aapaecklar/affc

Visualization of the analytical solution to tooling contact occurring during flow forming.

Introduction

An application has been developed in MATLAB to assist in visualizing the contact patch of a single roller during a flow forming operation with the means of a GUI. The details of how this contact is calculated appears in the paper "Analytical solution of the tooling/workpiece contact interface shape during a flow forming operation" published in the Journal of Materials Processing Technology, hereafter referred to as ‘the paper’. A preprint of this paper is available here.

Overview

The main window is accessed by running AFFC.m. Note that the companion subfunctions plot2Dsol.m, plot3Dsol.m, ToolContactArea.m and ToolContactPointCloudWrite.m are required on the MATLAB path at run time. Fig. 1 shows the interface highlighting the main features. On the far left of the GUI, section A shows the region where the geometrical variables describing the contact solution may be updated. The default values are those which were used to experimentally validate the contact solution, as described in the paper indicated above. Region B and C are output plots generated by pressing the ‘Update’ button indicated in D. The radio buttons in region E activate area calculation functionality and the ability to write the solution’s 3D point cloud to an external .csv file in the local directory. Buttons in region F activate navigation and data exploration modes. Finally, the radio button indicated in G permits showing the edges on graphical elements displayed in B and C. These regions/functions are described subsequently.

Fig. 1: AFFC interface with main features highlighted.

Functionality

Input

There are nine locations for the input of the solution variables and process geometry (Fig. 1-A), and these are described in the following table. Descriptions of each variable appear over each input field upon pressing the associated button/label. Note that aside from the angular dimensions, the solution is not dependent on units, as long as they are consistent. The tooling arrangement employed to validate the solution via a physical model as described in the publication appear as default values, input in millimetres. Note that the attack and planishing angles may only approach 90 and 0 degrees.

Variable	Description
R	Mandrel radius
to	Original workpiece thickness
tf	Final workpiece thickness
Rr	Roller radius excluding nose radius
R	Roller nose radius
a	Attack angle in degrees (<90°)
b	Exit or planishing angle in degrees (>0°)
P	Roller pitch
R*	Solution resolution

Output

There are three possible sources of output of the solution. The first is the default graphical output and the contact condition as documented in the paper, which is echoed to the command line. Secondly, the results of area calculations may be displayed as output echoed to the command line. Finally, raw output is available in the form of a 3D point cloud which is written by the application to a file specified by the user.

Graphical output and navigation

The default is the 2D and 3D graphical output shown in Fig. 1-B and C respectively, which update according to changes in variables. The 2D figure corresponds to Fig. 4 and 5 in the paper, while the 3D plot corresponds to Fig. 6 in the paper. These plots may be perused using the manipulation tools located in region F. An example of the ‘Rotate’ function is shown in Fig. 2. Pan and zoom are self-explanatory. To reset to the original view, double left-click the respective axis, or right-click and choose the appropriate option from the menu that appears.

Fig. 2: AFFC interface with 'Edges' on, showing how the 3D plot may be rotated.

The coordinates of any displayed point may also be interrogated in both the 2D and 3D plots by activating the ‘Data Cursor’. This is shown with the 2D plot in Fig. 3, where the Data Cursor has been used to display the values of R_i,,z₁₂ in the paper.

Fig. 3: AFFC interface showing the use of the 'Data Cursor'. The variable description for a has also been selected.

Contact area calculation output

In order to generate the results of the overall contact area as well as the area projected on the major planes, the 'Calculate area' radio button in region Fig. 1-E must be selected. The contact area in square units is then displayed on the console, just below the contact condition (please see paper for contact condition meaning):

Condition AI...

Calculated areas . . . 
Overall     |X plane    |Y plane    |Z plane
40.502342   |36.835296  |2.449122   |13.756200

Here, the overall contact area is displayed, with the projection of the contact area on the planes orthogonal to x, y and z axes, respectively.

Point cloud output

By selecting the 'Write points' radio button in region Fig. 1-E, the coordinates corresponding to each of the vertices plotted in the 3D display are written to a file specified by the user. This is accomplished by another GUI window launching from the current working directory, which will launch upon pressing 'Update'. The format of the data is x coordinate, y coordinate, z coordinate:

75.664,0,1.27
75.642,0,1.1815
75.642,0.19215,1.1815
75.643,0.38429,1.1815
75.644,0.57644,1.1815
75.646,0.76858,1.1815

Extensions

The subfuntions plot2Dsol.m and plot3Dsol.m can be run in standalone form from MATLAB. Note that output from plot2Dsol.m is required for plot3Dsol.m, and new figure handles need to be created in between to show discrete output:

%vars=[Rm to tf Rr R a b P]
vars=[69.33 8.05 6.17 56.23 5 45 60 2.54];
Rstar=60;
figure;
zlimits=plot2Dsol(vars,0); %2nd argument is for showing edges
figure;
[X Y Z]=plot3Dsol([vars Rstar],zlimits,0); % Rstar is appended to vars, 2nd argument is for showing edges