Some Basic Relationships for Identification of the Machining Processes

Some Basic Relationships for Identification of the Machining Processes (*) Janez Peklenik (1). Andrej J e r e l e ; D e p a r t m e n t of Control a n d Manufacturing S y s t e m s , University of Ljubljana Received on January 31,1992

Research into tlie machining processes was since E.WTaylor g e y intensive, t y i n g to understand and describe tlie process as n complex object of control. its modelling ions based predominatly on tlie deterministic approaclz, and well known lnzos of classical plzysics. This contribution reports on some resrarch results, where the process represents a part of the close loop machining systems and is described as a propagating and frictional surface interface. Its identification is based on stochastic inputs nnd outputs, related to the structure of the material. A n attempt is made to develop the process transferfunction, determining the gain factors. the process frequency bandruidtlzs and the damping factors in relation to the cutting speeds and structural chnrncteristics of the materials. Key Words: On-line process identification, transfer function, propagating surface interface

1.

SOME PROBLEMS IN MODELLING A MANUFACTURING PROCESS

The formal description of a manufacturing process such as cutting, grinding, spark erosion etc. represents a problem of considerable importance and attention. The reason is that the control and optimisation of a machining system depends decesivly upon the ability, to estimate the transfer characteristics of the manufacturing process. The requirement that a reliable estimate should be accomplished on line and in a very short time makes necessary, to develop a new approach for process identification. A manufacturing process is a complex object which can be modelled by two different ways: 0

deterministic modelling;

modelling of a process as a complex object of control. A brief review will indicate the difference in approach and the necessity to find new ways in order to establish more accurate modelling methods.

0

2.

THE DETERMINISTIC MODELLING OF MANUFACTURING PROCESSES

The majority of process models published, is based on the views that a process can be described by theoretical methods of classical physics, elastic plastic deformation and fracture theory, cristallography and others.

models have been inaccurate and of limited value due to the complexity of the object and the limitation of the approximations applied. However it should be stressed that this deterministic approach helped to answer many questions and contribute considerable in understanding the basic principles of the material removal.

3.

MODELLING OF A MACHINING SYSTEM

The objective of the research into the machining processes must be focused into the development of reliable methods for a n on-line identification, following the optimisation and finally, the adaptive control of the process. This means that the search for solution must include the entire machining system and not only the cutting process, as a separate entity. The idea to consider the machining process as a black box within the closed loop of the machining system, measuring selected input and output signals and correlating them was proposed already in 1964 by Peklenik for grinding process. The first attempt of modelling the cutting process in this way followed in 1967 by the same author. Further work in this direction was possible in the last years, due to the developments in sensing and data processing technology. Namely, the on-line process identification requires firstly, highly sensitive transducers with natural frequencies exceeding the expected dislocation frequencies and secondly, very fast data processing equipment, capable of processing a large amount of data obtained from the input/output signals and correlating them accordingly.

Already F.W.Taylor (1907) realized that the description of the machinability of a material is possible only, if one establish an empirical relationship between the tool life T and cutting process parameters v and /. The result of his research was a deterministic tool life model based on empirically established values of the exponents. Many researchers followed this approach, providing perhaps more detailed insight into the machining process itself, and trying to explain the material removal mechanism, resulting finally in an analytical model of the manufacturing process.

The second reason for considering the entire machining system, while identifying the process, is that the inputs and the outputs into the process depend considerably upon the machine tool and its dynamical and statical properties. And last but not least, the optimisation of the process followed the on-line identification is related to the adaption of the process conditions and can not be separated from the machine tool itself.

A major impact in this field was accomplished by M.E.Merchant (1945) developing the first shear plane model of the cutting process. This work was instrumental for an intensive research and further developments in process modelling, considering in addition to the classical mechanics, also the behaviour of the material under load, and in particular the dislocation theory.

Figure 1 yields the basic elements and relations of a close loop machining system in form of a block diagram. The following analysis will provide an insight into this complex object of control.

