OpenCASCADE 麻花钻头造型实例分析

OpenCASCADE 麻花钻头造型实例分析

eryar@163.com

Abstract. OpenCASCADE provides a simple twist drill bit modeling example in Tcl script. The blog will give a details of some key points, when you understand the key points, you can modeling the shape like that.

Key Words. OpenCASCADE, Twist Drill Bit Modeling, Tcl

1.Introduction

OpenCASCADE的Draw Test Harness中提供了一个麻花钻头造型的实例,如下图所示:

wps_clip_image-8478

Figure 1. A Simple Twist Drill Bit by OpenCASCADE

钻头造型主要涉及到旋转形状的造型方法,放样造型及布尔操作。本文结合钻头的Tcl脚本来详细说明造型过程。对于有同样造型需求的,可以在理解造型方法的基础上实现自己需要的参数化形状。

2.Modeling Tcl Script

通过Draw Test Harness的菜单Samples->View samples可以找到Drill例子,如下图所示:

wps_clip_image-20966

Figure 2. Drill bit modeling sample

对应的Tcl脚本位于samples/tcl文件夹中,列出如下:

# Sample: creation of simple twist drill bit

#Category: Modeling

#Title: Drill

pload MODELING VISUALIZATION

# drill parameters (some terms taken from http://www.drill-bits.cn/drill-bits-quality.asp)

dset R  4.    ;# outer radius

dset D  2*R   ;# diameter

dset Rr 3.5   ;# chisel radius (outer radius minus body clearance)

dset b  1.    ;# web thickness (approximate)

dset d  b/2

dset H  80.   ;# height of the spiral part

dset a  3.*pi ;# total angle of spiral rotation

dset sigma 118 ;# point angle, in degrees

# Create section profile by sequence of Boolean operations

# on simple planar objects

puts \"Creating the drill section profile...\"

polyline rectangle1 d -R 0  R -R 0 -d R 0 -R R 0  d -R 0

circle circle1 0 0 0 0 0 1 R

mkedge circle1 circle1

wire circle1 circle1

circle circle2 0 0 0 0 0 1 Rr

mkedge circle2 circle2

wire circle2 circle2

plane p0

mkface rectangle1 p0 rectangle1

mkface circle1 p0 circle1

mkface circle2 p0 circle2

bcommon sec rectangle1 circle1

# note use of \'fuse\' instead of \'bfuse\' -- we need to get single face

fuse sec sec circle2

# Construct flute profile so as to have cutting lip straight after sharpening.

# Here we need to take into account spiral shift of the flute edge

# along the point length -- the way to do that is to make spiral

# from the desired cutting lip edge and then intersect it by plane

polyline lip d -d/2 0  d -R -R/tan(sigma/2*pi/180)

polyline sp 0 0 0 0 0 H

cylinder cc 0 0 0 0 0 1 0 -4 0 4

line ll 0 0 a 80

trim ll ll 0 sqrt(a*a+H*H)

vertex v1 0 -R 0

vertex v2 0 -R H

trotate v2 0 0 0 0 0 1 180.*a/pi

mkedge ee ll cc v1 v2

wire gg ee

mksweep sp

setsweep -G gg 0 0

addsweep lip

buildsweep spiral -S

mkface f0 p0 -R R -R R

bsection sflute spiral f0

# here we rely on that section curve is parameterized from 0 to 1 

# and directed as cutting lip edge;

# note that this can change if intersection algorithm is modified

explode sflute e

mkcurve cflute sflute_1

cvalue cflute 0. x0 y0 z0

cvalue cflute 1. x1 y1 z1

vertex vf0 x0 y0 z0 

vertex vf1 x1 y1 z1

# -- variant: replace curve by arc with start at x0,y0,z0 and end at x1,y1,z1,

# -- such that tanget at start point is along Y

#dset Rflute ((x1-x0)*(x1-x0)+(y1-y0)*(y1-y0))/(2*(x1-x0))

#circle aflute x0+Rflute y0 0  0 0 1  Rflute

#mkedge sflute_1 aflute vf0 vf1

# make rounding in the flute; use circle with radius Rr/2

circle cround x0+Rr/2 y0 0 0 0 1 Rr/2

vertex vf3 x0+Rr y0 0

mkedge sflute_2 cround vf3 vf0

vertex vf2 R -R 0

edge sflute_3 vf3 vf2

edge sflute_4 vf2 vf1

wire w2 sflute_1 sflute_2 sflute_3 sflute_4

mkface flute p0 w2

# cut flute from profile

bcut sec sec flute

trotate flute 0 0 0 0 0 1 180.

