螺旋桨设计

螺旋桨设计计算书船舶原理·推进1.船体主要数据船型：单桨、集装箱船设计水线长L WL=215.00m垂线间长L PP=210.00m型宽B=32.00m设计吃水T=12.00m方形系数C B=0.655排水量∇=54000m3桨轴中心距基线Z P=4.00m 2.主机参数最大持续功率：32000kw转速：102r min⁄旋向：右旋3.推进因子伴流分数ω=0.24推力减额分数t=0.16相对旋转效率ηR=1.0船身效率ηH =1−t1−ω=1.1053船体有效马力曲线0.350.400.450.500.550.600.130.140.150.160.170.180.190.20τc =(T /A P )/(0.5ρV20.7R)σ0.7R =p 0/(0.5ρV20.7R)柏利尔空泡限界线图4.可以达到的最大航速的计算取功率储备15%，轴系效率 ηS =0.97螺旋桨敞水收到马力：P D =32000×0.85×ηS ×ηR =26384(kw )=35896.60hp假设有MAU5-70、MAU5-75、MAU5-80，按回归多项式以及回归系数计算。

（源代码见附表1）表1 按回归多项式以及回归系数计算表据表1中的计算结果可绘制P TE 、δ、P/D 及η0对V 的曲线，如图1所示。

图1 MAU5叶桨回归计算计算结果此处用MATLAB 求得相关曲线交点。

从P TE =f(V)曲线与船体满载有效马力曲线之交点，可获得不同盘面比所对应的设计航速及螺旋桨最佳要素P/D 、D 及η0。

如表2所列。

表2按图1设计计算的最佳要素5.空泡校核按柏利尔空泡限界线中商船上限线，计算不发生空泡之最小展开面积比。

桨轴沉深h s =T −Z P =12−4=8mP o −P v =P a +γh s −P V =10330+1025.24×8−174=18357.92kgf m 2⁄ 计算温度 t =15℃ ρ=104.63kgf ∙s 2m 4⁄ P V =174kgf m 2⁄ P D =35896.60hp图2空泡校核计算结果 表3空泡校核计算结果据表3计算结果作图2，用MATLAB 求得相关曲线交点。

可求得不发生空泡的最小盘面比以及所对应的最佳螺旋桨要素。

A E /A o =0.7443 P D ⁄=0.9724 D =7.5560m η0=0.6634 V max =22.9361kn6.强度校核按2001年《规范》校核t 0.25R 及t 0.6R ，如表4，应不小于按下式计算之值：t =√YK−X Y =1.36A 1N e Zbn eX =A 2GA d N 2D 31010Zb计算功率 N e =32000∙10009.8⁄75⁄∙0.97=42231.29hpA d =A E /A o =0.7443 P D ⁄=0.9724 ε=10° G =7.6g/cm 3 N =n e =102r/minb 0.66R =0.226D A d (0.1Z)⁄=0.226×7.5560×0.74430.5⁄=2.5420mb 0.25R =0.7212b 0.66R =1.8333m b 0.6R =0.9911b 0.66R =2.5194m表4强度校核计算表实际桨叶厚度按t 0.1R 0.25R t 0.2=309.72mm t 0.3=274.32mm t 0.4=238.91mm t 0.5=203.50mm t 0.6=168.09mm t 0.7=132.68mm t 0.8=97.27mm t 0.9=61.86mm7.螺距修正根据尾轴直径大小，决定毂径比d h D ⁄=0.17，此值比MAU 桨标准毂径比略小，对此项螺距进行修正。

所需的螺距比修正量为： ∆(P D )B =110[(d h D ⁄)′−d h D ⁄]=−0.001 0.7R 处标准桨厚度t 0.7=0.0171D =129.21mm由于实际桨叶厚度大于MAU 桨标准厚度，故需因厚度差异进行螺距修正。

