considering the differences in dynamics, cutting conditions, and cutting resistance for the central and peripheral inserts on the drill. The time-domain approach is chosen to be able to include nonlinearities in the model arising from the inserts jumping out of cut, multiple delays, backward motions of edges, and variable time delays in the system. The model is used to simulate cutting forces produced by each insert and responses of the system, in the form of displacements, to these forces. It is shown that displacements induced by dynamic torques are larger than those induced by dynamic axial forces. Finally, the vibration of a measurement point is simulated which is favorably comparable to the measurement results.

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“…In each time step, deflections are obtained from solving Eq. (16) and are then used to calculate axial and angular positions of the inserts, q, at the nth time step as follows:…”

Section: Mathematical Modelingmentioning

confidence: 99%