Thus, strain hardening parameters can be ignored in the neural network modeling of the velocity field. F F Roll force per unit width of the strip at the top and bottom rolls, respectively.
Rolling Processes
The need for an asymmetric spinning process depends on the application and product requirement. The asymmetric turning process requires less turning pressure, turning force and turning torque compared to the symmetric turning process.
Soft Computing Techniques
In the present work, the MATLAB function NEWRB is used to train the network. Salunkhe [2006] included the material strain hardening behavior and rolling deformation in the model.
Objective and Organization of Thesis
Introduction
The limitation of the curvature in the rolled product is important from a quality point of view. For these applications, a greater understanding of the relationship between the process parameters and strip curvature is needed.
Research on Symmetric Rolling Process
One-dimensional Models
The architecture of the RBF neural network used to predict the rolling force and torque is shown in Fig. Two separate soft inference models are created to predict rolling force and torque.
Slip-line Method Based Models
Upper Bound Theory Based Models
The upper bound method involves the construction of a kinematically admissible velocity field for a given deformation process. An upper bound method was proposed for the analysis of rolling by Avitzur [1964] assuming a continuous velocity field.
Finite Element Method Based Models
The authors demonstrated that the inclusion of elastic strain rates allows the estimation of residual stresses in strips. 1992] considered the elastic deformation of rolls in their finite element analysis for the rolling of thin strip.
Models Based on Visio-plasticity Technique
Only roll force values of the current model are therefore compared with the experimental results. The effect of roll flattening on the curvature of the rolled product is also studied in the current thesis.
Experimental and Theoretical Investigation of Friction at
Soft Computing Technique
Techniques like artificial neural network (ANN), fuzzy set theory, genetic algorithm (GA) are known as soft computing techniques. In the recent past, Samanta [2004] used radial basis function neural network for gear fault detection.
Research on Asymmetric Rolling Process
Experimental Research
They investigated the effect of differences in roller speed, differences in roller diameter, and differences in roller surface roughness on roller force, roller torque, and tape curvature. Pan and Sansome [1982] investigated the effect of roll speed mismatch on rolling force, torque and forward slip in cold rolling process.
Theoretical Research
The authors included the bar entry angle in the model as one of the causes of the asymmetry. 1988] are one of the early investigators who used the finite element (FE) model for the analysis of the asymmetric rolling process.
Detailed Objectives of the Present Thesis
The control of the curvature of the rolled product is important from a quality point of view. In this thesis, the situation with uncertain friction conditions at the upper and lower roller working surface will be modeled to estimate the unwanted curvature.
Introduction
The performance of the present finite element model with the help of neural network is validated against the finite element model of Dixit and Dixit [1996].
Finite Element Formulation
3.4) In Euler's formulation, the strain rate tensor εij, which is commonly used as a measure of strain, is given by. According to this formula, the ratio between the radius of the deformed contact arc R' and the radius of the cylinder R is given by.
Prediction of Velocity Field by Neural Networks
Study of Data
The correlation analysis shows that for node 1 (table 3.1), the horizontal and vertical components of velocity v1 and v2 respectively form a significant correlation with reduction randR h/ 1. For node 2 (table 3.2), the horizontal and vertical component of velocity respectively. v1 and v2 give significant correlation with reduction alone.
Neural Network (NN) Modelling
In this paper, the NEWRB function from the MATLAB toolbox was used for network training. The function uses an algorithm that starts with zero neurons in the hidden layer and keeps adding the input vector with the largest error as the center in successive runs until the error goal is reached.
Prediction of the Parameters Using Trained Neural
Here the output neuron corresponds to the arc length from output to neutral point divided by the total arc length. A similar procedure was adapted to train and test the model for predicting the location of a neutral point.
Results and Discussion
- Validation of the Neural Network Model
- Prediction of Roll Force and Roll Torque
- Comparison of Roll Pressure
- Comparison of Equivalent Strain Contours
- A Note on Computational Time
A general overview of the procedure using the NN predicted velocity field in the NN assisted FEM model. NN assisted FEM takes about one-tenth the time of the FEM code.
Summary
On the other hand, the computation time required to predict the speed of a neural network will be at most O N( 2). With this procedure, the calculation time is reduced by a factor of approx. 10 for the selected mesh.
Introduction
It is noted that the results of the current model and Dixit's [1997] model are quite similar. In this thesis, the results of the current model are compared with the experimental results of Hwang and Tzou [1997].
Problem Formulation
Data Generation Using RBF Neural Network
Fuzzy Inference Model for Prediction of Roll
The accuracy of the present TS model is further validated by comparing the results with FEM-based rolling force and torque predictions. A comparison of the proposed methodology with experimental results and finite element models available in the literature is performed.
Result and Discussion
Roll Force and Roll Torque Prediction
It is seen that NN predicted values lie between the lower and upper estimates of rolling force and rolling torque. The prediction of lower and upper estimates of rolling force and rolling torque is useful where the TS model is constructed with the experimental data.
Sensitivity Analysis for Roll Force and Roll Torque
The partial derivatives of the torsional and torsional forces with respect to Rh/1, f, and r are calculated from a finite difference scheme using data obtained from the FEM-based code [Dixit and Dixit, 1996]. The step size is taken as 10, 0.02 and 4 for the partial derivatives of the twisting force and the twisting torque with respect to R h/ 1, f and r respectively.
