SANLUIS Rassini has been working on a suspension design project that takes the conventional "Hotchkiss" (leaf spring) rear suspension used on all pickup trucks and adds new features which will allow it to live well into the 21^st century. The purpose of this article is to quickly identify how Surfer is used to couple the front and rear spring rates so the rider experiences smooth vertical motion and the vehicle does not pitch back and forth.

If you are not familiar with the traditional pick-up truck rear suspension, it consists of a 2-stage leaf spring bolted to a solid axle (Fig 1). The leaf spring is designed to have 2 distinctly different stiffness values (or rates) which change passively as a function of vertical axle deflection. When the vehicle is lightly loaded, you ride on what is known as the 1^st stage. When the vehicle is ballasted or loaded, the suspension compresses and engages a second stage plate which elevates the overall stiffness of the system (Fig 2 and 3).

Figure 1. The traditional pick-up truck rear suspension consists
of a 2-stage leaf spring (red) bolted to a solid axle (purple).

Figure 2. When the vehicle is heavily loaded,
the 4^th plate (shown in orange) is engaged (2^nd stage).

Figure 3. This image shows the traditional force/deflection diagram of a 2-stage
leaf spring. When the vehicle is loaded and the second stage plate is engaged
(indicated by red dot), the spring rate increases showing an increase is stiffness.

The front suspension on a pick-up truck is only 1-stage. It is important to understand the distribution of mass in the vehicle and to match the front and the rear suspension stiffnesses (spring rates) such that the vehicle does not behave erratically. Both the front and rear suspensions have individual stiffness maps like Figure 3, so it is important to understand how the rates need to change based on vehicle mass distribution to give the driver and passengers a sense of smooth ride without disturbing oscillations. This is known and Pitch and Bounce mapping.

The 3-dimensional relationship between the many possible front and rear suspension spring rates of a given vehicle and how they interact to provide driver comfort are shown in Figures 4-8. This is where Surfer is the tool of choice for visualizing how these values interact. The desired front and rear spring rate combination is where the pitch frequency is less than 1.7 (Figures 4 and 5), the bounce frequency is less than 1.4 (Figure 6), and the pitch frequency to bounce frequency ratio is less than 1.2 (Figure 7). These rates need to hold true for both maximum load (a full cargo bed) and passenger load (empty cargo bed).

Figure 4. Pitch frequency maps for (a) maximum load and (b) passenger load (b). Front and rear spring
rates are plotted using pitch frequency as the Z value. Based on the known maximum pitch frequency of
1.7 CPS, the ranges of front and rear spring rates for maximum and passenger loads were determined.
For maximum load, the front spring rate needs to be between 20-55 N/mm and the rear spring rate needs
to be 50 N/mm or less. For the passenger load, the front spring rate needs to be less than 30 N/mm
and the rear spring rate needs to be less than 27 N/mm.

Figure 5. "Go"/"No Go" maps for pitch frequency for (a) maximum load and (b) passenger load. This is a
visual depiction of acceptable pitch frequencies and compliments the Pitch Frequency Maps in Figure 4.
All pitch frequencies below 1.7 (which are desired) are given a Z value of 1. Pitch frequencies above 1.7
are given a Z value of 0. This immediately shows you what front and rear spring rate combinations
are compatible with an acceptable pitch frequency. These areas are shown as high values in blue.

Figure 6. Bounce frequency maps for maximum load (a) and passenger load (b). Front and rear spring
rates are plotted using bounce frequency as the Z value. Based on the known maximum bounce
frequency of 1.4 CPS, the ranges of front and rear spring rates for maximum and passenger loads were
determined. For maximum load, the front spring rate needs to be less than 25 N/mm and the rear spring
rate needs to be less than 50 N/mm. For the passenger load, the front spring rate needs to be
between 25-40 N/mm and the rear spring rate needs to be less than 22 N/mm.

Figure 7. “Go” / “No Go” maps for pitch:bounce frequency ratio for (a) maximum load and (b) passenger
load. This is a visual depiction of acceptable combinations of front and rear spring rates resulting in
satisfactory pitch:bounce frequency ratio of rear/front <1.2. All pitch:bounce frequency ratios below 1.2
(which are desired) are given a Z value of 1. Pitch:bounce frequency rations above 1.2 are given a
Z value of 0. This immediately shows you what front and rear spring rate combinations are compatible
with an acceptable pitch:bounce frequency ratio. These areas are shown as high values in blue.

Figure 7 clearly shows that although there are a number of front and rear spring rate combinations that would satisfy the pitch:bounce frequency ratio at maximum load, there is only one unique solution that satisfies the pitch:bounce frequency ratio at passenger load.

The rear spring is a dual rate, and the transition from 1^st to 2^nd stage is progressive. It can begin with 20-22 N/mm and progress to 50 N/mm or higher with the 2^nd stage plate. Therefore, there is larger tolerance in the spring rates allowed on the rear. The front spring is a single rate spring, which requires a tighter tolerance in the spring rates. Figure 7b focuses on the required rate for the front suspension.

When discussing the complex nature of spring rate mapping, a numeric spreadsheet of data causes people to "glaze-over". A 3D map of the same information using Surfer gets people excited and interested in understanding how everything converges, taking equations and large amounts of data and putting them into a picture anyone can understand.

Once we have mapped the many combinations of front and rear spring rates, Surfer makes it easy to "see" the proper combination to give the smoothest ride.

Mr. Juriga attended the General Motors Institute and worked for General Motors (8 years) and Eaton Suspension Division (9 years) before joining SANLUIS Rassini, the world's largest designer and producer of leaf springs for light vehicles, in 1997. For more information about SANLUIS Rassini, please visit www.sanluisrassini.com. SANLUIS Rassini received an Editor’s Choice award from Popular Mechanics for their work. Mr Juriga says that this is "thanks largely to the work Surfer helped me do in the design process."