1 Energy balance with mechanical actions measurement during

by its angle φand its thickness h1 (Figure 1). ... respectively the velocity and angular vectors of the workpiece compared to the tool. Ω. Vf ... two acquisition cards.
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1 Energy balance with mechanical actions measurement during a turning process Ph. Darnis Laboratoire de Génie Mécanique IUT A, Domaine Universitaire 33405 Talence Cedex. E-mail: [email protected]

O. Cahuc Laboratoire de Mécanique Physique UMR CNRS 5469, Université Bordeaux 1 351 cours de la libération, 33405 Talence Cedex. E-mail: [email protected]

Y. Couétard Laboratoire de Mécanique Physique UMR CNRS 5469, Université Bordeaux 1 351 cours de la libération, 33405 Talence Cedex. E-mail: [email protected]

ABSTRACT : In the orthogonal, oblique, then three-dimensional cut, the assumption of punctual contact between the tool and the workpiece often resulted in considering only the efforts according to the three principal directions [MER 45],[ALB 60]. Work presented disregards these assumption and confirms the existence of moments around the three principal directions through measurements of the mechanical actions during an operation of turning. The experimental principle used reveals through energy assessment the participation of the various components of the efforts and moments in the power consumed during a traditional operation of turning and hard turning operation.

KEY-WORDS : ENERGY BALANCE – TURNING – FORCES –MOMENTS - MEASUREMENT

1

Introduction

Predictive models of the cut are developed since the Forties. For a long time and in order to determine the various parameters relating to the cutting phenomenon of materials, works were limited to the orthogonal cut and more particularly to the turning operations. Merchant [MER 45-2] has developed the first two-dimensional model of cut . This model has been improved by Albrecht [ALB 60] by introducing the concept of edge acuity caused by wear of the tool or during the sharpening of the tool. More sophisticated thermo-mechanical models taking into account heat generation phenomena have then been developed [LEE 51][OXL 76][GIL 82][JOY 94], but in all cases, the workpiece/tool contact is considered as a punctual contact. Thus, it leads to consider only the three forces in the three principal directions in term of mechanical actions. Today's, numerically controlled machine have controlled axes which allow to carry out complex forms. So the cases of orthogonal cut are very rare and it is necessary to talk today about three-dimensional cut. Predictive models of three-dimensional cut have already been presented by Moufki [MOU 98], Stephenson [STE 88] and Toulouse [TOU 98]. Some of these models keep the assumptions of punctual contact between the tool and the workpiece. However, this assumption is strongly blamed because the observation of the cutting phenomenon shows that the tool/workpiece contact being itself on a non-negligible zone. So, it is necessary to take into account all the components of the mechanical actions between the workpiece and the tool. 2

Cutting Process Phenomenology Y

l : Chip thickness B γ: Rake angle

Shearing line

Tool A f : Feed rate

α : Clearance angle

Φ O

X

Vc

Figure 1. Geometrical and kinematics parameters

In machining and according to displacement speeds, selected trajectories and material hardness, a chip is created, coming up from the workpiece at the contact between workpiece and tool. In the case of turning, the main geometrical and kinematics parameters are presented in Figure 1. The analysis of the tool/workpiece/chip interfaces shows the existence of four principal zones (see Figure 2).

Chip 3

Tool

P M

Q

2

B E C

N

Workpiece

1

4

Figure 2. Main zones characterizing cutting process 2.1

Dead zone ¬

The material is divided into two parts. One will constitute the new outer surface of the workpiece and the other will be the chip. Here, strain speed is so important that the reaction is exothermic. The matter is completely plasticized in this zone. The matter is chased because tools always have a certain acuity coming either from their natural geometrical form due to the sharpening or from the tool wear. According to Albrecht [ALB 60], the metal workpiece located along BE (Figure 2) is chased in the tool whereas the workpiece located along EC is chased in the workpiece. 2.2

Primary shear zone-

Primary shear zone coincides with OA (Figure 1). The observed slip lines show that machined material is subjected to shear stress [JOH 54]. This is a slip plastic plane where the chip is formed. This plane is characterized by its angle φ and its thickness h1 (Figure 1). The variation of the cutting speed vector direction induces this shearing. In this study the material is homogeneous and isotropic, with a Von Mises plastic threshold material and a plastic incompressibility assumption is retained [WAS 68]. The line MN (Figure 2) denotes that the elastic limit is reached whereas the end of the plastic flow PQ becomes a solid flow. These phenomena generate strain rate

Vc (usually closed to 105s-1). Moreover, shearing strains f are very largely higher than 50% involving a complete plasticization of material.

