1. Steering Design Documentation
Northwestern Formula SAE 2013-2014
Derek Oung
Northwestern Formula SAE 2013-2014
Steering Design Documentation
Derek Oung
Steering Design CAD Model Dimetric View
2. Steering Design Documentation
Northwestern Formula SAE 2013-2014
Derek Oung
Goals
The steering system enables the driver to control the direction of movement of the car
Improved ergonomics:
Reduced angle of the steering wheel from the vertical plane
The steering wheel of the NFR 13 is 45° from the vertical plane. With the reclined seat, the driver was
not able to comfortably maneuver the steering wheel. Although this year’s car has an upright seat, the
angle of the steering wheel from the vertical plane will be reduced, making it more convenient for the
driver to steer.
Smaller steering wheel turn
The steering wheel of the NFR 13 has a total turn of 244°, 122° to the right and 122° to the left. A
smaller steering wheel turn compared to the NFR 13 will also make steering the car more comfortable
because the driver does not have to turn the steering wheel as much when going from turning back to
straight and vice versa.
Progressive Steering:
Progressive steering refers to having the wheels turn faster relative to the steering wheel as they turn to
the maximum and slower relative to the steering wheel the straighter they are. This enables the driver
to keep the car moving straight easily because turning the steering wheel by a little while it is at its
center only turns the car a little. Furthermore, when the driver needs to turn the car, the wheels will
have a greater response, allowing the driver to make the turn when required.
Minimal play:
The SAE rule for maximum amount of play is 7 degrees. This means the wheels have to respond to the
steering wheel before 7 degrees of steering wheel turn. Minimizing play will allow better response and
feedback of the wheels, making it easier to gauge how much the car is turning.
Design
Single universal joint:
Figure 1: Diagram of variables for the
universal joint. Axle 1 is perpendicular to
the red plane and axle 2 is perpendicular
to the blue plane at all times. These
planes are at an angle β with respect to
each other. The angular displacement
(rotational position) of each axle is given
3. Steering Design Documentation
Northwestern Formula SAE 2013-2014
Derek Oung
by and respectively, which are the angles of the unit vectors and with respect to their
initial positions along the x and y axes. The and vectors are fixed by the gimbal connecting the
two axles and so are constrained to remain perpendicular to each other at all times.
Reduced angle of the steering wheel from the vertical plane
Last year’s car did not use a universal joint. The steering wheel was connected to the rack and pinion via
one steering column. This angled the steering wheel such that it is 45° from the vertical plane. With a
single universal joint, two steering columns will be needed. This will reduce the angle of the steering
wheel from the vertical plane.
Progressive Steering
One possible problem using a single universal joint is that the angular velocity of the output shaft
relative to the input shaft will vary depending on the degree of turn. This is shown in Figure 2.
Usually, this is corrected by using another universal joint and an intermediate shaft in between the two
universal joints. However, a single universal joint can also be used to increase the angular velocity of the
output shaft at the edges of the turn. This will be used for progressive steering. Furthermore, a double
universal joint configuration will introduce more play to the system than a single universal joint.
From Figure 2, it can be seen that the maximum output shaft angular velocity occurs when the input
shaft angle is at 0 or 180 degrees. The minimum occurs when the input shaft angle is at 90 degrees.
Figure 2: Graph of output shaft speed relative to input shaft speed (Omega2) against input shaft angle
(Gamma1)
4. Steering Design Documentation
Northwestern Formula SAE 2013-2014
Derek Oung
The maximum and minimum output shaft angular velocities relative to the input shaft angular velocity
are shown in Table 1. The highlighted strip shows our desired angle between the output shaft and the
plane of the input shaft, which 30°. In other words, the angle between the input and output shaft is
180°-30°=150°. This angle is chosen because we want the ratio of steering wheel turn to wheel turn to
be 6° to 1° at the center and 4° to 1° at the edges. Thus, the desired Omega2prime/Omega2*100% value
is 133.3333%
Smaller steering wheel turn
For 33° of wheel turn, we are looking for 1.92’’ of rack travel. With the rack and pinion selected, the
steering wheel will have a total turn of 172°, 86° to the left and 86° to the right.
Table 1: Table showing different angles between the output shaft and the plane of the input shaft (Beta)
and the corresponding output shaft angular velocities (Omega2, Omega2’) when the input shaft angle
(Gamma1) is at 0 or 180 degrees and 90 degrees
Steering columns:
The steering columns will be made out of 4130 steel. Calculations were done for the steering column
between the steering wheel and the universal joint. The sample calculations are shown below.
Sample calculations: Using the values shown below,
𝐹 = 444.8222𝑁, 𝑟 = 0.1350𝑚, 𝑂𝐷 = 0.01905𝑚, 𝐼𝐷 = 0.017399𝑚,
𝑌𝑖𝑒𝑙𝑑τ = 435000000𝑃𝑎
𝑇 = 𝐹 ∗ 𝑟
𝑇 = 444.8222 ∗ 0.1350 𝑁𝑚
𝑇 = 60.051𝑁𝑚
5. Steering Design Documentation
Northwestern Formula SAE 2013-2014
Derek Oung
𝑚𝑎𝑥τ =
𝑇 ∗ 𝑂𝐷
𝜋
2 ∗ ((
𝑂𝐷
2
4
−
𝐼𝐷
2
4
)
𝑚𝑎𝑥τ =
𝑇 ∗ 𝑂𝐷 ∗ 32
𝜋 ∗ ((𝑂𝐷4 − 𝐼𝐷4)
𝑚𝑎𝑥τ =
60.051 ∗ 0.01905 ∗ 32
𝜋 ∗ ((0.019054 − 0.0173994)
𝑚𝑎𝑥τ = 290903298.3𝑃𝑎
𝐹𝑎𝑐𝑡𝑜𝑟 𝑜𝑓 𝑠𝑎𝑓𝑒𝑡𝑦 =
𝑌𝑖𝑒𝑙𝑑τ
𝑚𝑎𝑥τ
=
435000000
290903298.3
= 1.49534
The yellow highlighted strip indicates the column of the desired diameter and wall thickness. Its
diameter and wall thickness is the same with that of NFR 13. It has a factor of safety of 1.5 when
subjected to a torque of 60.051Nm as a result of a 100 lb (444.82216 N) force and a steering wheel
radius of 5.25 in (0.135 m).
6. Steering Design Documentation
Northwestern Formula SAE 2013-2014
Derek Oung
Figure 3: Calculations for a 4130 steel column of an outer diameter and wall thickness of sufficient factor
of safety
7. Steering Design Documentation
Northwestern Formula SAE 2013-2014
Derek Oung
Rack and Pinion:
Limiting the steering wheel turn to less than 180 degrees requires a rack and pinion that has more than
3.84 inches of rack travel with 1 revolution of the steering wheel.
We decided to use a Small Rack and Pinion Fast Ratio Steering Box from Speedwaymotors. An image of
it is shown The link to its specs are shown below:
Figure 4: Image of Speedwaymotors Small Rack and Pinion Fast Ratio Steering Box
http://www.speedwaymotors.com/Small-Rack-and-Pinion-Fast-Ratio-Steering-Box,3692.html
It has 4 inches of rack travel with 1 revolution of the steering wheel. It weighs 2.5 lb. Its length, height
and depth are 12, 2.38, and 2 in respectively.
Possible Issues and Further Investigations:
Smaller steering wheel turn
This may introduce a resistance that may be significant enough to cause discomfort when turning the
steering wheel because of the additional force needed to turn the steering wheel.
