Sitting comfort in next-generation cars: Theory, modelling, and experimentation

Abstract

The scientific study of ride quality, and especially of sitting comfort, requires a multidisciplinary approach that is appropriately established within the ambit of human factors and ergonomics. This research project was conducted within such a framework to contribute in paving the way for characterising, understanding, and predicting sitting comfort in next-generation (connected, autonomous, shared, and electric) cars. The contribution was divided into the three strands of theory, modelling, and experimentation, which resulted respectively in three theoretical studies, one modelling study, and one experimental study. Theoretical background and generalisations were reserved for a substantial appendix.

The first theoretical study allows obtaining the solution to the problem of expressing in the frequency domain the (possibly iterated) antidifferentiation in the time domain or, equivalently, the problem of expressing in the time domain the (possibly iterated) antidifferentiation in the frequency domain. The obtained solution results from using the theory of distributions, and it evokes singular distributions, such as ‘mysterious’ pseudofunctions as well as ‘hidden’ unit impulses and derivatives of them, all having the origin as singular support.

The second theoretical study allows obtaining a proper characterisation, both in the time domain and in the frequency domain, of each of the four basic two-terminal mechanical elements; these are the linear spring, the linear viscous damper, the linear inerter (including the rigid mass), and the linear hysteresis damper. In particular, a proper characterisation can be in terms of dynamic stiffness, mechanical impedance, and apparent mass as well as in terms of dynamic compliance, mobility, and accelerance (and their time-domain homologues). The obtained characterisation results from applying the findings of the first theoretical study, and, in the frequency domain, it generally features nonobvious behaviour on a neighbourhood of the origin (namely, of null frequency).

The third theoretical study allows obtaining a non-heuristic but application-oriented characterisation of a linear viscoelastic material both in the time domain and in the frequency domain. The obtained characterisation results from adopting the hereditary approach and from applying the findings of both the first theoretical study and the second theoretical study, and, in the time domain, it generally features nonobvious behaviour on a neighbourhood of the origin (namely, of null time).

The modelling study allows investigating whether it is possible to calibrate a finite-element model of a seat occupant in terms of both contact pressure at an interface with a rigid seat (not only at seat cushion but also at seat back) and apparent mass (not only of occupant buttocks but also of occupant back). The developed occupant model results from applying the findings of the third theoretical study, and it proves having too restrictive a minimum complexity requirement.

The experimental study allows establishing whether the concept of sitting configuration is appropriate to characterise a seat–occupant system as a whole with reference to performed activities as well as establishing whether there are significant main effects of, and interactions between, sex, vibration magnitude, and sitting configuration on objective responses of seat–occupant systems to vibration. The obtained experimental results may be used in follow-up studies to validate the occupant model developed in the modelling study.

In the theoretical studies, well-known physical aspects are omitted to focus on unclear mathematical aspects. The findings hold under mildly restrictive conditions (except in the ill-behaved case of the linear hysteresis damper) and contain specification of the input spaces. However, no attempt is made to specify the most general (ideally, necessary and sufficient) conditions for results to hold; rather, sets of incremental and reasonably general (sufficient) conditions are identified for formulations to be mathematically tenable.

The concept of sitting configuration proves appropriate to characterise the seat–occupant system as a whole with reference to performed activities. Indeed, at least as regards in-line transmission of vertical vibration at seat cushion, possible sitting configurations in next-generation cars are associated with distinctive objective seat–occupant responses to vibration. Specifically, when it comes to transmissibility plots, the scale is largely dependent on vibration magnitude, whereas the shape is largely dependent on sitting configuration; it therefore seems appropriate that, in future investigations, the long-standing emphasis on vibration magnitude be curtailed in favour of other factors. Results suggest that not only vibration magnitude but also sitting configuration (and possibly sex) affect sitting comfort in next-generation cars through in-line transmission of vertical vibration at seat cushion. Accordingly, in design and development of seating for next-generation cars, secondary activities and corresponding sitting configurations should be taken into account to optimise not only functionality but also comfort and protection (as well as related affective or emotional attributes).

The findings of this research project suggest that research and development for sitting comfort in next-generation cars benefits from introducing the concept of sitting configuration and from using relatively advanced mathematical methods such as the theory of distributions, which may prove helpful in elaborating a (currently unavailable) theory of human vibration.

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Identifiers

ORCID for Francesco D'Amore: orcid.org/0000-0002-6768-4043

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