機械原理課程設(shè)計 偏置直動滾子推桿盤形凸輪

1、凸輪大作業(yè)選題：凸輪5-C一：題目及原始數(shù)據(jù)：利用計算機輔助設(shè)計完成偏置直動滾子推桿盤形凸輪機構(gòu)的設(shè)計，已知數(shù)據(jù)如下所示，凸輪沿逆時針方向做勻速運動。具體要求如下：1.推程運動規(guī)律為等加速等減速運動，回程運動規(guī)律為五次多項式運動；2.近休凸輪轉(zhuǎn)角為0°-30°；推程凸輪轉(zhuǎn)角30°-210°；遠休凸輪轉(zhuǎn)角210°-280°；回程凸輪轉(zhuǎn)角280°-360。°3.初選基圓半徑為22mm；4.偏距為+14mm5.滾子半徑為18mm6.推桿行程為35mm7.許用壓力角為1=35°，2=65°。8.最小曲率

2、半徑為0.35rr9.計算點數(shù)取120.二：推桿運動規(guī)律及凸輪輪廓線方程1.推程加速階段：s1=70.*a1.*a1/pi/pi; x1=(s0+s1).*sin(a1)+e*cos(a1); y1=(s0+s1).*cos(a1)-e*sin(a1); k1=140*a1/pi2; i1=(k1-e).*sin(a1)+(s0+s1).*cos(a1).*(k1-e).*(k1-e)+(s0+s1).*(s0+s1).(-1/2); j1=-(k1-e).*cos(a1)+(s0+s1).*sin(a1).*(k1-e).*(k1-e)+(s0+s1).*(s0+s1).(-1/2); x1

3、0=x1-18*j1; y10=y1-18*i1;2.推程減速階段：s11=35-70.*(pi-a11).*(pi-a11)/pi/pi; x11=(s0+s11).*sin(a11)+e*cos(a11); y11=(s0+s11).*cos(a11)-e*sin(a11); k11=140.*(pi-a1)/pi2; i11=(k11-e).*sin(a11)+(s0+s11).*cos(a11).*(k11-e).*(k11-e)+(s0+s11).*(s0+s11).(-1/2); j11=-(k11-e).*cos(a11)+(s0+s11).*sin(a11).*(k11-e).

4、*(k11-e)+(s0+s11).*(s0+s11).(-1/2); x101=x11-18*j11; y101=y11-18*i11;3.遠休階段：x2=(s0+s2).*sin(a2)+e*cos(a2); y2=(s0+s2).*cos(a2)-e*sin(a2); k2=0; i2=(k2-e).*sin(a2)+(s0+s2).*cos(a2).*(k2-e).*(k2-e)+(s0+s2).*(s0+s2).(-1/2); j2=-(k2-e).*cos(a2)+(s0+s2).*sin(a2).*(k2-e).*(k2-e)+(s0+s2).*(s0+s2).(-1/2); x

5、20=x2-18*j2; y20=y2-18*i2;4.回程階段：a30=33*pi/18-a3; s3=(350.*a30.*a30.*a30/(4*pi/9)3-525.*a30.*a30.*a30.*a30/(4*pi/9)4+210.*a30.*a30.*a30.*a30.*a30/(4*pi/9)5); x3=(s0+s3).*sin(a3)+e*cos(a3); y3=(s0+s3).*cos(a3)-e*sin(a3); k3=-1050.*a30.*a30/(4*pi/9)3+2100.*a30.*a30.*a30/(4*pi/9)4-1050.*a30.*a30.*a30.*

6、a30/(4*pi/9)5; i3=(k3-e).*sin(a3)+(s0+s3).*cos(a3).*(k3-e).*(k3-e)+(s0+s3).*(s0+s3).(-1/2); j3=-(k3-e).*cos(a3)+(s0+s3).*sin(a3).*(k3-e).*(k3-e)+(s0+s3).*(s0+s3).(-1/2); x30=x3-18*j3; y30=y3-18*i3;5.近休階段：s4=0;x4=(s0+s4).*sin(a4)+e*cos(a4);y4=(s0+s4).*cos(a4)-e*sin(a4);k4=0;i4=(k4-e).*sin(a4)+(s0+s4)