Approximate Method for Prediction of Roll Force and Roll Torque
We can obtain the rolling force and torque for a hypothetical non-solidifying material with a uniform current voltage. If the multiplying factor for the other material is K2, the torque and rolling force for that material are given by. 4.14).
Identification and Suppression of Outliers in the TS Model
Using the rule base, the proposed procedure is followed to construct the modified TS fuzzy inference using Eq. Performance of the proposed TS model and original TS model in the presence of outliers.
Summary
It is shown by an illustration that the presence of outliers significantly degrades the performance of the TS model. The proposed methodology can also be extended to predict the lower and upper estimates in the presence of outliers.
Introduction
Pressure field correction in FEM flow formulation with the help of finite difference and neural networks. The proposed method is compared with a mixed pressure-velocity finite element method and experimental results available in the literature.
Problem Formulation
If there is no reverse voltage, the pressure at the inlet surface is considered to be zero. Using this equation, knowing the pressure at point (m, n), the pressure at the next point (m, n+1) in the vertical is calculated as an angle.
Neural Network Modelling
It is observed that the results of the present model are in good agreement with the FEM results of Shivpuri et al. The curvature of the strip in asymmetric rolling depends on the coefficient of friction for a given number of rolling conditions.
Result and Discussion
Results with Fuzzy Parameters for Steel Material
The only difference between the current model and Dixit and Dixit's model is the method of obtaining the pressure. 5.8-5.9 show that the current model and the Dixit and Dixit models largely differ in rolling force prediction.
Validation of the Model for Copper and Aluminium
Nadai, A., (1939), The forces required for rolling of steel strip under tension, Transactions of the American Society of Mechanical Engineers: Journal of Applied Mechanics, A, pp. Richelsen, AB, (1997), Elastic-plastic analysis of the stress and strain distributions in asymmetric rolling, International Journal of Mechanical Sciences, 39, pp.
Comparison with Slab Method
Summary
In the present work, cold flat rolling process is analyzed using finite element method and finite difference method assisted by neural network models. The new velocity field is used to find the pressure field by the finite difference method.
Introduction
Neural network and fuzzy set applications in curvature analysis in an asymmetric rolling process. The uncertain state of friction at the upper and lower interface of the rotating workpiece leads to the creation of asymmetry in the turning process.
Slab Method Formulation
Roll Force, Roll Torque and Strip Curvature
As the material undergoes deformation in the roll gap, the strip also bends due to differential shear deformations. So the total curvature of the tape will be the sum. curvature due to the difference in axial deformations and curvature due to the difference in shear deformations.
Validation and Parametric Study of the Model
- Roll Force and Roll Torque
- Effect of Friction Mismatch on Roll Force and Roll
- Comparison of Roll Force and Roll Torque in Symmetric and
- Power Dissipation for Different Speed Ratios
- Strip Curvature Analysis
- Effect of Roll Flattening on the Curvature
The rolling force and rolling torque are compared for three different speed ratios as shown in the figures. It is observed that in symmetric rolling case the rolling force and rolling torque values are higher than that of asymmetric rolling process.
Neural Network Model for the Prediction of Curvature
Study of Effect of Strain Hardening on the Curvature
In view of this, a preliminary study was carried out to understand the effect of strain hardening on curvature under different conditions. It is also observed that for moderate reductions and higher speed ratios VA, curvature is insensitive to the strain hardening parameters.
Neural Network Model
Final neural network parameters for radius of curvature prediction Network parameters for radius e. The neural network model can also be used for curvature estimation to control the curvature or to provide the desired curvature.
Effect of Frictional Asymmetry on the Curvature
Fuzzy Modelling of Parameters
Dixit, U.S., and Dixit, P.M., (1995), An analysis of the steady-state wire drawing of the stretch hardening materials, Journal of Material Processing Technology, 47, pp. Pittman (Eds.), Numerical Methods in Industrial Forming Processes, pp. 2008), An application of physics-based and artificial neural network-based hybrid temperature prediction schemes in a hot rolling mill, Transactions of the American Society of Mechanical Engineers: Journal of Manufacturing Science and Engineering pp.
Simulation with Fuzzy Material and Process Parameters
Control of Undesired Curvature
This leads to reducing the effect of frictional asymmetry and results in minimizing the curvature of the rolled strip. In the present work, the optimal speed ratio VA is found by using an exhaustive search method.
Summary
Radius of curvature (m) at optimal VA. 2006] to integrate the strain hardening behavior of the material and utilize the roll flattening effect. It is shown that the NN model can be effectively used to assess the sensitivity of the curvature to friction conditions.
Conclusions
It is observed that for a high roll radius to thickness ratio, the results obtained from the present model differ from the finite element results available in the literature [Dixit and Dixit, 1996] and are closer to the experimental results of Shida and Awazuhara [1973] ]. In the analysis of asymmetric cold rolling process, it is observed that rolling force and rolling torque are reduced compared to that of symmetric rolling process.
Scope for Future Work
Lenard, J.G., (1992), Friction and forward slip in cold strip rolling, Transactions of the American Society of Mechanical Engineers: Journal of Tribology, 35, s. Nepershin, R.I., (1999), Plane strain hot rolling of slab and strip , International Journal of Mechanical Sciences, 41, pp.
