Choosing a deflection valueįor reasonable 4mm scale finescale track, a recommended value for hornblock deflection, δ, under the final load of a locomotive, is 0.5mm. It is suggested that design should be based on a given deflection of a hornblock, and then determine what length, thickness and style of beam is most suitable for the specific force intended to be supported by each axle.įor locos weighted to be between 4 and 6 grams per prototype ton, the masses to be supported by each individual locomotive hornblock are likely to fall within the range 30 to 60 grams (equating to a prototype loading of between 14 and 20 tons per axle). There is also a considerable difference in the deflection of a beam, for a given force, depending on how it is supported and fixed and whether it is supported at one end only or at both ends. Application to model locomotive hornblocksĪs can be seen from the equations, the thickness of the material ( h or d) is very critical, and hence the incremental sizes in the range of guitar strings available make them very attractive for use as spring beams.
The proportion of the total weight acting on each axle of a loco or vehicle will depend on the position of its centre of gravity in relation to the axle (or the chassis fixing points of equalising beams where these are used).
In the following examples, only loads applying at a single point or single points are considered – the application point of force F in the diagrams is intended to denote a model locomotive hornblock (or vehicle axlebox) able to move vertically in a hornguide, and acting against the force of the spring beam fixed to or carried by the locomotive or vehicle mainframes. The equations given here are for homogenous, linearly elastic materials, and where the rotations of a beam are small. The deflection of a spring beam depends on its length, its cross-sectional shape, the material, where the deflecting force is applied, and how the beam is supported. ContentsĪpplication to model locomotive hornblocks Reference should be made to this work for the derivation of the equations. A particularly good exposition, and on which the equations given here are based, is contained in Mechanics of Materials (Fourth SI edition), by J M Gere and S P Timoshenko, Stanley Thornes, I3998 X. Deflection of beams Deflection of beams by Russ ElliottĪcknowledgements: There are a number of standard works addressing the principles of beam deflection.
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