CHATTER1

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Affects of Cutting Parameters (Chatter Theory)
Dynamics of High Performance/ High Speed
Machining
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SECTION OBJECTIVES

• Define Cutting Forces and Parameters.
• Explain Chatter Theory
• Explain Process Damping
• Affects of cutting parameters
• Case study

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The Cutting Force

• The cutting force F is in the first
  approximation proportional to the chip area
  obtained as chip width b times chip thickness h ,
  
• F Ks b h (1),
• where the coefficient Ks is the force per unit
  chip area, the specific force determined
  primarily by the work piece material.
• There are other influences such as tool geometry,
  tool material, cutting speed and chip thickness
  such that it is easier to cut thicker chips, but
  these are not strong and for most purposes can be
  neglected.
• So, we will assume the force to be proportional
  to both b and h.
• A Table of specific forces (discussed briefly) is
  included, using N/mm2 as the dimension.

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Mechanical and Thermal Properties of Selected
Work piece Materials
Column Heads represent the following UTS,
ultimate tensile strength, N/mm2(Mpa) Ks,
specific force, N/mm2 k, thermal conductivity,
N/(sec C) ?k/(?c), thermal diffusivity,
mm2/sec Tm, melting temperature, C (?c),
specific heat per volume, N/(mm2 C) Ts, shear
plane temperature, C
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Metal Removal Rate
MRR baf f nmc b axial depth of cut n
spindle speed a radial depth of cut m
number of teeth (width of cut) c chip
load f feed or feed rate v pdn v cutting
speed d cutting diameter
1) From the point of view of cutting speed v and
chip load c the limit is dictated by tool life
and breakage and potential increase of MRR
depends mainly on improving tool materials. 2)
From the point of view of the depth of cut b and
number of teeth m cutting simultaneously the
limit is caused by chatter and improvement of MRR
is possible by higher dynamic stiffness of the
machine tool as formulated by the condition of
limit of stability. This condition is the
primary reason for the dimensions and shapes of
the machine tool structural components.
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Simplified Formulations
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Definitions

• Chatter
• A self-excited vibration between the tool and
  work piece in cutting.
• It can create large forces, damage tools and work
  pieces, and create unacceptable surfaces.
• Particularly problematic in high-speed high-power
  machining.
• High-Performance/High-Speed
• Machining with such a spindle speed that the
  tooth passing frequency can approach the dominant
  natural frequency of the system.

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Stable Chatter
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High-Speed Benefits

• Along with losses and limitations, there are
  important benefits from phenomena which occur
  only in high-speed milling.
• An especially important phenomenon is that of
  stability lobes (stability pockets).
• Stability lobes permit dramatically larger axial
  depths of cut at high spindle speeds, but the
  spindle speed must be carefully selected.

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Basis for AnalysisThe Stability Chart
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Chatter Mechanism

• Most undesirable vibrations in milling are
  self-excited chatter vibrations.
• What mechanism is responsible for transforming
  the steady input of energy (from the spindle
  drive) into a vibration?
• The primary mechanism is-
• Regeneration of Waviness.

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Regeneration of Waviness
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Cutting Force and Chip Thickness

• The wavy surface leads to variable chip
  thickness, variable force, and vibration
• The variable part of the cutting force depends on
  the current vibration and the previously
  generated surface
• Depending on conditions (Ks, b, spindle speed)
  this vibration either grows or diminishes
• Diminishes - stable cut, no chatter
• Grows - unstable cut, chatter

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Derivation of Limit of Stability
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Limit of Stability Computation
Oriented FRF
For a SDOF system

Limit width of chip
Where k is stiffness, ? is damping
ratio, ? is orientation factor, and Ks
is specific force. This is a design
criterion. The actual structural systems are
more complex, with several prominent modes. The
criterion is then
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Limit of Stability Computation (cont.)
Where blim limit axial width of cut for no
chatter Ks cutting stiffness m direction
orientation factor -gt m cosb (b70º,
m0.34) ReG real part of the transfer
function.
blim is smallest (blim,crit) when ReG is
minimum EXAMPLE Plunge turning 1035 steel,
Ks300,00 lb/in2 Assume common z0.04, b70º and
choose a large, easy to remember stiffness k1
Mlb/in. For p times less stiffness blim,crit
0.8 in/p e.g. if stiffness 10 times less,
blim,crit0.080 in
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Directional Orientation
? cutting force angle f feed direction F
cutting force n cutter rotation N normal of
cut u directional orientation factor X
X-axis Y Y-axis
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Oriented Frequency Response Function (FRF)
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Formation of the Stability Lobe Diagram from the
Real Part of the FRF
Critical limit depth of cut (bcr)
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Stability Chart (Lobing Diagram)
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Chatter characteristics.

• The chatter frequency is usually close to, but
  not equal to the natural frequency.
• The lobes are more tightly packed at the left
  (smaller speed change for the same phase change).
• Large stable zones exist in the high speed
  ranges.
• Surprisingly, the largest such gap occurs where
  the tooth passing frequency is equal to the
  natural frequency. Why?
• When tooth frequency matches natural frequency,
  the surface waves and the tooth vibration are in
  phase. The chip thickness looks the same as if
  there were no vibration.

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Comparison of stable and unstable cut spectra
(frequency content)
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Process Damping

• Chatter vibrations are inhibited at low speeds by
  process damping.
• Interference between the rake face of the tool
  and the tool path produces a net damping force.

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General Tendencies

• Feed Rate
• By itself will not determine if a give cut
  chatters.
• If a cut chatters higher feed rates will chatter
  more than lower feed rates.
• Number of teeth
• For a given width and depth of cut a cutter with
  more teeth will chatter at lower depths of cut.
• For example, a 4 tooth cutter with similar
  length, diameter and cutting parameters will
  chatter at roughly half the depth of a 2 tooth
  cutter.
• Increasing the number of teeth will generally
  shift the stability pockets to a lower speed.
• Width (a or ar) and Depth (b or ae) of cut.
• Along with material machinability is the biggest
  influence for chatter.
• Generally the product of a and b will be constant
  for a given chatter limit, e.g., doubling depth
  usually requires reducing width by ½ if at the
  chatter limit.
• Direction of cut
• Both width of cut and direction will influence
  chatter limit.
• For long slender cutters the direction of cut is
  not as influential as it is for shorter and
  larger indexable cutters.