#
hotspotter 2.7 User's Manual

## Section One: Overview

### 1.1 About the program

Hotspotter is an engineering analysis software to determine the susceptibility of axisymmetric multidisk brakes and clutches to thermoelastic instability (TEI). An eigenvalue method is used to determine the exponential growth rate of eigenmodes of the system for a given rotational speed. The critical speed is then determined by searching for the lowest speed at which at least one mode has a positive growth rate Fourier decomposition is used in the circumferential direction so that discretization for the finite element analysis is needed only on the cross sectional plane. This greatly reduces computational time and increases numerical accuracy. The analytical basis of the model is described in the paper, Yun-Bo Yi, J.R.Barber and P.Zagrodzki, Eigenvalue Solution of Thermoelastic Instability Problems using Fourier Reduction, Proc.Roy.Soc. (London), in press.

User input to the program includes the geometric cross-sectional shape of all the components, the relevant elastic and thermal properties, the coefficient of friction and the boundary conditions at both internal and external surfaces. Output from the program includes the exponential growth rate and migration speed of the eigenmode for specified sliding speed, the critical speed as a function of wavenumber (number of hot spots around the circumference) and the spatial form of the dominant eigenmode in both the plane of the disks and the cross-sectional plane.

The program is particularly suitable for multidisk brakes or clutches, which are strictly axisymmetric. In contrast, a typical automotive caliper disk brake has a finite pad length and is therefore is non-axisymmetric. In some situations, however, the program still gives good estimates for critical speeds of brake problems if an equivalent friction coefficient is used in the axisymmetric model to describe the average heat input to the disk. This approximation is described in Section 2.7 below. For more information about the theoretical background of the program or the program itself please contact Professor J.R. Barber at the following address:

J.R.Barber
Professor of Mechanical Engineering and Applied Mechanics

E-mail: jbarber@umich.edu

Web: http://www-personal.engin.umich.edu/~jbarber/

Address:
J.R.Barber,
Department of Mechanical Engineering
University of Michigan
2350 Hayward Street
Ann Arbor MI 48109-2125

Office Phone: (734) 936-0406

FAX: (734) 647-3170

### 1.2 Program user interface

The user interface is a figure window consisting of 4 regions: the control buttons, the menus, the figure body and the message box, as shown in Figure 1.

- Control buttons: Located on the right of the main window These perform various controls on the program, such as start running the program, invoke the parameter editor, show results etc.;
- Menus: Located on the top of the window. These perform the same controls on the program as the control buttons. They provide an alternative method to control the program.
- Figure body: Located in the middle. All plots will appear here.
- Message box: Located on the bottom. Some useful messages are shown in this box while the program is running

Figure 1
The following is a brief description of the control buttons embedded in the main window.

- [My Model]:launch the MyModel window to display, modify or save the parametric description of your model.
- [Run]: start running the finite element analysis.
- [Show 3D model]: display a three-dimensional perspective view of the model you are working on.
- [Show mesh]: show the finite element mesh in the cross-sectional plane.
- [Show result]: show various results after a successful run of the program.
- [Help]: launch a browser to read the user's manual.
- [Quit]: exit the program.

Additional control buttons embedded in the `Show result' window are

- [T cross]: contour plot of the temperature field on the cross section for the dominant eigenmode
- [T surface]: contour plot of the temperature field on the surfaces for the dominant eigenmode
- [T thickness]: temperature distribution at the mid radius as a function of z.
- [Growth rate]: growth rates of temperature perturbation at given sliding speeds (only active when sliding speeds are specified).
- [Crt speed]: critical speed for given hot spot numbers (only active when sliding speed is not specified).
- [Mig speed]: migration speed at the critical speed for given hot spot numbers
- [Back]: back to the main frame of control buttons.

The menus in the menu bar have similar functions as the control buttons, except those listed in the `FILE' menu, which control file load/save, etc., and the `SET' menu, which control the appearance of your plots. In the `FILE' menu, there are following submenus,

- [load file]: load your model file and material property library.
- [save model]: save the model by inputting your preferred model file name at the prompt.
- [save material library]: save the material library by inputting your preferred material library name at the prompt.
- [print as]: print the current plot to a file (eps, ps, jpg). You will be prompted to give the file name. One of `eps', `ps' or `jpg' should be used as the file extension.

