Simple Shearing and Ploughing Cutting Force Model In Turning Operation with Nose Radius Tool

7/21/2019 Simple Shearing and Ploughing Cutting Force Model In Turning Operation with Nose Radius Tool

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University of RijekaFaculty of Engineering

Authors: Graciela Šterpin,

Zoran Jurković,Miran Brezočnik

15th International Scientific Conference on Production Engineering CIM 2015

June 10 ‐ 13, 2015, Vodice, Croatia



,

shearing and ploughing model,

turning

2

CIM 2015, June 10‐13, 2015, Vodice, Croatia



1. INTRODUCTION

Cutting force is affected by: the tool edge geometry,tool wear rate,

cutting temperature and

cutting parameters.

Analytical models can be very complex in order to reach good accuracy in

representing the effective cutting mechanics.

The pure empirical models are more frequent than the analytical ones:

- e compu er a e s a s ca es gn o exper men me o o ogy n par cu ar

regression analysis),

- computational neural network,

- .

However, pure empirical approach is both time and cost consuming.

One of the most applied techniques in cutting force modelling

3

Mechanistic or semi-empirical approach, mainly the shearing and ploughing modelCIM 2015, June 10‐13, 2015, Vodice, Croatia



1. INTRODUCTION

The specific cutting force k s

-k cs and k cp - shearing and ploughing coefficientsh

k A

k cp

csc

s

The main cutting force F c

Lk Ak F cpcsc

The shearing term The ploughing term

4

A - uncut chip areaL - length of the cutting edge engaged in the workpiece




1. INTRODUCTION

The shearing term The ploughing term

The effect of the chip pressure on The friction between the flank of,

uncut chip area

surface, proportional to theengaged cutting edge length

n e con rary o ana y ca cu ng orce mo e s, e s ear ng an p oug ng

model considers the changing of tool edge geometry due to tool wear. However,

this phenomenon is beyond the scope of presented research.

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2. CUTTING FORCE MODEL

ISO 3685 limits the maximum feed to 80% of the tool nose radius (i.e. f ≤ 0,8 r ε )

so that the end (or minor) cutting edge cannot be engaged in cutting.

There are two possible cases in practice:

–. p ε r

The uncut chip area can be divided into region (I) with curved cutting edge and

.

An ular limits:

ε r

f ζ

2arccos

1

6

κ r - approach angle

r κ ζ 902





The shearing and ploughing cutting force model is based on the assumption that

the resultant cutting force acting on the tool in region (I) is a sum of i = 1, 2, ..., N

.ˆddd

,ˆddd

l k Ak F

l k ζ Ak F cpi csci Local angle ζ i :

N

ζ ζ i ζ ζ i

121

The infinitesimal uncut chip area

d A(ζ ): product of the local uncut

After projection along the radial,

tangential and axial directions itcan be obtained:

chip thickness h(ζ i ) and theinfinitesimal cutting edge length

N

i

ci c y F F F

1

)I()I( ,dl d

i i

i ε i ε i ζ f r ζ f r ζ h 222 sincos

N

N

i

i r ni f z ζ κ F F F

1

)I()I( ,sind

7

d 12 π ζ ζ

r l ε

i

i r ni p x ζ κ F F F

1

)I()I( ,cosd


F p

- back forceF f - feed force




Local approach angle κ r (ζ i ): Region (II) derived geometry:

1 90i i r ζ ζ κ

r r ε p4

)II(

κ r al cos11 r κ s n

Cutting force components:

,sin

,

)II()II()II()II(

)II()II()II()II(

r npnsf z

cpcsc y

κ l k Ak F F

l k Ak F F

.cos)II()II()II()II( r npns p x κ l k Ak F F

8

, ,generated in regions (I) and (II):


qqq ,,,




Case 2. Cutting conditions: a p ≤ r ε (1 – cos κ r )

The uncut chip area for this case is again divided into two regions.

f aar

ar ζ

p pε

pε

22

2

arctan180

9ε

pε

r

ar ζ

arcsin1803


22)II( tan

2

ζ ζ h A




For a given k s, shearing and ploughing coefficients are usually located in the

following intervals:

,2,08,0 scs k k

,35,06,0

,04,005,0

,,,

npcp

csnp

csns

k k

k k

where the actual values ma in eneral de end on the local eometr of

cutting edge cross section (normal rake angle γ n, inclination angle λs, tool nose

radius r ε and other details) and on the actual thermo-mechanical conditions at

the chip.

