Relationship between measured apparent mass and seat-to-head transmissibility responses of seated occupants exposed to vertical vibration
Introduction
Apparent mass (APMS), driving-point mechanical impedance (DPMI), seat-to-head vibration transmissibility (STHT) and absorbed power have been widely used to characterize response characteristics of the seated subjects exposed to vibration. These functions describe “to-the-body” force–motion relationship at the human–seat interface, while the transmissibility function describes “through-the-body” vibration transmission properties. Although all these functions describe the body response to vibration, “to-the-body” and “through-the-body” functions yield considerably different information. Consideration of both types of functions may thus provide a better understanding of physical responses of the seated body to whole-body vibration (WBV), and could provide better means for formulating reliable biodynamic models.
Over the years, a quantity of the two types of biodynamic data has been generated by different investigators using different measurement methods under various sitting conditions, and types and magnitudes of whole-body vibration. The reported data on both types of measurements have shown significant differences that are mostly attributable to differences in test and analyses methods, experiment design, and subjects’ anthropometry, nature of whole-body vibration and muscles tension, employed in individual studies [1], [2], [3], [4], [5], [6]. Two studies (e.g. Refs. [7], [8]) presented a review of the reported data, and demonstrated significant variabilities among both datasets. The variabilities in seat-to-head transmissibility were particularly extreme. Apparent mass, ratio of force to acceleration at the driving-point, has been more frequently used to characterize the “to-the-body” biodynamic response to vertical or horizontal vibration, since it permits greater convenience for measurement and performing necessary corrections to account for inertia force due to seat structure [2], [9]. Moreover, apparent mass based on driving-point measurements alone, yields considerably smaller variability among the data sets when compared to that observed in seat-to-head transmissibility. It was further concluded that apparent mass responses yield lesser variability in the primary resonant frequency compared to that observed from driving-point mechanical impedance responses [10]. Consequently, the vast majority of the studies have focused on measurements of apparent mass responses, while the seat-to-head transmissibility measurements have been the subject of relatively fewer studies.
Although it is recognized that knowledge of a relationship between different forms of biodynamic functions would facilitate an understanding of vibration response of the human body [10], [11], [12], this relationship has not yet been thoroughly established, most likely due to excessive inter-subject variability of the measured seat-to-head vibration transmissibility responses. Only a few studies have attempted to identify relationships between the biodynamic functions (e.g., Refs. [10], [13]). Boileau et al. [13] investigated the relationships between driving-point mechanical impedance and seat-to-head transmissibility functions based upon 11 reported one-dimensional lumped parameter models. The majority of the models showed differences in frequencies corresponding to peak magnitudes of the two functions, which were expressed as resonant frequencies. The majority of the models considered, however, did not include the head substructure for evaluating seat-to-head transmissibility responses. The biomechanical models proposed by Patil and Palanichamy [14] and Payne and Band [15] with head substructure revealed 0.1 Hz difference in the primary resonant frequencies observed from the seat-to-head transmissibility and the apparent mass magnitudes. Wu et al. [10] investigated a relationship between the APMS/DPMI and seat-to-head transmissibility functions based upon four biodynamic models, ranging from single- to three-degrees of freedom models. It was shown that both the normalized apparent mass and seat-to-head transmissibility functions provide very similar fundamental resonant frequency, while the frequencies of higher modes of the higher order models differed. The apparent mass response was normalized with respect to seated body mass. The structures of models employed in this study, however, did not include a head substructure.
Although both the apparent mass and seat-to-head transmissibility response functions relate to the seated occupant responses to whole-body vibration, the two responses have shown some differences in resonant frequencies that are generally identified from the peak response magnitudes [7], [8], [16]. Synthesis of measured data presented in ISO-5982 [16] exhibits considerable differences in primary resonant frequency in the apparent mass and the seat-to-head transmissibility responses. Such differences may be inherent to “to-the-body” and “through-the-body” responses of the biological system to vibration or may be attributed to differences in subjects’ anthropometry and methods used to characterize the two measures. Moreover, the two measures have been acquired either by different investigators or during different test sessions that may also involve different subjects. The measurements of two functions under carefully controlled identical conditions could yield considerable insight into relationship between them, by reducing contributions due to inter- and intra-subject variabilities. Moreover, characterization of both “to-the-body” and “through-the-body” response functions for same subjects under identical test conditions could provide a better understanding of body response to whole-body vibration. In recent years, only one study has measured both functions with the same experimental condition using eight subjects exposed to vertical whole-body vibration, while a relationship between the two functions was not attempted [17]. Moreover, the seat-to-head transmissibility responses were measured using a bite-bar revealed excessively inter-subject variability.
Reported studies have invariably shown important influences of type and level of vibration, and sitting posture and muscles tension on both types of responses to whole-body vibration. The relations between the two biodynamic functions are thus also expected to depend upon the sitting and vibration conditions. The vast majority of the studies, however, have considered sitting with an unsupported back. Only a few studies have characterized vibration responses of seated body against an inclined back support, particularly the seat-to-head transmissibility [18]. Considering that the automotive seats are designed with inclined seat pan and backrest to provide comfortable and controlled sitting posture, the reported biodynamic data would be insufficient for identifying a relationship between the two types of functions. A study of seated body responses to vibration and the relationships between the two biodynamic functions, while sitting against a vertical or an inclined back support, thus forms an essential task.
In this study, the vertical apparent mass and seat-to-head transmissibility response characteristics of seated subjects are derived through measurements of total biodynamic force at the seat pan, and motions of the seat pan and head along the applied input acceleration direction, using 12 male subjects. The data were acquired under three different back support conditions and two different hands positions representative of drivers and passengers-like postures. The measurements were performed to establish the influences of back support condition, hands position and vibration magnitude on the acquired measures. Relationships between the measured vertical apparent mass and seat-to-head transmissibility biodynamic responses of the seated occupants under vertical vibration are investigated as functions of sitting posture and excitation conditions.
Section snippets
Measurement and analysis methods
A schematic representation of the experimental setup used in this study is shown in Fig. 1. The setup consists of a whole-body vehicle vibration simulator (WBVVS) capable of producing vertical vibration of deterministic as well as random nature. The whole-body vehicle vibration simulator comprises two vertical electro-hydraulic actuators with a number of safety control loops that limit the peak displacement, peak force and peak acceleration to preset levels. A rigid seat is installed on the
Vertical seat-to-head transmissibility responses
The data acquired in this study was analyzed to establish vertical seat-to-head transmissibility (Tv) responses of 12 subjects seated assuming three different back support conditions and both hands postures. The inter-subject variabilities [18] were also evaluated in the measured data. Despite considerable scatter between the seat-to-head transmissibility responses of different subjects, the peak moduli occur in the 4–5 Hz frequency range for all subjects, irrespective of the back support
Conclusions
The similarities and differences in the apparent mass and seat-to-head vibration transmission measures of biodynamic responses of seated occupants exposed to whole-body vertical vibration were investigated through measurements performed with 12 adult male subjects, and varying sitting conditions. Measured vertical seat-to-head transmissibility and apparent mass biodynamic responses were further characterized to examine the effects of three main factors: back support condition (no back, vertical
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