An excellent and comprehensive review of the cutting process models is given by M.C.Shaw /1984/. The models defining the structure of a process by shear angle, forces, wear, temperature etc. are structured as objects with predictable static and dynamic behaviours. In general these

Annals of the CIRP Vol. 41/1/1992

Description of the Machining System

The inputs. 0

0

the blank A is characterized by the structure and physicalchemical properties of the material, the shape and dimensions of the blank, the state of the surface etc. These properties are described by a set { A, );The material flow at the input is continuous; the tool 8, described by the cutting material properties, geometry and other parameters is specified by a set { Bi I ;

155

Figure I

Block dingram ofn machining system

The total energy Ul(tj required for the implementation of the cutting process is defined a s follows (Peklenik, Mosedale /1967/)

Udt) = UT(t)+ Uo(0

(1)

&(t)

energy time series requrredfor iniplententntion of the propagahng surface interface: Uo(t) - energy time series requiredjor implemmtntion of the frictional surface intqface.

The specification of the scales in cutting reveals that the system elements A and B define the macro level, both surface interfaces should, however, be observed on the micro level. T h e outputs. 0

0

a set of process conditions {CiI = (v,,J , a, Pi) under which the 3 material removal V,, Imm / s , take place, is provided by the machine tool MT. The power P, required for the process execution, is delivered on the blank A and the tool B;

The cutting process transforms the blank with the set of properties ( A ; ) into a workpiece with the set of properties [Aol, representing the major output and the objective, set by the subject.

the input energy Ui(t), capable of doing work (material removing, overcoming the friction between A and B etc.) is presented as a sum of $:) and X$ and considered as the inpuf energy time series, depending upon the input elements already discussed;

The secondary outputs are: the mass MA removed from the blank, the mass MB removed from the tool B, due to the wear in the firctional surface interface, changing the set of properties { Bo I, and the heat Q generated during the material removal in both surface interfaces.

the machine tool MT in the feedback loop provides by the positioning subsystem P, the relative position between the blank A a n d the tool 8, determining the depth of cut a , as the information I, requires. The kinematic subsystem K realises the cutting speed vi and the feedrates fi according the instructions Ik. The power Pi, necessary for the process implementation, is supplied by a motor, forming a part of the energy subsystem E. The power transmission to A and B is accomplished via positioning and kinematic mechanisms. The set of inputs constitutes the conditions for the implementation of the material volume V,, Vi to be removed in a unit of time, in form of a chip, and the generation of a new surface, forming the workpiece.

0

The interfacing of the elements A and B, under the conditions provided by the machine tool MT, generates two surface interfaces: the propagating surface interface, and the frictional surface interface, as proposed by Peklenik, Zun /1985/. The propagating surface interface is responsible for both parts of the cutting process: the deformation of the material Vi flowing into the transformation zone, and the generation of the out going surface by separation of the chip from the bulk A. In addition it affects also the vibration, tangential to the generaled surface of the workpiece, Figure 2 The frictional surface interface form the bulk A and the tool B on the clearance and rake face and is responsible basically for the tool wear and vibrations perpendicular to the generated work surface. Figure 2 Concept of surface interfaces in cutting DETAIL C

UACRO LEVEL

T h e feedbacks. The dynamics of the cutting process constitutes the feedbacks between the workpiece A, the tool B and the machine tool MT. Two types of feedbacks have been identified due to: 1. the potential energy UtBas a consequence of the elastic deformations between the workpiece A and the tool B; 2. the kinetic energy UfBresulting from the forced translatorial and torsional vibrations of both participants A and B.

The machine tool MT in the feedback loop with its subsystems P, K and E constitutes a close loop machining system, as shown in Figure 1. The external information I, and Ik is used to control manually or automatically the P- or/and K-subsystem of the MT. In conclusion i t should be stated that: 1. the functioning of a machining system is only possible due to a continuous in-flow of material into the process, and a continuous generation of shapes and surfaces of the workpiece A a t the output; 2. the research into the on-line process identification, a s one of the major objectives, has to follow the functioning mechanism, as explained in detail in the presented analysis.