bcut sec sec flute

donly sec

# sweep profile to get a drill body

puts \"Sweeping the profile...\"

mksweep sp

setsweep -G gg 0 0

explode sec w

addsweep sec_1

buildsweep base -S

# sharpen the drill (see http://tool-land.ru/zatochka-sverla.php)

puts \"Sharpening...\"

dset theta a*R/H*sin((90-sigma/2)*pi/180)

plane ax1 d 1.9*D \"H+1.9*D/tan(pi/180.*sigma/2.)\" 0 -1 -1

pcone sh1 ax1 0 100*sin((sigma-90)/2*pi/180.) 100

trotate sh1 0 0 0 0 0 1 -theta*180/pi

tcopy sh1 sh2

trotate sh2 0 0 0 0 0 1 180

box sh -D/2 -D/2 72 D D 20

bcommon qq sh1 sh2

bcut sharpener sh qq

bcut body base sharpener

# make a shank

puts \"Making a shank...\"

plane pl2 0 0 -40 0 0 1

pcylinder shank pl2 4 40

pcone transit R 0 R

plane pl3 0 0 -40 0 0 -0.5

pcone tail pl3 R 0 0.5

bfuse shank shank tail

bfuse shank shank transit

bfuse drill body shank

# check result

checkshape drill

# show result

puts \"Displaying result...\"

incmesh drill 0.01

vdisplay drill

vsetdispmode drill 1

vrenderparams -msaa 8

vfit

# show section and sweep path

ttranslate sec_1 0 0 H; trotate sec_1 0 0 0 0 0 1 a*180/pi; incmesh gg 0.01; vdisplay gg sec_1

 

下面结合Tcl脚本来对钻头的造型过程进行详细说明。

3.Twist Drill Bit Parameters

脚本首先加载相应的模块:造型模块和显示模块,分别为MODEING和VISUALIZATION。然后设置钻头相关参数变量:

wps_clip_image-20435

Figure 3. Drill Bit 

变量名及其说明:

变量名variable 说明 detail
R 外半径 outer radius
D 直径D
Rr Chisel Radius
b Web thickness(approximate)
d  
H 螺旋部分的高度Height of the spiral height
a 螺旋角度Total angle of spiral rotation
sigma 钻尖角度Point angle in degrees.

 

 

 

 

 

 

 

先定义这些变量的思想也是参数化的思想,将这些变量值改变就会得到不同的钻头模型。参数化的思想在CAD软件中比较常见,如AutoCAD中的动态块,PDMS中的设备模板Template等,都属于参数化的方法。通过修改参数让一个或多个几何体形状发生变化。

4.Create Drill Section Profile

创建钻头截面的Tcl脚本如下所示:

# Create section profile by sequence of Boolean operations

# on simple planar objects

puts \"Creating the drill section profile...\"

polyline rectangle1 d -R 0  R -R 0 -d R 0 -R R 0  d -R 0

circle circle1 0 0 0 0 0 1 R

mkedge circle1 circle1

wire circle1 circle1

circle circle2 0 0 0 0 0 1 Rr

mkedge circle2 circle2

wire circle2 circle2

plane p0

mkface rectangle1 p0 rectangle1

mkface circle1 p0 circle1

mkface circle2 p0 circle2

bcommon sec rectangle1 circle1

# note use of \'fuse\' instead of \'bfuse\' -- we need to get single face

fuse sec sec circle2

 

生成的图形如下图所示:

wps_clip_image-30324

Figure 4 Profile construction curves

其中变量Rectangle1是图中绿色表示的四边形,Circle1是黄色表示的外圆,Circle2是红色表示的内圆。通过布尔操作求取Rectangle1和Circle1的公共部分得到如下图所示的截面:

wps_clip_image-28102

Figure 5 Common of Rectangle1 and Circle1

将公共部分与内圆Circle2合并得到如图所示截面:

wps_clip_image-8412

Figure 6. Fuse of Common part and Circle2

下面在这个截面的基础上生成钻头的螺旋凹槽,这里是相对关键的地方,生成凹槽的时候还要考虑螺旋。

# Construct flute profile so as to have cutting lip straight after sharpening.

# Here we need to take into account spiral shift of the flute edge

# along the point length -- the way to do that is to make spiral

# from the desired cutting lip edge and then intersect it by plane

polyline lip d -d/2 0  d -R -R/tan(sigma/2*pi/180)

polyline sp 0 0 0 0 0 H

cylinder cc 0 0 0 0 0 1 0 -4 0 4

line ll 0 0 a 80

trim ll ll 0 sqrt(a*a+H*H)

vertex v1 0 -R 0

vertex v2 0 -R H

trotate v2 0 0 0 0 0 1 180.*a/pi

mkedge ee ll cc v1 v2

wire gg ee

mksweep sp

setsweep -G gg 0 0

addsweep lip

buildsweep spiral -S

mkface f0 p0 -R R -R R

bsection sflute spiral f0

 