In the `SET' menu, there are following submenus,

- [set grid on/off]: show grid in the plot or turn it off. Default:off
- [set colormap=grey]: select black & white colormap for contour plot(useful for B&W printer).
- [set colormap=default]: select colored plot option. Contrary to greycolor.
- [set layer number on/off]: show/not show the layer numbers on the middle of each layer. Default:on;
- [set Footnote on/off]: show/not show the footnote line on the bottom of the plot. Default:on
- [set PrintUI on/off]: print/not print control boxes and control buttons when generating plot files. Default: off
- [set Spacing larger/smaller]: make the distance of contact surfaces larger/smaller
- [set Zoom on/off]: make the zoom function capable/incapable. When Zoom is on, lick left button of your mouse to zoom in, click right button to zoom out. Default:on
- [set Mesh visible/invisible]: set FEA mesh lines visible/invisible while using `show mesh'.

### 1.3 Getting started

A few sample input files are included in the software package. We suggest you load the file `sample'. The model included in this sample file is the `modified Lee & Barber model' as shown in Figure 2. It consists of two sliding annular disks with a symmetric boundary condition on one exposed surface and and antisymmetric boundary condition on the other. You can use this sample problem to practice and get familiar with the program.

Figure 2

- step 1: run Matlab, at the prompt, cd to the directory where the program is installed
- step 2: type `tei'. This launches the main interface window
- step 3: click the menu `FILE' and then the submenu `Load' on the menubar.
- step 4: select `sample' and click on OK in the pop up box.
- step 5: click on `Show model' to see the 3D plot of the sample model; click on `Show mesh' to see the finite element mesh
- step 6: click on `run' to perform the analysis. While the program is running, you will see some information appearing in the message box. Wait until `Congratulations!!' appears, indicating that the analysis is complete.
- step 7: click on `Show result'. Then click on `Critical speed' to see a curve of the critical speed Vc as a function of hot spot number n.
- step 8: Go back to the main menu by clicking `Back'. Then click on `My model' to launch the MyModel window and see the model parameters.
- step 9: Change the parameters and repeat steps 1 thru 9. There are some other sample files named `sample_*' included in the software package. These models have more complicated geometries. You can load these files to further explore the capabilities of the program.

## Section Two: Change Your Model

To develop a model for a clutch or brake of your own specification,

- step 1: click the menu `FILE' and then the submenu `Load' on the menubar.
- step 2: select `temp' and click on OK in the pop up box.
- step 3: click on `My Model' to display the geometric and material description of the model (see Figure 3).
- step 4: modify this description in the `My Model' window, following the instructions given in sections 2.2 thru 2.7.
- step 5: click on `FILE' on the `My Model' window and select the submenu `Save Model'.
- step 6: change the name of the file in the pop-up window and click on `OK'.

Figure 3

### 2.1 Model description

The model is described in layers, each layer being an annular ring defined by an inner radius, an outer radius, a thickness and a set of material properties.

Each layer also has a flag indicating whether it is a rotor (moving) or stator (stationary). Two adjacent layers having the same status (both rotors or both stators) are assumed by default to be bonded together at the common interface. It is therefore possible to define more complex axisymmetric bodies as two or more layers with different dimensions bonded together. Composite friction disks (e.g. a steel core bonded to two friction material layers) can be defined in the same way. Internal interfaces between adjacent layers of different status are assumed to be in sliding contact with a specified coefficient of friction.

Alternatively, the layer can be assumed to make frictionless contact with an adjacent layer of the same status by specifying `frictionless contact' at the `Fric B.C.' option. Note that only the bottom surface of the layer is assumed to be frictionless. To make both interfaces frictionless, you need to specify `frictionless contact' for two layers - the current layer and the layer above it.

### 2.2 Geometry

To add or delete one layer, use `Next' to go to the layer on which you want to insert a new layer or delete. Then use `Add' or `Delete' buttons to insert or remove a single layer To make a copy for several layers, use `Next' to go to the layer on which you want to insert the new layers, clicking on Mcopy you will be prompted to specify the layers you want to duplicate. To delete several layers at a time, use `Mdel' button. You will be prompted to specify the layers you want to delete. The layer numbers should be separated by commas or blank spaces.

Figure 4
The program is capable of dealing with quite complicated geometries, as illustrated in Figure 4. This model is saved in the sample file named `sample_XClutch'. You can load this sample file by clicking 'Load' on the menubar and use it to see how to construct a model with a complicated geometry. There are several other sample model files. `sample_RealClutch' is a realistic clutch model; `sample_Brake' is a brake model;`sample_PaperClutch' is a multiple-disk clutch model studied in the paper mentioned at the beginning of the manual.

