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8/11/2019 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
8/11/2019 Prediction of Thrust and Torque in Drilling
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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
8/11/2019 Prediction of Thrust and Torque in Drilling
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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
8/11/2019 Prediction of Thrust and Torque in Drilling
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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%
8/11/2019 Prediction of Thrust and Torque in Drilling
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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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