library HasCASL/Real3D/SolidWorks/EN1591
version 0.1


%author: E. Schulz
%date: 24-02-2010

logic HasCASL

from HasCASL/Real3D/Basics get AffineRealSpace3DWithSets

%[
   This Specification formalizes the norm EN 1591 for flanges.
   We only consider the integral flange with spherical shell.

   Content:

   1. Application area
   2. Glossary
   3. Parameters for calculation
   4. Derived parameters
   5. Limit load equation


]%


%% 1. Application area

%% 2. Glossary

%[

@Indizes

A - Zusatz (FA, MA)
B - Schraube
C - Kriechen der Dichtung (gc)
D - Aequivalenter Zylinder (kegeliger Ansatz + angeschlossene Schale) zur Berechnung der Belastungsgrenze
E - Aequivalenter Zylinder (kegeliger Ansatz + angeschlossene Schale) zur Berechnung der Nachgiebigkeit
F - Flansch
G - Dichtung
H - Ansatz
I - Kennzahl fuer den Belastungszustand (mit den Werten 0, 1, 2 ...)
L - Loser Flansch
M - Moment
P - Druck
Q - Resultierende axiale Kraft durch Druck
R - Resultierende axiale Kraft durch aeussere Kraft
S - Schale, Scherbeanspruchung
T - Schale, modifiziert
X - Schwacher Querschnitt
Delta - Symbol fuer Aenderung oder Differenz
av - Mittelwert
c - berechnet
d - Auslegung
e - effektiv
max - Maximum
min - Minimum
nom - nominal
opt - optimal
req - erforderlich
s - Schaft (glatter Teil der Schraube)
t - theoretisch, Drehmoment, Gewinde
0 - Montagezustand (I = 0, siehe Index I)
]%


%% REMARK: A big deal for the specification of the parameters is their types.
%%         We don't want to spend a lot of space for type annotations (... as T)
%%         in order to have a well typed specifications.
%%         Sometimes we need, e.g., cos phi to be positive hence phi to be in [-pi/2, pi/2]
%%         , i.e, we need more fine-grained types (predicate subtypes).
%%         Another example is sqrt(e_1 - e_2), here we need e_1 >= e_2,
%%         or in 1/(e_1 - e_2) we need e_1 <> e_2
%%         This is not realizable by types, so we have to type-annotate the terms
%%         and leave the job to be done in the prover.

%% !Section Parameters for calculation

%% !Section Derived parameters

%[
@predecessors

DIN 2505:1927-01, 1964-10
DIN V 2505: 1986-01
DIN 2506: 1927-01
DIN 2507: 1927-07

]%

spec DerivedParameter = AffineRealSpace3DWithSets then

     %% * Flange ring

     %% ** Screw holes

     ops p_B, n_B, d_3, d_5, d_5e, d_5t, l_5t, e_Fb:RealPos;
         d_3e:Real

     %% distance between screws
     . p_B = Pi * d_3/n_B                    %(eq1)%
     %% effective diameter of screw hole
     . d_5e = d_5 * sqrt(d_5/p_B)            %(eq2)%
     %% diameter of blind hole
     . d_5 = d_5t * l_5t/e_Fb                %(eq3)%
     %% diameter of bolt circle
     . d_3e = d_3 * (1-2/n_B^2)           %(eq4)%

     %% ** Ring

     ops d_0, d_4, d_o:RealPos;
         b_F, d_F, e_F, b_L, d_L, e_L, A_F:Real

     . b_F = (d_4 - d_0)/2 - d_5e            %(eq5.1)%
     . d_F = (d_4 + d_0)/2                   %(eq5.2)%
     . e_F = 2 * A_F/(d_4 - d_o as NonZero)  %(eq5.3)%

     . b_L = 0                               %(eq6.1)%
     . d_L = 0                               %(eq6.2)%
     . e_L = 0                               %(eq6.3)%


     %% * Spheric shell

     ops beta, d_1, d_2, e_1, e_2, l_H:RealPos;
         e_E, d_E:Real

     . beta = e_2/e_1                        %(eq9.1)%
     . e_E = e_E %(eq9.2)% %% dummy for fast type checking
%%     . e_E = e_1 * (1 + (beta-1)*l_H/((beta/3) * sqrt(d_1*e_1) + l_H)) %(eq9.2)%
%%     . e_E = e_1 * (1 + ((beta-1)*(l_H/(((beta/3) * sqrt(d_1*e_1)) + l_H)))) %(eq9.2)%
%%     . e_E = e_1 * ((1:RealPos) + (beta-1)*l_H/((beta/3) * sqrt(d_1*e_1) + l_H)) %(eq9.2)%
%% second variant nearly four times faster
     %% REMARK: we interpret that - binds stronger than +
     . d_E = (min(d_1-e_1+e_E, d_2+e_2-e_E) + max(d_1+e_1-e_E, d_2-e_2+e_E))/2
       %(eq10)%

     %% * Lever arm

     ops d_Ge:RealPos;
         h_P, e_P:Real;

%[
@comment
 ANMERKUNG Im Falle einer Flachdichtung koennen die unten angegebenen
 Parameter $h_P und h_G nur errechnet werden nach Auswertung von $d_Ge,
 d. h. nachdem die Berechnungen in 4.3.2 durchgefuehrt wurden.
]%

     . h_P = h_P %(eq13)% %% dummy for fast type checking
%%     . h_P = ((d_Ge - d_E)^2 * (2*d_Ge + d_E)/6 + 2*e_P^2*d_F)/d_Ge^2 %(eq13)%


     %% * Elasticity related flange paramters

     ops gamma, phi_s:Real;
         %% TODO: outsource cos
         cos: Real->Real;

     . gamma = e_E * d_F/(b_F * d_E * cos(phi_s) as NonZero) %(eq17)%

     %% TODO: stopped at page 22(24), eq18
end


%% 5. Limit load equation