calculations for any size rotary engine

[modelbox]

how do you calculate the rotor and housing size for any size rotary you might want !i am english

[kanonkopdrinker]

I have just been sent this from 'Scottie' (a member of this grouip) who is having trouble posting to the site.....Hi there Modelbox,You ask if anyone can help you with the geometry of the Wankel engine. Perhaps I can help. All quiet on the ship at the moment.I trust you’re fairly competent at maths. Felix probably had one of those toys called a Spirograph as a kid, and that’s what got him going on this Wankel stuff. It’s quite easy to draw an epitrochoid. For best results imagine a gear wheel on the centre of your page. Then we are going to roll another gear around this gear. The diameter of the outer gear should be a simple fraction of the diameter of the centre gear. ie 1/2, 1/3, 1/5 etcNow, we are going to make a hole in the outer gear and insert a pencil. Now roll the outer gear round the inner gear. If the hole is in the centre of the outer gear, we generate an epitrochoid with no eccentricity – yes – a circle.If we make the hole right at the outside of outer gear, the pencil will again generate an epitrochoid. Note how your pencil very nearly comes to rest when adjacent to the inner wheel, and is moving at maximum speed when at the outside of the outer wheel. This is the maximum eccentricity case and gives rise to an epitrochoid chamber with sharp points between segments.Felix decided that for his engine the outer generating gear would be half the diameter of the inner gear, giving him the familiar epitrochoid with two chambers. Care had to be taken in determining the appropriate eccentricity. At maximum eccentricity the pencil point will momentarily be stationary when adjacent to the inner gear and will be moving much faster at the outside. This is what happens to rotor tip speeds!! Felix chose a moderate eccentricity.To fit nicely inside an epitrochoid with N chambers, you need a rotor with N+1 regularly spaced tips. So Felix used the three pointed rotor for his two chamber epitrochoid. This can be rotated eccentric to the geometric centre of the epitrochoid to always have its three tips in contact with the epitrochoid.The Wankel rotor has a central internal gear form of 2N teeth engaging with a gear, mounted central to the epitrochoid, with N teeth. A shaft rotates about the fixed gear centre and an eccentric journal passes through the centre of the rotor. Using this arrangement the rotor turns through 1/3 of a revolution for every revolution of the eccentric shaft. Because the rotor has 3 sides to it, this means that the single rotor engine does one 4 stroke cycle per revolution of the eccentric shaft.I expect you are anxious to get to the theory.First, measure your rotor housings across maximum diameter and minimum diameter. Let’s call that Md and mdMd = 6r + 2e + 2c…………………….(1Md = 6r – 2e + 2c…………………….(2WhereMd = Maximum internal diameter of your housingsMd = Minimum internal diameter of your housingsr = radius of the outer generating gear2r = radius of the inner generating geare = eccentricity. Measured from the centre of the outer generating gear.c = running clearance. Typically 0.2 mm, or 8 thou to you in USA. This is usually created by enlarging the epitrochoid to allow for temperature and build movements.If we subtract (2 from (1Md – Mr = 4e giving you a value for eIf we add (2 and (1Md + Mr = 12r + 4c. Assume c is 0.2 mm, and you have a value for rYou will need to plot the epitrochoid for a profile grinding machine. Taking the centre of the epitrochoid chamber as the origin (0,0) we can plot the epitrochoid in terms of (x, y)X = (3r+c)Cos $ + eCos3$Y = (3r+c)Sin $ + eSin3$You can try this on an excel spreadsheet and chart plotting $ at 1 degree intervals. Voila – your epitrochoid.The rotor geometry is a lot more empirical. The sides are made to bulge out so that they nearly touch the epitrochoid at it’s narrowest. This will usually be an arc, as it is far easier to have simple curved side seals and side seal grooves. The outer faces are usually sculpted to provide a reasonable shape combustion chamber. The displacement volume, the difference between the maximum chamber size and the minimum chamber size is :-3 x square root of {(3e) x (3r+c) x (Axial chamber length)}