Prediction of Thrust and Torque in Drilling

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PREDICTION OF THRUST AND TORQUE IN DRILLINGUSING CONVENTIONAL AND FEEDFORWARD NEURAL

NETWORKS

Vishy Karr i, Tossapol Kiatcharoenpol

School of Engineer ing, PO Box. 252-65, University of Tasmania, Australi a 7001

Abstract

Drilling performance prediction, using traditionalmechanics of cutting approach, is based on the extension of

three-dimensional oblique cutting theory. The quantitativereliability of such conventional models depend on a

numerous number process variables and quantitativeaccuracy of the data bank for a given work material. Thecomplexity of such models is increased when inevitable

eccentricity and drill deflections are incorporated into theanalysis. In this paper, using a novel neural networkarchitecture that optimises the output layer, the thrust and

torque in drilling operation are carried out. A set ofcomprehensive drilling tests is carried out to train and testthe architecture. It has been shown that the percentage

deviations of drilling predictions using the neural networkarchitecture is -0.56%, and 1.03% for thrust and torquecompared to 4.20% and 10.25% using traditional

mechanics of cutting approach.

Keywords : Drilling Performance Prediction, Neural

Networks

1. Introduction

Traditional mechanics of cutting approach and empiricalapproaches have been used for drilling performance

prediction, in the past. Artificial neural networks are used inthe recent year for cutting tool wear estimation, tool

condition monitoring, vibration control and surface finishdetection [12]. While these predictions are comparable with

conventional models, simultaneous estimation of more thanone performance feature is quite often necessary for on-linecontrol of a machining process. The conventional mechanicsof cutting models are efficient to the extent of predicting

individual performance but cannot estimate differentperformance features simultaneously. A brief descriptionof unified mechanics of cutting and empirical approaches to

drilling performance prediction are carried out in thi s workbefore the capabilities of neural network models are

presented.

2. Unified mechanics of cuttinganalysis and empirical models fordrilling performance

The thin shear zone (plane) analysis for drilling [1-3,6,10,11,16,18,19,20,22] uses elemental technique adoptedto allow for changes in tool geometry and cutting speed withradius for different points on the lips and chisel edge. Thegeometry for general-purpose drills is shown in fig.1. Figure1 shows basic geometry and variables involved in a general-

purpose drill. The cutting action in the lip region was treated

as a number of elemental classical oblique cutting elements

[14,20], each with different normal rake angle n, inclinationangle i and resultant cutting velocity Vw depending on the

mean radius of the element as shown in fig.2.

It is usual practice when predicting the forces and torque in

drilling to use the oblique model to represent the lip edgeand the orthogonal model to represent the chisel edge. Hence

the chisel edge can be modelled in two dimensions but theadded complexity of three dimensions is required for the lip

region. The angles nand i were found from the commonly

specified drill pint features 2p, 2W, oand D and the meanradius of the element r.

The elemental deformation forces dFp, dFQand dFR(fig.2)were then evaluated from the classical oblique cuttingequations [13,20] given the elemental area of cut dA and the

basic cutting data such as shear stress and the chip lengthratio rl. The edge forces [13] were also evaluated to give the

total force on each element. The forces thus found were usedto establish the elemental thrust and torque. Summing up theelemental values of thrust and torque, the total thrust and

torque generated by the lips during drilling were thenpredicted [13].

The cutting edge in the chisel edge region was also dividedinto a number of elements. The chisel edge wasapproximated to a straight line perpendicular to the drill axis

and the elemental static chisel edge normal rake angles nc[13,20] were treated as constant for all points on the chiseledge and numerically equal to the half of the wedge angle at

the chisel edge at the drill dead centre. The chisel edge

wedge angle could be obtained from measurement of thedrill, for the unspecified flank shape of a general-purpose

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drill. Due to the high negative rake angles and low cutting

velocities encountered at the chisel edge, a discontinuousorthogonal cutting model was applied [14,20].

Figure 1. Geometry and shape of general purpose drill

The elemental chisel edge length dLc, the mean radius r,dynamic angles and cut thickness at each element for theselected number of elements could be obtained, hence the

elemental thrust and torque on the chisel edge could bedetermined by summation of the elemental thrust and torquevalues. The total thrust and torque on the drill as a whole

were found by summing the corresponding values in the lipand chisel edge regions [4,13,14,17,21].

