机械原理课程设计 偏置直动滚子推杆盘形凸轮

1、凸轮大作业选题：凸轮5-C一：题目及原始数据：利用计算机辅助设计完成偏置直动滚子推杆盘形凸轮机构的设计，已知数据如下所示，凸轮沿逆时针方向做匀速运动。具体要求如下：1.推程运动规律为等加速等减速运动，回程运动规律为五次多项式运动；2.近休凸轮转角为0°-30°；推程凸轮转角30°-210°；远休凸轮转角210°-280°；回程凸轮转角280°-360。°3.初选基圆半径为22mm；4.偏距为+14mm5.滚子半径为18mm6.推杆行程为35mm7.许用压力角为1=35°，2=65°。8.最小曲率

2、半径为0.35rr9.计算点数取120.二：推杆运动规律及凸轮轮廓线方程1.推程加速阶段：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.推程减速阶段：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.远休阶段：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.回程阶段：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.近休阶段：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计算程序e=14;r0=22s0=sqrt(r02-e2);c111=1;c3=1; for(i=1:0.1:200) %由压力角条件循环求合适基圆半径 if (c111<35/180)&&(c3<65/180) %判断条件 else a1=0

8、:pi/60:pi/2; % 推程加速阶段 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; % 对s1求导 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; % 推程减速阶段 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; %凸轮远休阶段 s2=35; %推杆行程 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; %推杆回程阶段 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; %推杆近休阶

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*') %凸轮轮廓曲线绘制title(凸轮轮廓曲线绘制');xlabel('Variable X'); %X轴ylabel('Variable Y'); %Y轴text(-250,-200,'工作廓线&

15、#39;) %文字标注text(100,-100,'理论廓线'); grid on %加网格axis equal %坐标相等 a1=0:pi/60:pi/2; %压力角计算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; %每循环一次基圆半径+1 s0=sqrt(r02-e2); end end %求最大压力角位置 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) %求合适基圆半

19、径x1y1x11y11x2y2x3y3x4y4x10y10x101y101x20y20x30y30x40y40force1force11force2force3force4c111c3jiaodu11jiaodu3四：计算结果及分析：（1）工作廓线坐标：1;推程加速阶段X坐标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推程加速阶段Y坐标 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推程减速阶段X坐标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推程减速阶段Y坐标-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远休阶段X坐标-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远休阶段Y坐标-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减速阶段X坐标-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减速阶段Y坐标-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坐标-92.6420511766881-82.6518154464002-72.4350368350310-62.0197188225945-51.4344090718031-40.7081211809080-29.8702551594429-18.9505168448415-7.978836480802643.0147133194277613.999999999999910近休Y坐标1 188.4607395554201

33、93.050970998372 197.112063148625 200.632884834880203.603785729623 206.016622800007207.864782627336 209.143199533988209.848369468082 209.978359607845209.532813659341（2）理论廓线坐标;推程加速阶段X坐标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推程加速阶段Y坐标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推程减速阶段X坐标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推程减速阶段Y坐标-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远休阶段X坐标-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远休阶段Y

42、坐标-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回程阶段X坐标-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回程阶段Y坐标-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近休阶段X坐标-84.7013039329720-75.5673741224230-66.2263193920283-56.7037429235150-47.0257454370771-37.2188536511159-27.3099475743478-17.3261868295693-7.294936211019562.756309

47、3206196712.8000000000000近休阶段Y坐标172.306961879241 176.503744912797180.216743450172 183.435780420462186.152032667084 188.358055131435190.047801259279 191.216639573932191.861366370818 191.980214498602 191.572858202826凸轮压力角00.003544318559977650.007086575440251550.01062471312743390.01415668242241860.01768044655179030.02119398522475370.02469529861808280.02818241127214470.03165337588173310.03510627696624600.03853923440464810.04195040682166590.04533799481275080.04870024399651490.05203544788456750.05534195055995420.058