7、.*cos(a4).*(k4-e).*(k4-e)+(s0+s4).*(s0+s4).(-1/2); j4=-(k4-e).*cos(a4)+(s0+s4).*sin(a4).*(k4-e).*(k4-e)+(s0+s4).*(s0+s4).(-1/2); x40=x4-18*j4; y40=y4-18*i4;三：matlab計算程序e=14;r0=22s0=sqrt(r02-e2);c111=1;c3=1; for(i=1:0.1:200) %由壓力角條件循環(huán)求合適基圓半徑 if (c111<35/180)&&(c3<65/180) %判斷條件 else a1=0

8、:pi/60:pi/2; % 推程加速階段 s1=70.*a1.*a1/pi/pi; x1=(s0+s1).*sin(a1)+e*cos(a1); y1=(s0+s1).*cos(a1)-e*sin(a1); k1=140*a1/pi2; % 對s1求導(dǎo) i1=(k1-e).*sin(a1)+(s0+s1).*cos(a1).*(k1-e).*(k1-e)+(s0+s1).*(s0+s1).(-1/2); j1=-(k1-e).*cos(a1)+(s0+s1).*sin(a1).*(k1-e).*(k1-e)+(s0+s1).*(s0+s1).(-1/2); x10=x1-18*j1; y10

9、=y1-18*i1; a11=pi/2:pi/60:pi; % 推程減速階段 s11=35-70.*(pi-a11).*(pi-a11)/pi/pi; x11=(s0+s11).*sin(a11)+e*cos(a11); y11=(s0+s11).*cos(a11)-e*sin(a11); k11=140.*(pi-a1)/pi2; i11=(k11-e).*sin(a11)+(s0+s11).*cos(a11).*(k11-e).*(k11-e)+(s0+s11).*(s0+s11).(-1/2); j11=-(k11-e).*cos(a11)+(s0+s11).*sin(a11).*(k1

10、1-e).*(k11-e)+(s0+s11).*(s0+s11).(-1/2); x101=x11-18*j11; y101=y11-18*i11; a2=pi:pi/60:25*pi/18; %凸輪遠休階段 s2=35; %推桿行程 x2=(s0+s2).*sin(a2)+e*cos(a2); y2=(s0+s2).*cos(a2)-e*sin(a2); k2=0; i2=(k2-e).*sin(a2)+(s0+s2).*cos(a2).*(k2-e).*(k2-e)+(s0+s2).*(s0+s2).(-1/2); j2=-(k2-e).*cos(a2)+(s0+s2).*sin(a2).

11、*(k2-e).*(k2-e)+(s0+s2).*(s0+s2).(-1/2); x20=x2-18*j2; y20=y2-18*i2; a3=25*pi/18:pi/60:33*pi/18; %推桿回程階段 a30=33*pi/18-a3; s3=(350.*a30.*a30.*a30/(4*pi/9)3-525.*a30.*a30.*a30.*a30/(4*pi/9)4+210.*a30.*a30.*a30.*a30.*a30/(4*pi/9)5); x3=(s0+s3).*sin(a3)+e*cos(a3); y3=(s0+s3).*cos(a3)-e*sin(a3); k3=-1050

12、.*a30.*a30/(4*pi/9)3+2100.*a30.*a30.*a30/(4*pi/9)4-1050.*a30.*a30.*a30.*a30/(4*pi/9)5; i3=(k3-e).*sin(a3)+(s0+s3).*cos(a3).*(k3-e).*(k3-e)+(s0+s3).*(s0+s3).(-1/2); j3=-(k3-e).*cos(a3)+(s0+s3).*sin(a3).*(k3-e).*(k3-e)+(s0+s3).*(s0+s3).(-1/2); x30=x3-18*j3; y30=y3-18*i3; a4=33*pi/18:pi/60:2*pi; %推桿近休階

13、段 s4=0; x4=(s0+s4).*sin(a4)+e*cos(a4); y4=(s0+s4).*cos(a4)-e*sin(a4); k4=0; i4=(k4-e).*sin(a4)+(s0+s4).*cos(a4).*(k4-e).*(k4-e)+(s0+s4).*(s0+s4).(-1/2); j4=-(k4-e).*cos(a4)+(s0+s4).*sin(a4).*(k4-e).*(k4-e)+(s0+s4).*(s0+s4).(-1/2); x40=x4-18*j4; y40=y4-18*i4; plot(x10,y10,'-g*',x101,y101,'

