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.

Figure 1

The following is a brief description of the control buttons embedded in the main window. Additional control buttons embedded in the `Show result' window are 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, In the `SET' menu, there are following submenus,

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

Section Two: Change Your Model

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

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:

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:

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.

Section Five: FAQ