What About The 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

Thanks Rana. I find this to be quite invigorating and daunting at the same time. Invigorating, because I have actual bits of kit, dimensions can be measured, the model updated. This will bring me closer to a functional model. Daunting, because I may have to re-engineer some parts of the CAD. One example is the bull gear that the worm gear meshes with. I assumed straight teeth, not enveloped helical teeth. Because the envelopment prevents any lateral compliance, getting Twin Sisters around a 438 mm curve requires the 1st and 3rd axles provide all compliance. Further, the chassis cannot shift when the first and third axles contact it. I assumed straight teeth and point contact. This permits lateral compliance. Enveloped gears do not. I have to re-think that part of the design and modify the CAD. Bee

https://community.hornbyhobbies.com/forums/topic/36317-odd-behavior-resulting-in-multiple-resubmission/?do=findComment&comment=393056

My guess is that upon hitting the save / submit button, the page requests a reload of the page you are on. Then you see your submitted post. But if not on last page, there is a logic fault which presents the reply box all filled in, and since filled in, presents the save/submit button. Just a guess though Bee

I went to "What's on my Workbench" to add a post. I was on page 1, not page 59. It shouldn't matter, or so I thought. I created the post and pressed "save/submit". Instead of showing me my now saved post as usual, it presented me with the "save/submit" button again. So I thought perhaps a bad word or something like that. Nope, so I continued. Pressed save, same result. The issue: if you are not on the last page, it will not show your submitted (past tense) post, rather, it requests that you save / submit again. Which I did. Multiple times before the penny dropped Bee

My Scale Link parts have arrived! Scale Link parts for Swingback Church Pew I decided to explore using brass bearings for the pin point axles, as I was concerned about wear. These have a conical cup to suit the conical point of a pin point axle. The hornblocks will require some change to fit the bearings in. Scale Link parts for Experiment The carriage wheels and axles are supported by brass bearings (bushings). Now that the parts have arrived, critical dimensions can be measured and the model updated to permit it around an R2 438 mm radius turn. Exciting stuff! Scale Link Parts for Twin Sisters Although the model will only use one motor, two are here as well as two of the gear sets. Spare parts are a concept that begins at the beginning. Wheels, axles, crank pins and crank bushes, as well as tiny motor fixing screws have arrived. Twin Sisters also needs to go around an R2 curve. Further, the gear dilemma written about in the thread is now resolved. The gear is considered an enveloped gear set. Lots of parts to measure and install back into CAD. Details will be in the individual threads, rather than here. Updates to come Bee

Yes. Hello Ian and Welcome Aboard. The power controller appears under two names, Marshal II and Hornby II. Identical case and configuration. Late 1950s to 1960s. Bee

Thank you @Rana Temporia. Those data points tell the tale @DavewillRana measures less than ½ ampere. A 1 ampere supply is more than enough. Further, short circuit protection is sized against peak draw. You do not want to dump 2.5 amperes through that little motor before that controller trips. Heavy current will generate lots of heat and melt varnish on the coils. All the magic smoke will be let out. It will not matter if you use it only lightly or sparingly. Human reaction times may not be quick enough to prevent damage, and that is putting it kindly and gently. Bee

Whew! I was beginning to think I had communicated poorly. I was in the process of creating a diagram to clarify what I was relating, and still couldn't see the issue @ntpntpntp Over long term use, those elbows will wear and become unreliable, intermittent. In retrospect, TT points are too new to be at that stage yet. I still defer to you! Ha! 🙂 Bee

I defer to @ntpntpntp I could have sworn that power would still be switched via the blades and relied upon blade contact with the stock rails. The wing rails rely upon power from the blades, and the loop merely improves continuity over the sliding elbow. I stand corrected and accept error Bee