代码生成的图形如下图所示:

wps_clip_image-27754

Figure 7. Flute of the drill bit

通过将线lip沿着路径直线sp和螺旋线gg放样得到螺旋截面spiral,再将螺旋截面spiral和底平面f0求交得到sflute。

# here we rely on that section curve is parameterized from 0 to 1 

# and directed as cutting lip edge;

# note that this can change if intersection algorithm is modified

explode sflute e

mkcurve cflute sflute_1

cvalue cflute 0. x0 y0 z0

cvalue cflute 1. x1 y1 z1

vertex vf0 x0 y0 z0 

vertex vf1 x1 y1 z1

# -- variant: replace curve by arc with start at x0,y0,z0 and end at x1,y1,z1,

# -- such that tanget at start point is along Y

#dset Rflute ((x1-x0)*(x1-x0)+(y1-y0)*(y1-y0))/(2*(x1-x0))

#circle aflute x0+Rflute y0 0  0 0 1  Rflute

#mkedge sflute_1 aflute vf0 vf1

# make rounding in the flute; use circle with radius Rr/2

circle cround x0+Rr/2 y0 0 0 0 1 Rr/2

vertex vf3 x0+Rr y0 0

mkedge sflute_2 cround vf3 vf0

vertex vf2 R -R 0

edge sflute_3 vf3 vf2

edge sflute_4 vf2 vf1

wire w2 sflute_1 sflute_2 sflute_3 sflute_4

mkface flute p0 w2

 

通过求得的交线再构造圆弧和线段来构造出钻头凹槽的截面,如下图所示:

wps_clip_image-2949

Figure 8. Make flute section

将凹槽截面flute从前面构造的截面中去除:

# cut flute from profile

bcut sec sec flute

 

wps_clip_image-22613

Figure 9. Make drill bit profile

将凹槽截面绕Z轴旋转180度,再去布尔减原来的截面:

trotate flute 0 0 0 0 0 1 180.

bcut sec sec flute

 

wps_clip_image-9522

Figure 10. Make drill bit profile

这样钻头的截面就生成了。

5.Sweeping the Profile

将上面钻头截面沿着直线sp和螺旋线gg放样:

# sweep profile to get a drill body

puts \"Sweeping the profile...\"

mksweep sp

setsweep -G gg 0 0

explode sec w

addsweep sec_1

buildsweep base -S

 

生成图形如下图所示:

wps_clip_image-20384

Figure 11. Sweep the profile

通过放样得到了钻头的螺杆base。

6.Sharpening

得到钻头的螺杆后需要生成钻头的钻尖,根据钻尖角point angle变量sigma来造型。

# sharpen the drill (see http://tool-land.ru/zatochka-sverla.php)

puts \"Sharpening...\"

dset theta a*R/H*sin((90-sigma/2)*pi/180)

plane ax1 d 1.9*D \"H+1.9*D/tan(pi/180.*sigma/2.)\" 0 -1 -1

pcone sh1 ax1 0 100*sin((sigma-90)/2*pi/180.) 100

trotate sh1 0 0 0 0 0 1 -theta*180/pi

tcopy sh1 sh2

trotate sh2 0 0 0 0 0 1 180

box sh -D/2 -D/2 72 D D 20

bcommon qq sh1 sh2

bcut sharpener sh qq

bcut body base sharpener

 

先构造两个圆锥体(sh1和sh2)和一个长方体sh,再通过布尔运算得到两个圆锥体sh1,sh2的公共部分qq。如下图所示:

wps_clip_image-23669

wps_clip_image-5130

Figure 12. Modeling point angle

再从长方体sh中减去两个圆锥的公共部分得到如下图所示:

wps_clip_image-3000

wps_clip_image-24408

Figure 13. Modeling point angle

wps_clip_image-12972

将螺杆减去上面得到的sharpener就完成钻尖的造型,如下图所示:

wps_clip_image-4999

Figure 14. Modeling point angle

7.Make Shank

完成螺杆和钻尖造型后,就来实现麻花钻头的最后部分,钻头柄shank。

# make a shank

puts \"Making a shank...\"

plane pl2 0 0 -40 0 0 1

pcylinder shank pl2 4 40

pcone transit R 0 R

plane pl3 0 0 -40 0 0 -0.5

pcone tail pl3 R 0 0.5

bfuse shank shank tail

bfuse shank shank transit

bfuse drill body shank

 

钻头柄部由两个圆锥(transit和tail)和一个圆柱shank组成。最后将这三个形状合并得到完成的钻头的柄部shank。

wps_clip_image-20511

Figure 15. Modeling Shank

8.Conclusion

通过对OpenCASCADE中麻花钻头的造型实例分析,可见这个钻头造型用到的算法主要是放样及布尔操作。在生成螺旋线时主要是使用pcurve的方式。最后还要理解参数化的造型思想,通过定义变量来生成参数化的模型。

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