Force and Moments part #2
31 March 2014
Dr. Peter Tkacik
Book problems page 359 modified slightly and due 7 April 2014
1. Define the transformation matrices required to convert data from the SAE Tire Axis
System to the ISO Wheel Axis System.
2. What is the sense of the aligning moment and lateral force associated with a positive
inclination angle in the ISO Wheel Axis System?
3. Due to the width of the tire to be tested and clearance problems with respect to the load
cell system, a special adapter was manufactured to move the test wheel plane off-center
with respect to the design wheel plane location for the force and moment machine. The
assembly wheel plane is now 5 cm outboard (Y′+) of the location that the machine’s
programming assumes to be the origin of the Tire Axis System. Derive the equations that
properly express the data in the actual SAE Tire Axis System using the machine reported
data as input. Be sure to assume that inclination angle is present. Review the definition of
the origin of the Tire Axis System given in Section 8.1.1 before beginning this problem.
4. Write a Matlab program that transform the FY and MZ data used to generate figures 8.17
and 8.19 from the SAE Tire Axis System to the ISO Wheel Axis System. These data are
for a constant FZ. The data are in the problem 4 data set.
Problem 4: Data set:
SA (deg)
-10
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
Fy (N)
5689
5602
5440
5306
5155
4917
4595
4124
3275
2006
242
-1588
-2966
-3893
-4397
-4744
-5000
-5101
-5248
-5357
-5455
Mz (Nm)
-25
-34
-40
-52
-67
-83
-97
-117
-116
-79
-10
64
105
115
103
88
74
57
49
44
35