What About The Bee

If you are done, @Train Mad1707822774, remember to run the water reservoir dry. Its not a good idea to store it with water in the tank Bee

OO Twin Sisters has a geared axle. In my initial sketches, I supposed that the bull gear (disk, with gears on edge) had straight teeth. This would permit the geared axle to move side to side, relative to the chassis. I received the Romford 60:1 gear from Scale Link. The bull gear has enveloped teeth, that is, the teeth wrap around the worm gear. The geared axle is the middle of the three axles. My immediate concern was lateral compliance. How would this go around a OO R2 (438 mm) curve. The axle cannot shift relative to the chassis. I solve that here Fixed axle Computation in Round the Bend This alleviated my concern. The nominal gap between the F2F and the Track (Q=.148 mm) is far larger than the lateral compliance (Y = 0.012 mm). I can distribute this as I wish, it will be fine. On to my next poorly reverse engineered object, the crankpins. Bee

LT&SR_NSE pointed out that diagrams are helpful. This diagram illustrates chapter two, where we find the flange extension to the wheelbase. It should be evident that the distance X, from the axle centerline, the flange and rail meet geometrically. From this pure side elevation, you can see the exact point. For OO Twin Sisters, the center axle is captive by the enveloped gears. Therefore, it cannot shift side to side. How much lateral compliance does this axle need? Find X, the flange extension, 3.316 mm, using the process described in this post. The wheelbase, Wa is 0, as this is a single axle. Solve for Y, the chord formed by twice the flange extension and a 2nd radius curve. Answer? 0.012 mm. The track gap Q, chapter 1, is 0.148 mm. Thus, whatever lateral compliance we need for this axle will be easily accommodated by Q. There is no issue! Bee

That is very complimentary @Peter Stiles. While I do appreciate the sentiment, it may be unwarranted. I'm always in awe of those around me and strive to do better. Thank you. I share your enthusiasm for learning. Nothing like a new discovery, a novel approach, to invigorate the mind. I came to the Forum so as to learn from others who are more knowledgeable than I about model railways. There are plenty. I make plenty of mistakes, but writing a book will not be one. 😁 Bee

My only familiarity with Countdown are the episodes with Jimmy Carr. Which leads to my preference of Rachel Riley 😉 ÷÷÷÷ The problem so lends itself to trigonometry, as most of the solution is triangles within a circle. The flange extension (X) and the lateral wheel compliance (Y) are essentially trigonometric identities with a radius of wheel drum and track radius respectively. I moved OO Experiment from a straight to an R2 curve in my mind's eye, literally hundreds of times, checking and re-checking. And then formulated a set of equations and trialed them against the CAD. Repeatedly. The set of equations presented meet requirements. Bee

With the parts on hand, the final bits of OO Experiment can be resolved. The parts that were reverse engineered (guessed at) were measured and updated. The model was updated to permit OO Experiment around a 2nd radius curve (438 mm). You may read all about that here: Round The Bend Another update is couplings. It is clear that Locomotion is to run with the Accurascale Chaldrons. Carl stated as so, during a video update. The Accurascale Chaldrons come with extra magnetic chain couplings to attach to other rolling stock. They use a NEMA 362 pocket. I've installed that pocket, to spec, on OO Experiment. It is rendered as a separate color, as separate part in CAD, but in the 3D print, it will be fused with the chassis When Locomotion No.1, Accurascale Chaldrons and OO Experiment are coupled, it will be the same coupling throughout. I decided to install side skirts under the seats, outboard of the seat cradles The reason is apparent. John Backhouse was a first hand observer on Opening Day of the Stockton and Darlington Railway. When the CAD is viewed in side elevation with the chassis detail turned off, as Backhouse depicts the consist, something very magical happens Bee 1) Hopefully, this goes to the correct thread. Posted via search function 2) Would someone mind examining the metadata for Locomotion? I'd like to have OO Experiment on hand when Locomotion arrives. Thanks!

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I did see it here, but cannot remember who posted. At least, that is what my faulty memory tells me.... Tiny magnets. One in the shoe, the other in the object the figure is to stand on. Perfectly invisible in the base, need not even be exposed to the surface. Not visible in the figure, because it is inside the shoe. The figure can be moved about to other hidden magnets, leading to a more dynamic display, easier to clean, etc Bee

I should like to clarify what I thought would happen. I thought that I could enter my reply to Workbench from any page, and that it would add my reply to the bottom of the pages (it did) and then, upon page refresh, show me my post (it did not). It showed me the page I was on, page 1, with my reply populated in the reply box, still live. I did not expect that, at all. Normally, when on the last page of a thread, when you press the enter and submit, it reloads the page you are on, and DEPOPULATES the reply box. You can see your completed post. That was the expected behavior. This should be an easy error to recreate. Simply go to any thread with multiple pages. Navigate to page 1. Enter a reply. Observe that the reloaded page 1 still has a populated reply box. [Buzzer sound!] Bee