Therefore, the modelling of a cutting process can not be separated from the closed loop mechanism, enabling in the first place the process implementation and secondly, affecting its transfer characteristics { H I . It should also be stressed that the cutting process is basically a complex object of control, characterized by: 0

the lack of formal mathematical description;

0

stochastic properties;

0

non-stationarity;

SEPARATION MOITIOW VI0RATION4L SPEEO IN b U l S AND yJUS

GENERATED SURFACE

i

intolerance to control and

0 I >'

.,'

FRlCTlOW SURFACE INTERFACE

t

ilrl

irreproductibility of measurements. This state of art dictates new approaches in investigating manufacturing processes in general.

156

THE INPUT/OUTPUT CHARACTERISTICS OF THE CUTTING PROCESS AND ITS ESTIMATIONS

4.

and the estimate of the transfer function is expressed as

This research represents a continuation of the investigation for a n on-line identification of the cutting based on inPut/outPut introduced by Peklenik and Peklenikp Mosedale (1967)n the surface interface concept proposed by Peklenik, t u n (1985) and ('1989, initiating also the idea of the energy quanta, related to the Power of the time series U i ( t ) .

4.3 Experimental arrangements In order to obtain the on-line time series U l ( t )and U,(t), a measuring systems was set-up, as shown in Figure 3. The dynamic forces F:d(t) and Fud(t) have been assessed by a two component dynamometer (natural frequency fn = 10 kHz) during cutting of various materials. The shape of the tool exhibits Figure 3. For the estimating of the transfer function H(f) the following arrangements have been made. The cutting speeds are very low Di = 1.21,Z.j and 5 mm/s. The depth of cut n = ;Dc - diameter

4'1 The estimation Of the input/output energy time series Ui(t)/Uo(t)

Figure 3 Measuring system and experimental arrangement

The input energy time series Ul(t), responsible for forming the propagating surface interface, Figure 2, is expressed according Peklenik, Mosedale (1967) as follows

(3)

In order to assess the influence of the structural and mechanical properties of the materials selected for this investigation, representing one of the major input into the process, the effects of speeds and vibrations should be eliminated. The Eq (2) yields

Fz Fzd

Fz vi

+

Fzdt) Vi

(4)

DT

I+

j

I PLOrnR

RECORDER

of the equivalent circle in pm for estimating the grain size of the material. Table 1 yields the results of statistical evaluations of the grain sizes Dc of the materials. The evaluation of the cutting tests on materials shown in Table 1 contains the time series Fzd(t), Fyd(tj and its correlation or/and covariance functions, power spectra and the statistical distribution of the force components.

average cutting force, dynamic component of the cutting force.

The same approximation applies also for the estimate of the output energy U&).

Considering that the input and output speeds are very low, i t can be assumed, that vi = vg. By not considering the average forces Fz and Fv, the fluctuation of the input and output energies can be estimated by measuring and processing the dynamic part of the forces Fzd(t) and Fydft). The speeds v, and vg are assumed to be constant. The Eq (4) and (5) become expressed as estimates Ci(t ) = Ci F z d t )

AMPJFIER

[(q +,

-.--"

'i.,oo

Ui(t)

~

~

-0s

[~ ot )( f y( t )3

i

CHARGE IMR FlER

..,

The output energy time series U,(t) responsible for generating the frictional surface interface is given in a analoguous way a s

U d t ) = Fy( t)

7

_---__

(2)

{-z&zzrp?-

- - - - ---, -- - - - - - - - -- - - - - -

g&\:zE

OVNRf4OMETERO

3

,

- - - -- -

(6)

Figure 4 yields a measuring and evaluation example for cutting the innoculated cast iron GGG40 (Werkstoffnummer 0.7040). The signals measured in these tests contain random as well as periodic components. In order to assess the accuracy of the estimations of power spectra, (auto-and cross), as well as the coherence functions, it is necessary to determine the number of data sets required. If one accepts an allowable error of 10 % the number of data sets is smaller than ten. Table 1: Sfatisfical parameters of grain sizes D C in prn HIN

STD.DEV.

MAX

MEAN

VARIAN.

