©Hal Gurgenci 2001
The function of the steering system is to enable the driver to control the orientation of the front wheels and thereby control the overall direction of the vehicle. The steering performance is generally linked with the design of the suspensions.
As in the other parts of this exercise, follow the KISS rules. I also strongly suggest you read through the HowStuffWorks page on steering. It will make the following much clearer. You may also want to visit the web page of Team Orion, which provides a concise treatment of elementary car dynamics.
The simplest way of turning the front wheels is by turning the wheel axle as shown below:
This is how the horse-drawn carriages were being steered. Not surprisingly, the first automobiles were designed as horseless carriages and they were steered as shown in the second figure on the left by rotating the entire axle.
You want to keep your design simple, but this is probably too simple. This steering configuration suffered from the fact that the horizontal component of any shock load acting on either wheel had substantial leverage on the steering direction. This made the vehicle very difficult to control.
DOUBLE-PIVOT (ACKERMANN) STEERING
If you examine the single wheel above, you will notice that you only need a stub shaft coming out of the wheel to turn that wheel; you do need a whole axle. If both front wheels have similar stub shafts, then they will be rotating on their individual pivot points rather than around the centre of the wheel base. This idea is summarised in the following figure:
This system was patented in London by Rudolph Ackermann in 1817. Ackermann was not the inventor of the arrangement but he was astute enough to see its importance. The double pivot arrangement still is the most favoured steering arrangement even today and it has come to be known as Ackermann steering.
The steering wheel is connected to the tie rods attached to each wheel by means of shafts, universal joints and vibration isolators. Two most common options to convert the steering wheel rotation to translation at the tie rod ball joints are
In this project, you are advised to design a rack and pinion joint. The following figure should define the basic components of a rack-and-pinion arrangement.
In the Ackermann system, the wheels swivel at equal angles when driving along a curve. At low speeds, this may cause scrubbing of the wheels and heavy steering loads. This was vaguely alluded to in the original Ackermann patent. A French carriage builder, Charles Jeantaud, modified it in 1878 to overcome this problem. Ackermann steering as we know it today includes the Jeantaud modification.
The Ackermann system with Jeantaud modification requires the axes of the steered front wheels to intersect on the axis of the unsteered rear wheels. This is shown in the following figure:
All four wheels are rotating around the same centre. This means none of them will slip. This can only be accomplished if the two front wheels are not parallel but there is an angle between them. This angle is called the Ackermann angle. The above figure was for a wide turn. The situation is clearer for a tighter turn:
From the geometry, one can show that the two front wheel angles are
where the approximation is only valid for small turning angles. The Ackermann angle is the difference between these two angles, ie
This Ackermann angle is not constant of course but varies with the turning radius, R. A so-called Ackermann factor is the ratio between the actual angle between the front wheels and the full Ackermann angle as shown in the above figure. For parallel steering, the Ackermann factor is zero. When Ackermann geometry is fully implemented as in the above figure, the Ackermann factor is 100%.
Having a high Ackermann factor is useful in taking tight corners at low speed. At higher speeds its usefulness is dubious. In fact, during high-speed cornering the dynamic effects compensate for the Ackermann effect and some even suggested using a negative Ackermann angle, which is sometimes referred to as anti-Ackermann steering. For a racing car, it is common to use zero Ackermann (ie parallel steering).
FRONT WHEEL GEOMETRY
The above analysis should be of help in getting the kinematics right. One also needs to be careful about the geometry around the wheel itself. The local wheel steering geometry determines how the forces and the moments are transmitted and is an important consideration. The steering axis for the wheel is not vertical but inclined in both longitudinal and cross-sectional planes. This steering axis is traditionally referred to as the kingpin. The castor and the inclination angles associated with the kingpin orientation are defined in the following figure:
As it is seen, the kingpin is tipped outward at the bottom. For passenger cars, typical values for the kingpin inclination angles are 10-15o. You should also note that the kingpin intercepts the ground slightly inside of the wheel contact. The distance is called the "kingpin offset" or "scrub". Such an offset is not only necessary to create space for things like brakes, suspension and steering components; it also adds to the "feel of the road" and reduced static steering efforts.
In the longitudinal plane, the kingpin is intercepts the ground ahead of the wheel axis as shown in the above figure. The associated angle is called the castor angle. Typical values range from 0 to 5o.
The wheel is seen to be vertical in the above figure. This may not always be the case. Camber describes the angle between the tire's centerline and the vertical plane. If the wheels of the car lean inwards, the camber angle is said to be negative, if they lean outward, the angle is said to be positive. It is usually measured at ride height. Too large a camber angle will act to reduce the grip during cornering when further camber change occurs due to suspension action. The camber is demonstrated in the following figure.
Here are the inertias and etc of those wheels, courtesy of Mark Casey and Frank Evans. I copy Mark's e-mail to me here. I have no reason to believe that they may be inaccurate but use it at your own risk:
Dear Prof Gurgenci
I have attained some approximate values for moment of inertias and radii of gyration through the uni team solid edge model. These would be good estimates for people doing suspension in other groups so Frank was wondering if you would like to make these figures available.
I1=250 I2=200 I3=60 kg.m^2
radii of gyration: k1=800 k2=750 k3=400
where axis 1 is the direction if the driver was to point to the sky
axis 2 is if the driver were to point sideways
axis 3 in the direction of the drivers legs