Simcenter Amesim Project with Bearcats Motorsports

UC’s own FSAE team, Bearcats Motorsports (BCMS), is mostly comprised of senior-year students who start the 9-month design cycle around mid-summer for the next year’s competition. After working on designing, ordering &/or manufacturing required parts and building the car, the team sets aside some time before the competition to test their car and gather data. Besides making sure that the build-quality is up to the mark, the testing phase gives the team the performance data that is invaluable when you are competing against other world-class teams. Even though FSAE releases the course layouts prior to the competition, replicating the track to do test runs on it is unimaginably difficult.

One possible solution to that is lap simulations, and this is objective of this project. Using Simcenter Amesim, we first build the suspension model, perform a parametric analysis on the suspension hard-points to finalize the design. I have chosen to dive deeper into the suspension subsystem because it is critical to replicate the behavior of the actual car. With Simcenter Amesim, you can build detailed models of any one or all your subsystems: suspension, aerodynamics, engine, etc. Once the suspension model is validated, we integrate the different subsystems into a single 15DOF vehicle model. Then, we import the characteristics of each real subsystem to replicate their performance in the vehicle model. For example, for the chassis subsystem, we import parameters like pitch, roll, yaw inertias, sprung and unsprung masses to name a few. We then, use the sensor models or other inbuilt tools to validate the performance of the vehicle model with the data from the real car. The final step would be to import the track of interest and incorporate path-following control to make sure that the vehicle model follows the reference trajectory.

Graphic showing roadmap for Lap Simulation

Figure 1: Roadmap for Lap Simulation; 1. Design 2019 BCMS suspension in Amesim 2. Parametric analysis of the hardpoint locations 3. Design an Amesim model of the 2019 BCMS car 4. Import the 2019 FSAE Endurance track into Amesim 5. Incorporate path-following control to the vehicle model

Suspension Design in Simcenter Amesim

Automotive Suspensions

The two most commonly used suspension systems in the automotive industry are the double-wishbone and McPherson strut suspensions. Both configurations have their respective advantages and disadvantages. The McPherson strut is relatively simple suspension model because of the fewer number of links to the chassis while the increased number of hardpoints in the double-wishbone system gives the designer more degrees of freedom to achieve the required performance characteristics. In addition to that, using the double-wishbone enables the designer to lower the ride height of the car to a much higher degree. For these reasons, the double-wishbone suspension is very commonly used in racecar applications as a lower center of gravity is a desirable attribute. In accordance with that, 2019 BCMS team also adopted this configuration.

Diagram of a double-wishbone and McPherson strut suspension

Figure 2: Double-wishbone and McPherson strut suspension

Simcenter Amesim Model

In this section, the Amesim model for the double-wishbone suspension is presented. The model is built using different blocks available in the 3D Mechanical library. This model is now available as a template in Simcenter Amesim. To use this model to design your suspension, you need to either import the hardpoint locations, shown in Fig. 3, or manually enter them in the Global Parameters list.

Diagram of double-wishbone suspension hardpoints

Figure 3: Double-wishbone suspension hardpoints

A screenshot of the template in Amesim is shown in the image below. This model takes the amount of steering rack input, wheel vertical motion, and the forces and moments acting on the wheel center as the inputs. And it computes the toe, camber, self-rotating angles along with the variation in wheelbase and half-track. This particular model can also be used for generating Kinematic & Compliance analysis data which will be discussed later.

Screenshot of Double-wishbone suspension template

Figure 4: Double-wishbone suspension template

Once the hardpoint locations are set, we can visualize and animate the suspension model based on our inputs using Amesim’s 3D Assembly block. All we need to do is import that block and Amesim will build the 3D model of our suspension and animate it.

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Parametric Analysis of Hardpoints

Now that we have completed building a base suspension model in Amesim, we can use Amesim’s Batch Analysis feature to do a parametric analysis and visualize the effect that the change in certain inputs will have on the outputs of interest. To demonstrate this, we take the case where each suspension hardpoint locations were shifted by 0.5” in every direction and the respective characteristic curves like camber and toe were plotted against each other. This, along with other key performance parameters like caster, KPI etc., are used to finalize the locations of the hardpoints. 

Diagram of Batch plots for parametric analysis for changes in hardpoint K

Figure 6: Batch plots for parametric analysis for changes in hardpoint K

Vehicle Model

When building a model that will be used for simulations, the most crucial aspect is to maintain a decent fidelity in the model. If not, the simulation model will not behave like its real-life twin and the data collected from the simulations will not be useful for making strategic decisions in the real-world scenario.

High-level breakdown of an automobile into subsystems

Figure 7: High-level breakdown of an automobile into subsystems

To maintain a respectable fidelity in vehicle simulations, the automobile has to be broken down into subsystems and the performance of each subsystem has to be replicated in the vehicle model to a desired degree of fidelity. Amesim’s modular block-building nature allows you to connect different subsystems and define the respective characteristics individually, if required, with ease. In addition to that, the complexity of each model can be chosen based on the user’s requirement using the Submodel mode. This allows the user to set the degree of fidelity of each subsystem depending on the area of application.  

The following image shows a fully decked up vehicle model built in Simcenter Amesim using the Mechanical, Control, Powertrain and Vehicle Dynamics libraries. You can see that all the different subsystems are connected to a central 15DOF Chassis model. As I have previously mentioned, apart from the necessary subsystems, the other subsystems’ influence can be ignored by not including them in the model. For example, if you do not have the aerodynamic characteristics of your real car or you just do not want to consider its effect, you can remove the blocks related to it.  