3.34 4 8 . 7

23.9

64.9

8.1

11.96 47.1

27.6

46.9

6.85

9.9

39.5

24.7

35.5

5.96

All constituents Pearlite Ferrite

2.25 9.51 2.25

41.17

15.61 22.21 8.9

71.52 41.95

8.46 6.48 3.38

All constituents

8.53 20.7 8.53

Ferrite

________.____.___.._._____________.__ lnnoculated cast iron Pearlite Graphite

........................................................................ Carbon steel (normalized)

and

41.17 19.38

11.64

Carbon steel

The estimates of the power spectra for Ui(f) and U J t ) yield

Pearlite Ferrite

(8)

79.6

28.7

79.6

39.!

198.6 142.6

14.1 11.9

46.1

18.2

36.8

6.1

Carbon steel (spec. heat-treated) 19.8 182.8 203.8 35209. All constituents Pearlite 47.4 t82.8 358.8 21481. 244. 47.4 95.8 19.8 Ferrite

_ _ _ _ . _ _...._.......... .___.____.

187.6 146.6 15.6

Gray cast iron

157

Figure 4 Example o/measurenzent and evaluatron of theforce signal obtained on innoculated cost iron

Fzd(t)

PDF

POWER SPE( 1 .O

r

10.0 r

ml

rms

~

v2 j

Real

I

Rea 1

I

I

v2 1--1 lO.

0.0 0

5.0

S

0

L

11

ji

t

0.0; I 15

I

i

!\I I i I 1

i

v

-3.0

3.0

INNOCULATED CAST IRON =

-8. 0

I

rn

I

I

I

Kd

I

f

4.5 4.4

=

3,73mV2 218,~m

= 12,5Hz

Analysis of t h e experiments

Experimental results

The tests conducted within this investigation yield the results (Jerele 1991) indicating: the relation between the correlation lenght Kd of the cutting force time series Fzd(t) and the cutting speed Vi, Figure 5; the dependance of the process frequency bandwidth 9ffrom the cutting speed u;, Figure 6; the dependance of the average gain Kp(Afl from the cutting speed vi, Figure 7 and Table 2; the correlation between the average gain of amplification

Kp(wand specific force F p ~ z= PA -

PA

expected value of

the cristal surface of the cutting cross section area), Figure 8; the effect of cutting speed

Vi

on damping factor f3, Figure 9.

Figure 5 Correlation lenght of the autocovariance function in relation to the cutting speed o f o r various nznterials

The objective of the analysis is to gain some basic understanding of how the structure of the materials affects the factors constituting the transfer characteristics of cutting.

The characteristic frequences of the autocovariance functions increase with the cutting speed. The increase is, however, not proportional. The explanation yields the measurements, indicating that the disloctions in the cristal, due to the external stresses, cause the movements of parts of the cristal within an order of magnitude of the lattice constant. This is also the reason that the characteristic frequencies, related to the distribution of the grain sizes, in correlation functions and power spectra d o not appear very clearly. The influence of the microstructure which is evident in the force signal &d(t), is decesively affecting the propagating interface. The results of the measurements of Fyd(f) reveal that the output energy &(t) = c,+,d(t) predominantly affects the frictional surface interface. The correlation lenght K d of the autocovariance functions remain almost constant as function of cutting speed, Figure 5. Figure 6 Relation between the process frequency bandwidth Af and cutting speed v f o r various materials

40

--

I

1

N

/

i

10

0 :

-

0

. Fe 42

A

+

- G G 40 M.6040l - GGG 40 #3.7040/

v

0

x

- Ck 45 /1.1191/normalized - Ck 45 /1.1191/ . Ck 45 /1.1191/ qec.hea1-treated

6

v ( mm/s 1

0

. Fe

t

- GG 40 m.6040/

0

158

__

3

2

1

42

GGG 40

7040/

A

- Ck 45 H.11911 normalized

x

. Ck 45

v

/I 11911

. Ck 45 11.11911 spec heal-treated

5

:

Table 2

Average gain factors arid specific forces for steel Ck 45 (WN 1 . 11 91 j

[45(n)i

278

Ck45

108

CkGW

11 8

76

’-

1

281 117

145

76

261

;1

138

77

~

124 04

Figure 9 Duntping koeflicient p in relation to the cutting speed

0961

10:

0761

077

047‘

0581

067

--

34

-

35

-

3.7

i

(.10-~ N I ~ ~ * )

Figure 7 Average values of the KPly) as function of the cutting speed and the materials

VI

-

oa 12

I?