And that is why this is titled Round the Bend Its driven me there! 🤪 Bee

Chapter Six If you have made it this far, I congratulate you on your perseverance. This topic is by necessity a trigonometric exercise. But can we put this all together? Yes we can Here is the closed form series of equations and values for Experiment. Each equation relates to a previous chapter and will help us to define the value to be used in CAD And that is how we go from this To this Okay, but that is for an even number of axles. Suppose the number of axles is an odd value. The above solution still works, selecting pairs of axles from the outside in. The final axle will be just itself, and: Wₐ=0 Wₜ = Wₐ + X + X That is, twice the flange extension. The chord is merely across the flange extension in both directions, the nominal wheelbase doesn't exist, it is a point. What is the shift in chassis? You will note that Cₛ' is less than T. So when we require the axles to shift by more than Cₛ', the chassis will also shift by T - Cₛ. This means that the first and last axles, on the inside of the curve, will come very near to the chassis. And that, lads, is why back to back opposing curves are not recommended. You have no idea what lateral compliance a designer has put in. I've put in just enough to get around a 2nd radius curve, but if they go back to back, then the front and rear of the chassis is forced in opposite directions, leading directly to derailment

Chapter Five: Build up of Tolerance Cs will be fed from the equations into the CAD model, as this is the line to line, precise minimum value for a OO R2, 438 mm curve. The technical term used is "Build up of tolerance". Can I set the back to back (which achieves the F2F) to within 1 micron? No. Can the chassis be 3D printed to within 1 micron (0.001 mm)? No. Can I place both bearings relative to the chassis to within 1 micron? No. Even if I could, there is 3 microns of uncertainty, right there. Each object's dimensions has a tolerance. For example, the flange of a 2mm axle bushing is measured at 0.24 mm. But plus or minus what? Now add up my inability to position each component with the inability of the manufacturer to make any part precisely to the print (CAD). Shazzam! Build up of Tolerance. Cₛ' = Cₛ + BoT Bot is an arbitrary, but small number. I selected 0.1016 mm (0.004") per side. I may regret this, or relax it even more as I commit to print, depending upon my level of panic

Chapter Four: Distribution of Compliance Experiment is running from a straight section of track onto a 438 mm radius curve in OO. Because the drums are a section of a conic, all the axles will be centered. For the purposes of this discussion, I will assume that the chassis is also centered to the track, although we will find this does not really matter. Nothing happens until ½ of Q is taken up by the first axle. The wheel sets are centered and so until the flange touches the rail in the curve, no adjustment in lateral displacement need occur, except by the conic section of the drum As Experiment moves forward from the touch point, the axle is shoved over, relative to the chassis, by another ½Q. That is, the entirety of Q is consumed by the curve, the wheel on the outside of the curve will have no gap to the track. All of Q will be allocated to the inside wheel v track. Thus we can reduce the required lateral compliance (Y) by the gap (Q) Y' = Y - Q = 1.455 - 0.148 = 1.307 mm Y' is now the defined lateral distance the first and last axles must be shoved over. What of the interior axles, numbered 2 and 3? As Experiment continues forward, the identical process occurs. The second axle utilizes ½Q and then another ½Q, and then lateral shift due to the chord of the curve. Simply define the wheel base as a function of X and the distance between the 2nd and 3rd axles. Again axle 2 to axle 3 is CAD data Wₐ₍₂₊₃₎ = 21.930 mm Wₜ₍₂₊₃₎ = Wₐ₍₂₊₃₎ + X + X = 28.150 mm From this, the lateral distance (Y₍₂₊₃₎) can be found Y₍₂₊₃₎ = (1-cos(sin⁻¹((Wₜ₍₂₊₃₎/2)/Rₜ))) × Rₜ Y₍₂₊₃₎ = 0.222 mm Deducting the gap, as before Y'₍₂₊₃₎ = Y₍₂₊₃₎ - Q = 0.222 - 0.148 = 0.074 mm Y'₍₂₊₃₎ is now the defined lateral distance the second and third axles must be shoved over. So at last, we know the maximum travel (T) for the axles. Y' to Y'₍₂₊₃₎ is 1.307 - 0.074 T = 1.233 mm T is a critical value, as it defines the total requirement of gap . T is the Total Travel! The gap between the left wheel and its bearing + the gap between the right wheel and its bearing. Because track can bend to the left or to the right, it is best to centralize the chassis relative to the permitted lateral axle play. Thus, in the initial condition, the gap on the left should be equal to the gap on the right. The axle bearings are fixed to the chassis. The outside of the bearing defines the limit of side to side travel, until we permit the chassis itself to move over. Put another way, the first and last axles get shoved over, relative to the chassis to fit into the curve by Y'. But what happens if the inside of the wheel touches the outside bearing surface and continues to shove over? It moves the chassis over! Thus, we can say: Cₛ= T/2 Awesome Sauce! Except that is completely impractical in the real world.