设计桨 (t b )0.7R =0.132680.9964×2.5420=0.05238 标准桨 (tb )0.7R =0.0171×D0.9964×0.750.1×5×0.226×D=0.05062 （取MAU5-75为基准桨）1−s =V A NP =(1−ω)V ×30.866NP =0.76×22.9361×30.866102×7.3475=0.7179 ∆(t b )0.7=[(t b )0.7设−(t b )0.7标×0.750.7443]×0.75=0.00103 ∆(P D )t =−2(P D )0(1−s)∆(tb )0.7R =−2×0.9724×0.7179×0.00103=−0.001438 修正后的螺距比P D =(P D )0+∆(P D )t +∆(PD)B =0.9724−0.001−0.001438=0.9700 8.重量及惯性矩计算根据中国船舶及海洋工程设计研究院提出的公式：桨叶重 G b1=0.169γZb max (0.5t 0.2+t 0.6)(1−dD )D(kgf) 桨榖重 G n =(0.88−0.6d0d)L K γd 2(kgf )螺旋桨重量 G =G b1+G n螺旋桨惯性矩 I mp =0.0948γZb max (0.5t 0.2+t 0.6)D 3(kgf ∙cm ∙s 2) (d D ⁄≤0.18) 式中：桨叶最大宽度b max =2.542m ；主机最大持续功率情况下的螺旋桨收到马力P D =35896.60hp ； 螺旋桨在相应收到马力下的转速N =102r/min ；0.2R 和0.6R 处切面的最大厚度t 0.2=0.30972m ，t 0.6=0.16809m ； 轴毂配合的锥度K =1/13； 毂长L K =d +0.1=1.4m ；材料重量密度γ=7.6g cm 3=7600kgf m 3⁄⁄； 桨叶数Z =5；桨榖直径d =1.3m ；螺旋桨直径D =7.5560m ；桨榖长度中央处轴径d 0=0.045+0.108（P D N ⁄）13⁄−KL K 2=0.7537m ；代入上式计算得到：桨叶重量 G b1=32982.07kgf 桨榖重量 G n =9568.70kgf 螺旋桨总重 G =42550.77kgf螺旋桨惯性矩 I mp =1279023.7kgf ∙cm ∙s 2 9.敞水性征曲线之确定按回归多项式以及回归系数计算，得到设计桨MAU5-74.43，P D ⁄=0.9724的敞水性征曲线如图3，其数据见表5。

（源代码见附表2）图3设计桨的敞水性征曲线表5设计桨的敞水特性数据表10.系柱特性计算由图3及表5得J=0时，K T=0.4753K Q=0.0672计算功率P D=32000×0.97×1000÷9.8÷75=42231.29hp 系柱推力减额分数取t0=0.04主机转矩Q=P D×60×752πN=42231.29×60×752π×102=296528.78kgf∙m系柱推力T=K TK QQD=0.47530.0672296528.787.5560=277570.59kgf螺旋桨转速N=60√TρD4K T=78.51r/min11.航行特性计算取转速为102r/min，94r/min，86r/min进行按回归多项式以及回归系数计算，结果如表6所示。

（源代码见附表3）表6航行特性计算表图4航行特性曲线将上述计算结果绘成图4。

由图中可求得压载航行时可达到最大航速约为V=23.53kn，主机马力为33311hp。

超满载航行时可达最大航速约为V=21.95kn，主机马力为36950hp。

满载航行，N=102r/min时，可达到最大航速约为V=22.79kn，主机马力为V=34852hp，与设计要求基本一致。

12.螺旋桨计算总结螺旋桨直径D=7.5560m⁄=0.9700螺距比P D型式MAU叶数Z=5盘面比A E/A o=0.7443纵倾角ε=10°=0.6634螺旋桨效率设计航速V max=22.9361kn⁄=0.17毂径比d h D旋向右旋材料Cu3镍铝青铜重量42550.77kgf惯性矩1279023.7kgf∙cm∙s213.设计总结本次设计整体上经过了基本参数的初步确定、通过各项性能校核确定最佳基本参数、对选区参数的螺旋桨进行强度的校核和性能的修正、预测该螺旋桨的实际航行性能并与设计要求相比较。

设计总体的关键实际上在于第一步，基本参数设定时选取的方法不同，将直接导致的设计精度和参数设计优良程度，进而影响后续的所有参数处理过程。

通过设计的过程，个人认为对于技术已经成熟的系列桨设计，利用系列桨图谱进行设计可以得到比较好的精度和与设计要求相符的程度，个人采取的利用回归多项式和回归系数辅以计算机而完成的参数计算，与其他方法比较可以发现，该种方法设计的桨的参数要略大于其他方法设计得到的参数。

