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

Multi-frequency Chatter Analysis Using the Shift Theorem

During machining, the use of variable helix tools can potentially improve the system's stability to regenerative chatter. However, this configuration of tool has a distributed time delay, which makes the stability analysis more complex. The analysis is further exacerbated by the time-periodic coefficients that occur during milling. The present contribution demonstrates how the Fourier transform and harmonic transfer function approach can be used to analyse the system stability. This provides new insight into the stability of these tools, based on a mathematically elegant approach that makes extensive use of the shift theorem

On the approximation of delayed systems by Taylor series expansion

It is known that stability properties of delay-differential equations are not preserved by Taylor series expansion of the delayed term. Still, this technique is often used to approximate delayed systems by ordinary differential equations in different engineering and biological applications. In this brief, it is demonstrated through some simple second-order scalar systems that low-order Taylor series expansion of the delayed term approximates the asymptotic behavior of the original delayed system only for certain parameter regions, while for high-order expansions, the approximate system is unstable independently of the system parameters

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

Az emberi egyensúlyozás mechanikai modellezése PIDA szabályozó segítségével

Ebben a cikkben két egyszerű problémán keresztül vizsgáljuk az emberi egyensúlyozás folyamatát. Vizsgáljuk az ujjhegyen történő rúdegyensúlyozást és az egy helyben állás egyensúlyozási folyamatát, a posturalis kilengést. Az egyensúlyozási problémákat egyszerű mechanikai modellekkel írjuk le, majd egy, az iparban is gyakran használt, PIDA szabályozó segítségével modellezzük az emberi agy szabályozási mechanizmusát egyensúlyozás közben. A mozgást leíró differenciál-egyenletben konstans időkéséssel figyelembe vesszük a reflex-késés hatását és a leíró egyenletek stabilitási vizsgálatával ellenőrizzük a felírt modell stabilizálhatóságát. Végül a kapott számítási eredményeket összevetjük a szakirodalomban található kísérleti eredményekkel

The Critical Length is a Good Measure to Distinguish between Stick Balancing in the ML and AP Directions

Seven novice subjects participated in experiments of stick balancing on a linear track in the anterior-posterior (AP) and the medio-lateral (ML) directions. The goal of the experiments was to test how the depth perception in the subjects' AP direction affects balancing performance compared to balancing in the ML direction, where depth perception does not play a role. It is easier to balance longer sticks than shorter ones, therefore balancing performance is measured by the length of the shortest stick that subjects can balance. Subjects were found to be able to balance shorter sticks in the ML direction than in the AP direction: the ratio of the shortest stick lengths in the ML direction relative to the AP direction was in average 0.53. Thus, the additional challenge posed by depth perception in the AP direction is clearly observable. Additionally, repeated trials were carried out for 5 consecutive days to assess the development of balancing skill by using stabilometry analysis. The maximal balance time of the subjects significantly increased with the days of practice

STABILITY TRANSITION BETWEEN 1 AND 2 DEGREE-OF-FREEDOM MODELS OF MILLING

Chatter prediction for 2 degree of freedom (DOF) milling model is presented. The workpiece is assumed to be flexible and the tool to be stiff. Non-linear cutting force model is used, and the linearized equation of motion is derived. Stability charts are constructed for different stiffness values in the directions x and y. The charts for the 1 DOF models associated with the x and the y directions are also given. It is shown that the 2-DOF case can not be given via the pure overlaying of the charts of the two single DOF cases