Effects of Varying Dynamics of Flexible Workpieces in Milling Operations

2019 ◽  
Vol 142 (1) ◽  
Author(s):  
Adam K. Kiss ◽  
Daniel Bachrathy ◽  
Gabor Stepan
Keyword(s):  
Closed Form Solution ◽  
Form Solution ◽  
Depth Of Cut ◽  
Stability Conditions ◽  
Flexible Beam ◽  
Milling Operations ◽  
Radial Depth ◽  
Distributed Transfer Function ◽  
Relative Errors ◽  
The Stability

Abstract In this study, surface error calculations and stability conditions are presented for milling operations in case of slender parts. The dynamic behavior of the flexible beam-type workpiece is modeled by means of finite element method (FEM), while the varying dynamical properties related to the feed motion as well as the material removal process are incorporated in the model. The FEM-generated direct frequency response function is verified through a closed-form solution based on the distributed transfer function method. Relative errors and convergence of the FEM are investigated based on the analytical solutions of the continuum model, from which appropriate element size and mode number can be selected for modal coordinate transformations. The pattern in the variation of the natural frequencies is explored using the analytical model in case of high radial depth of cut relative to the original cross section of the beam-like workpiece. Both the stability conditions and the resulted surface errors are predicted as a function of the tool position. The presented approach and the results are validated by laboratory tests.

Dynamics and Stability of Turn-Milling Operations With Varying Time Delay in Discrete Time Domain

2018 ◽  
Vol 140 (10) ◽  
Author(s):  
Alptunc Comak ◽  
Yusuf Altintas
Keyword(s):  
Time Domain ◽  
Chip Thickness ◽  
Body Motion ◽  
Depth Of Cut ◽  
Time Varying Delay ◽  
Milling Operations ◽  
Varying Time Delay ◽  
The Stability ◽  
Five Axis ◽  
Turn Milling

Turn-milling machines are widely used in industry because of their multifunctional capabilities in producing complex parts in one setup. Both milling cutter and workpiece rotate simultaneously while the machine travels in three Cartesian directions leading to five axis kinematics with complex chip generation mechanism. This paper presents a general mathematical model to predict the chip thickness, cutting force, and chatter stability of turn milling operations. The dynamic chip thickness is modeled by considering the rigid body motion, relative vibrations between the tool and workpiece, and cutter-workpiece engagement geometry. The dynamics of the process are governed by delayed differential equations by time periodic coefficients with a time varying delay contributed by two simultaneously rotating spindles and kinematics of the machine. The stability of the system has been solved in semidiscrete time domain as a function of depth of cut, feed, tool spindle speed, and workpiece speed. The stability model has been experimentally verified in turn milling of Aluminum alloy cut with a helical cylindrical end mill.

Stability and Imperfections in Quasistatic Viscoplastic Solutions

1990 ◽  
Vol 43 (5S) ◽  
pp. S251-S255 ◽  
Author(s):  
T. Belytschko ◽  
B. Moran ◽  
M. Kulkarni
Keyword(s):  
Strain Field ◽  
Strain Softening ◽  
Fourier Spectrum ◽  
Shear Bands ◽  
Closed Form Solution ◽  
Step Function ◽  
Form Solution ◽  
Viscoplastic Material ◽  
Strain Fields ◽  
The Stability

The effect of imperfections on the structure of shear bands in strain-softening viscoplasticity is studied via a closed form solution. The stability of various solutions is then examined by varying the data through imperfections. It is shown that a step-function imperfection, such as commonly used in finite element solutions, leads to a step-function shear strain field, which is an unstable solution. Arbitrary C0 and C1 imperfections lead to C0 and C1 strain fields, respectively. Fourier analyses show that the imperfection scales the response of the viscoplastic material: the Fourier spectrum of the strain field is strongly influenced by the Fourier spectrum of the imperfection.

Stability Analysis of Mechanical Seals With Two Flexibly Mounted Rotors

1998 ◽  
Vol 120 (2) ◽  
pp. 145-151 ◽  
Author(s):  
J. Wileman ◽  
I. Green
Keyword(s):  
Dynamic Properties ◽  
Equations Of Motion ◽  
Closed Form Solution ◽  
Form Solution ◽  
Fluid Film ◽  
Mechanical Seals ◽  
Stability Threshold ◽  
Seal Design ◽  
The Stability ◽  
Gyroscopic Effects

Dynamic stability is investigated for a mechanical seal configuration in which both seal elements are flexibly mounted to independently rotating shafts. The analysis is applicable to systems with both counterrotating and corotating shafts. The fluid film effects are modeled using rotor dynamic coefficients, and the equations of motion are presented including the dynamic properties of the flexible support. A closed-form solution for the stability criteria is presented for the simplifled case in which the support damping is neglected. A method is presented for obtaining the stability threshold of the general case, including support damping. This method allows instant determination of the stability threshold for a fully-defined seal design. A parametric study of an example seal is presented to illustrate the method and to examine the effects of various parameters in the seal design upon the stability threshold. The fluid film properties in the example seal are shown to affect stability much more than the support properties. Rotors having the form of short disks are shown to benefit from gyroscopic effects which give them a larger range of stable operating speeds than long rotors. For seals with one long rotor, counterrotating operation is shown to be superior because the increased fluid stiffness transfers restoring moments from the short rotor to the long.