总体而言，通过这次的设计，主要得到了一下几个方面的认识。

(1)对螺旋桨的设计和计算过程有了实际的操作经历。

(2)对于不同的设计方法的优缺点有了直接的认识。

(3)了解了螺旋桨的各个参数的重要程度，从而得到了螺旋桨设计过程的侧重点。

附表1最大航速确定源代码#include"stdio.h"#include"math.h"int n;double pd=35896.60;double N=102;double w=0.24;double t=0.16;double bp,va,bps,v;void calculator(){va=(1-w)*v;bp=N*pow(pd,0.5)/pow(va,2.5);bps=sqrt(bp);}double delta(double x){int i;double del=0;doublec[8]={13.34629,10.57914,-0.01699188,0.7553662e-5,-0.2363072e+2,0.1271846e+2,0.8845788, -0.4082846e-6};double ii[8]={0,1,3,6,0,0,1,7};double jj[8]={0,0,1,2,1,2,4,3};for(i=0;i<=7;i++)del=del+c[i]*pow(bps,ii[i])*pow(x,jj[i]);return(del);}double pD(double x){int i;double pD=0;doubled[11]={0.2020720e+1,-0.5540289,0.7619289e-1,-0.1940969e-2,-0.2383249e-3,0.1738893e-5 ,-0.654265e-7,0.1872267,-0.7578786e-1,0.6260398e-7,0.3688448};double ii[11]={0,1,2,3,4,6,7,0,1,6,0};double jj[11]={0,0,0,0,0,0,0,4,1,4,1};for(i=0;i<=10;i++)pD=pD+d[i]*pow(bps,ii[i])*pow(x,jj[i]);return(pD);}double kt(double x,double y,double z){int i;double kt=0;doublea[16]={0.5367018e-1,-0.3023566,0.4333625,-0.1065471,-0.6582904,0.1189101,-0.4408557e-3, -0.3317857e-1,0.1151124e+1,0.1960773,-0.9747062e-1,0.2036384,-0.2566153,-0.1370242,-0.2 874294,-0.2851609};double ii[16]={0,0,1,0,2,1,6,1,2,0,3,1,1,0,0,2};double jj[16]={0,1,0,2,0,3,0,4,0,0,0,1,1,2,0,0};double kk[16]={0,0,0,1,3,1,0,1,2,3,1,0,1,0,2,1};for(i=0;i<16;i++)kt=kt+a[i]*pow(x,ii[i])*pow(y,jj[i])*pow(z,kk[i]);return(kt);}double kq10(double x,double y,double z){int i;double kq10=0;doubleb[23]={-0.9251390e-1,-0.1229000,0.3050697,-0.2935303,-0.3991474,-0.1022050e+1,0.10228 33e-1,0.3521100e-2,0.2552059e-2,0.2143532,0.7131110e-3,0.2078488,0.6397053,0.9404846e-3,-0.2930044e-1,-0.7807623e-1,-0.3025523,0.1855105,-0.6724210,-0.2087142,0.9400654,0.9 316346,-0.4348397e-1};double ii[23]={0,2,1,0,2,1,7,1,5,0,4,1,1,7,0,0,2,1,2,4,3,2,6};double jj[23]={0,0,1,2,0,1,0,0,2,1,4,2,0,1,1,4,2,3,1,0,0,1,0};double kk[23]={0,0,0,0,1,1,0,3,0,3,0,1,0,0,1,0,3,1,2,3,1,3,0};for(i=0;i<23;i++)kq10=kq10+b[i]*pow(x,ii[i])*pow(y,jj[i])*pow(z,kk[i]);return(kq10);}void main(){int i,j;double ae[3],delt,PD,J,KT,KQ10,efficiency,pt;FILE *fp;fp=fopen("data.txt","w+");printf("输入计算航速的个数:\n");scanf("%d",&n);printf("输入所取的三个盘面比:\n");for(i=0;i<3;i++){printf("输入第%d个盘面比:",i+1);scanf("%lf",&ae[i]);printf("\n");}for(i=0;i<n;i++){printf("\n输入航速V:\n\n");scanf("%lf",&v);fprintf(fp,"\n航速=%lf\n",v);for(j=0;j<=2;j++){fprintf(fp,"\n盘面比=%lf\n\n",ae[j]);calculator();delt=delta(ae[j]);PD=pD(ae[j]);J=30.86/delt;KT=kt(PD, J, ae[j]);KQ10=kq10(PD, J, ae[j]);efficiency=10*KT*J/(KQ10*6.283185307);pt=pd*efficiency*(1-t)/(1-w);fprintf(fp,"δ=%-10.4lf ",delt);fprintf(fp,"P/D=%-8.4lf ",PD);fprintf(fp,"η0 =%-8.4lf ",efficiency);fprintf(fp,"Pte =%-15.4lf\n ",pt);}}fclose(fp);}附表2敞水性征曲线计算源代码#include"stdio.h"#include"math.h"int n;double pd=35896.60double N=102;double w=0.24;double t=0.16;double va,v;double kt(double x,double y,double z){int i;double kt=0;doublea[16]={0.5367018e-1,-0.3023566,0.4333625,-0.1065471,-0.6582904,0.1189101,-0.4408557e-3, -0.3317857e-1,0.1151124e+1,0.1960773,-0.9747062e-1,0.2036384,-0.2566153,-0.1370242,-0.2 874294,-0.2851609};double ii[16]={0,0,1,0,2,1,6,1,2,0,3,1,1,0,0,2};double jj[16]={0,1,0,2,0,3,0,4,0,0,0,1,1,2,0,0};double kk[16]={0,0,0,1,3,1,0,1,2,3,1,0,1,0,2,1};for(i=0;i<16;i++)kt=kt+a[i]*pow(x,ii[i])*pow(y,jj[i])*pow(z,kk[i]);return(kt);}double kq10(double x,double y,double z){int i;double kq10=0;doubleb[23]={-0.9251390e-1,-0.1229000,0.3050697,-0.2935303,-0.3991474,-0.1022050e+1,0.10228 33e-1,0.3521100e-2,0.2552059e-2,0.2143532,0.7131110e-3,0.2078488,0.6397053,0.9404846e-3,-0.2930044e-1,-0.7807623e-1,-0.3025523,0.1855105,-0.6724210,-0.2087142,0.9400654,0.9 316346,-0.4348397e-1};double ii[23]={0,2,1,0,2,1,7,1,5,0,4,1,1,7,0,0,2,1,2,4,3,2,6};double jj[23]={0,0,1,2,0,1,0,0,2,1,4,2,0,1,1,4,2,3,1,0,0,1,0};double kk[23]={0,0,0,0,1,1,0,3,0,3,0,1,0,0,1,0,3,1,2,3,1,3,0};for(i=0;i<23;i++)kq10=kq10+b[i]*pow(x,ii[i])*pow(y,jj[i])*pow(z,kk[i]);return(kq10);}void main(){int i;double ae,PD,KT,KQ10;double J[10]={0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9};FILE *fp;fp=fopen("data.txt","w+");printf("输入最佳航速:\n");scanf("%lf",&v);va=(1-w)*v;printf("输入最佳盘面比:\n");scanf("%lf",&ae);printf("输入最佳螺距比:\n");scanf("%lf",&PD);fprintf(fp,"\n航速=%lf\n",v);fprintf(fp,"\n盘面比=%lf\n",ae);fprintf(fp,"\nP/D=%lf\n",PD);for(i=0;i<=9;i++){KT=kt(PD,J[i],ae);KQ10=kq10(PD,J[i],ae);fprintf(fp,"J=%lf,KT=%lf,10KQ=%lf\n",J[i],KT,KQ10);}fclose(fp);}附表3航行特性曲线源代码#include"stdio.h"#include"math.h"double w=0.24; //伴流分数double t=0.16;double kt(double x,double y,double z){int