35.1 Introduction

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Regenerative chatter is a major limitation in machining operations. This phenomenon is a result of an

unstable interaction between the machining forces and the structural deflections. The forces generated

when the cutting tool and part come into contact produce significant structural deflections.

These structural deflections modulate the chip thickness that, in turn, changes the machining forces.

For certain cutting conditions, this closed-loop, self-excited system becomes unstable and regenerative

chatter occurs. Regenerative chatter may result in excessive machining forces and tool wear, tool failure,

and scrap parts due to unacceptable surface finish, thus severely decreasing operation productivity and

part quality.

35-1

© 2005 by Taylor & Francis Group, LLC

A typical chatter stability chart, the so-called

stability lobe diagram, is shown in Figure 35.1.

If the process parameters are above the stability

borderline, chatter will occur, and if the process

parameters are below the stability borderline,

chatter will not occur. The asymptotic stability

borderline is the depth-of-cut below which

stable machining is guaranteed regardless of the

spindle speed. The lobed nature of the stability

borderline allows stable pockets to form; thus,

at specific ranges of spindle speeds, the depth-ofcut

may be substantially increased beyond the

asymptotic stability limit. These pockets become

smaller as the spindle speed decreases. The

stability borderline is “pulled up” for low spindle speeds due to process damping (i.e., the back

side of the tool rubbing on the part surface). If accurate models of the structural components and the

cutting process are available, the stability lobe diagram may be used to plan chatter-free machining

operations.

The analysis of regenerative chatter as the interaction between the cutting forces and structural

vibrations was established by Tobias (1965) and Koenigsberger and Tlusty (1971). Merritt (1965) used

systems theory to determine stability and construct the stability lobe diagram by generating specialized

plots from the harmonic solutions of the system’s characteristic equation. Chatter analysis reveals a

natural delay in the system leading many researchers to use Nyquist techniques to generate stability

lobe diagrams (Minis et al., 1990a, 1990b; Lee and Liu, 1991a, 1991b; Minis and Yanushevsky, 1993).

A set of process parameters is selected and the characteristic equation is formed. The Nyquist criterion

is applied to determine if the system for this process parameter set is stable. The depth-of-cut

is adjusted and the procedure is repeated until the critical depth-of-cut is determined. Another

chatter analysis technique capable of generating stability lobe diagrams analytically for linear

systems has recently been introduced (Altintas and Budak, 1995; Budak and Altintas, 1998a, 1998b).

This technique is utilized in this chapter.

The theoretical analysis of regenerative chatter laid the foundation for developing techniques to

automatically detect its occurrence and to automatically suppress it. Since there is a dominant chatter

frequency, which is near a structural frequency, that occurs when chatter develops, most monitoring

techniques analyze the frequency of a process variable, and chatter is detected when significant energy is

present near a structural frequency. Most automatic chatter suppression routines either adjust the spindle

speed to be in a pocket of the stability lobe diagram or vary the spindle speed to bring the current and

previous tooth passes into phase. While automatic monitoring and control of regenerative chatter shows

great promise, it has been mostly limited to laboratory applications. Therefore, commercial tools are not

currently available.

While regenerative chatter in turning and face-milling operations is discussed in this chapter, this

phenomenon is not limited to these specific manufacturing operations. Other machining operations

for which chatter has been analyzed include end milling (Budak and Altintas, 1998a, 1998b), grinding

(Inasaki et al., 2001), drilling (Tarng and Li, 1994), and so on. Also, the regenerative chatter

phenomenon occurs in other manufacturing operations, most notably in rolling (Yun et al., 1998;

Tlusty, 2000).

Section 35.2 and Section 35.3 present an analytical method to examine regenerative chatter in

turning and face-milling operations, respectively. Section 35.4 discusses a numerical technique

known as time domain simulation that may be used to analyze regenerative chatter for nonlinear

systems. The subject of chatter detection is presented in Section 35.5, then methods to perform chatter

suppression are discussed and illustrated in Section 35.6. Section 35.7 presents a case study of a facemilling

operation.

stable

Spindle speed

Depth-of-cut

unstable

stability borderline

asymptotic borderline

FIGURE 35.1 Stability lobe diagram.

35-2 Vibration and Shock Handbook

© 2005 by Taylor & Francis Group, LLC

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