approximated by the ratio

2.3

Secondary shear zone®

Kato [KAT 72] has found that this zone is a slip zone with intense friction between chip and tool Microscopic analyses showed the existence of slip strips called shearing strips [JOH 54] Generally, we consider that, in the secondary shear zone, strains are quite higher than 200 or 300% [HAS 80]. However with these values work hardening will be saturated as soon as a strain of 100% is reached. We suppose that segment OC is the seat of a connection which makes it possible to transmit to the tool a pure couple which comes from a constant distribution m of stress torque [TOU 98] along OC in the Z direction (see Figure 3). This assumption is based on the following report : any material can be comparable according to the scale of observation to a material of COSSERAT [STO 74], [HJA 78], [SAL 88] . We consider that the microstructure of material can then transmit stress torque. The stress continuity in O allows to determine σOB from σOA . Then, shearing is constant and equal to σ OB on segment OC and decreases to be cancelled in B.

Chip Y’ l

σΟΒ

P (t)

z Y

t

B

pI

C

A

Y σΟΑ

X’

Tool

m φ− γ c pO

Z'

O

K Workpiece

Figure 3. Stress distribution along KOB

2.4

Principal clearance zone ¯

In this zone, a penetration of the tool in the workpiece (zone IJK, Figure 3) is considered ant it is supposed that the material remains in an elastic state [TOU 98]. Thus, the workpiece is subjected to an elastic state of stress in IJK zone (Figure 4). Stresses (given from hydrostatic pressure) and shear stresses in I can be taken equal to those in O. Then, the pressure distribution along IK will be considered linear and decreasing to cancel each other in K [JOH 54], [JOH 58], [JOH 71]. Moreover, this distribution is supposed to be constant in the depth of cut direction.

Chip

Tool

Shear zones O

K

Ra

I

J

Workpiece L’

L

Figure 4. Principal clearance zone model 3

Mechanical assessment

During a turning operation, the energy provided to the workpiece by the turning machine can be quantified by: A power part provided to the spindle, A power part provided to the mobile head-stock (longitudinal in slide lathing). If all of the tool mechanical actions on the workpiece are considered, the complete mathematical expression of the mechanical power is defined by: PC = F ⋅V + M ⋅Ω

where

r M = MX

PC

is

MY

MZ

the

consumed

[1] power.

r F = FX

FY

FZ

and

are respectively the forces and moments resulting vectors

r r from the tool on the workpiece. V = VX VY VZ and Ω = ω X ω Y ω Z are respectively the velocity and angular vectors of the workpiece compared to the tool. Workpiece

Chip

Vf

r D

Ω z

X Tool insert

Z

VcD (Workpiece/Tool) Tool holder

Y

Figure 5. Turning process description. During a slide lathing operation, the only non null components speeds are VY, VZ and ω Z. Calculation of the consumption gives: PC = FY .VY + FZ .VZ + M Z .ω Z

[2]

It is shown in experiments that the part of power consumed by the FZ .VZ term is negligible compared to the others (about 2%). Then the second stage of the study consists in determining the spindle power PE which can be expressed by :

PE = ω S .C S

[3]

where ω S and CS are respectively the spindle speed and the torque provided to the workpiece by the spindle. If the workpiece/tool system is considered into steady state, if the power consumed by the feed is neglected and according to the conservation energy principle, the balance of the powers can be expressed by:

PC = PE

[4]

Torque-meter/tachymeter

Turning machine motor

PE = ω S .C S

1

Workpiece

Instrumented tool

2

6 components dynamometer

3

PC = FY .VY + M Z .ω Z

Figure 6. Power balance (energy conservation principle) in the turning process. The measurement of the various parameters (speed, forces and moments) allows to check the energy balance of the system in steady state. 4

Experimental procedure As it is necessary to exactly identify the spindle speed and the torque provided to the workpiece, an instrumented torque-meter/tachymeter • (see Figure 6) has been designed in order to deduce the power involved during slide lathing operation from experimental measurements. On the tool, it is necessary to measure the forces and the moments related to the power assessment. A tool holder ‚ allowing two components of force (FY and FZ) and 2 components of moment (MY and MZ) to be measured has been designed. The instrumented tool holder is fixed on the table saddle on which is interposed a 6 components dynamometer developed by Couétard [COU 93]. This dynamometer is able to measure independently the three components of force and the three components of moment ƒ. 4.1

Description The test workpiece to be machined is maintained in position between the torque-meter and the mobile head-stock (see Figure 7). For reasons of confidentiality, the torque-meter is not represented on this figure. An electromagnetic system allows us to recover information on the torque provided by the spindle and the real rotation speed of this one. The torque-meter, the tool and the dynamometer are connected to two PC via two acquisition cards.