### 2.3 Material properties

All material properties are in SI units. Use `Add' to add a new material into the material library. Use `Delete' to remove an existing material from the material library. Use menu `Save Material Library' and change the file name at the prompt to one of your own choosing. Note that the friction coefficient is defined in the model file, not in the material library.

The isotropic material properties are assumed in the program by default. However, you may also specify an anisotropic material by clicking the `isotropic' button. A new window will come up and you will be asked to input the required anisotropic properties for that material. Specifically, you need provide two matrices: the matrix C and thermal expansion matrix A. Please see Figure 5 for the definition. Note that C is the inverse of the corresponding stiffness matrix, and it is symmetric. After you fill out the matrices, click `apply anis' to switch the material to anisotropic; click `unapply' to switch the material back to isotropic. In the current version, the anisotropic definitions for other properties, such as thermal conductivity, are not provided, and may be included in future versions.

Figure 5

### 2.4 Boundary conditions

The boundary conditions are specified in the two popup buttons the MyModel window. The first and second B.C. represent the B.C. applied on the bottom surface and the top surface of the stack respectively. You are able to obtain different B.C.s by selecting different combinations of the two popup buttons.
*******************************************************
Note--
a) The degree of freedom (DOF) are r-radial, z-axial, t-circumferential
b) Ur, Uz, Ut are displacements
c) Srr, Szz, Stt are the normal tractions
d) Qz is heat flux in the z direction
e) T is the temperature
*******************************************************
B.C.definitions:

- Free -- mechanically free;thermally insulated;(Srr=Stt=Szz=0; Qz=0)
- Symm -- mechanically symmetric; thermally insulated (Uz=0,Srr=Stt=0;Qz=0)
- Anitisym -- mechanicall antisymmetric; thermally T=0 (Ur=Ut=0, Szz=0; T=0)
- Fixed -- mechanicall fixed; thermally insulated (Ur=Ut=Uz=0; Qz=0)
- Floating -- mechanicall fixed on r, free in z, t; thermally insulated(Ur=0,Szz=0;Qz=0)
- Cyclic -- All physical quantities on the upper boundary have the same values as on the lower boundary.
- 2PointSymm -- same as Symm, except the B.C. is only applied on the in-most radius and out-most radius.
- 2PointFixed -- same as Fixed, except the B.C. is only applied on the in- most radius and out-most radius.
- 2PointFloating -- same as Floating, except the B.C. is only applied on the in-most radius and out-most radius.

### 2.5 Sliding speed and hot spot number

If the sliding speed is not specified in the `sliding speed' box, the program performs iterations to find the critical speeds for the hot spot numbers specified in the `hot spot numbers' box. If the sliding speed is specified, the growth rate is computed. You can input multiple hot spot numbers rather than a single number. For example: if you want to run the program for hot spot numbers 4, 6, 8 and 10, you can input 4,6,8,10 or 4 6 8 10 or 4:2:10. They are all valid inputs. Multiple sliding speeds are also acceptable. The growth rate is computed subsequently for all the sliding speeds.

### 2.6 Mesh size

The mesh size for the finite element analysis can be modified by clicking on the popup menu `mesh size' in the MyModel window. There are several options ranging from `super coarse' to `super fine'. Starting from `coarse'(the third option) and beyond, the skin layer is suitably discretized such that there are enough number elements within this region. However, no such guarantees for `super coarse' and `very coarse' options.

The finite element mesh is highly biassed in the thermal skin region in the poor conductor to prevent poor computational accuracy. To make use of the axisymmetric geometry of the problem, a Fourier reduction method is used and therefore the standard Garlerkin finite element analysis is performed in the program. Please refer to the paper mentioned at the beginning of this manual.

### 2.7 Brake model

As mentioned in the Overview Section, the program only gives an approximation solution for the brake model since the brake geometry is nonaxisymmetric (the pad length is finite circumferentially). To specify a brake model you need to specify a number less than 360 in the `pad angle' box in the MyModel window. If the number is 360 then the model is regarded as a clutch problem rather than a brake probem. In the `fric coeff' you should give a real number (not the `equivalent friction coefficient' defined by the real friction coefficient multiplied by the pad angle divided by 360). In addition, the model does not include vents.

In the current version of program, `Show 3D model' only supports 9-layer brake model, as shown in Figure 6. These nine layers are defined as follows:
Layer 1-backing plate of the inboard pad
Layer 2-friction material of the inboard pad
Layer 3,4,5,6,7- rotor, where the hat parts are 6 and 7
Layer 8-friction material of the outboard pad
Layer 9-backing plate of the outboard pad

Figure 6
You can specify a brake model with more than the 9 layers. You will still get correct results from the analysis. But you may not be able to get a correct 3D picture of your model, if you use `Show 3D model' menu in that case.

