Manually Cutting a Radius

[rake60]

Forming a small radius on a manual machine is easy.
You grind a form tool and plunge it into the work piece to make the curve.
As the radius gets bigger that may not be an option.
Two of the jobs I hated at work were manually cutting the rope groove in
wire rope sheaves, and cutting the big clearance radius on the top ID of large
brass bushings. I worked with guys who could manually free hand cut a
perfect radius. I never could so I found an easier way.

First you need a bolt circle calculator. I use Marv's BOLTCIRC.ZIP .
The program will give you coordinates to the center of a tool.
To keep it simple, say I want to cut a 1/2" radius using a .030" nose radius
tool. Add 1/2 that nose radius to the formula. In the program I'd enter:

Number of holes? = 360
Radius of bolt circle? = .515
Diameter of holes? = .020 (You can put ANY value in there.)
Angular offset of first hole? Zero is fine.
X offset of bolt circle? Once again Zero is fine.
Y offset of bolt circle? Again Zero works.

You end up with a set of coordinates that look like this.
(It's a long list. Don't bother reading all of it! )

Bolt circle specification:
Radius of bolt circle = 0.5150
Bolt hole diameter = 0.0200
Spacing between hole edges = -0.0110
Angular offset of first hole = 0.0000 deg
X offset of bolt circle center = 0.0000
Y offset of bolt circle center = 0.0000

