Closed-Form Solution of Road Roughness-Induced Vehicle Energy Dissipation

Abstract

A major contributor to rolling resistance is road roughness-induced energy dissipation in vehicle suspension systems. We identify the parameters driving this dissipation via a combination of dimensional analysis and asymptotic analysis. We begin with a mechanistic model and basic random vibration theory to relate the statistics of road roughness profile and the dynamic properties of the vehicle to dissipated energy. Asymptotic analysis is then used to unravel the dependence of the dissipation on key vehicle and road characteristics. Finally, closed form expressions and scaling relations are developed that permit a straightforward application of the proposed road-vehicle interaction model for evaluating network-level environmental footprint associated with roughness-induced energy dissipation.

Smartphone-enabled road condition monitoring: from accelerations to road roughness and excess energy dissipation

“…The starting point is the realization that the only source of dissipation is the damping mechanism within the Kelvin-Voigt suspension system. The expected value of the energy dissipation per travelled length, δ , considering the stochastic nature of the road profile, therefore reads (24) can be approximated using asymptotic analysis for a small unsprungto-sprung mass ratio [7], γ = m u /m s 1. This is achieved by first approximating the poles of H z (ω) for an undamped system as…”

“…The integral on the r.h.s. of equation (2.4) can be approximated using asymptotic analysis for a small unsprung-to-sprung mass ratio [7], γ = m u / m s ≪ 1. This is achieved by first approximating the poles of H z ( ω ) for an undamped system as ω 1 ≈ 1 − 1/2 β 2 γ and ω 2 ≈ β (1 + 1/2 β 2 γ ).…”

“…The need for such a dramatic change is also driven by recent developments in smart roads, which are poised to be vital elements of the built environment in smart cities of the future [3]. The road surface condition, in particular, impacts the ride comfort, contributes to the vehicle's operating costs [4][5][6][7] and, more importantly, increases the greenhouse gas emissions associated with road transportation [8,9]. It is, furthermore, considered an important piece of information for successful implementation of autonomous driving in urban environments [10].…”

Roughness-induced vehicle energy dissipation from crowdsourced smartphone measurements through random vibration theory

“…A Gaussian roughness profile, for instance, results in a normally distributed suspension motion with χ ¼ ffiffiffiffiffiffiffi ffi 2=π p (for other marginal probability distributions; see Louhghalam et al, 2015). A convenient asymptotic solution for Equation (43) has recently been proposed in the function of only the road roughness PSD parameters, gΩ w 0 À Á and w (Louhghalam et al, 2019):…”

“…where H z S,i and H z U,i respectively denote the sprung mass and unsprung mass FRFs of the front i ¼ 1 ð Þand rear ði ¼ 2Þ suspension system, that is, from the solution of Equation (36). Since the integral expression in Equation (51) converges rapidly, an estimate of the energy dissipated in the suspension system can be obtained from an asymptotic solution of Equation 50for the quarter-car model (Louhghalam et al, 2019). Using the model invariants (30) and (32), this asymptotic model holds-in first order-for the front and rear suspension system as:…”