35.6 Chatter Suppression

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Most machining process plans are derived from handbooks or from a database. Since these plans do not

consider the physical machine that will be used, chatter-free operations cannot be guaranteed. Thus,

multiple iterations, where the feed or spindle speed are adjusted using the operator’s experience,

are typically required. The tool position may also be adjusted (e.g., the depth-of-cut may be decreased)

to suppress chatter and, while this is guaranteed to be effective due to the presence of the asymptotic

stability borderline, this approach is typically not employed since part program must be rewritten to

add multiple passes, thereby drastically decreasing productivity. The stability lobe diagram can be used

as a tool to plan chatter-free machining operations and productivity can be greatly increased by

selecting the process parameters to lie in a pocket between two lobes. A cutting tool design methodology

(Altintas et al., 1999) has also been proposed for milling tools where the pitch is slightly adjusted

such that the teeth are not evenly spaced. The variable pitch has the effect of changing the phase

difference between successive teeth vibrations and, if designed properly, will suppress chatter. These

design techniques are very sensitive to parameter variations and model uncertainty, and may not be used

reliably for a large range of operating conditions. This section will describe methods for automatic

chatter suppression.

35.6.1 Spindle-Speed Selection

For the stability lobe diagram generated from a system modeled as having a one-dimensional

structure, it is seen that the maximum depths-of-cut are located at the tooth-passing frequencies

(i.e., the number of teeth multiplied by the spindle speed) corresponding to the dominant structural

frequency and integer fractions thereof. If the dominant structural frequency is known, it may be

used as an aid in selecting spindle speeds; however, the structural dynamics are often unknown

and may be determined only through costly testing. Further, structural dynamics change drastically

over time.

It is known, however, that during chatter, the dominant frequency seen in the cutting-process output is

close to a dominant structural frequency. This fact is used in Smith and Delio (1992) to suppress chatter

automatically. The following steps are taken:

1. Implement a chatter detection routine to determine the presence of chatter.

2. If chatter is detected, determine the chatter frequency, vc: This will be the frequency at which the

process signal has the greatest energy.

3. Set the new spindle speed to be Ns ¼ vc = ½NtðN þ 1Þ􀀉; where N is the smallest positive integer such

that the new spindle speed does not violate the maximum spindle speed constraint.

4. Repeat Steps 1 to 3 until the chatter has been suppressed.

The equation Ns ¼ vc = ½NtðN þ 1Þ􀀉 may be interpreted as selecting the tooth-passing frequency,

or an integer fraction thereof, corresponding to the approximate dominant structural frequency.

Note that if the depth-of-cut is too large and the maximum spindle speed is too small, this technique

will not be effective and the feed or depth-of-cut must be adjusted, or the spindle speed must be

continuously varied.

35.6.2 Example 6

The feed force for a turning operation is given by Equation 35.1, and the structural dynamics are

given by Equation 35.26. The system parameters are P ¼ 0.75 kN/mm2, fnom ¼ 0.1 mm,

vn ¼ 750 Hz, z ¼ 0.1, and k ¼ 15 kN/mm. The depth-of-cut is 5 mm. The spindle speed that

should be selected to suppress chatter if the chatter frequency is 725 Hz, when the spindle speed is

not constrained, is determined. The spindle speed that should be selected to suppress chatter if the

maximum spindle speed is 15,000 rpm is also determined. The system is simulated for a spindle

speed of 10,000 rpm for ten spindle revolutions and then for ten spindle revolutions for the spindle

35-20 Vibration and Shock Handbook

© 2005 by Taylor & Francis Group, LLC

speed calculated when the spindle speed is not constrained. The simulation is then repeated for the

spindle speed calculated when the spindle speed is constrained. Feed force and tool displacement are

plotted for both cases.

For a chatter frequency of 725 Hz, the optimal spindle speed is 60(725) ¼ 43,500 rpm. Other possible

spindle speeds are 43,500/2 ¼ 21,750 rpm, 43,500/3 ¼ 14,500 rpm, 43,500/4 ¼ 10,875 rpm, and so on.

Therefore, when the maximum spindle speed is 15,000 rpm, a spindle speed of 14,500 rpm is used.

The time domain simulations are in Figure 35.20 and Figure 35.21. The results illustrate that a depth-ofcut

of 5.3 mm is stable at 43,500 rpm, but not at 14,500 rpm. Therefore, if the spindle speed is

limited to 15,000 rpm, spindle-speed selection may not be used to suppress the chatter present in the

machining operation.

0.01 0.02 0.03 0.04 0.05 0.06 0.07

0.3

0.4

0.5

Time (s)

Feed force (kN)

Tool displacement (mm)

0.01 0.02 0.03 0.04 0.05 0.06 0.07

−0.04

−0.03

−0.02

−0.01

0

Time (s)

FIGURE 35.20 Time-domain simulations using spindle speed selection with Ns ¼ 43,500 rpm.