14、;-g+',x20,y20,'-r*',x30,y30,'-b*',x40,y40,'-k*',x1,y1,'-g*',x11,y11,'-g+',x2,y2,'-r*',x3,y3,'-b*',x4,y4,'-k*') %凸輪輪廓曲線繪制title(凸輪輪廓曲線繪制');xlabel('Variable X'); %X軸ylabel('Variable Y'); %Y軸text(-250,-200,'工作廓線&

15、#39;) %文字標(biāo)注text(100,-100,'理論廓線'); grid on %加網(wǎng)格axis equal %坐標(biāo)相等 a1=0:pi/60:pi/2; %壓力角計算force1=abs(atan(k1).*(s0+s1).-1); c1=max(force1); a11=pi/2:pi/60:pi; force11=abs(atan(k11).*(s0+s11).-1);c11=max(force11);c111=max(c1,c11);a2=pi:pi/60:25*pi/18;force2=abs(atan(k2).*(s0+s2).-1);c2=max(force2

16、); a3=25*pi/18:pi/60:33*pi/18; force3=abs(atan(k3).*(s0+s3).-1);c3=max(force3); a4=33*pi/18:pi/60:2*pi;force4=abs(atan(k4).*(s0+s4).-1);c4=max(force4); r0=r0+1; %每循環(huán)一次基圓半徑+1 s0=sqrt(r02-e2); end end %求最大壓力角位置 c111 c3 m1,n1=sort(force1); bend1=n1(end-1+1:end) jiaodu1=(bend1(end)-1)*3 m11,n11=sort(for

17、ce11); bend11=n11(end-1+1:end) jiaodu11=(bend11(end)-1)*3+90 m3,n3=sort(force3); bend3=n3(end-1+1:end) jiaodu=(bend3(end)-1)*3+250 vv=i1./j1;vv1=diff(vv);vv2=diff(vv,2);vv22=0,vv2;p=(1+vv1.2).(3/2)./vv22;g=min(p) vv1=i11./j11;vv11=diff(vv1);vv21=diff(vv1,2);vv221=0,vv21;p1=(1+vv11.2).(3/2)./vv221;g1

18、=min(p1) vv2=i2./j2;vv222=diff(vv2);vv223=diff(vv2,2);vv2211=0,vv223;p2=(1+vv222.2).(3/2)./vv2211;g2=min(p2) vv=i3./j3;vv1=diff(vv);vv2=diff(vv,2);vv22=0,vv2;p=(1+vv1.2).(3/2)./vv22;g3=min(p) vv=i4./j4;vv1=diff(vv);vv2=diff(vv,2);vv22=0,vv2;p=(1+vv1.2).(3/2)./vv22;g4=min(p) ) ro=sqrt(s02+e2) %求合適基圓半

19、徑x1y1x11y11x2y2x3y3x4y4x10y10x101y101x20y20x30y30x40y40force1force11force2force3force4c111c3jiaodu11jiaodu3四：計算結(jié)果及分析：（1）工作廓線坐標(biāo)：1;推程加速階段X坐標(biāo)1424.9479312972938 35.833579542701846.6331664128873 57.323071617132667.8798591305935 78.280303424130088.5014157831108 98.5204708048515108.315033160764 117.8629847

20、04875127.142552005136 136.132334367976144.811332419744 153.158977301315161.155160523920 168.780264525614176.015193958402 182.841407726263189.240951783976 195.196492695966200.691351943287 205.709540955551 210.235796832989 214.255618712129217.755304716715 220.721989423648223.143681761924 225.009303250

21、807226.308726472013 227.0328136593412推程加速階段Y坐標(biāo) 209.532813659341 208.532370629552206.998924199561 204.935879972465202.347567871334 199.239236813805195.617049448531 191.488076931747186.860293712014 181.742572281261 176.144677840557 170.077262819810163.551861181761 156.580882432274 149.177605251176141.

