Direct Fixation Fastener (DFF) Spacing and Stiffness Design

Direct fixation fasteners are one of the most important elements in trackwork design. Elastomeric pads are incorporated in the fastener to provide vertical and horizontal flex and they assist in the reduction of noise, vibration and impact. The spring rate in DFF is often adjusted to mitigate ground borne vibration, that adjustment then affects the track modulus. Currently no industry-wide specifications exist for the design, definition or procurement of direct fixation fasteners. A thorough examination of the characteristics and past performance of available fasteners, as well as the characteristics of the proposed transit vehicle should be undertaken prior to fastener selection for any specific application. In this paper a procedure is suggested to calculate the spacing and desirable (vertical) stiffness of DFF that would mitigate noise, vibration and impact. There are two issues to consider enabling proper vibration isolation. The dominant issue is spring rate and the secondary issue is damping constant. Both are considered. Rail can be defined as a beam supported by DFF, directly fixed to a concrete slab. Usually light mass-spring ballast less track systems have a natural frequency varying from 12 Hz up to 18 Hz. Firstly a natural frequency for the direct Fixation Track is chosen. This choice must conform to the fact that exciting frequency such as train passing frequency should not go close to the natural frequency level so as to avoid resonance. Using a load-deflection formula for the track, a formula for natural frequency of a mass-spring system, a DFF passing frequency formula and relation between track modulus and characteristic length, DFF stiffness can be calculated. The design of stiffness and spacing of DFF does not lead to a unique value. There will always be a range of value depending on the choice of frequency ratio, r. It is found that spacing and stiffness are strongly correlated with R² = 0.991. At the end a discussion follows on how to choose the value of natural frequency, f_n stiffness amplification factor, R and the frequency ratio, r. Finally an application of the proposed design procedure is shown.