Stress concentration factor kt determination for a crankshaft in bending loading: An artificial neural networks approach

Krank milleri


INTRODUCTION
Crankshaft is one of the critical components of an engine.This machine element is connected with the other components of engine.Cranckshaft carries the connecting rod(s) and pistons.In generally engines have different number of cylinders and pistons for instance 1, 2, 3, 4, 6 or 8. Cranckshafts design has eccentric shape.The crankshaft is subjected to bending and torsion during operation.The crankshaft design is performed according to bending and torsional stress.The crankshaft must be capable of withstanding the intermittent variable loads acting on them.During transfer of torque to the output shaft, the force deflects the crankshaft.This deflection occurs due to bending and twisting of the crankshaft.Bending and torsional stresses can be achieved by using material with the correct physical properties and by minimizing stress concentration.The crankshaft is put in series to all the other components of the engine in the fault crankshaft analysis and the reliability of the whole system heavily depends on the reliability of the crankshaft.The crankshaft is a geometrically relatively complex component which is often obtained by machining a forged piece of steel or cast iron.Mechanical, thermo-mechanical or thermo-chemical surface treatments, such as shot peening, rolling, nitriding or case-hardening allow to increase the surface hardness and induce beneficial compressive residual stresses at the surface that prevent crack nucleation and propagation [1].Arai and Peterson were researched to maximum stress in the fillet of pin and journal of crackshafts in bending state and studied about the parameters of crankshaft design in guided by earlier works [2,3,4].Staul and Pfender et al. made use of extensometers to determine stresses in crankshafts [5,6].Fessler & Sood utilized the technique of photoelasticity [7].The crankshaft is a critical component and any damage occurring to the crankshaft may put the mechanical system out of order.The numerical finite element simulation of crankshafts with multiple rods is often time consuming even quite accurate if the aim is to evaluate the stress -strain behavior at the notched area and verify the component.The development of a simplified numerical model would prove effective to reduce the time needed to reach a good approximation design of the crankshaft [8].The design of a new crankshaft, or the upgrade of a crankshaft to higher power engines, is always a big challenge for the designer [9].Recent years, some studies interested in crankshafts bending fatigue tests [10].In this study contains stress concentration factors (Kt ) for a crankshaft in bending loading state.This study is an updating study.Graphs by obtained Peterson and Arai was converted into numerical values.The charts data converted numerical data.An ANN model was developed in new format.With using the method, interval values can be obtained without perform any interpolation etc. with high reliability.

MATERIAL AND METHOD
Stability conditions of machine elements against stress in terms of stress concentration were examined in general.To what extent the machine parts can be challenged depends on the strength of the product, the design of the product and the material properties.Machine parts can be found under different difficulties according to work environments.The irregular form on the machine elements such as; the channels, grooves, radius etc is varied the magnitude of the stress.FEM, photoelastic, experimental, numerical, statistical, artificial intelligence techniques, etc. were used to investigate the stress conditions of the machine element in more detail.Previously, obtained from experimental and validated data tables are already available and are used in the design.The main problem is that there are no mathematical formulas of these tables.The user only obtains these values by reading the relevant table.Value reading from table is a very tedious and error-prone process.The values obtained vary from user to user.So, a new techniques is need to read each parametric value.New computer based techniques have been begun the invetigate of the stress concentration in deeply.In the last century, computer graphical specification have been developed very impressive scale.Thus, graphical material can be converted into very sensitive numerical values.Converted numerical values were classified in an excell file according to their origin.A new ANN model was created in the sensitivity that the classical regression model can not reach.It is necessary to increase the degree of equation to improve the sensitivity of the formula in the classical regression.When degree of equation increases, calculation becomes quite complex to obtain a result by using these equations.Usage of the ANN method, the user don't need to use any formulae and calculator.Dertermination for the Kt, A software has been created in the Matlab editor.
Arai was researched about fillets of the pin and journal of a series of crankshafts in bending [2].Design parameters were determination to optimum with using experimental techniques.The stress concentration factor is defined (eq.1-7) as σ max /σ nom , where The most important design variables are web thickness ratio t/d, fillet radius r/d, web width ratio b/d and the crank "throw" as expressed by s/d (Figure 1).These parameters are effected the stress concentration factor.An empirical formula was developed by Arai to cover the entire range of tests [11].By using Eq.  .4  (6)