Chapter Three: We must fit the wheels on their axles within the curve. Each axle will be shifted laterally. I just need to slide each axle, from side to side, such that they fit into the track. When this is done, you should see that the first and last axles form a chord to the curve of the track. We know the given radius of the track R2=438 mm in OO. This, however, is the the centerline of the track. The true radius (Rₜ) of the curve we care about is to the outside of the track. This is easy to find Rₜ = R2 + Gₜ/2 = 446.25mm The nominal wheelbase is the distance from the first axle centerline to the last axle centerline. This is merely a design criteria, so obtain it from the CAD. In my case, the axle wheelbase (Wₐ) for S&DR 'Experiment' is 65.791 mm. The true wheelbase (Wₜ) is the axle wheelbase (Wₐ) plus the flange extension (X) for the leading and trailing axles Wₜ = Wₐ + X + X = 72.013 mm So to fit those leading and trailing SW1412B wheelsets into the R2 curve, we have required lateral compliance (Y). Y = (1-cos(sin⁻¹((Wₜ/2)/Rₜ))) × Rₜ For SW1412B and R2 in OO, Y = 1.455 mm

Chapter Two: This factor is the extension of the wheelbase, as a function of the drum radius and flange height. In an automobile, the wheelbase is simple, it is the distance between the first and last axles. Railway wheels have flanges, which extend the wheelbase. What is that extension? For SW1412B, the drum radius R𝒹 7mm and the height of flange (H) is 0.66 mm. Therefore the distance from the axle centerline to the flange top of rail intersection (X) is X = sin(cos⁻¹(R𝒹 / (R𝒹 + H))) × (R𝒹 + H) For SW1412B, X = 3.111 mm

Chapter One: Track Gap This factor is the gap between the gauge of the track (Gₜ) and the Front to Front (F2F) of the wheelset. The gap is required, since both wheels are hard coupled to the axle. The wheel drum is conical in section. Thus, lateral motion permits different diameters of the drum presented to the track, thus the axle and wheels go around a turn without wheel slip. This was a fundamental patent from the early days of railways. Gₜ is obvious for OO, 16.5 mm. What is not so obvious is the F2F dimension, since the profile of the tire of the wheel involves conical and curved sections. F2F is the dimension from the front side of one wheel to the front side of the other wheel, at the flange. I will be using Scale Link Bogie wheels for S&DR 'Experiment'. SW1412B, to be specific. I can set the B2B to anything I like, here 14.54 mm, which is identical to the Romford locomotive drive axle dimensions, with the wheels mounted. Yet we know that the B2F is critical for going through points. Using a set of Peco points (SLE-192), the Scale Link SW1412B wheelset and a feeler gauge, I can determine the check rail gap to within 0.0005 inches or 0.0127 mm (12.7 microns). Once I know the B2F and the B2B, algebra will permit the determination of one flange or front. From this, I measure F to be 0.906 mm. Therefore I find the F2F to be 14.54 mm + .906 mm + .906 mm = 16.352 mm. I will emphasize that this dimension is for Scale Link wheels, not to be used for Hornby wheels & etc. Thus, the first factor (Q) is merely the difference between the track gauge (Gₜ) and the F2F. Q = Gₜ - F2F Q= 0.148 mm

This discussion is how to permit a multi axle system go around a curve. I will be using my S&DR Experiment and an R2 (438mm curve), but the equations are suitable for any system in which all axles can move side to side. As decision time nears for a commitment to print, I have been giving a tremendous amount of thought to going around a curve. To be explicit, this defines how thin the chassis must be to accommodate the side to side travel of the axle. This is so because the axle and wheels are fixed dimensions; to work as a system with the track. The thing we adjust is the chassis, not the wheels. In particular, the axle bushings must be slightly proud of the plastic chassis, so in fact, we define the location of the bushings to permit travel round the bend, and fit the chassis to the bushings. It should be clear that if the axles are not permitted to travel laterally (side to side) then the wheels will not fit into the track gauge on a curve. They will beautifully fit on a straight section of track. Without lateral axial compliance, they will not fit. Lateral axial compliance is the same as side to side play. So how do I get from this To this How much compliance? How to define Cₛ'? There are several factors to consider. One factor is the gap between the gauge of the track and the Front to Front dimension of the wheel set. That is, when the axle and wheels are placed on a track, they can be moved side to side (laterally). Another factor is the flange of the wheel as it faces the track. The drum touches the track at a point, but the flange inside the rail extends forwards and backwards from that point. This is a chord of a circle, a function of the radius of the drum and the flange height. Another factor is the chord of circle formed by the track and the wheelbase. The wheelbase must include consideration of the flange of the wheels. Each practical pair of axes must be considered. Another factor is the distribution of the lateral compliance. Is the chassis permitted to shift off center, or must the full lateral compliance be on both sides of the chassis? Another factor is a practical one. Once the mathematical minimum is met, can the parts manufactured and assembled meet that minimum solution or should we expect build up of tolerance? Since this is a fairly complex topic, I have broken this up into chapters. Each chapter will focus on an individual factor. Finally, there will be a chapter tying it all together. Note: all equations were developed on a blank sheet of paper. It is very likely that there are other ways to solve this. I am not saying that this is the way to solve the problem, rather, it is how I solve the problem. All errors are mine alone. Bee