Target audience: Vehicle dynamists, Research scholars, FSAE/Baja students
Read time: 10 minutes
Author: Aravind R Nair
We might generally go under the assumption that the reason we feel general comfort inside a vehicle could be because of “perfect” flatness in newly paved roads. However, that is far from the truth, as any “perfect” road will have realistic elevation profile and on top of that an additional roughness profile based on the road material.
A good measure of road profile roughness is the International Roughness Index (IRI) which is the ratio between meters of accumulated suspension travel with respect to the vehicle’s forward distance travelled in kilometers. It should also be know that most countries use measures as such to classify their roads (A-class, B-class etc.) to lawfully control road quality on motorways and highways.
The following table shows the quality checklist for Indian expressways, National highways and state highways based on material of surface used using Roughness Index (RI) and IRI as the metrics.
The study of vibrational behaviors of a vehicle going a constant speed along a bumpy road is defined as ride. It mainly deals with frequencies between 0.25 Hz – 25 Hz. Tires, being the primal contact has the ability to absorb high frequency roughness vibrations due to its vertical stiffness properties and lower mass in comparison. However, in frequencies below 3 Hz, Tires can have only minimal effect, leaving the major road loads to be dealt with by the vehicle suspensions.
Currently, It is known to us that Vehicle suspension includes all non-linear springs (Including bushes, and solid flexes), non-linear damping (Including hysteresis) and a component called inerter, which gives off reaction forces based on acceleration as input. Inerter will have a higher effect at high frequency of oscillation (higher acceleration), as it acts against the spring force, It can gradually release the spring load and have a good effect on improving road holding capabilities.
Ride and Road-holding vehicle models
During the initial phase of the vehicle development, it is important to have a good analogy in developing a dependable vehicle model for ride analysis and optimization. It would be unwise to go for a higher degree of freedom model used for handling studies, hence, on a general basis, Half-car and quarter car models are usually used. An important consideration to be made is that both models, due to its restricted freedom and assumptions increases the level of its approximation. However, they provide a good idea and general direction for each particular vehicle model.
Transmissibility and suspension tuning
Using the formulated model and consideration that the vehicle will act as a Linear Time-Invariance system, thereby including complex system behaviors, we may arrive at variables that depend on vibration frequencies and suspension parameters. Transmissibility is the behavioral advantage a suspension system has after the component tuning based on vertical motion ratios between the sprung mass or the unsprung mass with respect to the vertical road inputs. It helps us understand the suspension chassis created and the unsprung mass reactance to road inputs respectively.
A typical transmissibility plot for the sprung mass (left) and unsprung mass (right) is show in the figure below.
We may observe two natural frequency zones for the undamped spring-mass model curves namely Body hop resonance (1-2 Hz) and Wheel hop resonance (10 to 15 Hz). Within this, the first resonance shall have little effect on change in damping properties, when compared to the second resonance, which can have drastic changes. Factors such as sprung and unsprung masses, spring stiffnesses, damping coefficients and the inerter effects.
Optimizing Ride vs Road holding:
Choosing which suspension setup to go for in a particular vehicle is dependent on its use cases, design limits and rulebooks. How Engineers make adjustments in the same is through deriving the optimal tuning strategy for ride comfort and road holding respectively for a given vehicle and providing reasonable compromises as per their conditions.
For ride comfort, it can be a reasonable assumption that the value of damping coefficient for the curve that passes through point A shall be tangential to the undamped curve. In other words, the derivative of the plot shall be 0 at point A.
Thereby, we’ll arrive at a value for the damping coefficient that is suitable for a “theoretical” perfect ride comfort for the system by:
It is to be noted that using such a damping coefficient shifts both the natural frequencies along with interference with the wheel hop frequency spectrum. This means, the optimal damping is an unsuitable setup in concerns of road holding, which is also a vital part of vehicle ride design.
Therefore, for road holding, it is a good design practice to reduce the unsprung mass of the system and higher values of damping than optimal damping.
Summing up:
In general, the overall ride modelling, the basic idea is extraction of both half and quarter car models for free and forced oscillation study of the system respectively. As the actual ride of the vehicle differs a bit and it harder to compute, both models are only approximations.
Generally for normal vehicles, the sprung mass for a vehicle ranges up to 10 times its unsprung mass. The tire stiffness is up to 6-12 times the spring stiffness chosen. This means that tire will be having less effect on controlling low frequency road vibrations, which leaves the entire task to be taken up by the vehicle suspensions. However, for high frequency oscillations, it does have an effect in filtering the road noise.
It is worth knowing that for racing applications like Formula 1, the tire stiffness ranges only 1-2 times the spring stiffness, which amplifies the need of good tire modelling due to having a bigger impact for both low and high frequency road disturbances.
The physical evidence of how the vehicle perform as per design can be analyzed using a power spectral density check on the vehicle’s sprung and unsprung mass movements based on different road inputs. Usually, much more changes shall be made during vehicle integration testing by swapping the settings with different bushings or damper settings as per driver’s preference.
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References
Heißing, B., & Ersoy, M. (2011). Ride Comfort and NVH. Chassis Handbook, 421–448. https://doi.org/10.1007/978-3-8348-9789-3_5