Torque-meter Workpiece

Instrumented tool

6 components dynamometer Dyn 6

Figure 7. Operative workpiece of the breadboard assembly Thus, the breadboard assembly allows the simultaneous acquisition of : Äthe torque transmitted by the spindle test workpiece, Ä the 3 efforts and the 3 moments transmitted to the tip of the tool by the 6 components dynamometer, Äthe 2 efforts and the 2 moments transmitted to the instrumented tool, Ä the spindle speed. 5 Results 5.1 Conditions of tests and results obtained A first test in hard turning was carried out according to described conditions below: Treated steel XC48 (case hardening) workpiece test (hardness : 65 HRc) Depth of cut: a p = 1.06 mm Cutting speed: Vc = 142.35 m / mn Machined diameter: φext = 83.6 mm Feed rate : f = 0.1 mm / rev Insert : TNMA 16 04 08 CBN Insert Figure 8 shows forces and moments obtained during this test. The results obtained in term of consumed power are described in Table 1. The residue is calculated by taking as reference the spindle power and can be defined by : P − PE * 100 Residue (% )= C [5] PE

Table 2 highlights the participation of the moments (at the tip of the tool D) in the energy balance.

Dynamometer Dyn 6 Tool Torque-meter

FY(N) M z ,D ( Nm ) 392.4 -3.02 370

-2.84 -12.36 (Torque)

PE(W)

PC(W) 759.8

Residue (%) 8.14

703.3

0.09

-702.6

Table 1. Powers related to a hard turning operation

Dynamometer - Dyn 6 Tool

% (P (M Z ) PE )*100

P(FY)

P(MZ)

931.1 862.3

-171.24 -159.06

24.4 22.6

Table 2. Participation of the moments in the energy balance Forces (N)

Instrumented Tool and Dyn6 Forces

450 400 350 300

Tool Fy Dyn 6 Fy

250 200 150 100 50

Time

0 0

a)

0.1

0.2

0.3

0.4

0.5

0.6

Instrumented Tool and Dyn6 Moments Moments (Nm) 0

0.2

0.4

0.6

Time -1 -2 -3 -4 -5

Tool Mz,D Dyn 6 Mz,D

-6

b) Figure 8 a & b. Experimental forces and moments results for the Table 1 example (Dyn 6 and instrumented tool).

Other tests were carried out in traditional turning but by using two types of inserts: (TNMA 16 04 08 CBN Insert and Carbide TNMG 16 04 08 23). The workpiece is then made of XC38 steel. For all the tests, the feed rate has been fixed to 0.1mm/rev. The test results are indexed respectively in Table 3 and Table 4. N° 1 2 3 4

Ap PC(Dyn6) PC(tool) PE Rd Rt (%) (P (M ) P )*100 (mm) (%) (%) 1.06 603 682.81 -714.4 15.6 4.4 12.3 1.25 744.6 821.7 -818.2 9 0.4 16.6 1.25 768.9 855.6 -818.2 6 4.6 22.1 1.33 809.6 866.9 -875.1 7.5 0.9 15.4 Table 3 . Energy balance on a XC38 test workpiece for a TNMA 16 04 08 CBN insert Z

E

The quantities Rd and Rt respectively represent the power residues for the six components dynamometer and the tool. N° 7 8

Ap PC(Dyn6) PC(tool) PE Rd Rt (%) (P (M ) P )*100 (mm) (%) (%) 1.14 451.1 633.1 537.1 16 17.9 11.6 1.29 645.8 749.9 730.6 11.6 2.64 15.2 Table 4 . Energy balance on a XC38 test workpiece for a carbide TNMG 16 04 08 23 insert. Z

E

5.2

Discussion The results obtained show that: The energy assessment is balanced with an accuracy ranging between 0% and 4.6% in the case of an operation of hard turning. There is an excellent correlation between the results obtained by the tool and the torque-meter for all the parameters of cut. In all cases, the energy assessment can be balanced only if moment Mz is taken into account. According to the cutting conditions used, the participation of the moments in the energy assessment in term of power varies from 10% to 23%. According to the cutting conditions used during the tests, moment Mz is driving (it contributes to the cut). The results obtained are correlated jointly by the instrumented tool and the six components dynamometer. 6

Conclusions An energy balance with mechanical action measurements during a turning process has been established. Efforts and moments to the tip of the tool measurements have been made by to different systems. The existence of moments in the cutting process has been shown during an operation of slide lathing in hard turning.