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1

0.3

0.4

0.5

Time (s)

Feed force (kN)

Tool displacement (mm)

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1

−0.04

−0.03

−0.02

−0.01

0

Time (s)

FIGURE 35.21 Time-domain simulations using spindle speed selection with Ns ¼ 14,500 rpm.

Regenerative Chatter in Machine Tools 35-21

© 2005 by Taylor & Francis Group, LLC

35.6.3 Feed and Depth-of-Cut Selection

When chatter occurs, operators will sometimes increase the feedrate via the feedrate override button

on the machine tool control panel. This has the effect of increasing the feed, assuming the spindle

speed remains constant. When linear chatter analysis techniques are employed, the force process

gains are linearized about the nominal feed, and stability does not appear to be affected by the

nominal feed. However, the stability results are only valid for a small region about the nominal feed.

It is well known that there is a nonlinear relationship between the machining forces and the feed of

the form F ¼ Pðf Þdf : The pressure can be expressed in the form Pðf Þ ¼ Kf a where a , 0; thus, the

pressure decreases as the feed increases. Since the stable depth-of-cut is inversely proportional to

the pressure, the stability limit will increase as the feed increases, assuming the spindle speed

remains constant. An illustration of this phenomenon was shown in Example 3: when the feed was

increased from 0.1 to 0.2 mm, chatter was suppressed. While increasing the feed can suppress

chatter, the sensitivity of chatter to feed is limited and other adverse phenomenon, such as tooth

chippage, may occur.

Another method to suppress chatter is to decrease the depth-of-cut (Weck et al., 1975). This method is

guaranteed to work as evidenced by stability lobe diagrams. However, this method is typically not

preferred as it dramatically decreases operation productivity by increasing the total number of tool passes

that are required to complete the operation.

35.6.4 Spindle-Speed Variation

Spindle speed variation (SSV) is another technique that has shown the ability to suppress chatter

(Inamura and Sata, 1974; Lin et al., 1990). The spindle speed is varied about some nominal value,

typically in a sinusoidal manner. Although SSV is a promising technique, the theory required to guide the

designer in the selection of suitable amplitudes and frequencies is in its infancy (Radulescu et al., 1997a,

1997b; Sastry et al., 2002). Also, in some cases, SSV may create chatter that would not occur when using a

constant spindle speed.

0.05 0.1 0.15 0.2 0.25 0.3

0.2

0.3

0.4

0.5

Time (s)

feed force (kN)

tool displacement (mm)

0.05 0.1 0.15 0.2 0.25 0.3

−0.06

−0.04

−0.02

0

0.02

Time (s)

FIGURE 35.22 Time-domain simulations using spindle-speed variation with A ¼ 0.1 and V ¼ 20 Hz.

35-22 Vibration and Shock Handbook

© 2005 by Taylor & Francis Group, LLC

35.6.5 Example 7

The feed force for a turning operation is given by Equation 35.1 and the structural dynamics are given

by Equation 35.26. The system parameters are P ¼ 0.75 kN/mm2, fnom ¼ 0.1 mm, vn ¼ 750 Hz, z ¼ 0.1,

and k ¼ 15 kN/mm. The depth-of-cut is 5 mm. The system is simulated for a nominal spindle speed

of Nnom ¼ 10,000 rpm for 10 spindle revolutions and then for 30 spindle revolutions for the spindle

speed calculated from Equation 35.67 for the following three cases: A ¼ 0.1 and V ¼ 20 Hz, A ¼ 0.25

and V ¼ 20 Hz, and A ¼ 0.25 and V ¼ 160 Hz. Feed force and tool displacement are plotted for all

three cases.

NsðtÞ ¼ Nnom½1 þ A sinðVtÞ􀀉 ð35:67Þ

0.05 0.1 0.15 0.2 0.25 0.3

0.25

0.3

0.35

0.4

0.45

Time (s)

Tool displacement (mm) Feed force (kN)

0.05 0.1 0.15 0.2 0.25 0.3

−0.04

−0.03

−0.02

−0.01

0

Time (s)

FIGURE 35.23 Time-domain simulations using spindle-speed variation with A ¼ 0.25 and V ¼ 20 Hz.

0.05 0.1 0.15 0.2 0.25 0.3

0.25

0.3

0.35

0.4

0.45

Time (s)

Tool displacement (mm) Feed force (kN)

0.05 0.1 0.15 0.2 0.25 0.3

−0.04

−0.03

−0.02

−0.01

0

Time (s)

FIGURE 35.24 Time-domain simulations using spindle-speed variation with A ¼ 0.25 and V ¼ 160 Hz.

Regenerative Chatter in Machine Tools 35-23

© 2005 by Taylor & Francis Group, LLC

The time-domain simulations are in Figure 35.22 to Figure 35.24 for the respective cases. The results

illustrate that SSV may be utilized to suppress chatter; however, the amplitude and frequency of the

spindle speed vibration must be carefully chosen.

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