(This is rather long, so if you do not wish to read it all please scroll down to ‘The Problem')(adsbygoogle = window.adsbygoogle || []).push({});

This is my situation:

I am designing a powered-bicycle that will feature a two-wheel-drive capability. I need to calculate the diameter of the drive shaft that transfers power to the front wheel (it needs to be as small as possible).

In order to calculate this diameter first I need to identify all of the resistive forces acting on the bike (to determine how much power will pass through it). So, to be able to do that I need to know how much the bike will weigh and how much power the components will absorb (mechanical loss).

How would you go about doing this?

How I went about doing this was to, concerning the estimated weight of the bike, look at other bikes, both motorcycles and bicycles. I looked at how much other bikes weigh and determined what the maximum weight of my bike will be by comparing the power of the motorcycles, that I looked at, to their weights, and also by noting the frame-weights of the bicycles, that I looked at (down hill mountain bikes because they are the strongest). I also noted the combined weight of the small engine I will use and also (because my bike will be a hybrid petrol/electric-powered design) the weight of the electric drive components (motor and battery). My conclusion was 50kg, which is the maximum I would want the bike to be, as it needs to be light enough to carry over fences and gates, etc., during long distance cross-country tours. Of course I factored into this 50kg estimation figure the materials I wish to use.

Now that I know how much my bike will weigh I can calculate most of the forces acting on it. I know how big the bike will be and what sort of tyres it will use, so I am able to calculate the drag forces from the air and also from rolling resistance. I can workout how much force is required to propel the bike, with rider and cargo, up an inclined plane, I am able to workout how much force is needed to accelerate the bike (F = MA) and I am also able to calculate the rotational inertia of the wheels.

I have in mind minimum performance figures (such as top speed, acceleration, etc) that the bike needs to be capable of, so I measured estimated forces up to these limits.

This leaves the problem of trying to estimate the drag forces of the bikes’ drive components. I need to estimate the efficiency of bearings, drive shafts, drive chains, CV-joints (at varying angles), spiral bevel gears and one-way clutches. I have drag force figures for bearings and one-way clutches, although not at different speeds (the manufactures tend not to have this information) and not during acceleration (for acceleration I will calculate the rotational inertia for the individual components and calculate the force that way). Drive shaft efficiency is easy enough to calculate and, once I know the exact dimensions, spiral bevel gear efficiency, I hope, will be a straightforward calculation thanks to a formula I found.

The Problem:

Although I found a formula for calculating bicycle drive chain efficiency, I am not confident that I can use it properly. I do not know what units parts of the formula need to be expressed in and I am also not confident that I will be able to source the information, such as various coefficients of friction for parts of the chain, needed for the equation. Drive chain power-loss formulae are hard to come across, as are equations for CV-joint efficiency, to name just two drive components. Also, there is a possibility that my spiral bevel gear formula will prove impossible for me as well!

So, what am I to do? I know that these drive components absorb power (cause a resistive force) but I have no accurate way of identifying exactly how much. Most mechanics people say a good drive chain that is well maintained will be about 98% efficient and spiral bevel gears should not be less than about 95% efficient (grease lubrication). Should I just use these figures in my force estimations? It does not seem very scientific to me; it seems to be making a guess based on hearsay!

Until the bike is built this project is purely theoretical, and with little opportunity (at this stage) for conducting experiments with models, etc. I am writing-up how I went about this project, how I determined component (TWD drive shaft) dimensions and generally the fundamental mathematics involved in basic design work. I will be presenting this project to a university in an attempt to gain a place on a degree course in Engineering, and I do not have very much time at all to finish it (I currently have a place in the Foundation Year). The project (write-up) has to be scientifically based and it has to be of academic standard (albeit 1st year entry standard), so it cannot be based on guesswork.

Would you just assume 98% for a drive chain, or 95% for a bevel gear? Is this how professional engineers would go about making an estimation (estimation, not guesstimation)? In the absence of available formulae, what other option do I have?

What is the standard design modus operandi for such scenarios?

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# Design M.O.

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