The thrust and torque predictions using the mechanics of

cutting models were 15% to the experimental values while

machining S1214 free machining steel [14]. While theapproach above seems most promising for thrust and torque

prediction, it should be noted the commonly specified drill

point features 2p, 2W, oand D and r, together with cuttingconditions N and f should be given to predict the thrust andtorque in drilling. The accuracy of the mechanics of cutting

approach depended on these features along with theorthogonal cutting data bank. Therefore the accuracy of thistraditional approach to predictions, was found to be

dependent on the reliable orthogonal cutting data bank, theaccuracy of the edge forces and the reliable estimation of

drilling geometrical features. Neural network modellinginvolved a fewer parameters for the simultaneous prediction

of thrust and torque as discussed below.

Figure 2. Elemental deformation forces in drilling [2]

3. Brief Description of BackPropagation and Optimised Layer byLayer (OLL) Neural NetworkArchitectures

While the specified literature provides adequate theory on

the neural network models studied in this paper, it is usefulhere to consider the basic theory associated with each of

these neural networks with an understanding of the industrialapplication applied. It is important to note that while theobjective of each neural network is to predict the values of

thrust and torque in drilling, the architecture and algorithmsused by each network to achieve this are significantlydifferent. A brief note on the BP and OLL networks is

discussed below.

The standard backpropagation network [5,6,8,15,23,24]comprises 3 layers of processing elements, fully feedforwardconnected. With the sigmoid on the hidden layer as shown in

the figure 3 below, only the basic equations are :

y u zk kj jj

H

==

1

1

zj j

=+

1

1 exp( ) 2

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j ji i

N

w x==

0

3

The Least Mean Square error

( )E y tk kk

M=

=

12

2

1

4

All the data is scaled between 0..1 but it can be scaled

between -1..1 to standardise all the inputs with variousdimensions. The weights wji and ukj are assigned randomnumbers in the range -1..1, and a random pair of input /

output vectors are picked from the training set. The inputvector is fed through the network to get an output vector(feed forward process), this is then compared with the output

vector and an error is found.This error is then passed back through the neural network(back propagation process) to modify the weights using thefollowing equations

u u ukjnew

kjold

kj= + 5

w w wjinew

jiold

ji= + 6The gradient descent optimisation technique is used tocalculate the change in each weight. This is then repeated by

picking another random pair of input / output vectors andcontinuing until the error is at a minimum.

3

2

1

H

0=1..N j=1..H k=1..Mw u

j,i k,j

Input layer Hidden layer Output layer

z

Nx

w41

w4N

w42

z

1

x 2

x1N

z

w

w12

z11

w

y23

2Hu

2122

u

uu

M

y11

u12

u13

u1H

u

1

Figure 3. Multi-Layered Back Propagation Neural

Network

Momentum can be used to decrease times in training and thechance of the network getting stuck in a shallow minimum.This is done by accelerating the convergence of the error but

is not applied in this situation.

The architecture of an OLL network [9], shown in Figure 4,

consists of an input layer, one or more hidden layers and anoutput layer. All input nodes are connected to all hiddennodes through weighted connections, wji, and all hidden

nodes are connected to all output nodes through weightedconnections, Vkj.

VkjWji

.

.

.

.

.

Input Layer

i = 0..M

Ouput Layer

k =1..N

Hidden Layer

= 0..H

.

.

.

.

.

.

x1

x2

xM

y2

y1

yN

f(net1)

f(net2)

f(netH)

o1

o2

oH

o0 = 1x0 = 1V10W10

Figure 4. Basic Structure of an OLL Network [9]

Training Algorithm of OLL with one hidden layer(fig.4.)

Step 1 Initialize weights : set all weights to small randomvalue range(-1,1)

Wji: weight connecting input node ito hidden layer nodejVkj: weight connecting hidden nodejto output layer node k

Set weight factor = 0.0001, set Bias value = 1

{ Optimization of output-hidden layer weight Step 2 to 3 }Step 2.1 Calculate the response of each hidden layer node by

the activation function, the Sigmoidal function, until the endof training patterns by following equation.

