scholarly journals The Effect of Non-Symmetric FRF on Machining: A Case Study

2015 ◽  
Author(s):  
David Hajdu ◽  
Tamas Insperger ◽  
Gabor Stepan
Keyword(s):  
Frequency Response ◽  
Degrees Of Freedom ◽  
Stability Diagram ◽  
Domain Model ◽  
Practical Applications ◽  
Stability Diagrams ◽  
Machining Center ◽  
Milling Operations ◽  
The Stability ◽  
Machining Operations

Stability prediction of machining operations is often not reliable due to the inaccurate mechanical modeling. A major source of this inaccuracy is the uncertainties in the dynamic parameters of the machining center at different spindle speeds. The so-called tip-to-tip measurement is the fastest and most convenient method to determine the frequency response of the machine. This concept consists of the measurement of the tool tip’s frequency response function (FRF) usually in two perpendicular directions including cross terms. Although the cross FRFs are often neglected in practical applications, they may affect the system’s dynamics. In this paper, the stability diagrams are analyzed for milling operations in case of diagonal, symmetric and non-symmetric FRF matrices. First a time-domain model is derived by fitting a multiple-degrees-of-freedom model to the FRF matrix, then the semi-discretization method is used to determine stability diagrams. The results show that the omission of the non-symmetry of the FRF matrix may lead to inaccurate stability diagram.

Dynamic Stability Characteristics of Axially Accelerated Beams

2006 ◽  
Vol 321-323 ◽  
pp. 1654-1658 ◽  
Author(s):  
Hong Hee Yoo ◽  
Sung Jin Eun
Keyword(s):  
Dynamic Stability ◽  
Natural Frequencies ◽  
Equations Of Motion ◽  
Stability Diagram ◽  
Accelerated Motion ◽  
Stability Diagrams ◽  
Divergence Type ◽  
The Stability ◽  
Direct Numerical Integration ◽  
Free Beam

Dynamic stability of axially accelerated beams is investigated in this paper. The equations of motion of a fixed-free beam undergoing axially accelerated motion are derived. Unstable regions due to the acceleration are obtained by using the Floquet’s theory. Stability diagrams are presented to illustrate the influence of the acceleration characteristics. Large unstable regions of flutter type instability exist around the first, twice the first, and twice the second bending natural frequencies. Divergence type instability also occurs when the acceleration exceeds a certain value. The validity of the stability diagram is confirmed by direct numerical integration of the equations of motion.

On Instability Pockets and Influence of Damping in Parametrically Excited Systems

2018 ◽  
Vol 140 (5) ◽  
Author(s):  
Ashu Sharma ◽  
S. C. Sinha
Keyword(s):  
Degrees Of Freedom ◽  
State Transition ◽  
Degree Of Freedom ◽  
Transition Matrices ◽  
Stability Boundaries ◽  
Parametrically Excited ◽  
Parametric Space ◽  
Stability Diagrams ◽  
Wide Range ◽  
The Stability

In most parametrically excited systems, stability boundaries cross each other at several points to form closed unstable subregions commonly known as “instability pockets.” The first aspect of this study explores some general characteristics of these instability pockets and their structural modifications in the parametric space as damping is induced in the system. Second, the possible destabilization of undamped systems due to addition of damping in parametrically excited systems has been investigated. The study is restricted to single degree-of-freedom systems that can be modeled by Hill and quasi-periodic (QP) Hill equations. Three typical cases of Hill equation, e.g., Mathieu, Meissner, and three-frequency Hill equations, are analyzed. State transition matrices of these equations are computed symbolically/analytically over a wide range of system parameters and instability pockets are observed in the stability diagrams of Meissner, three-frequency Hill, and QP Hill equations. Locations of the intersections of stability boundaries (commonly known as coexistence points) are determined using the property that two linearly independent solutions coexist at these intersections. For Meissner equation, with a square wave coefficient, analytical expressions are constructed to compute the number and locations of the instability pockets. In the second part of the study, the symbolic/analytic forms of state transition matrices are used to compute the minimum values of damping coefficients required for instability pockets to vanish from the parametric space. The phenomenon of destabilization due to damping, previously observed in systems with two degrees-of-freedom or higher, is also demonstrated in systems with one degree-of-freedom.

Modeling of Drillstrings

2005 ◽  
Author(s):  
M. A. Elsayed ◽  
Chin Chin Phung
Keyword(s):  
Frequency Response ◽  
Response Function ◽  
Frequency Response Function ◽  
Laboratory Data ◽  
Stability Diagram ◽  
Test Rig ◽  
Real Component ◽  
Reasonable Degree ◽  
Representative Model ◽  
The Stability

In this paper we show how a drillstring can be modeled in terms of limited numbers of masses and springs for the purpose of building a test rig. The model should represent the drillstring dynamics to a reasonable degree of accuracy. We will use the real component of the Frequency Response Function and the stability diagram as measures of dynamic similarity between the model and drillstring. We will also show how the chosen modes can be decoupled and used in obtaining the bit displacement. The decoupled modes will be used in a proposed test rig configuration that would increase flexibility in adding or removing modes from the system. Obtaining a representative model of the test rig is critical to our ability to extrapolate laboratory data into field applications.

