Roughness-Induced Vehicle Energy Dissipation: Statistical Analysis and Scaling

Arghavan Louhghalam, Mazdak Tootkaboni, Franz-Josef Ulm
2015 Journal of engineering mechanics  
4 The energy dissipated in vehicle's suspension system due to road roughness affects rolling 5 resistance and the resulting fuel consumption and greenhouse gas emission. The key parame-6 ters driving this dissipation mechanism are identified via dimensional analysis. A mechanistic 7 model is proposed that relates vehicle dynamic properties and road roughness statistics to 8 vehicle dissipated energy and thus fuel consumption. Scaling relationship between the dissi-9 pated energy and the most
more » ... rgy and the most commonly used road roughness index, International Roughness 10 Index (IRI), is also established. It is shown that the dissipated energy scales with IRI 11 squared and scaling of dissipation with vehicle speed V depends on road waviness number 12 1 w in the form of V w−2 . The effect of marginal probability distribution of road roughness 13 profile on dissipated energy is examined. It is shown that while the marginal distribution of 14 road profile does not affect the identified scaling relationships, the multiplicative factor in 15 these relationships does change from one distribution to another. As an example of practical 16 application, the model is calibrated with the empirical HDM-4 model for different vehicle 17 classes. 18 Keywords: roughness-induced dissipation, pavement vehicle interaction, IRI, roughness 19 power spectral density, stationary stochastic process, translation process theory 20 21 Pavement roughness affects rolling resistance (Beuving et al., 2004), and thus vehicle fuel 22 consumption. In fact, when a vehicle travels at constant speed on an uneven road surface, 23 the mechanical work dissipated in the vehicle's suspension system is compensated by ve-24 hicle engine power, resulting in excess fuel consumption. In addition to pavement texture 25 effects (Sandberg et al. (2011)) and viscoelastic dissipation in the pavement material (see 26 e.g., Pouget et al. (2011), Akbarian et al. (2012), Louhghalam et al. (2013), Louhghalam 27 et al. (2014b)), pavement roughness manifesting itself as surface unevenness with wave-28 lengths above 50 mm (Flintsch et al., 2003), has been recognized as a main contributor 29 to Pavement Vehicle Interactions (PVI) affecting vehicle operating costs (VOC) (Zaabar 30 and Chatti (2010)). While the phenomenon is well known, the intricate links between road 31 roughness parameters, vehicle dynamic characteristics, and vehicle speed remain yet to be 32 established. The mechanistic model developed herein, aims at quantitatively assessing the 33 impact of these parameters on roughness-induced vehicle fuel consumption and the relating 34 greenhouse gas emission. Such models are in high demand for evaluating the environmental 35 footprint of pavement structures during their use-phase, contributing to the development of 36 2 a quantitative frameworks for pavement sustainable design and maintenance. The develop-37 ments presented in this paper aim at contributing to the growing field of mechanics-based 38 quantitative engineering sustainability. In contrast to empirical approaches, the originality of 39 the approach herein developed relies on a combination of a thermodynamic quantity (energy 40 dissipation) with results from random vibration theory in order to identify scaling relations 41 of roughness-induced vehicle energy dissipation. 42 To motivate the forthcoming developments, consider the classical two-degree-of-freedom 43 (2-DOF) quarter-car model (Sayers (1995)) shown in Figure 1: a two-mass system in series 44 composed of a tire (stiffness k t ) and a spring-dashpot parallel suspension unit (stiffness k s 45 and viscosity coefficient C s ). We are interested in the dissipation rate (δD) of mechanical 46 work into heat form due to the relative motion,ż = dz/dt (with z the relative displacement 47 of sprung mass m s with respect to the unsprung mass m u ) of the suspension unit. This 48 dissipation depends on the vehicles dynamic properties (m s , m u , k t , k s , C s ), the vehicle speed 49 V ; and parameters that quantify the pavement roughness. This roughness, ξ, is typically 50 assessed by longitudinal profile data, and condensed, after Fourier transformation, into the 51 power spectral density (PSD) of roughness which describes the distribution of roughness 52 across various wavenumbers (Ω) in the form of S ξ (Ω) = cΩ −w , where c is the unevenness 53 index and w is the waviness number (Dodds and Robson (1973), Robson (1979), Kropac and 54 Mucka (2008) ). We thus seek a relationship between the dissipation per distance traveled 55 (δE = δD/V ) and these parameters; that is: It is useful to perform a dimensional analysis of Eq. (1) by considering an extended 58 3 base dimension system (L x L z M T ) that considers, in addition to mass (M ) and time (T ), 59 two independent characteristic length dimensions, one for the driving direction (L x ), the 60 other for the vertical direction of vehicle motion (L z ). For instance, in this extended base 61 dimension system, the dissipation per lane mile traveled δD has dimension [δE] = [δD/V ] = 62 [F z ] [dz/dt] [V ] −1 = L −1 x L 2 z M T −2 (where F z stands for the force in the dashpot); while the 63 speed has dimension [V ] = L x T −1 . Similarly, we obtain [k t ] = [k s ] = M T −2 , [C s ] = M T −1 , 64 [Ω i ] = L −1 x , whereas for the unevenness index [c] = [S ξ ] [Ω w ] = L 1−w x L 2 z , since [S ξ (Ω)] = L x L 2 z . 65 129 Fourier transformation, the steady-state response in frequency domain z (ω) can be expressed 130 as: 131 z (ω) = H z (ω) ξ (ω)
doi:10.1061/(asce)em.1943-7889.0000944 fatcat:xjhwlwtijfc6rlvicypjdtmsa4