billbedford wrote:Proto87Stores wrote:
So far, given a few days to allow for extra consideration, no-one seems to have found fault with the above Physics.
However, if instead we consider the methodology of pure Equalization, the static weight carried on each wheel of a similar well balanced vehicle remains constant, regardless of track twist or any combination of bumps/dips in the track. Flexi-chas is of a course a methodology based on equalization, but was somewhat affected by the limited range of practical and economic options and parts available to modellers back at that time.
Quoting from the suspension section of the Digest:
. . . .
"2 Introduction
The term 'better running' may be looked at from several viewpoints; of these, the most important is freedom from derailment, followed closely by controllability of locomotives and their performance in terms of balance, stability and haulage capacity."
. . . .
My ongoing concern is why almost all the other threads on this forum are heavily into recommending some form of chassis springing, when equalization clearly and fundamentally is better at providing consistent wheel weighting over less than perfectly flat track, and meets the primary goals of better running as expressed above?
Andy
After 15 or 20 years of explaining to you why springing is superior to 'equalisation' you still don't get the point, and I suspect that most people that have tried to help you have just given up.
To recap: Springing is a dynamic system, and while the static loads may vary within small limits, the benefits of the absorption of minor perturbations in the ride height due to irregularities in the track or wheels gives a smoother ride.
Flexi-chas does
not provide any equalisation, except in the case of four wheeled vehicles, and even then sprung or rigid systems provides better road holding than rocking 3-point suspensions. Flexi-chas is compensation system where the proportion of weight carried by each axle is fixed by the geometry. So in the case of a flexi-chas three axle loco frame one axle carries as much weight as the other two combined.
For equalisation both springing and compensation are used so that loads are shared and averaged between springs. This is evident on US designed bar-framed locos where springs are linked together by compensation beams, or on many diesel loco bogies.
Bill,
You are getting quite far ahead of me here. I'm only interested in first getting agreement on the basic underlying physics. That of multiple wheels on axles sharing the weight of the vehicle they are carrying. If that Physics isn't understood by all interested parties, then there is no way of assessing comparisons of existing methods, or validating potential improvement suggestions.
My understanding of any form of LINEAR springing on a wheel without intermediate stops is as follows: The recommended needed range of movement = +/- 0.5 mm
When resting on the track, the correct default static equilibrium position under the per wheel weight of the vehicle is the 50% (midway) compression point.
The spring is essentially unloaded when and while the vehicle is lifted off the track.
Setting the required spring rate vs. the wheel position and the location of the c of g in the chassis to obtain the correct/desired per/wheel weight carried requires a smart computer program.
It then follows that if the wheel drops a full 0.5 mm relative to the chassis, there is zero weight carried by the spring and the wheel. And if the wheel rises 0.5 mm relative to the chassis, the max weight the wheel carries while still sprung is twice its equilibrium per wheel weight before it becomes merely rigid.
If the spring is softer than required for the full movement range, then there will either be rigid stops at the top and bottom of the =/- 0.5 mm movement range, or a larger range of movement for the same loads. So, in the former case, a dropping wheel will hit the lower stop before there is zero weight and hit the higher stop before carrying twice the equilibrium weight.
For springs that are proportionally harder, the wheel will not hit an upper stop, or movement limit, unless the weight on the wheel is proportionally increased. Correspondingly,, the wheel will become unloaded proportionally before the lower stop.
My understanding of purely longitudinal (chassis) equalization is as follows:Consider each side of the loco or passive vehicle chassis separately.
Divide up the wheel bearings identically along each side into separate adjacent pairs, or triplets of overlapping adjacent pairs
Each adjacent pair of wheel bearings on one side of a chassis are then connected by by a rigid beam which is pivoted at a fulcrum point between them. The weight to be carried by the pair of wheels is applied to the beam at the fulcrum point. A similar duplicated beam on the other side if the chassis connects the matching wheel bearings on the other side. But the two beams may move independently. Add as many beams and fulcrum points separately per side as needed to cover all the load carrying wheels fitted to the vehicle.
Set the fulcrum of each beam where it will divide its downward force in the weight ratio between the pair of wheels that you want. (default is 50:50 for a pair weighted equally, or 66:33 for each beam of an over-lapping pair triplet all weighted equally).
If you end up with more than two fulcrums per side, add another layer of similar beams pressing down on those fulcrums (again your choice of ratio) until you end up with only 2 fulcrum points per side.
The necessity of going beyond chassis only pure longitudinal equalization.Pure longitudinal equalization alone will not solve any of the “twisted track issues”. But there are several options for going beyond just equalizing the chassis sides and mounting the body to the chassis. I have listed three possible options below. There may well be others. The best option in a particular case typically will be based on where the c of g of the vehicle is and the performance/stability desired.
The three options I considered include:
1. Attach/support the body and/or chassis fixed sideframes on the four remaining fulcrum points via vertically flexible joints or springs.
2. Add a single transverse equalizing beam to two opposite fulcrums on each side. Support the body on the center fulcrum of the transverse beam and the two remaining fulcrums. Springs optional.
3. Add or use one more beam layer to the sides so that you only have one fulcrum on each side. Add two transverse equalizing beams to both ends of the top longitudinal side beams. Attach/support the body at four points on the fulcrums of the two side beams and the center fulcrums of the two transverse beams. Springs optional.
Now the body will be stable on the all equalized chassis.
To keep this post of manageable size, I’ll stick with just the descriptions above for now. This is still checking to make sure we have common ground as to what springing and equalization are and do. And of course these are open for comment.
I’ll save what I believe are the various justifications and advantages for later.
Andy