2

1 ~

0 3

3 v(rnrnis1

J

.

4

’

- Ck 45 /1.11911 . Ck 45 11.11911 specheat-lreated - Ck 45 /1.11911 normalized

the distruction of the grain. Figure 8 yields the relation between the average gain and the FP,+ explaining the reasons for the increase of the gain with the physical properties of the grains. The estimation of the damping factor !3, assessed by the impulse response function

0 - Fe 42 + . GG 40 10.6040/ 0 . GGG 40 0.7O40/

A

. Ck

45 11.11911 normalized

- Ck 45 11.11911 v - Ck 45 11.11911spec.heat-treated I

in relation to the cutting speed, reveals almost constant values of p, Figure 9. The influence of the material structure on dampintr is, o n the other hand, considerable.

This can be interpreted with the homogenity of the microstructure and mechanical properties of the grains. The frequency bandwidth of the process increases with the cutting speed almost proportional, Figure 6. These are in relation to the spatial fluctuation of the microstructural properties of the material under investigation. In order to assess properly the frequency bandwidth, the mherance function was constantly determined. The measurement of a/ are correct, if coherance function is approx. equal one. The effect of material structure on frequency bandwidth is evident. The average gain Kp (Af) is little affected by the cutting speed. The material structure, however, influences strongly this parameter of the transfer function as Figure 7 and Table 2 indicate. This can be explained by the specific force, necessary for Figure 8 Relation between the average gain factor and specijc cristalforce

l2 1.1

1

/ -

I

-P 0 9 1 07

1

0.4

rn 0 0

- Ck 45 11.11911 normalized

- Ck 45 i1.11911

. Ck 45 11.11911 specheal-treated

”’

, ,

5.

CONCLUSIONS

In this investigation the cutting process is described by the concept as a propagating and frictional surface interface, which can formaly be described by the Output/Input relation in form of the transfer function estimates. In order to obtain the elements, constituting the formal expression of a transfer function, a number of reference tests have been conducted in order to assess the influence of the material structure and the cutting speed on the gain factor, frequency bandwidth and damping. The results indicate the viability of the surface interface concept and the input/output approach in developing the on-line process identification a s basis for the process optimisation and adaptive control. The reference tests helped to understand the physics of the process, which is a prerequisite for mapping the results in to the real situations.

REFERENCES Bendat, 1.. Piersol A.. 1980. Engineering Applications of Correlntion and Spectral Analysis, John Wiley and Sons Ltd, New York. DIN 66141. 1974. Jerele, A., 7991, Some Fundamentals of On-Line ldentficntion of the Cutting and Wenr Processes, M.Sc.Thesis, Depnrtrnent of Control und Manufacturing Systems, University of Ljubljnnrr. Merchant, M . E., 1945, Mechanics of the Mefnl Cutting Process. lourn. AppLPhysics 16, No.5. pp.267-275, pp.318-324. Peklenik, J., 1964, Contribution to the Correlation Theoryfor the Grinding Process, Trans.ASME 1964, Vol.86, pp.97-106. Peklenik, J., Mosedale T., 1967, A Statistical Analysis of the Cutting System Based on an Energy Prinnple, Pmc. of the 8th International MTDR Conference, Manchestq Pergnnm Press-Oxford, New York 1968, pp.209-231. Pew~l*1..tun, I., 1985,SUW [nie$ice in Cuttiiig fmxss, roc c$f/w Intemah o d Gn$ of h4etals, New Grimn$ Pub. Amerium Soclrtyfir Metals, pp.2%2. Peklenik I., 1987, S u r w Interlhcp Concept in MmujiWuring Pmcesses, CIRPPw. on Mnn~fachiringSystems, Vd.16, N0.2, ~p.161-174. Shaw,M.C.. 1984 Metal Cutting Principles, CaMemn Press, O.+rd. (10) Tuyfor, F.W., 1907, Trans. Am.Soc.MEch.Engrs. (28). pp.31.

159