Artificial Neural Network (ANN) Model
ANN is a subfield of Artificial Intelligence.ANN has a mathematical operational context in its back ground.ANN works with different learning algorithms.A neuron is the basic element of ANN.Neurons duties, shapes and size can be varried.Neurons activities is important.An ANN may be seen as a black box which contains hierarchical sets of neurons (e.g.processing elements) producing outputs for certain inputs.Each processing element consists of data collection, processing the data and sending the results to the relevant consequent element.The whole process may be viewed in terms of the inputs, weights, the summation function, the activation function and outputs (Figure 2) .A neural network usually consists of input layer, hidden layer(s), and output layer [12][13][14][15][16][17].
In this study contains determination of stress concentration factors (Kt ) for a crankshaft in bending loading.For this aim; Peterson's stress concentration factor charts were investigated.These charts are drawn as a result of the experimental study and are not identified by a mathematical function.These charts are still used today to define the stress concentration.It is necessary to read the data in these curves when defining the stress concentration for a particular problem.Value reading from table is a very tedious and error-prone process.The values obtained vary from user to user.A numerical data bank was created for these curves.An ANN database was created using obtained from graphs data and a new ANN model was developed.The data were obtained according to study parameters (t/d, s/d, b/d, r/d.andKt (Table 1)) that has 3654 lines x 4 columns.Among them, 30% data have been randomly selected and used as the test data and other 70 % data were used training are determination of the Kt for a crankshaft in bending loading.Figure 3a shows Improved an ANN Model using MATLAB.Figure 3b shows The ANN predictions; training, test and validation performance.Figure 3c shows training performance of ANN model and Figure 3d shows Validation performance of ANN. Figure 3e shows Training performance of ANN and Figure 3f shows Error Histogram of ANN and These figures have been getting from prepared Matlab code.Training ANN model results were compared with the statistically (Table 2).

TESTING THE ACCURACY OF ANN MODELLING
In order to understand an ANN modelling is making good predictions, the test data which has never been presented to the network is used and the results are checked at this stage.The statistical methods of R 2 , RMSE and MEP values have been used for making comparisons [11][12][13][14][15][16].The same data obtained from the regression analysis is used to determine the mentioned values.These values are determined by the following Eqs (12)(13)(14): Using the trial error method, the structure of the network (i.e. the number of neurons and hidden layers) is altered and the training operation is repeated.To be able to get accurate results we have used three hidden layers.Number of neuron in the hidden layer were changed (e.g. from 5 to 150) to determine the best network architecture.

RESULTS AND DISCUSSION
In this study, we have composed the chart data and network predicted output results t/d, s/d, b/d, r/d and Kt for the stress concentration factor parameters for statistical error analysing methods.As presented in Table 2, the statistical error levels for both training and testing data sets are evaluated.As the table illustrates the network with three hidden layers of [3+9+11+11+1] neurons at each layer has provided the best results (Figure 4).ANN model has been illustrated Figure 4.In this model, it is consist of 4 input layer(s) and with processing element at 3 hidden layer(s) and finally 1 output layer.In terms of the statistical error analysis methods, using Levenberg-Marquardt (LM) learning algorithm technique for Output.It is easier and more practical to determine these values using auxiliary software instead of using formulas.These charts are still used today to define the stress concentration factor.It is necessary to read the data in these curves when defining the stress concentration for a particular problem.These curves have been converted into numerical values with the help of highly sensitive computer software.An ANN database was created using these data.A new ANN model was developed using Matlab software.Different ANN models were tried and the best model was determined To determine the stress concentration factor according to diffrent bending loading states in design of crankshaft was explored.The ANN model was provided high accuracy for prediction of stress concentration factor (Kt).This model has R 2 =0.999869,MEP%=0.610405 and RMS=0.139119.User can be read fault value that getting from chart.
Using the ANN model these faults were eliminated.Easy and economical method was improved using An ANN model.This model was effective and usefull method.This method can be used with more reliability.

Fig. 1 .
Fig. 1.Model of a crankshaft in bending loading

n:
Number of processing elements in the previous layer.whereNET is the weighted sum of the input.An ANN model was developed using Matlab NN tool.For this aim a new ANN code has been prepared and developed.Different models have been tested.Best model was determined.

Fig. 2 .
Fig. 2. Basic artificial neural network model back propagation learning algorithm has been used with Scaled Conjugate Gradient (SCG) learning algorithm and Levenberg-Marquardt (LM) learning algorithm versions at the training and testing stages of the Networks.The number of hidden layers and the number of neurons for each hidden layer were determined.Then, the number of iterations were entered by the user, and the training starts.The training continues either to the end of the iterations or reaching the target level of errors.

Fig. 4 .
Fig. 4. ANN architecture with [3+9+11+11+1] processing elements at four hidden layers Figure 5 shows Kt values was determined according to t/d, s/d. Figure 5 shows comparison of emprical values (chart values) and ANN model values.Figure6shows Kt values was determined according to s/d, r/d.Figure6 Figure5shows Kt values was determined according to t/d, s/d.Figure5shows comparison of emprical values (chart values) and ANN model values.Figure6shows Kt values was determined according to s/d, r/d.Figure6

Figure 6 shows
Figure5shows Kt values was determined according to t/d, s/d.Figure5shows comparison of emprical values (chart values) and ANN model values.Figure6shows Kt values was determined according to s/d, r/d.Figure6shows comparison of emprical values (chart values) and ANN model values.Both ANN models results and emprical values were compatibled with graphical data.

Table 1 .
Stress concentration factors Kt variable parameters for a crankshaft in bending loading

Table 2 .
Statistical Performance of training ANN model In this study contains stress concentration factor determination using Peterson's Stress Concentration Factor charts and ANN modelling.Peterson's graphs have been accepted as scientifically valid, but a mathematical equation has not yet been transformed.Peterson's charts were drawn as a result of the experimental study and were not identified by a mathematical function.The values in these graphs can be defined only with the result of experimental studies.