22、356170650697133.131574562033 124.519659744732115.537106908501 106.20142493273596.5309400655771 86.5447839816669 76.2628805759777 65.705931370278654.8953994088027 43.8534915206956 32.603138828747321.16797538678679.57231483194954 -2.15887505719948-14.00000000000003推程減速階段X坐標(biāo)227.032813659341 227.1346196

23、85286226.568905051752 225.331644205755223.421214513810 220.838411540547 217.586454974950213.670985176905209.100050353069 203.884084407342 198.035875547330191.570525763878184.505401336072 176.860074548737 168.656256843411159.917723656843150.670231233150 140.941425726738 130.760744942876120.1593130912

24、03109.169828954466 97.8264479001947 86.164658186856474.221152038085562.0336919788640 49.6409729459048 37.0824807009210 24.398347089867511.6292027035831 -1.18397249451846-14.00000000000004推程減速階段Y坐標(biāo)-14.0000000000000-25.9228338599749-37.8904674143353-49.8635381159681-61.8024134893063-73.6673405558026-8

25、5.4185959941913-97.0166364509177-108.422248415730-119.596697079292-130.501873593764-141.100440163605-151.355972402351-161.233098401750-170.697633972432-179.716713530067-188.258916117849-196.294386074865-203.794947880574-210.734214728044-217.087690402739-222.832864069368-227.949297596606-232.41870507

26、8147-236.225024238547-239.354479443456-241.795636066125-243.539445995213-244.579284102998-244.910975527746-244.5328136593415遠休階段X坐標(biāo)-14.0000000000000-26.7786721222032-39.4839457654822-52.0809966579133-64.5352971586108-76.8127108955902-88.8795863311907-100.702848998602-112.250092156677-123.48966561455

27、9-134.390762482652-144.923503612169-155.059019491793-164.769529377011-174.028417435196-182.810305697758-191.091123619391-198.848174053764-206.060195464824-212.707420203182-218.771628687875-224.236199344965-229.086154166116-233.3081997622826遠休階段Y坐標(biāo)-244.532813659341-243.464986549453-241.729838834477-2

28、39.332126433691-236.278421310122-232.577093457254-228.238287957455-223.273897175014-217.697528159994-211.524465352257-204.771628687875-197.457527222762-189.602208400634-181.227203104369-172.355466641343-163.011315824535-153.220362321829-143.009442456216-132.406543649295-121.440727709697-110.14205117

29、6688-98.5414829372844-86.6708193426842-74.56259705668027減速階段X坐標(biāo)-234.573962542258-237.924423961410-240.528414701632-242.301034179885-243.179109387654-243.122053300159-242.111828793401-240.152099129043-237.266657296952-233.497236106624-228.900808808014-223.546496133102-217.512199933386-210.88108601493

30、2-203.738039329490-196.166213373622-188.243792502170-180.041080919969-171.618025436311-163.022270727289-154.287835944964-145.434490148429-136.467891333878-127.380539946257-118.153582814159-108.759487623767-99.16559150875688減速階段Y坐標(biāo)-70.4794512845940-58.1011116825609-45.5418784536957-32.8365161989020-2

31、0.0390090002643-7.216945791302505.55380225566372 18.194003075560030.6254874984057 42.7749931638176 54.5773610652433 65.978032703814576.9348117792082 87.4188705720677 97.4149974868349 106.921098432862115.946980634777 124.512462892978 132.644871079527 140.375991577690147.738568287212 154.762440563530

32、161.470429890068 167.874092062809173.969459073374 179.732900602872 185.1172389914419近休X坐標(biāo)-92.6420511766881-82.6518154464002-72.4350368350310-62.0197188225945-51.4344090718031-40.7081211809080-29.8702551594429-18.9505168448415-7.978836480802643.0147133194277613.999999999999910近休Y坐標(biāo)1 188.4607395554201

33、93.050970998372 197.112063148625 200.632884834880203.603785729623 206.016622800007207.864782627336 209.143199533988209.848369468082 209.978359607845209.532813659341（2）理論廓線坐標(biāo);推程加速階段X坐標(biāo)12.8000000000000 22.872827317908432.8885297342726 42.825360681316652.6617133932777 62.3761432336542 71.9473900632018

34、81.354400741436490.5763518517692 99.5926727370081 108.383068927807 116.927546041764125.206434225271 133.200413203958140.890538000620 148.258265371979155.285481007489 161.954527524708168.248233286539 174.149942056033179.643543494319 184.713504496809189.344901352090 193.523452696839197.235553228942 20

35、0.468308129584 203.209568133643 205.447965176251207.172948531918 208.374821351328 209.044777489697推程加速階段Y坐標(biāo)191.572858202826 190.652383395923189.241484022951 187.343250393275184.961604006512 182.101293199539178.767888983898 174.967781050798170.708173911217 165.997083129187160.843331597179 155.2565457