## Section Three: See Results

By clicking on Results menu on the control buttons or on the menu bar, you are able to see the computational results in the following ways:

- [T cross]: temperature field on the cross section. To see the temperature of a different mode, click the right button of your mouse to launch the context menu, and then select a suitable option.
- [T surface]: temperature field on the surfaces. The default surface is the first surface from the bottom. To see the temperature on a different surface or a different mode, Right click your mouse to launch the context menu, and then select a suitable option.
- [T thickness]: temperature distribution thru the z direction at mid radius. To enlarge the skin region(usually the skin layer is extremely thin), Right click your mouse to launch the context menu, and then select a suitable option.
- [Growth rate]: growth rates of temperature perturbation at given sliding speeds
- [Crt speed]: critical speeds for given hot spot numbers
- [Mig speed]: migration speeds at the critical speeds for given hot spot numbers
- [print as]: print the plot to a file (eps, ps, jpg). You need to give the file name with correct file extension. The file style is determined by the file extension. To include the control buttons and boxes in your plot, switch 'PrintUI on' in the menu bar on the top of the main figure window.

Figure 7

## Section Four: Version 2.7 against 1.5

Some users may have the old version 1.5x and they are familiar with the usage of that version. Compared with Version 1.5x, the new Version 2.7x has the following improvements.

- The freezing window problem has been completely solved. There is a brand new message box appearing on the lower part of the main window. The terminal window with Matlab prompt is no longer useful and can thus be ignored.
- A menu bar is added on the top of the main window. In stead of the standard root menus provided by Matlab Figure, there are four additional user menus, i.e., MAIN, RESULT, MODE and OTHERS, each of them containing a few sub-menus.
- Multiple sliding speeds are acceptable in the new version. The plot option for sliding speed vs. growth rate is also a new option of result showing.
- One can duplicate one or more existing layers for several times to construct a model with repeating disks. Also one can delete several layers at a time.
- The user's manual (in HTML) is now available by clicking the Help button on the main menu (or the equivalent menu on the menu bar on top of the window)
- A 'context menu' can be launched by clicking the right button of your mouse. These menus can be used to change the current mode, current layer surface or other plot operations.
- Three new B.C. types are added. They are 2PointSym, 2PointFixed and 2PointFloating. These B.C.s are the same as Sym, Fixed and Floating except that they are applied on the two nodes at the inner-most radius and the outer-most radius rather than on the entired surface.
- In addition to eps format supported in the previous version, PS and JPG file formats are now available, by using suitable file extension, .eps, .ps, or .jpg.

## Section Five: FAQ

- The program takes too long time to finish. How can I quit it anyway?
  Answer: method 1, Click 'Quit' button on the main figure window, and you may have to click it for more than one time; method 2, use Ctrl-C; method 3, use Alt-Ctrl-Delete on PC, select job ID to kill it.
- How to insert a composite disk instead of a layer into my model?
  Answer: In MyModel window, go to the layer you want to add a disk on. Use 'Madd' button to insert multiple layers to you model. You need to specify the layers you want to copy from.
- How to see temperature field on different surfaces rather than the first surface?
  Answer: right click on you mouse, you will get a context menu, select 'next surface' to see T on the next surface and so on. Or you can use the same menu named 'others' in the menu bar.
- Can I input multiple hot spot numbers and multiple sliding speeds at the same time?
  Answer: Yes. The program gives you the sliding speed-growth rate curve for each hot spot in a same plot when you use Growth Rate menu option.
- Do I have to save the modified model before I start running the program?
  Answer: No. The model parameters are immediately updated when you change the edit boxes in the MyModel window.
- I do not like EPS or PS print format. Can I save my plot as JPG file?
  Answer: Yes. You can specify ps, eps, jpeg format by using suitable file extension .ps, .eps, and .jpg when you are prompted to input the print file name.
- I want to start running the analysis when I use the result controls. Should I go back to the main window to click on Start button?
  Answer: No, you do not have to. You can use the menu bar on the top of the window instead. You can use menu bar at any time without having to switch the windows back and forth looking for buttons.
- I could not launch the context menu when I click on the right button of my mouse. Why?
  Answer: The context menu cannot be launched when there is a plot axis box and your mouse is inside this axis box. Please move your mouse outside the box, then click the right button. Generally speaking, the context menu does not show when the mouse is on top of any existing graphic object.