01-Principles of Cutting

8/10/2019 01-Principles of Cutting

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Content

Tooth pitch vs Fill ratio

Saw blade vs Excavator

Tooth pitch, intake surface area

Tooth f illratio

Fill ratio vs cutting speed


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Why?

Why all the math?

Based on facts instead of feelings Uniform

Consequent

Can be used on all materials

Can be used on any size or type of products

Improves process dependability

Result:

One or two blades cut all products

Better understanding how to choose cutting parameters

Easier to introduce new cutoff applications

and obtain good results right from the start


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Tooth pitch vs. fill ratio


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The gullet area is very much like the size of the bucket


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How big the gullet area is, is determined by the distance between the teeth

This distance between teeth we call the tooth pitch


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Which blade has 1m

circumference (perimeter):

a) 225x2x32

b) 315x2,5x40c) 325x3x32

d) 350x2,5x40

e) 370x3x40

Circumference

P = 2r = x D

0,707 m

0,989 m1,021 m

1,099 m

1,162 m

It all started with Archimedes

Circumference of the blade

rD


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P x D

T = =

Z Z

____

Tooth pitch

_______

circumference of blade xDiameter

Tooth pitch = =

number of teeth number of teeth

_____________________ _________________


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To calculate how much material can be removed by one tooth (bucket)

we need to calculate the size of the gullet area: the surface of the orange

area

To make calculation easier we asume the surface is a circle

The gullet


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Intake surface

Maximumintake surface:

100% = D

The diameter of this circle

is half of the pitch

Maximumintake surface:

100% =r = (D/2)

= D / 2 = D/4

But T being a Tooth pitch, intake surface is also

= ( T) = T

100% = 1/16 T

Intake surface or gullet area is the size of the

bucket


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Intake surface

Sawblade diameter D = 315 mm

Amount of teeth Z = 180 teeth

Toothpitch T= 315 x / 180 = 5.5 mm

100% intake surface ( T) = 5.93 mm2


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During cutting, the gullet fills with chip material

The surface of the chip is decided by its length and thickness

Chip forming


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Question: What determines how full the bucket/gullet is going to be?

Answer: forward speed of bucket + length of arc of contact bucket/soil

This arc of contact is what we call the longest cut length (LCL)


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Longest cutting length (LCL)

D

W

Longest Cut Length (LCL)


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A typical example of overfill: sand overflow.

When sand falls back to the ground, energy is wasted.

By choosing a good balance between feed rate and arc of contact,

the efficiency of the chip/soil evacuation process can be optimized.

Overfill


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Fill ratio

To allow the chip to be removed, and to prevent damage to the tooth, the

surface of the chip may not exceed a certain percentage

Standard value for this fil l ratio is: 10%


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Overfill

What all cutting processes have in common, is that material must be

removed.

Just like the Excavator, you need to choose

The right size of the bucket (tooth pitch)

The forward speed (Fz, tooth load)

When a incorrect combination of parameters is used, a problem of

Overfill can be encountered!


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Normal filling of the gullets / buckets Good choice of tooth pitch and feed rate

Good chips, right fill


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Chips too thick, danger zone

Pitch too small or feed rate too high for applicable longest cutting length

Danger zone


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Overfill: chips too thick, overload, vibration, breakage of saw blade.

Feed to high for LCL, pitch too small

Overfill


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Fill ratio

Overfill

Normal

Danger zone


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So: we need to figure out the arc of contact

Between sawblade and cut product

Longest cutting length (LCL or Lmax)

Lmax = 2 x (D W) x W)___________

D

W

Lmax Longest cutting lengthD diameter

W Wall thickness

D 25 mm

W 2,0 mm

Lmax = 2 x (25 2) x 2) = 13,56 mm

___________

Lmax


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Chip surface calculation

Chip surface =

Lmax x Fz(Feedrate mm / tooth)

DW

LCL

Fz

x

Chip surface


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Tooth Fill ratio calculation

Sawblade 315 mm

Z = 180

T = Tooth pitch = 5.5 mm

Tube 25 x 2,0 mm

Feed rate = 0,08 mm/tooth

Lmax=2 x(D W) x W) = 2 x(25 2) x 2) = 13,56 mm

Chip surface = Lmax x Feed rate = 13,56 x 0,08 = 1,08 mm2

Intake surface = ( T) = T = 1/16 T =

= 1/16 x 3,14x 5,5 = 5.93 mm2

_____________ _____________

Tooth fill ratio = Chip surface / max intake surface x

100 % = (1,08 / 5,93) x 100% = 18,2 %


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Speed and limitations

When speed is limited, one can get away with a high fill ratio

and still manage to go around a corner


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When speed increases,

the max fill ratio is reduced

and so is max corner speed



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When speed is very high, one needs to be even more careful with the fill ratio

When speed is increased, more room is required to prevent accidents.



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How fast can you go?

Trials show, a good balance between blade life and chip evacuation, is

obtained when fill ratio does not exceed the limits mentioned above.

- Mechanical limitations of cutoff machine can also limit maximum possible

fill ratio (vibration, motorpower)

- Fully coated sawblades can be run at 30% fill ratio, even at high cuttingspeeds!

25%

50 m/min

20%100 m/min

15%200 m/min

The same applies to chips. When cutting speed is raised, max fill ratio is

reduced.


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Thank you for your attention

Documents

01-Principles of Cutting