clear
%?parameters
N?=?2;??????????????%?number?of?teeth
Kt?=?6e8;???????????%?tangential?cutting?force?coef?cient（N/m2）
Kn?=?2e8;???????????%?normal?cutting?force?coef?cient（N/m2）
w0?=?922*2*pi;?????%?angular?natural?frequency?（rad/s）
zeta?=?0.011;??????%?relative?damping?（1）
m_t?=?0.03993;?????%?mass?（kg）
aD?=?0.05;??????????%?radial?depth?of?cut
up_or_down?=?-1;???%?1:?up-milling??1:?down-milling
if?up_or_down?==?1?%?up-milling
???fist?=?0;????????%?start?angle
???fiex?=?acos（1?-?2*aD）;?%?exit?angle
elseif?up_or_down?==?-1?%?down-milling
???fist?=?acos（2*aD?-?1）;?%?start?angle
???fiex?=?pi;?%?exit?angle
end
stx?=?400;?%?steps?of?spindle?speed
sty?=?200;?%?steps?of?depth?of?cut
w_st?=?0e-3;?%?starting?depth?of?cut?（m）
w_fi?=?10e-3;?%??nal?depth?of?cut?（m）
o_st?=?5e3;?%?starting?spindle?speed?（rpm）
o_fi?=?25e3;?%??nal?spindle?speed?（rpm）
%?computational?parameters
k?=?40;?%?number?of?discretization?interval?over?one?period
intk?=?20;?%?number?of?numerical?integration?steps?for?Equation?（37）
m?=?k;?%?since?time?delay?=?time?period
wa?=1/2;?%?since?time?delay?=?time?period
wb?=1/2;?%?since?time?delay?=?time?period
D?=?zeros（m?+?2?m?+?2）;?%?matrix?D
d?=?ones（m?+?1?1）;
d（1?:?2）?=?0;
D?=?D?+?diag（d?-1）;
D（31）?=?1;
%?numerical?integration?of?speci?c?cutting?force?coef?cient?according?to?Equation?（37）
for?i?=?1?:?k
????dtr?=?2*pi/N/k;?%t?if?=?2?/N
????h_i（i）?=?0;
????for?j?=?1?:?N?%?loop?for?tooth?j
????????for?h?=?1?:?intk?%?loop?for?numerical?integration?of????h
?????????????fi（h）?=?i*dtr?+?（?j?-?1）*2*pi/N?+?h*dtr/intk;
?????????????if（fi（h）?>=?fist）*（fi（h）?<=?fiex）
?????????????????g（h）?=?1;?%?tooth?is?in?the?cut
?????????????else
?????????????????g（h）?=?0;?%?tooth?is?out?of?cut
?????????????end
????????end
????????h_i（i）?=?h_i（i）?+?sum（g.*（Kt.*cos（fi）?+?Kn.*sin（fi））.*sin（fi））/intk;
????end
end
%?start?of?computation
for?x?=?1?:?stx?+?1?%?loop?for?spindle?speeds
????o?=?o_st?+?（x?-?1）*（o_fi?-?o_st）/stx;?%?spindle?speed
????tau?=?60/o/N;?%?time?delay
????dt?=?tau/（m）;?%?time?step
????for?y?=?1?:?sty?+?1?%?loop?for?depth?of?cuts
????????w?=?w_st?+?（y?-?1）*（w_fi?-?w_st）/sty;?%?depth?of?cut
????????%?construct?transition?matrix?Fi
????????Fi?=?eye（m?+?2?m?+?2）;
????????for?i?=?1?:?m
????????????A?=?zeros（2?2）;?%?matrix?Ai
????????????A（12）?=?1;
????????????A（21）?=?-w0^2?-?h_i（i）*w/m_t;
????????????A（22）?=?-2*zeta*w0;
????????????B?=?zeros（2?2）;?%?matrix?Bi
????????????B（21）?=?h_i（i）*w/m_t;
????????????P?=?expm（A*dt）;?%?matrix?Pi
????????????R?=?（expm（A*dt）?-?eye（2））*inv（A）*B;?%?matrix?Ri
????????????D（1?:?2?1?:?2）?=?P;
????????????D（1?:?2?m?+?1）?=?wa*R（1?:?2?1?:?1）;
????????????D（1?:?2?m?+?2）?=?wb*R（1?:?2?1?:?1）;
????????????Fi?=?D*Fi;?%?transition?matrix
????????end
????ss（xy）?=?o;?%?matrix?of?spindle?speeds
????dc（xy）?=?w;?%?matrix?of?depth?of?cuts
????ei（xy）?=?max（abs（eig（Fi）））;?%?matrix?of?eigenvalues
????end
stx?+?1?-?x
end
figure
contour（ssdcei[

?屬性????????????大小?????日期????時間???名稱
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?????文件????????3100??2013-03-19?15:38??lobe_semi.m