Stability Predictions for End Milling Operations With a Nonlinear Cutting Force Model

2009 ◽  
Vol 131 (6) ◽  
Author(s):  
Alex Elías-Zúñiga ◽  
Jovanny Pacheco-Bolívar ◽  
Francisco Araya ◽  
Alejandro Martínez-López ◽  
Oscar Martínez-Romero ◽  
...  
Keyword(s):  
Experimental Data ◽  
Cutting Force ◽  
End Milling ◽  
Stability Conditions ◽  
Force Model ◽  
Process Stability ◽  
Cutting Force Model ◽  
Stability Lobes ◽  
Milling Operations ◽  
The Stability

The aim of this paper is to obtain the stability lobes for milling operations with a nonlinear cutting force model. The work is focused on the generation of stability lobes based on a formulation with Chebyshev polynomials and the semidiscretization method, considering a nonlinear cutting force model. Comparisons were conducted between experimental data at 5% radial immersion with aluminum workpiece and predictions based on Chebyshev and semidiscretization. In all cases, the use of nonlinear cutting force model provides better prediction of process stability conditions.

Initial Post-Buckling and Growth of a Circular Delamination Bridged by Nonlinear Fibers

2000 ◽  
Vol 67 (4) ◽  
pp. 777-784 ◽  
Author(s):  
S. Li ◽  
J. Nie ◽  
J. Qian ◽  
Y. Huang ◽  
Y. Hu
Keyword(s):  
Fracture Toughness ◽  
Three Dimensional ◽  
Closed Form Solution ◽  
Dynamic Effect ◽  
Form Solution ◽  
Delamination Growth ◽  
Nonlinear Fibers ◽  
Post Buckling ◽  
Bridging Model ◽  
The Stability

Axisymmetric buckling, initial post-buckling and growth of a circular delamination bridged by nonlinear fibers in three-dimensional composites are studied by a perturbation method. The through-thickness fibers are assumed to provide nonlinear restoring traction resisting the deflection of the delaminated layer. A closed-form solution for the central deflection of the delamination due to on applied compressive stress during initial post-buckling is obtained. In addition, some simple formulas for calculating the strain energy release rate and the mixed mode stress intensity ratio (i.e., Mode II versus Mode I) at the delamination crack tip are also established. Some interesting conclusions arising directly from the perturbation solutions are drawn. These include: (1) initial post-buckling behavior of a circular delamination is unstable for a softening bridging model; this may result in initial delamination growth for some materials with lower fracture toughness when the delamination buckles rather than post-buckles. However, stable growth is obtained for a hardening bridging model; (2) with an increase of the nonlinear fiber bridging parameter β¯, the residual stiffness of a three-dimensional composite structure with a circular delamination increases gradually; (3) bridging force changes the catastrophic nature of the delamination growth and increases the stability of the delamination. The range and the dynamic effect of the unstable delamination growth diminish or disappear as the bridging parameters increase; (4) for the bridged delamination, the higher the material fracture toughness, the higher the stability of the delamination growth, and the smaller the range and dynamic effect of its unstable growth. [S0021-8936(00)03203-7]

Stability Analysis for the Milling of Lateral Walls

2011 ◽  
Vol 346 ◽  
pp. 190-196
Author(s):  
Ai Jun Jiang ◽  
Kai Wu
Keyword(s):  
Three Dimensional ◽  
Depth Of Cut ◽  
Milling Cutter ◽  
Milling Parameters ◽  
Stability Lobes ◽  
Radial Depth ◽  
Stability Model ◽  
The Stability ◽  
Stable Zone ◽  
Lateral Walls

The stability model was established and the two-dimensional and three-dimensional lobes were plotted for the milling of lateral walls in order to avoid chatter occurring in the milling of lateral walls. The combination of milling parameters of free chatter can be selected in the stable zone of stability lobes. The stability of milling lateral walls influenced by radial depth of cut and teeth number of the milling cutter was analyzed. It is shown that the stable zone of stability lobes expands gradually as the spindle speed increases. The stable zone become wider as the radial depth of cut increases. The axial depth of cut limits is increased and higher productivity can be obtained as the teeth of the milling cutter decreases.

