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Peritrochoid Formulae - how to implement these formulae in Solidworks so they are smart models?

Question asked by Sher Shishe on Jun 25, 2020
Latest reply on Jul 2, 2020 by Josh Brady
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Peritrochoid Formulae How to implement these formulae in Solidworks so they are smart models?

1. Rotor Housing

Inner Surface

X = e cos α + R cos (α/3) + a cos ((α/3)+φ)

Y = e sin α + R sin (α/3) + a sin ((α/3)+φ)

e = 19

R = 130

a = 3

φ = 26.2

 

2. Rotor

X = R cos 2v + (3/2)(e^2/R)(cos 8v - cos 4v)

+/- e(cos 5v + cos v)(1-(9e^2/R^2)sin^2 3v)^(1/2)

+/- (3/2)(ea’/R)(cos 5v - cos v)

+ a’ cos 2v (1-(9e^2/R^2)sin^2 3v)^(1/2)

Y = R sin 2v + (3/2)(e^2/R)(sin 8v + sin 4v)

+/- e(sin 5v + sin v)(1-(9e^2/R^2)sin^2 3v)^(1/2)

+/- (3/2)(ea’/R)(sin 5v + sin v)

+ a’ sin 2v (1-(9e^2/R^2)sin^2 3v)^(1/2)

 

These functions are cyclic functions with the period of 2π.

The inner envelope corresponds to:

v = (1/6)π ~ (1/2)π, (5/6)π ~ (7/6)π, (3/2)π ~ (11/6)π

Generally a’ can be determined as follows:

a’ = a - Sp

where    

a: amount of parallel transfer of trochoid    

Sp: minimum clearance between rotor and rotor housing

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