36、93692149.247151954669 142.826372082411136.006219708068 128.799495316842121.219781338553 113.281436600464104.999590134052 96.390134222989187.4697165758390 78.2557315040260 68.766309983443159.020308476717649.0372963926355 38.8375420595755 28.4419970910307 17.87227902341457.15065210936054 -3.6999938463

37、5310 -14.6561667163081推程減速階段X坐標(biāo)209.193734991700 209.188778273809208.573036193737 207.342473187261205.495287697520 203.031928716014 199.955103403567196.269775760348191.983156349172 187.104683111356181.645993349332 175.620886984768169.045281235120 161.937156885096154.316496362355 146.205213858842137.6

38、27077770212 128.607625755855119.174072750844 109.35521228870799.1813115200797 88.684000336947677.8961550352902 66.851776970326355.5858666782191 44.1342939559169 32.533664406729620.82118297320159.03451499079487 -2.78835469420737-14.6092639913715推程減速階段Y坐標(biāo)-16.4015145824514-27.3181030218633-38.276089049

39、0105-49.2392576762938-60.1711110106104-71.0350090000076-81.7943109934888-92.4125175513741-102.853411943058-113.081200770624-123.060653160544-132.757237971647-142.137258475553-151.167983975963-159.817777845352-168.056221471851-175.854233625249-183.184184769079-190.020005865654-196.337291242469-202.11

40、3395111709-207.327521359409-211.960806247121-215.996393696655-219.419502857395-222.217487685822-224.379888298036-225.898473888143-226.767277038293-226.982619279687-226.543127798025遠休階段X坐標(biāo)-12.9711482618274-24.8107233108544-36.5822938918588-48.2535949481094-59.7926362546736-71.1677901013991-82.3478779

41、822689-93.3022560535201-104.000899126289-114.414482963567-124.514464655894-134.273160855494-143.663823654403-152.660713898624-161.239171737366-169.375684213972-177.047949713308-184.234939088932-190.916953302526-197.075677417593-202.694230799421-207.757213383730-212.250747887182-216.162517844044遠休階段Y

42、坐標(biāo)-226.562241489795-225.572888364055-223.965255630689-221.743749699274-218.914459563151-215.485140109924-211.465190865844-206.865630232365-201.699065285474-195.979657220565-189.723082537593-182.946490072876-175.668453995324-167.908922895934-159.689165110094-151.031710422544-141.960288314811-132.4997

43、62924347-122.676064893652-112.516120296192-102.047776833901-91.2997275085610-80.3014319762869-69.0830358006497回程階段X坐標(biāo)-217.335260464284-220.421346316413-222.795183195622-224.398577389943-225.188547506355-225.137585355545-224.233655449440-222.479896624979-219.893983296304-216.507098988589-212.36248811

44、6223-207.513585489574-202.021768715920-195.953825087341-189.379262026933-182.367612804067-174.985894648424-167.296364561343-159.354690783951-151.208619312605-142.897173644983-134.450395994491-125.889635960919-117.228428433346-108.474068637267-99.6300563428237-90.6995930141100回程階段Y坐標(biāo)-65.2999580017652

45、-53.9008411016096-42.4544037000726-30.9651421357433-19.4561855319938-7.964550465698053.46312822959339 14.774462367317425.9148401896814 36.830647892016847.4721553190688 57.795992842225267.7671217377121 77.3601986319145 86.5602513186570 95.3626114072227103.772082503801 111.801357318003119.468732676936

46、 126.795209558515133.801107529679 140.502367786106146.906758880859 153.010222047587158.793589895652 164.219890434419169.232439040273近休階段X坐標(biāo)-84.7013039329720-75.5673741224230-66.2263193920283-56.7037429235150-47.0257454370771-37.2188536511159-27.3099475743478-17.3261868295693-7.294936211019562.756309

47、3206196712.8000000000000近休階段Y坐標(biāo)172.306961879241 176.503744912797180.216743450172 183.435780420462186.152032667084 188.358055131435190.047801259279 191.216639573932191.861366370818 191.980214498602 191.572858202826凸輪壓力角00.003544318559977650.007086575440251550.01062471312743390.01415668242241860.01768044655179030.02119398522475370.02469529861808280.02818241127214470.03165337588173310.03510627696624600.03853923440464810.04195040682166590.04533799481275080.04870024399651490.05203544788456750.05534195055995420.058