Forj=1 to the last node at hidden layer

netj= i=M [xi Wji]where netj = weighted summed input to hidden layer nodej

i=M = summation from i=0 to M (fig.4.)Forj=1 to the last node at hidden layer

f(netj) = 1/( 1 + exp(-netj) )oj= f( netj)

where oj: the output value of hidden layer nodejStep 2.2 Calculate weights Vjk= A

-1xB

A(j,j1)= matrix { aj,j1} ;

aj,j1 = q=P[oj oj1] : j,j1 = 0..H

B(j,k)= matrix { bj,k} ;

bj,k= q=P[tk oj] : k= 1..N (number of output nodes)

where tk= target output for node k

P = number of training patterns

q=P= summation from q=1 to P

Step 3.1 Calculate the response of each output layer node by

the activation function, the linear function :For k=1 to the last node at output layer

netk= j=H[oj Vkj]

yk= f( netk)where netk= weighted summed input to output layer node k

yk= the output value of output layer node k

j=H = summation from j=0 to H (fig.4.)Step 3.2 Calculate Root Mean Square error (RMS)

RMS = q=Pk=N1/2(tk- yk)2

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{Optimization of the input-hidden layer weight Step 4 to 8 }

Step 4.1 Calculate linearized weights in each output layernode :

For k=1 to the last node at output layer

Vlinkj= j=H[f(netk) Vkj]Where Vlinkj= linearized weight connecting hidden nodej

to output layer node k

f(x) = derivative of the sigmoidal function= f(x)[1-f(x)]

Step 4.2 Calculate weight correction term :

Wopt = Au-1 xbuAu(s,s)= matrix { a(ij,hm)} ;

a(ji,hm): for (j h) = q=Pk=N((Vlinkjxi)(Vlinkhxm)): for (j = h) = q=Pk=N((Vlinkjxi)(Vlinkhxm))

+ (/H)*abs(Vkj)f(netj) xixmbu(s) = vector { b(ji)};

bji = q=Pk=N[(tk yk) Vlinkjxi]

where k=N = summation from k=1 to N (fig.4.)abs(x) = absolute value of x

Remark : matrix Au is (S x S ) dimension square matrix.

vector bu, Wopt is (S) dimension vector.S= H x (M+1) dimensions (fig.4)

Step 4.3 Calculate Wtest by adding weight correction term :

Forj=1 to the last node at hidden layerFor i=0 to the last node at input layer

Wtestji(new) = Wji(old) + Wopt

Step 5 Calculate Root Mean Square error (RMStest) byusing Wtest

RMStest = q=Pk=N1/2(tk- yk)2

Step 6 Compare between RMS and RMStest :

If (RMSTest > RMS) then = *1.2 (increase )

Go back to Step 4

Step7 If (RMSTest < RMS) then

Wji = WtestjiRMS = RMStest

Step 8 Decrease weight factor

= *0.9 (decrease )

Step 9 Do Step 2 to Step 8 until the end of iterations

4. Development of Training DataResults and Discussion

In order to train the network on a comprehensive range ofcutting conditions and process variables, drillingexperiments were carried out. ANCA automatic drilling

machine was used to carry out the experiments. The thrustand torque were measured using three component

dynamometer and associated data acquisition system. Taking

the handbook recommendations and associated feasible drill

geometrical features a total of 72 experiments were carried

out. The training of the network is carried out for the 57cutting conditions above. All the input variables were scaled

between 0-1 and the training was carried out over 57

combinations of cutting conditions.

Figure 5a,5b. Prediction of the neural network models at

training stage and comparison with conventional

methods and experimental values

The training was found to be excellent accuracy with a smallerror at training stage indicating that the network is well

trained with only 10 inputs and meets the target thrust and

torque accurately. The ten inputs were P1, P2, dP, , oandD and W/R, together with cutting conditions eR and eandf. It can be seen that the BP and OLL neural networks havetrained well with great quantitative accuracy highlighting the

predictive capability of the networks

The error was calculated using the deviation formula(Predicted-Exp./Exp.)*100 and the percentage deviations at

the training stage were excellent as shown in Table I for thethrust and for the torque respectively. It can be seen fromTable I that at the training stage for both thrust and torque

there is no significant bias either for over prediction or underprediction for both BP and OLL neural network models.