Dynamics and Stability of Five-Axis Ball-End Milling

2010 ◽  
Vol 132 (2) ◽  
Author(s):  
Erdem Ozturk ◽  
Erhan Budak
Keyword(s):  
Time Domain ◽  
End Milling ◽  
Milling Process ◽  
Ball End Milling ◽  
Part Quality ◽  
Stability Diagrams ◽  
Milling Operations ◽  
The Stability ◽  
Milling Dynamics ◽  
Five Axis

Being one of the most important problems in machining, chatter vibrations must be avoided as they result in high cutting forces, poor surface finish, and unacceptable part quality. Using stability diagrams is an effective method to predict chatter free cutting conditions. Although there have been numerous works in milling dynamics, the stability of five-axis ball-end milling has not been studied in detail. In this paper, the stability of the five-axis ball-end milling is analyzed using analytical (frequency domain), numerical (time-domain), and experimental methods. The models presented consider 3D dynamics of the five-axis ball-end milling process including the effects of all important process parameters such as the lead and tilt angles. Both single- and multi-frequency solutions are presented. Unlike other standard milling cases, it is observed that adding multi-frequency effects in the solution has marginal influence on the stability diagrams for five-axis ball-end milling operations due to effects of the ball-end milling geometry on the engagement region, thus, on the directional coefficients. The stability limits predicted by single- and multi-frequency methods are compared with time-domain simulations and experiments. Using the models and experimental results, the effects of the lead and tilt angles on the stability diagrams are also shown. The presented models can be used in analysis of five-axis ball-end milling dynamics as well as in the selection of the milling conditions for increased stability.

scholarly journals Inviscid Faraday waves in a brimful circular cylinder

2013 ◽  
Vol 724 ◽  
pp. 671-694 ◽  
Author(s):  
R. Kidambi
Keyword(s):  
Circular Cylinder ◽  
Contact Line ◽  
Stability Diagram ◽  
Bond Number ◽  
Faraday Waves ◽  
Almost Periodic ◽  
Contact Lines ◽  
Stability Diagrams ◽  
The Stability ◽  
Subharmonic Resonances

AbstractWe study inviscid Faraday waves in a brimful circular cylinder with pinned contact line. The pinning leads to a coupling of the Bessel modes and leads to an infinite system of coupled Mathieu equations. For large Bond numbers, even though the stability diagrams and the subharmonic and harmonic resonances for the free and pinned contact lines are similar, the free surface shapes can be quite different. With decreasing Bond number, not only are the harmonic and subharmonic resonances very different from the free contact line case but also interesting changes in the stability diagram occur with the appearance of combination resonance tongues. Points on these tongue boundaries correspond to almost-periodic states. These do not seem to have been reported in the literature.

Chatter Stability of Serrated Milling Tools in Frequency Domain

2021 ◽  
pp. 1-26
Author(s):  
Nima Dabiri Farahani ◽  
Yusuf Altintas
Keyword(s):  
Frequency Domain ◽  
Discrete Time ◽  
Time Domain ◽  
Angular Distance ◽  
Domain Model ◽  
Chatter Stability ◽  
Stability Diagrams ◽  
Time Marching ◽  
The Stability ◽  
Milling Tools

Abstract Serrated milling tools are widely used for chatter suppression in roughing difficult-to-cut Titanium and Nickel alloys in the aerospace industry. Due to the complexity of chip generation and serration wave geometries ground on the flutes, the chatter stability diagrams are predicted with time marching numerical simulation or semi-discrete time-domain methods, which are computationally too costly to use in practice. This paper presents a frequency domain model of milling dynamics with variable delays caused by the flute serrations. The endmill is divided into discrete cylindrical elements, each having a different radius from the cutter axis. As the cutter rotates and cuts metal, the angular distance between the subsequent tooth varies as a function of serration amplitudes and feedrate; hence the regenerative delays vary. The angular delays and effective directional factors are averaged for each tooth to form a time-independent but serration-dependent characteristics equation for all discrete cutter elements. The stability of the resulting characteristic equation of the system is solved using Nyquist theory and compared against the experimental results and existing time marching and semi-discrete time-domain solutions. The proposed analytical model predicts the stability charts about thirty times faster than the time-domain models while providing acceptable accuracy.