Screenshot of Vehicle model in Simcenter Amesim

Figure 8: Vehicle model in Simcenter Amesim

Kinematic & Compliance Analysis

In vehicle performance simulations, the interaction between the vehicle and the track beneath is crucial, and because the unsprung mass is the link between both, modeling its performance will define the interplay. To enable this, the 15DOF Chassis model requires us to provide data which define the suspension’s behavior with respect to the movement of the wheel and the forces that are acting on it. In order get that data, we need to carry out an analysis called the Kinematic & Compliance analysis.  

The Kinematic section treats the suspension components as kinematic elements where the forces and moments are not considered. The data gives us a mapping from vertical displacement of the wheel (Z), steering rack input (Yn) and the influence of the opposite wheel (for a linked suspension) to toe, camber, dive angles, wheelbase and half-track variations. The compliance segment gives the same outputs but based on the forces and moments acting on the wheel. 

Diagram of Suspension Kinematics & Compliance;

Figure 9: Suspension Kinematics & Compliance;

Usually, getting this data is a very tedious process, but Amesim has a dedicated inbuilt app that does this for us. We just need to import the app to the suspension model, shown in Fig. 4, and set the range of wheel movement, steering inputs and anticipated vertical force on the wheel.

Screenshot of KnC Data Generator App

Figure 10: KnC Data Generator App

The app will give us the data which we should save and import into our 15DOF Chassis model. Once we do that, our suspension’s dynamic behavior will be like that of our real vehicle. Along with the kinematic tables data and the compliance coefficients, the app also gives us information about other key suspension geometric parameters like king-pin inclination angle, caster, rollcenter height, etc. These parameters can be used to validate the suspension model with already existing data to get sense check. BCMS Suspension team gave me the data from their suspension model in Optimum K. I used that to validate the suspension model, as seen in Fig.  

Suspension model validation using KnC app with Optimum K data

Figure 11: Suspension model validation using KnC app with Optimum K data

Virtual Sensor Models

For the simulation to be accurate, the vehicle model that we are building needs to be of good fidelity. Then, after applying control to the developed model, the collected data of the dynamics of the vehicle can be used for analysis. Now that we have validated the suspension model in the previous section, we can make use of Amesim’s sensor models to measure key vehicle characteristics like yaw rate, longitudinal and side slip (the tire modeling section will be added to in the next version of the tutorial), camber of each wheel to name a few. This “measured” data can be used to validate the dynamics of the simulation model with actual data collected from the real vehicle during the testing phase. We can develop the same track or scenarios that were used to collect the data from the real vehicle in Simcenter Amesim to run the simulation model. That will give us a way to compare data of the two models (real and simulation) over the same track.

Different types of sensors available in Simcenter Amesim

Figure 12: Different types of sensors available in Simcenter Amesim

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Import Reference Track

Once the vehicle model has been validated, we can start thinking about incorporating control to the model such that it follows the reference track. One final step before that is to import the track of interest into Amesim. The first step is to find the track layout in SVG format. If the track is not available in this format, we can use software like Inkscape to convert PDF or PNG into SVG format. In addition to that, we also need Open Street Map data of the track. If the track is well renowned, we can find this in Open Street Map editor. If not, we need to create/upload our track on to OSM and then download the data. Amesim documentation regarding this has some steps to generate the required OSM data.

Inputs required to import the track to Amesim

Figure 14: Inputs required to import the track to Amesim

The next step would be to generate the profile waypoint information that will be used by the Trajectory Designer app to define the track trajectory in data points. This is done by using Ametrack app which can be opened from the VDGROUND0 component used for ground description. The app takes the OSM data as input. Then, open the Trajectory Designer app, import the SVG file and the waypoints generated by Ametrack. This app will generate the data points which will be used by the lateral controller to make the vehicle follow the track. In addition to that, the app will also generate a reference velocity map that will be used by the longitudinal controller to control the speed of the vehicle through the track. The directories of these corresponding data files must be carefully specified as inputs for both the controller models. For more details on how to use the app, kindly follow the comprehensive Amesim documentation of the same.  

Trajectory app designer in Simcenter Amesim

Figure 15: Trajectory app designer in Simcenter Amesim

Path-following Control

To summarize what we did till now, we first developed the double-wishbone suspension model and used Amesim’s inbuilt apps for validation and Kinematic and Compliance. Then, we built an integrated vehicle model accounting for all the necessary subsystems with varying fidelity based on the application. Then, we used sensors to measure variables for validation. The last step was to import the track of interest into Amesim. Now that we have our vehicle model and our track, the final piece of the puzzle is to design a controller that controls the vehicle such that it follows our track trajectory. 

Lap simulation schematic

Figure 16: Lap simulation schematic

Diagram of Control logic

Figure 17: Control logic

Amesim accomplishes this by combining two controllers. One controller is setup to control the throttle and brake inputs to the vehicle model. The magnitude of the control input is computed such the actual vehicle velocity matches closely with the reference velocity generated by the Trajectory Designer app. This is done using a feedforward-feedback control strategy. Amesim uses a Model Predictive controller for the lateral control of the vehicle to effectively reduce the error between the trajectory and the path followed by the vehicle. Controller parameters like the feedback gain for the longitudinal controller and prediction horizon, control horizon, state error and control input weight matrices for MPC must be tuned to achieve desired performance. We can use the displacement sensors to plot the trajectory followed by the vehicle to check whether our model is behaving as planned or not. In addition to that, we can use the base vehicle dynamics animation model ‘Vehicle_Dynamics_Global_Analysis’ to visualize our vehicle following the track of interest. 

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Graphic showing roadmap for Lap Simulation

Figure 19: Roadmap for Lap Simulation; 1. Design 2019 BCMS suspension in Amesim 2. Parametric analysis of the hardpoint locations 3. Design an Amesim model of the 2019 BCMS car 4. Import the 2019 FSAE Endurance track into Amesim 5. Incorporate path-following control to the vehicle model