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[solution]: CSE/EEE 230 Spring 2015 Assignment 4 Due March 1 3PM 20


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__________________________________________________| M

 


 

43.

 


 

|X-02 | 2/29/16| 1/2

 


 

PROBLEM STATEMENT

 

AREA AVERAGED LINING TEMPERATURE OF BRAKE PADS

 

In order to simulate the thermal characteristics of disk brakes D. A. Secrist and R. W.

 

Hornbeck needed to approximate numerically the area averaged lining temperature, T,

 

from the equation:

 

r0

 


 

T

 


 

T (r )r dr

 


 

r dr

 

p

 


 

re

 


 

r0

 


 

re

 


 

p

 


 

Where re represents the radius at which the pad-disk contact begins. r0 represents the

 

outside radius of the pad-disk contact. p represents the angle subtended by sector brake

 

pads, and T(r) is the temperature at each point of the pad, obtained numerically from

 

analyzing the heat equation .

 


 

If re=.308 ft. r0 =.478 ft. and p= .7051 radians, and the temperatures given in the

 

following table have been calculated at the various points on the disk, answer the

 

following questions:

 

1. Find an approximation for T at r = .315 ft.

 

2. Find an approximation for T at r = .380 ft.

 

3. Find an approximation for T at r = .455 ft.

 

INPUT

 

1. re=.308 ft.

 

2. r0 =.478 ft.

 

3. rp= .7051 radians

 

r (feet)

 


 

T(r)(F)

 


 

/usr/share/prizm/cache/WorkfileCache/tlwuBO9WeS-GFR2l33Bg2Q/WorkfileContents.doc

 

Page 1 of 2

 


 

gvk

 


 

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.308

 

.325

 


 

|X-02 | 2/29/16| 2/2

 


 

640

 

794

 


 

.342

 

.359

 

.376

 

.393

 

.410

 

.427

 

.444

 

.461

 


 

43.

 


 

885

 

943

 

1034

 

1064

 

1114

 

1152

 

1204

 

1222

 


 

Report

 

1. (page one): Difference Table

 

2. (page 2, 3, 4):

 


 


 

Case #: r = x.xxx using 3rd order NGF

 


 

u

 

=

 

1

 


 


 

u

 

=

 

2

 


 


 

u

 

=

 

3

 


 


 

u

 

=

 

4

 


 


 

error =

 

f(x.xxx ) =

 


 

Note: Error is the fourth term of the NGF

 


 

/usr/share/prizm/cache/WorkfileCache/tlwuBO9WeS-GFR2l33Bg2Q/WorkfileContents.doc

 

Page 2 of 2

 


 

gvk

 


 

 


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