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1. Vehicle Suspension
The design of vehicle suspension has a critical functioning role in ground vehicles. Various conflicting functions must be satisfied by the vehicle suspension, namely body attitude and wheel attitude. The suspension needs to provide enough compliance to cope with uneven terrain and isolate the chassis from the induced forces and vibration. Many vehicle vibration models can be used to analyze the modes of vibrations ranging from a 1 degree of freedom (DOF) to 16 DOF for a complete vehicle model. In this particular tutorial, we will look at the 2DOF 1/4 car model to analyze the vertical vibration of a vehicle.
2. Quarter Car Model Simulation
The quarter car model encompasses 1/4th of the sprung mass and incorporating associated un-sprung mass as shown in Figure 1. The dynamics of the sprung mass absorbs excitations from aerodynamics, engine, and drive train where are the imbalanced forces from tire are applied to the un-sprung mass.
Fig 1. Quarter Car Vehicle Model. Vehicle Representation (Left) Simplified Representation (Right)
The dynamics of the quarter car model can be derived by applying Newton's law to each mass and identifying the forces induced on each mass. This leads to the following equations, where W represents road disturbance.
For sprung mass
For un-sprung mass
Using LabVIEW Control Design and Simulation Module, we can build the simulation model from the differential equations above as shown in Figure 2.
Fig 2. Block Diagram of Quarter Car Suspension Model
Let's emulate the vehicle coming out from a pothole that is 0.1 m. You can see that the masses oscillate quite a bit from Figure 3 . We can determine the natural frequencies for both masses by assuming the response of each variable has the form of
substituting into the undamped and unforced system will lead us with the characteristic equation with two solutions
where
Using LabVIEW MathScript RT Module shown in Figure 4, we've determined that the natural frequencies for each of the mass is
Fig 3. Quarter Car Suspension Response
Fig 4. Calculating Natural Frequency
Fig 5. Block Diagram of Quarter Car Simulation
3. Controllable Suspensions
The simulation result shown above for the 1/4 car model motives the need of having a controllable suspension to minimize oscillation thus improving the rider's experience. There are several different controllable suspensions which we can categorized by how active they are
• Passive
o There's no external energy needed. This type of suspension utilize the nonlinearity to be able to adjust the suspension system itself.
• Semi-active
o There's little control power which may only be active at some instances. A slow acting load-leveler system may be integrated.
• Hybrid-Active
o These type of systems might be engaged at only low frequencies and utilize passive or semi-active suspension for high frequencies.
• Fully-Active
o These type of systems has high bandwidth and require the most external energy source.
In this tutorial, we will focus on passive suspension design and in particularly, the concept of skyhook damping.
4. Skyhook Damping
The concept of skyhook damping or so called fictional absolute damper, is to separate the function of absolute body motion and the relative motion between body and wheels. In another words, there will be an additional damping force Fb added to the sprung mass where
It is important to note that a high pass filter is usually coupled with skyhook damper so the skyhook damper will not respond to constant velocities. The modified quarter car suspension model can be found in Figure 6.
Fig 6. Schematic of Skyhook Damper (Left) Block Diagram of 1/4 Car Suspension with Skyhook Damper (Right)
As shown in Figure 7, the skyhook damper passively reduces the oscillation of the vehicle coming out of the pothole hence improve ride stability.
Fig 7. Quarter Car Simulation Results Comparison
5. Conclusion
This article briefly introduces the concept of vehicle suspension and simulate a 2 DOF quarter car suspension using LabVIEW Controls and Simulation Module. The concept of passive suspension is also discussed. By implementing a skyhook damper, the quarter car model reduces its oscillation drastically. It is feasible to implement pitch and bounce dynamics with the quarter car model to simulate a half car response. Notice when performing a half car simulation, it is critical to determine the correct initial conditions.
You can download an evaluation copy of the modules here
LabVIEW Control Design and Simulation Module
NI LabVIEW Robotics Starter Kit
Please contact andy.chang@ni.com to request more information about this article.
6. Related Links
Hybrid Vehicle Test and Simulation using NI's Hardware-In-The-Loop (HIL) Platform
7. Reference
ME 390: Vehicle Dynamics and Controls (Spring 2011)
Prof. Raul. G. Longoria, ME, University of Texas, Austin