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3. EXPERIMENTAL VALIDATION

The instantaneous cutting forces predicted by the model have beencompared to cutting force signals measured during the turning operation.

The laboratory experiments:

The laboratory experiments

-"Georg Fisher NDM-16" lathe

-KISTLER 9257A dynamometer

-instantaneous cutting forces F c , F f and F p-were measured during the turning

-operation

-LabVIEW software

-wor p ece ma er a : an e

-SPK-DDJNL 3225P15 tool holder with the

-Sandvik Coromant DNMG 150608 PM4025

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- -tool geometry

γ n λs κ r r ε


17 -8 93 0,8 mm




The feed and the depth of cut were varied in order to compare the experimentaland estimated cutting forces on a larger variety of conditions.

Experimental results and model validation

Cutting parametersDynamometer

forcesEstimated forces Percentage error

v c m/min f mm a p

mm F c N F f N F pN F c

N F f N F pN F c % F f % F p%

1. 400 0,10 0,8 222,2 102,0 123,3 190,5 106,3 93,5 14,26 -4,19 24,22

2. 400 0,15 0,8 306,0 131,8 163,3 273,9 130,7 113,0 10,50 0,84 30,76

3. 400 0,20 0,8 372,7 156,2 199,9 361,6 155,6 134,2 2,97 0,42 32,89

4. 400 0,10 1,2 337,9 191,1 149,8 274,8 164,8 90,5 18,67 13,76 39,59

5. 400 0,15 1,2 435,6 208,5 171,7 394,9 203,9 109,3 9,34 2,24 36,32

6. 400 0,20 1,2 492,9 203,6 186,0 519,7 243,6 129,7 -5,42 -19,65 30,27

, - , ,

Analytical cutting forces were calculated by applying the model coefficients,

which were estimated in [3] and are similar to values reported in other

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Coefficient Value

k cs 1809 N/mm2

publications and technical reports for Ck45.


k cp 28,47 N/mm

k Ns 723,1 N/mm2

k Np 73,51 N/mm




There is a good agreement between the

experimental and predicted cutting force

.

Back force F p -considerably underestimated

The current model coefficients are not

ade uate for re resentin all the force

components at the same time with good

accuracy.

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Predicted vs. measured forces



4. CONCLUSION

A simple semi-empirical approach to the modelling of cutting force, which is

based on the shearing and ploughing theory, is proposed and experimentally

validated for a turning operation.

Estimated cutting force components have been compared to measured onesand their good agreement was observed.

The comparison between the predicted and measured cutting force components

ver y e mo e rea ness or e cu ng orce es ma ons ur ng a rea urn ng

operation.

ur er n eres : o nc u e e n uence o oo wear n e presen e mo e .

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5. ACKNOWLEDGEMENT

University of Rijeka, Croatia, contract. . . . .

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REFERENCES

[1] Prosperi, F., 2014, Manufacturing of high precision mechanical

components, Doctorate Thesis, University of Udine.

, ., ,

Mechanics, Machine Tool Vibrations, and CNC Design,

Cambridge University Press., ., , ., , ., , ., ,

of cutting forces and cutting conditions in complex turning

operations, 12th International Scientific Conference on

-, , . .

[4] Totis, G., Sortino, M., 2011, Development of a modular dynamometer for triaxial cutting force measurement in turning,

International Journal of Machine Tools & Manufacture, Vol. 51,

pp. 34-42.

[5] ISO Standard 3685, 1993, Tool Life Testing with Single-Point

Turning Tools, pp. 1-48.

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[6] Totis, G., Sortino, M., 2014, Robust Analysis of Stability in

Internal Turning, Procedia Engineering, Vol. 69, pp. 1306-1315.




Thank you for your attention!!!

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Simple Shearing and Ploughing Cutting Force Model In Turning Operation with Nose Radius Tool