Chaotic vibrations in a regenerative cutting process

Litak, Grzegorz

doi:10.1016/s0960-0779(01)00176-x

Cited by 72 publications

(35 citation statements)

References 13 publications

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“…In calculations the following parameters [3,5] have been used: c 1 = 1.25 × 10 9 N/m 2 , c = 86 Ns/m, w = 3.0 × 10 −3 m, h 0 = 0.3 × 10 −3 m, ω 0 = 816 rad/s, and m= 17.2 kg. Furthermore, the feed velocity v 0 has been assumed to be fairly large.…”

Section: Into Eqs (2) We Derive a Delay Differential Equation (Dde) mentioning

confidence: 99%

“…Thus a better understanding of the physical phenomena associated with a cutting process becomes necessary. A cutting process is inherently nonlinear and may exhibit a wide range of complex behavior due to frictional effects, delay dynamics, or structural nonlinearities [1][2][3][4][5]. Moreover it may also involve loss of contact between the tool and the workpiece.…”

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confidence: 99%

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Identification of chaos in a regenerative cutting process by the 0‐1 test

Litak

Radons

Schubert

2009

Proc Appl Math and Mech

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We examine the regenerative cutting process by using a single degree of freedom non-smooth model with a friction component and a time delay term. Instead of the standard Lyapunov exponent calculations, we propose a statistical 0-1 test for chaos. This approach reveals the nature of the cutting process signaling regular or chaotic dynamics. We are able to show that regular or chaotic motion occur in the investigated model depending on the delay time. In a cutting process chaotic vibrations and chatter are known to develop harmful operating conditions leading to poor final surface quality. The technological demand is to improve the final surface properties of the workpiece and to minimize the production time with higher cutting speeds. Thus a better understanding of the physical phenomena associated with a cutting process becomes necessary. A cutting process is inherently nonlinear and may exhibit a wide range of complex behavior due to frictional effects, delay dynamics, or structural nonlinearities [1][2][3][4][5]. Moreover it may also involve loss of contact between the tool and the workpiece. After the first pass of the tool, the cutting depth can be expressed aswhere y(t−T ) corresponds to the position of the workpiece during the previous pass, and T is the time delay scaled by the period of revolution of the workpiece 2π/Ω 0 , cp. Fig. 1a. The motion of the workpiece can be determined from the model proposed by Stepan [2]where ω 0 = k/m is the frequency of free vibration, v 0 is the feed velocity, and 2γ = c/m is the damping coefficient. F y (h) is the thrust force, which is the horizontal component of the cutting force, and m is the effective mass of the workpiece. The thrust force F y is based on dry friction between the tool and the chip. It is assumed to have a power law dependence on the actual cutting depth h and to be proportional to the chip width w and a friction coefficient c 1 . Θ denotes the Heaviside step function. The restitution parameter β = 0.75 is associated with the impact after contact loss, while t − and t + denotes the time instants before and after the impact. Substituting Eq. (1) into Eqs. (2) we derive a delay differential equation (DDE) for workpiece motion y(t). Plugging its solution into eq. (1) results in the history of cutting depth h(t).

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Section: Into Eqs (2) We Derive a Delay Differential Equation (Dde) mentioning

confidence: 99%

mentioning

confidence: 99%

Identification of chaos in a regenerative cutting process by the 0‐1 test

Litak

Radons

Schubert

2009

Proc Appl Math and Mech

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“…As described through the paper, a repetitive path tracked by the RT end-effector can produce a nonperiodic motion in the joint space. This non-periodic joint trajectory presents a chaotic behavior, an undesirable nonlinear effect which can appear during some machining processes [16] [17]. This chaotic behavior has embedded a large number of Unstable Periodic Orbits (UPOs).…”

Section: Introductionmentioning

confidence: 99%

Dynamic visual servo control of a 4-axis joint tool to track image trajectories during machining complex shapes

Pomares

Perea

Jara

et al. 2013

Robotics and Computer-Integrated Manufacturing

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A large part of the new generation of computer numerical control systems has adopted an architecture based on robotic systems. This architecture improves the implementation of many manufacturing processes in terms of flexibility, efficiency, accuracy and velocity. This paper presents a 4-axis robot tool based on a joint structure whose primary use is to perform complex machining shapes in some non-contact processes. A new dynamic visual controller is proposed in order to control the 4-axis joint structure, where image information is used in the control loop to guide the robot tool in the machining task. In addition, this controller eliminates the chaotic joint behaviour which appears during tracking of the quasi-repetitive trajectories required in machining processes. Moreover, this robot tool can be coupled to a manipulator robot in order to form a multi-robot platform for complex manufacturing tasks. Therefore, the robot tool could perform a machining task using a piece grasped from the workspace by a manipulator robot. This manipulator robot could be guided by using visual information given by the robot tool, thereby obtaining an intelligent multi-robot platform controlled by only one camera.

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“…Finally, the role of the dry friction and the stick-and-slip motion [10][11][12] was indicated and studied extensively. Recently, apart from the widely studied conditions of regular chatter vibrations, noise like chaotic oscillations caused by various system nonlinearities were predicted and detected [13][14][15][16][17][18][19][20][21][22][23][24][25].…”

Section: Introductionmentioning

confidence: 99%

Dynamics of a stainless steel turning process by statistical and recurrence analyses

Litak

Rusinek

2012

Meccanica

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This paper explores the cutting force oscillations. Forces have been measured during the stainless steel turning. We provide the results of standard statistical analysis of the corresponding time series together with their recurrence properties. We claim that the system, which initially exhibits regular vibrations, is unstable to chaotic oscillation for some fairly larger cutting depths. This characteristic transition in the cutting dynamics can be monitored by recurrences and could have the important implications to design a new control procedure.

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Chaotic vibrations in a regenerative cutting process

Cited by 72 publications

References 13 publications

Identification of chaos in a regenerative cutting process by the 0‐1 test

Identification of chaos in a regenerative cutting process by the 0‐1 test

Dynamic visual servo control of a 4-axis joint tool to track image trajectories during machining complex shapes

Dynamics of a stainless steel turning process by statistical and recurrence analyses

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