The tests have pointed out that the power consumed by the moment MZ is considerable and it can reasonably think similar results during raising in turning or in milling could be obtained. The advent of machine such as high speed milling machines shows that it is necessary to take in account the components of moments because their importance in the power assessment is directly dependent on workpiece rotation speed in turning or the spindle speed in milling. The good dimensioning of a tool, a tool holder or a machine need forces and moments to which they are subjected to be identified. To modelize a cutting process, every predictive models in three dimensional cutting must take into account moments. 7

Bibliography [ALB 60] ALBRECHT, P., "New developments in the theory of metal cutting process. Part I : The ploughing process in metal cutting.", Journal of Engineering for Industry, (ASME), Vol.82, 1, pp. 348-358, 1960. [BAL 2000] BALAJI, A., K., JAWAHIR, I., S., "Variable tool-chip interfacial friction in 2-D and 3-D machining operations", International workshop on friction and flow stress in cutting and forming, ENSAM- PARIS, 2000. [COU 93] COUETARD Y. "Capteur de forces à deux voies et application à la mesure d’un torseur de forces", Brevet français N°93403025.5, 1993. [GIL 82] GILORMINI,P., "Contribution à la modélisation de la formation du copeau en usinage des métaux", Thèse à l' Ecole Nationale Supérieure des Mines de Paris, 1982. [HAS 80] HASTING, W., F., MATHEW, P., OXLEY, P., L., B., "A machining theory for predicting chip geometry, cutting forces etc.. from work material properties and cutting conditions", Proceeding of the Royal Society of London, Vol. 371, pp. 569-587, 1980. [HJA 78] HJALMAR, S., "Non-linear micropolar theory", The Royal Institute of Technology, Stockholm, Sweden, 1978. [JOY 94] JOYOT., P, "Modélisation numérique et expérimentale de l’enlèvement de matière (application à la coupe orthogonale)", Thèse Université Bordeaux 1 (ENI Tarbes), 1994. [JOH 54] JOHNSON, K., L., "Surface Interaction Between Elastically Loaded Bodies Under Tangential Forces", Proceeding of the Royal Society of London, A Vol. 230, plate 13, pp. 531-548., 1954 [JOH 58] JOHNSON, K., L.,M.,A., PH., D., "A note on the adhesion of elastic solids", British Journal of Applied Physics, Vol. 9, pp. 199-200., May 1958 [JOH 71] JOHNSON, K., KENDALL, K., ROBERTS, A., D., "Surface energy and the contact of elastic solids", Proceeding of the Royal Society of London, A Vol. 324, pp. 301-313., 1971

[KAT 72] KATO, S., YAMAGUSHI, K., YAMADA, M., "Stress distribution at the interface between tool and chip in machining", Journal of Engineering for industry, pp. 683-689, 1972. [LEE 51] LEE, E.,H., SCHAFFER,B.,W., "The theory of plasticity applied to the problem of machining", USA American Society of Mechanical Engineers, Journal of Applied Mechanics, Vol. 18, pp. 405-413 , 1951. [MER 45] MERCHANT, E., "Mechanics of the metal cutting process. I. Orthogonal cutting and a type 2 chip", Journal of Applied Physics, Vol. 16 pp267-275, May 1945. [MER 45-2] MERCHANT, E., "Mechanics of the metal cutting process. II. Plasticity conditions in orthogonal cutting", Journal of Applied Physics, Vol. 16 pp318-324, June 1945. [MOU 98] MOUFKI, A., RAUSH, M., DUDZINSKI, D.,MOLINARI, A., "Modélisation de la coupe oblique, calcul des efforts et détermination de l'écoulement du copeau,( application au chariotage et au fraisage de face)", Bulletin du Cercle d'Etudes des Métaux pp. 10.1 10.8, 1998 [OXL 76] OXLEY P. L. B., HASTING W. F., "Minimum work as possible criterion for determining the frictional conditions at the tool interface machining", Philosophical Transactions of the Royal Society of London, Vol. 282, A 1310, pp. 565-584, 1976. [SAL 88] SALENCON, "Mécanique des milieux continus", Paris, Ellipse, 1988, Tome. 1. [STE 88] STEPHENSON, D., A., WU, S., M., "Computer Models for the mechanics of three dimensional cutting process. Part I : Theory and numerical method", Journal of Engineering for Industry ASME , Vol. 110, pp. 32-37, 1988. [STO 74] STOKANOVIC, R., "Non linear micropolar elasticity", CISM courses and lectures No. 151, Springer Verlag, Wien-New-York, 1974. [TOU 98] TOULOUSE, D. "Contribution à la modélisation et à la métrologie de la coupe dans le cas d'un usinage tridimensionnel."161 p. – Thèse Université Bordeaux 1, 1998. [WAS 68] WASHIZU, K., "Variational methods in elasticity and plasticity", Pergamon Press , 1968.