The starting point for the MSC Adams and Creo models was a spreadsheet that defined the hardpoints of the suspension structure and some anti-characteristics of the system. As mentioned, many MSC Adams simulations were required to consider all the kinematic and dynamic aspects of the suspension.

• Suspension kinematics testing, i.e., parallel wheel displacement, opposite wheel displacement, and steering displacement. These simulations were necessary to evaluate the kinematic characteristics and behavior of the suspension architecture.
• Modal analysis of the vehicle, which generated knowledge of the first natural frequency and the ideal stiffness and damping values for the vehicle system at different workload conditions (e.g., unladen vehicle weight, gross vehicle weight, etc.).
• Dynamic performance simulations, necessary to measure the comfort, handling, and traction performance of the vehicle. These were obtained by performing: ISO5008 simulations at different vehicle speeds; ramp steering and moose test simulations; and traction tests on a 4-poster test bench.

Most of the objective functions of the optimization were outputs of these simulations, such as selected kinematic characteristics of the suspension or the dynamic performance in terms of comfort, handling, and traction. Some other outputs, however, served as inputs to other models.
For example, ideal stiffness and damping values from the Adams modal analysis were considered as inputs for hydraulic circuit sizing in Simcenter Amesim. At the same time, the actual stiffness and damping force curves were evaluated in the hydraulic circuit sizing and were inputs for the dynamic simulations in Adams.

The static loads on the suspension actuators and the corresponding ideal stiffness and damping values were inputs to the sizing of the hydraulic circuit. The circuit was then sized to support these loads and achieve the target stiffness and damping values. In addition, it was sized so that the overall dimensions and cost met the targets. The main parameters to be considered were the dimensions of the hydraulic actuators, the dimensions of the hydro-pneumatic accumulators, and the damping valves and/or orifices. The correct working pressure range also had to be verified. To do this, a spreadsheet and some Amesim templates were deployed. In particular, an Excel sheet was exploited to size the stiffness part of the circuit while the Simcenter Amesim models were used to set the dimensions of the damping valves and/or the dimensions of the orifices.
These models were also used to evaluate the actual stiffness and damping force curves, which are different from the ideal ones identified in the modal analysis. These curves were needed by the Adams dynamic simulations to consider the actual behavior of the suspension system.

The optimization process required control so that there was no static and dynamic interference between the individual mechanical parts and the elements of the hydraulic circuit. It was therefore necessary to integrate two simplified 3D CAD models developed in Creo, one for static and one for dynamic interference.
The input parameters of these models were the coordinates of the structure’s hardpoints, the overall dimensions of the hydraulic circuit elements, and the maximum vertical and steering displacement of the suspension. This ensured the feasibility of the solution in each suspension configuration.

Fig. 4 - Simplified CREO model for evaluating interferences

Fig. 5 - First concept of the optimization workflow

The first concept of the optimization workflow illustrated in Fig. 5 was characterized by a large number of input variables and objectives.
This resulted in a significant number of designs being evaluated in the optimization stage to obtain reliable and accurate results. In addition, each simulation model had to be run for each design, and some of these simulations were quite long, which would have made the process inefficient.
Therefore, we decided to split the workflow into three cycles or loops, each of which had fewer input variables, fewer objectives, and thus fewer designs to evaluate than the initial workflow. As shown in Fig. 6, each loop represented the optimization of some aspect of the entire system.
This was possible because some of these aspects were independent of each other, while we used the optimized outputs from previous loops as inputs for the dependent aspects. Finally, the workflow was structured to clearly describe the method of investigating the phenomena and to manage the strategic analysis more easily.

Fig. 6 - Workflow split into three loops

Loop 1

Loop 1 was used to define the kinematics of the suspension, hence the structure of the hardpoint positions that influence the main kinematic parameters. The objective of this loop was to find the best architectural solution that would guarantee the best kinematic characteristics of the suspension, while ensuring that there was no mechanical interference.
The design parameters for Loop 1 were as follows:

• Input variables - 23 variables between independent hardpoint coordinates and kinematic requirements.
• Output variables - dependent hardpoint coordinates, kinematic characteristics, steady-state roll stability factor, and possible interference.
• Objective functions - minimization of camber loss and maximization of roll stability factor.

These objectives were chosen after a sensitivity analysis. Other objectives suggested in the first optimization concept were turned into constraints:

• constraints - kinematic features have minimum values and no static/dynamic interference.

The workflow concept for Loop 1 is illustrated in Fig. 7.

Fig. 7 - Loop 1 workflow

Loop 2

The block diagram of Loop 2’s workflow is shown in Fig. 8. The goal was to define both some remaining hardpoint locations and the suspension stiffness and damping in order to minimize the first natural frequency of the system.
The optimized coordinates from Loop 1 were held constant while the hardpoints affecting the vehicle’s anti-dive were set as variables. This is because the anti-dive value affected the modal analysis of the vehicle. The modal analysis was repeated in the workflow for different load conditions.
In addition, a nested optimization of the hydraulic circuit sizing was integrated with the information from the Adams modal analysis (i.e., static cylinder loads and corresponding stiffness values). This loop focused on the stiffness aspect of the circuit while the damping aspect was studied in Loop 3.

