Stress distributions on the rake face during orthogonal machining

Buryta, D.; Sowerby, R.; Yellowley, I.

doi:10.1016/0890-6955(94)90054-x

Cited by 66 publications

(43 citation statements)

References 7 publications

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“…Here D denotes the tool diameter, hence ε is equivalent to the ratio of the contact length l 0 = Ah 0 and the workpiece perimeter Dπ. Typical values of this ratio are in the range 0.0005 < ε < 0.05 [5,7]. However, in case of the state-dependent short delay described by Eq.…”

Section: State-dependent Delay Modelmentioning

confidence: 99%

“…According to the literature on shear stress distribution measurements, two different types of shear stress distributions were identified. Several measurements [43,8,24,5,9,7] showed that the shear stress has a plateau near the tool tip along a certain sticking length l s , and then decays to zero at the point of chip separation. The corresponding shape function f (θ) can be approximated using a constant and an exponential function as shown in panel (a) of Fig.…”

Section: State-dependent Delay Modelmentioning

confidence: 99%

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State-dependent distributed-delay model of orthogonal cutting

2015

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In this paper we present a model of turning operations with state-dependent distributed time delay. We apply the theory of regenerative machine tool chatter and describe the dynamics of the tool-workpiece system during cutting by delay-differential equations. We model the cutting-force as the resultant of a force system distributed along the rake face of the tool, which results in a short distributed delay in the governing equation superimposed on the large regenerative delay. According to the literature on stress distribution along the rake face, the length of the chip-tool interface, where the distributed cutting-force system is acting, is function of the chip thickness, which depends on the vibrations of the tool-workpiece system due to the regenerative effect. Therefore, the additional short delay is state-dependent. It is shown that involving statedependent delay in the model does not affect linear stability properties, but does affect the nonlinear dynamics of the cutting process. Namely, the sense of the Hopf bifurcation along the stability boundaries may turn from sub-to supercritical at certain spindle speed regions.

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Section: State-dependent Delay Modelmentioning

confidence: 99%

Section: State-dependent Delay Modelmentioning

confidence: 99%

State-dependent distributed-delay model of orthogonal cutting

2015

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“…We assume that the cutting-force distribution can be decomposed into a magnitude function F T x (t, s) and a time-independent weight function W (s). This assumption was verified experimentally for stable stationary cutting using a split-tool [11,12] and using a sapphire tool [13]. Here we assume that this decomposition is valid in case of small perturbations around the stationary cutting, too.…”

Section: Cutting-force Modelsmentioning

confidence: 99%

“…In the past decades several models were built and measurements were carried out to provide data on the normal and the shear stress distributions along the rake face, see e.g. [11][12][13][18][19][20][21]. Here, we are interested in the x-directional component of stresses, which, in case of zero rake angle, is the shear stress.…”

Section: Cutting Force Distributionmentioning

confidence: 99%

Investigating Multiscale Phenomena in Machining: The Effect of Cutting-Force Distribution Along the Tool’s Rake Face on Process Stability

Molnár

Insperger

Hogan

et al. 2015

Volume 6: 11th International Conference on Multibody Systems, Nonlinear Dynamics, and Control

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Regenerative machine tool chatter is investigated in a nonlinear single-degree-of-freedom model of turning processes. The nonlinearity arises from the dependence of the cutting-force magnitude on the chip thickness. The cutting-force is modeled as the resultant of a force system distributed along the rake face of the tool. It introduces a distributed delay in the governing equations of the system in addition to the well-known regenerative delay, which is often referred to as the short regenerative effect. The corresponding stability lobe diagrams are depicted, and it is shown that a subcritical Hopf bifurcation occurs along the stability limits in the case of realistic cutting-force distributions. Due to the subcriticality a so-called unsafe zone exists near the stability limits, where the linearly stable cutting process becomes unstable to large perturbations. Based on center-manifold reduction and normal form calculations analytic formulas are obtained to estimate the size of the unsafe zone.

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“…In the past decades several measurements were performed to determine the distribution of stresses along the rake face of the tool. According to [9][10][11][12][13], there are two kinds of widely accepted shapes for both the normal and the shear stress distributions. Namely, some of the above measurements showed that the normal stress peaks at the tool tip and decays exponentially to zero at the end of contact.…”

Section: Mechanical Modelmentioning

confidence: 99%

On the Effect of Distributed Regenerative Delay on the Stability Lobe Diagrams of Milling Processes

Molnár

Insperger

2015

Period. Polytech. Mech. Eng.

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Regenerative machine tool chatter is investigated for milling operations with helical tools. The stability of a two-degreesof-freedom milling model is analyzed IntroductionThe occurrence of harmful vibrations (chatter) during metal cutting processes is an important problem in manufacturing technology. Machine tool chatter has many unfavorable effects: it reduces the productivity and the surface quality, causes noise, enhances tool wearing, and even leads to tool damage in some cases. Therefore, avoiding or suppressing chatter is highly important for the machine tool industry. In the past few decades, a significant amount of research was conducted to find the governing physical phenomena behind chatter in order to understand its nature and describe methods to avoid or suppress it.One of the most widely accepted explanations of machine tool chatter is the theory of surface regeneration introduced by Tobias [1] and Tlusty [2]: the vibrating tool leaves a wavy surface behind, which results in a varying cutting-force in the consecutive cut. Accordingly, delay effects appear in the models of metal cutting operations since the cutting-force exciting the tool motion is determined by the chip thickness, which depends both on the actual tool position and the delayed position at the previous cut. Hence, machine tool vibrations can be described using delay-differential equations, and the regenerative machine tool chatter can be considered as the manifestation of self-excited oscillations in a time-delay system.Following the works of Tobias and Tlusty, a large effort has been put lately into the more accurate modeling of machine tool chatter. In this paper we follow the model of [3], where the stability of turning processes is investigated taking the distribution of the cutting force along the tool's rake face into account. The concept was experimentally verified in [4]. Extension to interrupted turning operation was presented in [5]. Here, we will extend the distributed cutting-force model to milling processes and perform the stability analysis.The outline of the paper is the following. Section 2 presents the mechanical model of the system, the description of the cutting-force expression, and the final form of the governing equation. In Section 3, the semi-discretization technique [6] is applied to analyze the stability of the system numerically. Some numerical issues regarding computational efficiency are also highlighted. Section 4 considers the special cases of the

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Stress distributions on the rake face during orthogonal machining

Cited by 66 publications

References 7 publications

State-dependent distributed-delay model of orthogonal cutting

State-dependent distributed-delay model of orthogonal cutting

Investigating Multiscale Phenomena in Machining: The Effect of Cutting-Force Distribution Along the Tool’s Rake Face on Process Stability

On the Effect of Distributed Regenerative Delay on the Stability Lobe Diagrams of Milling Processes

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