The neural network architecture was tested over 15 variousconditions. The multi-layer perceptron with back

propagation program was run to check the predictability of

the neural network model for the testing stage.

PredictionVsMeasuredThrustforTrainngData(Fig.5a)

600

900

1200

1500

1800

2100

2400

2700

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57

NumberofTrainingData

PredictionThrust(N.

Conv.

BP

OLL

Measured

Prediction Vs Measured Torque for Training Data (Fig.5b)

250

500

750

1000

1250

1500

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57

NumberofTrainingData

PredictionTorque(N.mm.

Conv.

BP

OLL

Measured

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Method % Deviation

Thrust Torque

Training training

Conv 3.91 -8.79

BP -1.25 0.19

OLL 0.07 0.18

Table I. Average percentage deviations for training

predictions for BP and OLL compared to

conventional methods

From testing point of view, the histograms in the Fig.6a-fhighlight the comparison of the quantitative accuracy of

three different approaches to thrust and torque prediction.The average percentage deviations of predicted thrust andtorque by conventional methods are 4.20% and 10.25%

respectively (Fig.6a and d). For neural network basedpredictive models, BP had an average percentage deviationsof -4.68 and 2.00% (Fig.6b and 6e) and OLL had average

percentage deviations of 0.56% and 1.03% for thrust andtorque respectively (Fig.6c and 6f). Comparing withconventional method, neural network approaches yield

higher quantitative accuracy. While the dispersions ofhistograms of all three models are similar, it is evident thatneural network approaches can offer high accuracy

prediction.

Figure 6a. Thrust testing conventional

Figure 6b. Thrust testing BP

Figure 6c. Thrust testing OLL

Figure 6d. Torque testing conventional

Figure 6e. Torque testing BP

Figure 6f. Torque testing OLL

Figure 6a-f. Histograms of percentage deviation of

conventional methods and BP and OLL networks intesting data.

Frequency

0

1

2

3

4

5

6

-14 -12 - 10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 16

% Error (Fig. 6a)

Thrust : Avg. error = 4.20%

Frequency

0

1

2

3

4

5

6

-21 -18 - 15 -12 -9 -6 -3 0 3 6 9 12 15 18 21 24

% Error (Fig. 6b)

Torque : Avg. error = 10.25%

Frequency

0

1

2

3

4

5

6

-14 -12 - 10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 16

% Error (Fig. 6c)

Thrust : Avg. error = -4.68%

Frequency

0

1

2

3

4

5

6

-21 -18 -15 -12 -9 -6 -3 0 3 6 9 12 15 18 21 24

% Error (fig. 6d)

Torque : Avg. error = -2.00%

Frequency

0

1

2

3

4

5

6

-14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 16

% Error (Fig. 6e)

Thrust : Avg. error = -0.56%

Frequency

0

1

2

3

4

5

6

-21 -18 -15 -12 -9 -6 -3 0 3 6 9 12 15 18 21 24

% Error (Fig. 6f)

Torque : Avg. error = 1.03%

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5. Conclusion

The need for reliable and simultaneous prediction of thrustand torque in drilling operations is highlighted. Mechanics of

cutting approach to thrust and torque predictions has beenextensively used in the past. The mechanics of cuttingapproach and its complexity is highlighted in this paper from

predictive point of view. It has been shown that a number ofprocess parameters is required together with for the drillingperformance prediction. The accuracy is further tested when

reliable geometrical features are not established. In this workthe well-established multi-layer back propagation neuralnetwork (BP) with 2 outputs has been chosen as a first

architecture together with optimised layer by layer feedforward network (OLL) for performance prediction as a

second architecture. Experiments were carried out over arange of cutting conditions to gather thrust and torque

components in drilling operations. A range of drillingconditions covering 57 different cutting conditions and toolgeometrical features were selected as a training set. Theneural network algorithm has trained well with excellentquantitative accuracy with less that 2% average percentagedeviation to the experimental values using both BP and OLLnetworks. The network is tested with 15 different cutting

conditions and showed excellent predictive capability. Theaverage percentage deviation of predicted thrust and torque

by conventional methods are 4.20% and 10.25%respectively. For neural network based predictive models,BP had an average percentage deviation of -4.68 and 2.00%

and OLL had average percentage deviations of 0.56% and

1.03% for thrust and torque respectively.

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