Application of the stability lobes theory to milling of thin workpieces, experimental approach

The optimisation of cutting conditions in High Speed Machining (HSM) requires the use of a vibratory approach in order to avoid a fast deterioration of the tool and of the spindle, as well as a loss of quality of the surface rough- ness. We suggest a transposition of the method of stability lobes to the case of the milling thin parts, which is very typical from the aeronautical manufacturing context. After having modelled the dynamic behaviour of a blade and of the cutting efforts in side milling, we describe the zones of machining instability. An experimental validation permits us to emphasise the transition from stability to instability, in accordance to our theoretical results. The experimental profile is then compared with a computed profile. A decomposition of the different situations of contact between the tool and the part permits to show the influence of back cutting in the model. Tests of machining permit then to quantify its role. The objective of these works is the definition of a quick methodology for deter- mining the optimal cutting conditions in a given industrial machining configuration

Chatter milling modeling of active magnetic bearing spindle in high-speed domain

A new dynamical modeling of Active Magnetic Bearing Spindle (AMBS) to identify machining stability of High Speed Milling (HSM) is presented. This original modeling includes all the minimum required parameters for stability analysis of AMBS machining. The stability diagram generated with this new model is compared to classical stability lobes theory. Thus, behavior’s specificities are highlighted, especially the major importance of forced vibrations for AMBS. Then a sensitivity study shows impacts of several parameters of the controller. For example, gain adjustment shows improvements on stability. Side milling ramp test is used to quickly evaluate the stability. Finally, the simulation results are then validated by HSM cutting tests on a 5 axis machining center with AMBS

Experimental study of thin part vibration modes in machining

The machining of thin walls generally generates milling chatter, that damage surface roughness and manufacturing tools. Stability lobes which include natural frequencies are successful in case of tool chatter. When milling thin webs models are less adequate, because the interaction with the tool disrupts the behaviour of the work piece. The modal approach generally used for stability charts may be not adequate enough because of neglecting the tool and the work piece contact. This paper presents the experimental phase of a work aiming at analyse vibration modes of a thin web during machining. A finite element calculation shows the influence of a contact on natural frequencies of the part. For a better investigation, field displacements of the work piece are analysed. This work eventually aims at better knowledge of the contact between the tool and the part to improve the hardiness of models

Chatter Control by Spindle Speed Variation in High-Speed Milling

High-speed milling operations are often limited by regenerative vibrations. The aim of this paper is to analyze the effect of spindle speed variation on machine tool chatter in high-speed milling. The stability analysis of triangular and sinusoidal shape variations is made numerically with the semi-discretization method. Parametric studies show also the influence of the frequency and amplitude variation parameters. This modeling is validated experimentally by variable spindle speed cutting tests with a triangular shape. Stable and unstable tests are analyzed in term of amplitude vibration and surface roughness degradation. This work reveals that stability must be considered at period variation scale. It is also shown that spindle speed variation can be efficiently used to suppress chatter in the flip lobe area

The variational theory of complex rays for the calculation of medium-frequency vibrations

A new approach called the ``variational theory of complex rays’’ (VTCR) is developed for calculating the vibrations of weakly damped elastic structures in the medium-frequency range. Here, the emphasis is put on the most fundamental aspects. The effective quantities (elastic energy, vibration intensity, etc.) are evaluated after solving a small system of equations which does not derive from a finite element discretization of the structure. Numerical examples related to plates show the appeal and the possibilities of the VTCR

Influence of material removal on the dynamic behavior of thin-walled structures in peripheral milling

Machining is a material removal process that alters the dynamic properties during machining operations. The peripheral milling of a thin-walled structure generates vibration of the workpiece and this influences the quality of the machined surface. A reduction of tool life and spindle life can also be experienced when machining is subjected to vibration. In this paper, the linearized stability lobes theory allows us to determine critical and optimal cutting conditions for which vibration is not appar- ent in the milling of thin-walled workpieces. The evolution of the mechanical parameters of the cut- ting tool, machine tool and workpiece during the milling operation are not taken into account. The critical and optimal cutting conditions depend on dynamic properties of the workpiece. It is illustrated how the stability lobes theory is used to evaluate the variation of the dynamic properties of the thin- walled workpiece. We use both modal measurement and finite element method to establish a 3D rep- resentation of stability lobes. The 3D representation allows us to identify spindle speed values at which the variation of spindle speed is initiated to improve the surface finish of the workpiece

Integration of dynamic behaviour variations in the stability lobes method: 3D lobes construction and application to thin-walled structure milling

Vibratory problems occurring during peripheral milling of thin-walled structures affect the quality of the fin- ished part and, to a lesser extent, the tool life and the spindle life. Therefore, it is necessary to be able to limit these problems with a suitable choice of cutting conditions. The stability lobes theory makes it possible to choose the appropriate cutting con- ditions according to the dynamical behaviour of the tool or the part. We introduce the dynamical behaviour variation of the part with respect to the tool position in order to determine optimal cutting conditions during the machining process. This general- ization of the classical lobes diagram leads us to a 3D lobes diagram construction. These computed results are compared with real experiments of down-milling of thin-walled structures

Influence d'une vitesse de rotation variable sur les vibrations d'usinage en UGV

Les opérations de fraisage à grande vitesse sont couramment limitées par les vibrations régénératives. Dans cet article, nous allons étudier une solution de réduction du phénomène de broutement, basée sur la variation de la vitesse de rotation de l’outil. Afin de quantifier les gains de productivité, deux modélisations différentes du fraisage dynamique ont été adaptées et confrontées : la simulation temporelle et la semi-discrétisation. La comparaison de ces deux méthodes a montré une bonne cohérence des résultats aussi bien à vitesse constante qu’à vitesse variable. Ces deux modélisations ont été validées expérimentalement à vitesse constante et variable. Les essais d’usinage à vitesse variable ont permis de mettre en évidence la différence entre la stabilité théorique et expérimentale

Suppression of period doubling chetter in high-speed milling by spindle speed variation

Spindle speed variation is a well known technique to suppress regenerative machine tool vibra- tions, but it is usually considered to be effective only for low spindle speeds. In the current paper, spindle speed variation is applied to the high speed milling process, at the spindle speeds where the constant speed cutting results in period doubling chatter. The stability analysis of triangular and sinusoidal shape variations is made numerically with the semi-discretization method. It is shown that the milling process can be stabilized by increasing the amplitude of the spindle speed variation, while the frequency of the variation has no significant effect on the dynamic behaviour. The results are validated by experiments. Based on the analysis of the machined workpieces, it is shown that the surface roughness can also be decreased by the spindle speed variation technique

The Effect of High School Employment on Educational Attainment: A Conditional Difference-in-Differences Approach

Using American panel data from the National Educational Longitudinal Study of 1988 (NELS:88) this paper investigates the effect of working during grade 12 on attainment. We exploit the longitudinal nature of the NELS by employing, for the first time in the related literature, a semiparametric propensity score matching approach combined with difference-in- differences. This identification strategy allows us to address in a flexible way selection on both observables and unobservables associated with part-time work decisions. Once such factors are controlled for, insignificant effects on reading and math scores are found. We show that these results are robust to a matching approach combined with difference-in-difference-in-differences which allows differential time trends in attainment according to the working status in grade 12.education, evaluation, propensity score matching