i;double kt=0;doublea[16]={0.5367018e-1,-0.3023566,0.4333625,-0.1065471,-0.6582904,0.1189101,-0.4408557e-3, -0.3317857e-1,0.1151124e+1,0.1960773,-0.9747062e-1,0.2036384,-0.2566153,-0.1370242,-0.2 874294,-0.2851609};double ii[16]={0,0,1,0,2,1,6,1,2,0,3,1,1,0,0,2};double jj[16]={0,1,0,2,0,3,0,4,0,0,0,1,1,2,0,0};double kk[16]={0,0,0,1,3,1,0,1,2,3,1,0,1,0,2,1};for(i=0;i<16;i++)kt=kt+a[i]*pow(x,ii[i])*pow(y,jj[i])*pow(z,kk[i]);return(kt);}double kq10(double x,double y,double z){int i;double kq10=0;doubleb[23]={-0.9251390e-1,-0.1229000,0.3050697,-0.2935303,-0.3991474,-0.1022050e+1,0.10228 33e-1,0.3521100e-2,0.2552059e-2,0.2143532,0.7131110e-3,0.2078488,0.6397053,0.9404846e-3,-0.2930044e-1,-0.7807623e-1,-0.3025523,0.1855105,-0.6724210,-0.2087142,0.9400654,0.9 316346,-0.4348397e-1};double ii[23]={0,2,1,0,2,1,7,1,5,0,4,1,1,7,0,0,2,1,2,4,3,2,6};double jj[23]={0,0,1,2,0,1,0,0,2,1,4,2,0,1,1,4,2,3,1,0,0,1,0};double kk[23]={0,0,0,0,1,1,0,3,0,3,0,1,0,0,1,0,3,1,2,3,1,3,0};for(i=0;i<23;i++)kq10=kq10+b[i]*pow(x,ii[i])*pow(y,jj[i])*pow(z,kk[i]);return(kq10);}void main(){int i,m,n,j;double ae,PD,KT,KQ10,v[20],N[20],va,J,D,pte,ps;FILE *fp;fp=fopen("data.txt","w+");printf("输入最佳盘面比:\n");scanf("%lf",&ae);printf("输入最佳螺距比:\n");scanf("%lf",&PD);printf("输入直径:\n");scanf("%lf",&D);fprintf(fp,"\n盘面比=%lf\n",ae);fprintf(fp,"\nP/D=%lf\n",PD);printf("输入选择航速的个数:\n");scanf("%d",&n);printf("输入选择的航速:\n");for(i=0;i<n;i++){printf("v(%d)=:",i+1);scanf("%lf",&v[i]);}printf("输入计算转速的个数:\n");scanf("%d",&m);printf("输入选择的转速:\n");for(i=0;i<m;i++){printf("N(%d)=:",i+1);scanf("%lf",&N[i]);}for(i=0;i<m;i++){fprintf(fp,"N=%lf\n\n",N[i]);N[i]=N[i]/60;for(j=0;j<n;j++){va=0.5144*(1-w)*v[j];J=va/N[i]/D;KT=kt(PD,J,ae);KQ10=kq10(PD,J,ae);pte=KT*104.63*pow(N[i],2)*pow(D,4)*(1-t)*v[j]/145.6;ps=KQ10/10*2*3.14159*pow(N[i],3)*pow(D,5)*104.63/75/0.97;fprintf(fp,"v=%lf\n",v[j]);fprintf(fp,"J=%lf, KT=%lf, 10KQ=%lf pte=%lfps=%lf\n\n",J,KT,KQ10,pte,ps);}}fclose(fp);}附表4 AU 型螺旋桨回归多项式及回归系数对叶数Z 固定后分别进行回归分析，得到以下计算推力系数K T 、转矩系数K Q 、最佳直径系数δopt 及相应螺距比P D ⁄的回归多项式，如下：K T =∑∑∑A ijk (P/D)i (J)j (A E /A O )k n 3k=0n 2j=0n 1i=010K Q =∑∑∑B ijk (P/D)i (J)j (A E /A O )k n 3k=0n 2j=0n 1i=0δopt =∑∑C ij (√B P )i (A E /A O )j n 2j=0n 1i=0P/D =∑∑D ij (√B P )i (A E /A O )j n 2j=0n 1i=0回归系数如下列表格所示：AU 型五叶螺旋桨回归系数AAU型五叶螺旋桨回归系数C。