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MetalMAX Training Manufacturing Laboratories, Inc. CHATTER-1 Affects of Cutting Parameters (Chatter Affects of Cutting Parameters (Chatter Theory) Theory) Dynamics of Dynamics of High Performance/ High Performance/ High Speed High Speed Machining Machining
24
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Page 1: Chatter Overview

MetalMAX Training Manufacturing Laboratories, Inc. CHATTER-1

Affects of Cutting Parameters (Chatter Affects of Cutting Parameters (Chatter Theory)Theory)

Dynamics of Dynamics of High Performance/High Performance/High Speed High Speed MachiningMachining

Page 2: Chatter Overview

MetalMAX Training Manufacturing Laboratories, Inc. CHATTER-2

SECTION OBJECTIVESSECTION OBJECTIVES

Define Cutting Forces and Parameters.

Explain Chatter TheoryExplain Process DampingAffects of cutting parametersCase study

Page 3: Chatter Overview

MetalMAX Training Manufacturing Laboratories, Inc. CHATTER-3

The Cutting ForceThe 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.

Page 4: Chatter Overview

MetalMAX Training Manufacturing Laboratories, Inc. CHATTER-4

Mechanical and Thermal Properties Mechanical and Thermal Properties of Selected Work piece Materialsof Selected Work piece Materials

No. Material UTS Ks k Tm c

1 grey cast iron HBN 200 1500 43 12 1220 3.7

2 carbon steel 1020 N 400 2100 43 12 1520 3.7

3 carbon steel 1035 N 500 2300 43 12 1500 3.7

4 carbon steel 1045 N 650 2600 43 12 1490 3.7

5 stainless steel 302 700 2700 15 4.4 1425 3.6

6 alloy steel 4140 H 900 2800 38 10 1510 3.7

7 alloy steel 5140 H 950 2800 40 11 1500 3.7

8 Ni based Inconel X 1450 3500 12 3.2 1370 3.7

9 Ni based Udimet 500 1500 3550 12 3.2 1370 3.7

10 Co based L605 1250 3700 10 2.8 1370 3.6

11 Ti (A16,V4) 1350 2000 7 2.6 1600 2.7

12 Al 7075-T6 530 850 140 60 540 2.3

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/secTm, melting temperature, °C(c), specific heat per volume, N/(mm2 °C)Ts, shear plane temperature, °C

Page 5: Chatter Overview

MetalMAX Training Manufacturing Laboratories, Inc. CHATTER-5

Metal Removal RateMetal Removal RateMRR = b*a*f f = n*m*cb = axial depth of cut n = spindle speeda = radial depth of cut m = number of teeth (width of cut) c = chip loadf = feed or feed rate

v = *d*nv = cutting speedd = 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.

Page 6: Chatter Overview

MetalMAX Training Manufacturing Laboratories, Inc. CHATTER-6

Simplified FormulationsSimplified Formulations

cff

cf

Tf

sss

ss

st

vFP

vvv

FF

vFP

vvFF

bhKF

tan

tan

cos )cos(

1

Page 7: Chatter Overview

MetalMAX Training Manufacturing Laboratories, Inc. CHATTER-7

Definitions: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.

Page 8: Chatter Overview

MetalMAX Training Manufacturing Laboratories, Inc. CHATTER-8

Stable ChatterStable Chatter

Page 9: Chatter Overview

MetalMAX Training Manufacturing Laboratories, Inc. CHATTER-9

High-Speed BenefitsHigh-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.

Page 10: Chatter Overview

MetalMAX Training Manufacturing Laboratories, Inc. CHATTER-10

Basis for Analysis:Basis for Analysis:The Stability ChartThe Stability Chart

ProcessDampingRegion

Full Stability Chart

Page 11: Chatter Overview

MetalMAX Training Manufacturing Laboratories, Inc. CHATTER-11

Chatter MechanismChatter 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”.

