SetDirectory[NotebookDirectory[]]

Freno a ceppo traslante

Componenti della risultante e momento frenante

Rx[α_,β_,rr_,f_,pp0_]= Integrate[(pp0 Cos[θ] Cos[θ] -f pp0 Cos[θ] Sin[θ])rr,{θ,-α,β}]//Simplify

Ry[α_,β_,rr_,f_,pp0_]= Integrate[(f pp0 Cos[θ] Cos[θ] + pp0 Cos[θ] Sin[θ])rr,{θ,-α,β}]//Simplify

Mo[α_,β_,rr_,f_,pp0_]=Integrate[f pp0 Cos[θ] rr^2,{θ,-α,β}]//Simplify

solo pressioni

Rpx[α_,β_,rr_,f_,pp0_]= Rx[α,β,rr,0,pp0]//Simplify

Rpy[α_,β_,rr_,f_,pp0_]= Ry[α,β,rr,0,pp0]//Simplify

solo azioni di attrito

Rtx[α_,β_,rr_,f_,pp0_]= Rx[α,β,rr,f,pp0]-Rx[α,β,rr,0,pp0]//Simplify

Rty[α_,β_,rr_,f_,pp0_]= Ry[α,β,rr,f,pp0]-Ry[α,β,rr,0,pp0]//Simplify

Inner[Times,{Rpx[α,β,rr,f,pp0],Rpy[α,β,rr,f,pp0]},{Rtx[α,β,rr,f,pp0],Rty[α,β,rr,f,pp0]},Plus]

Norm[{Rpx[30 Degree,45 Degree,0.13,f,3000],Rpy[30 Degree,45 Degree,0.13,f,3000]}]//Simplify

Norm[{Rtx[30 Degree,45 Degree,0.13,f,3000],Rty[30 Degree,45 Degree,0.13,f,3000]}]//Simplify

Manipulate[(βn = (α + Δβ) ;

p0=First[pp0/. Solve[Rx[α Degree,βn Degree,r,f,pp0]==15,pp0]];

RRx=Rx[α Degree,βn Degree,r,f,p0];
RRy=Ry[α Degree,βn Degree,r,f,p0];
MMo=Mo[α Degree,βn Degree,r,f,p0];


figura=Show[{

Graphics[{
Darker[Green],EdgeForm[Thin],
Opacity[0.35],
Disk[{0,0},1.6 r,{-α Degree,βn Degree}],

Rectangle[{1.58 r,-0.2 r},{4 r, 0.2 r}],
Opacity[1],

White,
Disk[{0,0},r,{-α Degree,βn Degree}],

Orange,
Tooltip[Circle[{0,0},Mo[α Degree,βn Degree,r,f,p0]/10],
"raggio prop. al mom. frenante"],

Black,Thick,
Circle[{0,0},r],

Line[{{2 r,0.25 r},{4 r, 0.25 r}}],
Line[{{2 r,-0.25 r},{4 r, -0.25 r}}],
Gray,
Disk[{0,0},2,{0,2Pi}],

Black,
PointSize[0.00715],
(*Point[{Mo[α Degree,α Degree,r,f,p0]/Ry[α Degree,α Degree,r,f,p0],0}],*)


Arrowheads[0.0175],
Circle[{0,0},2,{0,2Pi}],
AbsoluteThickness[3],
Arrow[BezierCurve[4{{0.9,0.5},{0,1.65},{-0.9,0.5}}]],


(*Arrow[{{0,0},{RRx,
RRy}}],*)


Brown,
Tooltip[Arrow[{{MMo/RRy,0},{MMo/RRy+RRx,0*RRy}}],
"Rx = -Q"],

Tooltip[Arrow[{{4 r+RRx,0}, {4 r,0}}],
"Q"],

Orange,
Tooltip[Arrow[{{MMo/RRy,0},{MMo/RRy+0*RRx,RRy}}],
"Ry"],

Blue,
Tooltip[Arrow[{{0,0},{Rpx[α Degree,βn Degree,r,f,p0],Rpy[α Degree,βn Degree,r,f,p0]}}],
"risultante sole pressioni = N"],

Magenta,
Tooltip[Arrow[{{0,0},{Rtx[α Degree,βn Degree,r,f,p0],Rty[α Degree,βn Degree,r,f,p0]}}],
"risultante sole azioni di attrito = T = f N"],

Red,
Tooltip[Arrow[{{MMo/RRy,0},{MMo/RRy+RRx,RRy}}],
"risultante totale"],

Red,
Tooltip[Arrow[{{0,-MMo/RRx},{RRx,-MMo/RRx+RRy}}],
"risultante totale"],


Thin,
Line[{{r*Cos[βn Degree],r*Sin[βn Degree]},{r/Cos[βn Degree],0}}]}],

PolarPlot[Tooltip[r+p0/3*r Cos[t],
"pressione"],{t,-α Degree,βn Degree},PlotStyle->{Blue,Thick}]
},
Axes->True,Ticks->None,

PlotLabel->"Freno a tamburo (M. Guiggiani - 9/3/2020 - all rights reserved)",

PlotRange->1.63{{-15,80},{-15,15}},
ImageSize->1000]),
{{r,15},5,20 },
{{f,0.5},0.0001,2,Appearance->"Labeled" },
{{α,45},-90,90,Appearance->"Labeled" },
{{Δβ,0},-120,120,Appearance->"Labeled" },ControlPlacement->Top,
SaveDefinitions->True
]

figura

asimm2=

Export["asimm2.eps",asimm2]

asimm1=

Export["asimm1.eps",asimm1]

simm2=

Export["simm2.eps",simm2]

simm1=

Export["simm1.eps",simm1]

SystemOpen[DirectoryName[AbsoluteFileName["simm1.jpg"]]]

p0

rRy

Rx[α,α,r,f,p00]//Simplify

p0sol= p00 /.Solve[Rx[α,α,r,f,p00]== NN,p00]//First

Ry[α,α,r,f,p00]//Simplify

Ry[α,α,r,f,p0sol]//Simplify

Rpx[α,α,r,f,p00]//Simplify

Rty[α,α,r,f,p00]//Simplify