Design and Implementation of a Distributed Variable Impedance Actuator Using Parallel Linear Springs

2016 ◽  
Vol 8 (2) ◽  
Author(s):  
Mohammad Hasan H. Kani ◽  
Hamed Ali Yaghini Bonabi ◽  
Hamed Jalaly Bidgoly ◽  
Mohammad Javad Yazdanpanah ◽  
Majid Nili Ahmadabadi
Keyword(s):  
Degrees Of Freedom ◽  
Piecewise Linear ◽  
Angular Position ◽  
Morphological Structure ◽  
System Stability ◽  
Practical Applications ◽  
Wearable Robots ◽  
Linear Spring ◽  
The Stability ◽  
Actuator Design

This paper introduces a distributed variable impedance actuator that provides independent control of the actuator's angular position and its impedance. The idea for the actuator was inspired by the morphological structure of muscles and tendons. The system to be presented can be used as both a variable impedance actuator as well as a passive piecewise linear spring. Moreover, the actuator has an adequate number of degrees-of-freedom to approximate any nonlinear spring characteristics because of its distributed nature. Using distributed torque production subsystems with small and low power motors makes it possible to use this actuator in many applications such as prosthesis, artificial limbs, and wearable robots. The stability of the system discussed and the conditions that ensure the system stability are presented. Finally, a proof-of-concept actuator design is presented, as well as experimental results which confirm that the proposed distributed variable impedance actuator can be implemented in practical applications.

Effect of Process Damping on Longitudinal Vibrations in Drillstrings

1994 ◽  
Vol 116 (2) ◽  
pp. 129-135 ◽  
Author(s):  
M. A. Elsayed ◽  
R. L. Wells ◽  
D. W. Dareing ◽  
K. Nagirimadugu
Keyword(s):  
Shock Absorber ◽  
Stability Diagram ◽  
Field Observations ◽  
Longitudinal Vibrations ◽  
Process Damping ◽  
Stability Diagrams ◽  
Drag Bits ◽  
The Stability ◽  
Cut Surface ◽  
Cutting Speeds

This paper shows the effect of process damping—caused by the interference between the cutter and the previously cut surface—on the stability of drillstrings. The method of including process damping in the calculation of the stability diagram is outlined. Previously published stability diagrams of drillstrings equipped with drag bits showed decreased stability at low cutting speeds, and that the addition of a shock absorber decreased the size of stability pockets. In this paper, we show that the introduction of process damping confirms field observations of increased stability at low speeds. We also show that a properly designed shock absorber produces large stability pockets where drilling is most effective.

Non-adhesive lotus and other hydrophobic materials

2008 ◽  
Vol 366 (1870) ◽  
pp. 1539-1556 ◽  
Author(s):  
David Quéré ◽  
Mathilde Reyssat
Keyword(s):  
Solid Surface ◽  
Room Temperature ◽  
Water Repellency ◽  
Short Review ◽  
Water Repellent ◽  
Practical Applications ◽  
Hydrophobic Materials ◽  
Volatile Liquid ◽  
Air Cushion ◽  
The Stability

Superhydrophobic materials recently attracted a lot of attention, owing to the potential practical applications of such surfaces—they literally repel water, which hardly sticks to them, bounces off after an impact and slips on them. In this short review, we describe how water repellency arises from the presence of hydrophobic microstructures at the solid surface. A drop deposited on such a substrate can float above the textures, mimicking at room temperature what happens on very hot plates; then, a vapour layer comes between the solid and the volatile liquid, as described long ago by Leidenfrost. We present several examples of superhydrophobic materials (either natural or synthetic), and stress more particularly the stability of the air cushion—the liquid could also penetrate the textures, inducing a very different wetting state, much more sticky, due to the possibility of pinning on the numerous defects. This description allows us to discuss (in quite a preliminary way) the optimal design to be given to a solid surface to make it robustly water repellent.

scholarly journals Velocity and acceleration level inverse kinematic calculation alternatives for redundant manipulators

Meccanica ◽  
2021 ◽  
Author(s):  
Dóra Patkó ◽  
Ambrus Zelei
Keyword(s):  
Degrees Of Freedom ◽  
Direct Method ◽  
Tracking Error ◽  
Inverse Kinematic ◽  
Linear Feedback ◽  
Joint Position ◽  
Stability Properties ◽  
Acceleration Level ◽  
Error Elimination ◽  
The Stability

AbstractFor both non-redundant and redundant systems, the inverse kinematics (IK) calculation is a fundamental step in the control algorithm of fully actuated serial manipulators. The tool-center-point (TCP) position is given and the joint coordinates are determined by the IK. Depending on the task, robotic manipulators can be kinematically redundant. That is when the desired task possesses lower dimensions than the degrees-of-freedom of a redundant manipulator. The IK calculation can be implemented numerically in several alternative ways not only in case of the redundant but also in the non-redundant case. We study the stability properties and the feasibility of a tracking error feedback and a direct tracking error elimination approach of the numerical implementation of IK calculation both on velocity and acceleration levels. The feedback approach expresses the joint position increment stepwise based on the local velocity or acceleration of the desired TCP trajectory and linear feedback terms. In the direct error elimination concept, the increment of the joint position is directly given by the approximate error between the desired and the realized TCP position, by assuming constant TCP velocity or acceleration. We investigate the possibility of the implementation of the direct method on acceleration level. The investigated IK methods are unified in a framework that utilizes the idea of the auxiliary input. Our closed form results and numerical case study examples show the stability properties, benefits and disadvantages of the assessed IK implementations.

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