Mathematical Model for Closed-Form Solution of Parameters of Cylinder Exhaust Port in Variable-Stroke Engine

2010 ◽  
Vol 97-101 ◽  
pp. 2724-2727
Author(s):  
Li Ming Di ◽  
Chun Jing Yang ◽  
Yong Sheng Zhao
Keyword(s):  
Mathematical Model ◽  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
Alignment Method ◽  
Specific Time ◽  
Exhaust Port ◽  
Initial Stage ◽  
Relative Errors ◽  
Stroke Engine

A mathematical model for getting the closed-form solution of main parameters of cylinder exhaust port is present, based on a few known parameters of variable-stroke engine (VSE). Considering lack of parameters in the initial stage of design, empirical formula is applied to solve the initial specific time-area value of exhaust port, and the initial port timing angle is solved by using logarithmic alignment method, thereby height and width of the exhaust port can be solved, then the precise specific time-area value and port timing angle are solved by using the coefficient calculation method and logarithmic alignment method respectively, so that the relative errors between initial and precise values of specific time-area value and port timing angle are defined as the relative errors of the mathematical model. Application examples show that the relative errors of the model is less than 3%.

Stability Prediction for Low Radial Immersion Milling

2002 ◽  
Vol 124 (2) ◽  
pp. 217-225 ◽  
Author(s):  
M. A. Davies ◽  
J. R. Pratt ◽  
B. Dutterer ◽  
T. J. Burns
Keyword(s):  
Stability Theory ◽  
High Speed ◽  
Depth Of Cut ◽  
Machining Parameters ◽  
Peripheral Milling ◽  
Flexible Mode ◽  
Milling Operations ◽  
Radial Depth ◽  
Tool Diameter ◽  
Low Radial Immersion

Traditional regenerative stability theory predicts a set of optimally stable spindle speeds at integer fractions of the natural frequency of the most flexible mode of the system. The assumptions of this theory become invalid for highly interrupted machining, where the ratio of time spent cutting to not cutting (denoted ρ) is small. This paper proposes a new stability theory for interrupted machining that predicts a doubling in the number of optimally stable speeds as the value of ρ becomes small. The results of the theory are supported by numerical simulation and experiment. It is anticipated that the theory will be relevant for choosing optimal machining parameters in high-speed peripheral milling operations where the radial depth of cut is only a small fraction of the tool diameter.

Study on Surface Roughness in Micro End Milling of Mold Material

2011 ◽  
Vol 325 ◽  
pp. 594-599 ◽  
Author(s):  
Hiroo Shizuka ◽  
Koichi Okuda ◽  
Masayuki Nunobiki ◽  
Yasuhito Inada
Keyword(s):  
Surface Roughness ◽  
End Milling ◽  
Milling Process ◽  
Cutting Conditions ◽  
Mold Material ◽  
Depth Of Cut ◽  
Milling Operations ◽  
Radial Depth ◽  
Micro End Milling ◽  
End Milling Process

The effects of cutting conditions on the surface roughness in a micro-end-milling process of a mold material are described in this paper. Micro-end-milling operations were performed under different cutting conditions such as feed rate and depth of cut, in order to investigate the factors that had the greatest influence on the finished surface during micro-end-milling. It was revealed that the surface roughness begins to deteriorate when the radial depth of the cut exceeds the tool radius. In addition, it was found that this phenomenon is peculiar to micro-end-milling processes.

Stability-Based Spindle Design Optimization

2006 ◽  
Vol 129 (2) ◽  
pp. 407-415 ◽  
Author(s):  
Vincent Gagnol ◽  
Belhassen C. Bouzgarrou ◽  
Pascal Ray ◽  
Christian Barra
Keyword(s):  
High Speed ◽  
Modal Identification ◽  
Design Parameters ◽  
Depth Of Cut ◽  
Chatter Vibration ◽  
High Rotational Speed ◽  
Milling Operations ◽  
Critical Requirement ◽  
The Stability ◽  
Gyroscopic Coupling

Prediction of stable cutting regions is a critical requirement for high-speed milling operations. These predictions are generally made using frequency-response measurements of the tool-holder-spindle set obtained from a nonrotating spindle. However, significant changes in system dynamics occur during high-speed rotation. In this paper, a dynamic high-speed spindle-bearing system model is elaborated on the basis of rotor dynamics prediction and readjusted on the basis of experimental modal identification. The dependency of dynamic behavior on speed range is then investigated and determined with accuracy. Dedicated experiments are carried out in order to confirm model results. They show that dynamic effects due to high rotational speed and elastic deformations, such as gyroscopic coupling and spin softening, have a significant influence on spindle behavior. By integrating the modeled speed-dependent spindle transfer function in the chatter vibration stability approach of Altintas and Budak (1995, CIRPS Ann, 44(1), pp. 357–362), a new dynamic stability lobe diagram is predicted. Significant changes are observed in the stability limits constructed using the proposed approach and allow accurate prediction of cutting conditions to be established. Finally, optimization studies are performed on spindle design parameters in order to obtain a chatter vibration-free cutting operation at the desired speed and depth of cut for a given cutter.

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