Page 12: Chatter Overview

MetalMAX Training Manufacturing Laboratories, Inc. CHATTER-12

Regeneration of WavinessRegeneration of Waviness

Page 13: Chatter Overview

MetalMAX Training Manufacturing Laboratories, Inc. CHATTER-13

Cutting Force and Chip ThicknessCutting 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 chatterGrows - unstable cut, chatter

F K b f z zs ( )0

F K b z zs ( )0

Page 14: Chatter Overview

MetalMAX Training Manufacturing Laboratories, Inc. CHATTER-14

Derivation of Limit of StabilityDerivation of Limit of Stability

minlim,

lim

0

0

1

0

0

)Re(2

1

)Re(2

1

1

)/(1

)cos(cos

)(

)(

)(

GKb

GKb

Y

YG

GbK

Y

Y

GuG

u

FGY

YYbKF

eYYhh

bhKF

scr

s

s

iii

iii

s

tjm

s

Page 15: Chatter Overview

MetalMAX Training Manufacturing Laboratories, Inc. CHATTER-15

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

For a SDOF system:

Limit of Stability ComputationLimit of Stability Computation

i

n

GuG ior 1

ReRe

k

Gor minRe

ss K

k

GKb

2

Re2

1

min

lim

min

lim Re2

1

ors GKb

“Oriented” FRF:

Limit width of chip:

Page 16: Chatter Overview

MetalMAX Training Manufacturing Laboratories, Inc. CHATTER-16

Limit of Stability Computation Limit of Stability Computation (cont.)(cont.)

Where:blim = limit axial width of cut for no chatterKs = cutting stiffnessm = direction orientation factor ->

m =cosb (b=70º, m=0.34)Re[G] = real part of the transfer function.

k

G4

1Re min

blim is smallest (blim,crit) when Re[G] is minimumEXAMPLE: Plunge turning 1035 steel, Ks=300,00 lb/in2

Assume common z=0.04, b=70º and choose a large, easy to remember stiffness k=1 Mlb/in.

For p times less stiffnessblim,crit=0.8 in/pe.g. if stiffness 10 times less, blim,crit=0.080 in

)34.0)(53)(2(

)04.1)(04.0)(61)(4()20(800.0lim, E

Emminb cr

min

lim Re2

1

ors GKb

Page 17: Chatter Overview

MetalMAX Training Manufacturing Laboratories, Inc. CHATTER-17

Directional OrientationDirectional Orientation

= cutting force angle= cutting force anglef = feed directionf = feed directionF = cutting forceF = cutting forcen = cutter rotationn = cutter rotationN = normal of cutN = normal of cutu = directional orientationu = directional orientation factorfactorX = X-axisX = X-axisY = Y-axisY = Y-axis

Page 18: Chatter Overview

MetalMAX Training Manufacturing Laboratories, Inc. CHATTER-18

Oriented Frequency Response Oriented Frequency Response Function (FRF)Function (FRF)

Page 19: Chatter Overview

MetalMAX Training Manufacturing Laboratories, Inc. CHATTER-19

Formation of the Stability Lobe Formation of the Stability Lobe Diagram from the Real Part of the Diagram from the Real Part of the FRFFRF

Critical limit depth of cut (bcr)

Page 20: Chatter Overview

MetalMAX Training Manufacturing Laboratories, Inc. CHATTER-20

Stability Chart (Lobing Stability Chart (Lobing Diagram)Diagram)

Page 21: Chatter Overview

MetalMAX Training Manufacturing Laboratories, Inc. CHATTER-21

Chatter characteristics.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.

Page 22: Chatter Overview

MetalMAX Training Manufacturing Laboratories, Inc. CHATTER-22

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

Page 23: Chatter Overview

MetalMAX Training Manufacturing Laboratories, Inc. CHATTER-23

Process DampingProcess 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.

Page 24: Chatter Overview

MetalMAX Training Manufacturing Laboratories, Inc. CHATTER-24

General TendenciesGeneral 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.