Figs. 8 - Loop 2 workflow

The design parameters of Loop 2 are described below:

MAIN

• Input variables - 23 variables including independent hardpoint coordinates, suspension anti-characteristics, stiffness, and damping values.
• Output variables - dependent hardpoint coordinates, modal analysis results.
• Objective functions - minimization of the first eigenmode frequencies. The first natural frequency should be as low as possible, while not descending below the motion sickness value (about 1 Hz).
• Constraints - kinematics have minimum values, motion sickness, absence of interference.

NESTED

• Input variables - 12 variables between hydraulic circuit parameters and input of constants from the modal analysis.
• Output variables - min/max effective suspension stiffness for each load condition, min/max levelling pressure for each load condition, penalty function, cylinder footprint, effective stiffness force curves.
• Objective functions - penalty function minimization, footprint and cost minimization. The penalty function was defined to reach 0 when all stiffness requirements are met. The lower the value of the penalty function value, the better the solution.
• Constraints — achieving the most important stiffness values.

Fig. 9 - Loop 3 workflow

Loop 3

The optimization goal for Loop 3 was the definition of the suspension’s damping requirements. The minimum and maximum damping coefficients found in the Loop 2 modal analysis were the starting points for this optimization. This workflow was divided in two sub-optimizations, a valve pre-selection and a dynamics optimization.
The first was aimed at continuous sizing of the damping part of the hydraulic circuit and subsequent selection of the most suitable valves from a portfolio. Starting from these best valves, the goal of the second sub-optimization was to improve the dynamic performance in terms of comfort, handling, and traction. The variable parameters were the input current to the damping valves, which define the damping of the entire system. Every other parameter was taken from the previous loops and set as a constant.
The design parameters for Loop 3 were:

OPT.1 – Valve pre-selection

• Input variables - 12 variables between hydraulic circuit parameters and input of constants from the modal analysis.
• Output variables - list of best damping valves.
• Objective functions - minimization of hydraulic circuit size and cost.
• Constraints - achieving the min/max damping coefficients.

OPT.2 — Dynamic optimization

• Input variables - valve index, valve input currents.
• Output variables - effective damping force curves, Adams dynamic simulation results.
• Objective functions - minimization of whole-body vibration (comfort), maximization of roll stability factor (handling), maximization of total contact factor (traction).
• Constraints - no constraints.

Each of the three dynamic simulations in Opt.2 (i.e., comfort, handling, and traction) had a dedicated project node with a nested optimization.
This made it possible to evaluate the corresponding best valve current, and hence damping value, for the three different aspects. The conceptual workflow for Loop 3 is shown in Fig. 9.

Each loop presented in the previous section required a multi-objective optimization approach since there was more than one objective function per loop.
Due to the large number of input variables, the optimization strategy required a robust optimization followed by an accurate one.
modeFRONTIER enabled each best-solution cluster to be identified with the first step, while refining the best values more accurately with the second.
Regarding Loop 1, an NSGA-II controlled system algorithm was selected for the robust optimization and an NSGA-II variation population size for the accurate one. The DOE of the first robust optimization was created in modeFRONTIER starting from the lower and upper bounds of the input variables and using the Incremental Space Filler and Uniform Latin Hypercube algorithm.
In contrast, the DOE of the second and accurate optimization was the set of best designs from the robust optimization.
As Fig. 10 shows, the reference design was far from the Pareto frontier. This implies that one or more better solutions in terms of kinematic characteristics could easily be found among the analysed ones. With more than one best solution available, it is up to the user to choose which direction to take regarding the Pareto frontier.
Almost the same optimization strategy was chosen for Loop 2, both for the main and the nested workflows (i.e., an NSGA-II controlled system for the robust optimization, an NSGA-II variation population size for the accurate optimization). The creation of the Loop 2 DOE was also similar to the previous loops.
Fig. 11 shows the results of the optimization of the hydraulic circuit from Loop 2. The best solutions highlighted are of particular interest with regard to the reference design. Both had a better penalty function value, but one had the same cost and footprint as the reference design, while the other had a lower cost.
Other Pareto frontier designs were not as interesting due to their higher cost and footprint. As mentioned in the previous section, Loop 3 was divided in two sub-optimizations. The optimization strategy for Loop 3 Opt. 1 was the same as for the other loops, with a robust step and an accurate one.
The strategy for Loop 3 Opt. 2 was a little different. The goal was to optimize the valve input currents only for the valve combinations present in the best valves list obtained from Opt. 1. We therefore decided to select a DOE sequence for the main workflow of Opt. 2 while a gradient-based optimizer (B-BFGS) was chosen for the nested optimizations related to comfort, handling, and traction. The DOE was created using an Incremental Space Filler, which ensured that all possible valve combinations were covered. An IF node was then used to check whether the current DOE design was in the list. If so, the optimization was allowed to continue, whereas the optimization would advance directly to the next design if not.