HOLE ANGLE X-COORD Y-COORD

1 0.0000 0.5150 0.0000
2 1.0000 0.5149 0.0090
3 2.0000 0.5147 0.0180
4 3.0000 0.5143 0.0270
5 4.0000 0.5137 0.0359
6 5.0000 0.5130 0.0449
7 6.0000 0.5122 0.0538
8 7.0000 0.5112 0.0628
9 8.0000 0.5100 0.0717
10 9.0000 0.5087 0.0806
11 10.0000 0.5072 0.0894
12 11.0000 0.5055 0.0983
13 12.0000 0.5037 0.1071
14 13.0000 0.5018 0.1158
15 14.0000 0.4997 0.1246
16 15.0000 0.4975 0.1333
17 16.0000 0.4950 0.1420
18 17.0000 0.4925 0.1506
19 18.0000 0.4898 0.1591
20 19.0000 0.4869 0.1677
21 20.0000 0.4839 0.1761
22 21.0000 0.4808 0.1846
23 22.0000 0.4775 0.1929
24 23.0000 0.4741 0.2012
25 24.0000 0.4705 0.2095
26 25.0000 0.4667 0.2176
27 26.0000 0.4629 0.2258
28 27.0000 0.4589 0.2338
29 28.0000 0.4547 0.2418
30 29.0000 0.4504 0.2497
31 30.0000 0.4460 0.2575
32 31.0000 0.4414 0.2652
33 32.0000 0.4367 0.2729
34 33.0000 0.4319 0.2805
35 34.0000 0.4270 0.2880
36 35.0000 0.4219 0.2954
37 36.0000 0.4166 0.3027
38 37.0000 0.4113 0.3099
39 38.0000 0.4058 0.3171
40 39.0000 0.4002 0.3241
41 40.0000 0.3945 0.3310
42 41.0000 0.3887 0.3379
43 42.0000 0.3827 0.3446
44 43.0000 0.3766 0.3512
45 44.0000 0.3705 0.3577
46 45.0000 0.3642 0.3642
47 46.0000 0.3577 0.3705
48 47.0000 0.3512 0.3766
49 48.0000 0.3446 0.3827
50 49.0000 0.3379 0.3887
51 50.0000 0.3310 0.3945
52 51.0000 0.3241 0.4002
53 52.0000 0.3171 0.4058
54 53.0000 0.3099 0.4113
55 54.0000 0.3027 0.4166
56 55.0000 0.2954 0.4219
57 56.0000 0.2880 0.4270
58 57.0000 0.2805 0.4319
59 58.0000 0.2729 0.4367
60 59.0000 0.2652 0.4414
61 60.0000 0.2575 0.4460
62 61.0000 0.2497 0.4504
63 62.0000 0.2418 0.4547
64 63.0000 0.2338 0.4589
65 64.0000 0.2258 0.4629
66 65.0000 0.2176 0.4667
67 66.0000 0.2095 0.4705
68 67.0000 0.2012 0.4741
69 68.0000 0.1929 0.4775
70 69.0000 0.1846 0.4808
71 70.0000 0.1761 0.4839
72 71.0000 0.1677 0.4869
73 72.0000 0.1591 0.4898
74 73.0000 0.1506 0.4925
75 74.0000 0.1420 0.4950
76 75.0000 0.1333 0.4975
77 76.0000 0.1246 0.4997
78 77.0000 0.1158 0.5018
79 78.0000 0.1071 0.5037
80 79.0000 0.0983 0.5055
81 80.0000 0.0894 0.5072
82 81.0000 0.0806 0.5087
83 82.0000 0.0717 0.5100
84 83.0000 0.0628 0.5112
85 84.0000 0.0538 0.5122
86 85.0000 0.0449 0.5130
87 86.0000 0.0359 0.5137
88 87.0000 0.0270 0.5143
89 88.0000 0.0180 0.5147
90 89.0000 0.0090 0.5149
91 90.0000 -0.0000 0.5150
92 91.0000 -0.0090 0.5149
93 92.0000 -0.0180 0.5147
94 93.0000 -0.0270 0.5143
95 94.0000 -0.0359 0.5137
96 95.0000 -0.0449 0.5130
97 96.0000 -0.0538 0.5122
98 97.0000 -0.0628 0.5112
99 98.0000 -0.0717 0.5100
100 99.0000 -0.0806 0.5087
101 100.0000 -0.0894 0.5072
102 101.0000 -0.0983 0.5055
103 102.0000 -0.1071 0.5037
104 103.0000 -0.1158 0.5018
105 104.0000 -0.1246 0.4997
106 105.0000 -0.1333 0.4975
107 106.0000 -0.1420 0.4950
108 107.0000 -0.1506 0.4925
109 108.0000 -0.1591 0.4898
110 109.0000 -0.1677 0.4869
111 110.0000 -0.1761 0.4839
112 111.0000 -0.1846 0.4808
113 112.0000 -0.1929 0.4775
114 113.0000 -0.2012 0.4741
115 114.0000 -0.2095 0.4705
116 115.0000 -0.2176 0.4667
117 116.0000 -0.2258 0.4629
118 117.0000 -0.2338 0.4589
119 118.0000 -0.2418 0.4547
120 119.0000 -0.2497 0.4504
121 120.0000 -0.2575 0.4460
122 121.0000 -0.2652 0.4414
123 122.0000 -0.2729 0.4367
124 123.0000 -0.2805 0.4319
125 124.0000 -0.2880 0.4270
126 125.0000 -0.2954 0.4219
127 126.0000 -0.3027 0.4166
128 127.0000 -0.3099 0.4113
129 128.0000 -0.3171 0.4058
130 129.0000 -0.3241 0.4002
131 130.0000 -0.3310 0.3945
132 131.0000 -0.3379 0.3887
133 132.0000 -0.3446 0.3827
134 133.0000 -0.3512 0.3766
135 134.0000 -0.3577 0.3705
136 135.0000 -0.3642 0.3642
137 136.0000 -0.3705 0.3577
138 137.0000 -0.3766 0.3512
139 138.0000 -0.3827 0.3446
140 139.0000 -0.3887 0.3379
141 140.0000 -0.3945 0.3310
142 141.0000 -0.4002 0.3241
143 142.0000 -0.4058 0.3171
144 143.0000 -0.4113 0.3099
145 144.0000 -0.4166 0.3027
146 145.0000 -0.4219 0.2954
147 146.0000 -0.4270 0.2880
148 147.0000 -0.4319 0.2805
149 148.0000 -0.4367 0.2729
150 149.0000 -0.4414 0.2652
151 150.0000 -0.4460 0.2575
152 151.0000 -0.4504 0.2497
153 152.0000 -0.4547 0.2418
154 153.0000 -0.4589 0.2338
155 154.0000 -0.4629 0.2258
156 155.0000 -0.4667 0.2176
157 156.0000 -0.4705 0.2095
158 157.0000 -0.4741 0.2012
159 158.0000 -0.4775 0.1929
160 159.0000 -0.4808 0.1846
161 160.0000 -0.4839 0.1761
162 161.0000 -0.4869 0.1677
163 162.0000 -0.4898 0.1591
164 163.0000 -0.4925 0.1506
165 164.0000 -0.4950 0.1420
166 165.0000 -0.4975 0.1333
167 166.0000 -0.4997 0.1246
168 167.0000 -0.5018 0.1158
169 168.0000 -0.5037 0.1071
170 169.0000 -0.5055 0.0983
171 170.0000 -0.5072 0.0894
172 171.0000 -0.5087 0.0806
173 172.0000 -0.5100 0.0717
174 173.0000 -0.5112 0.0628
175 174.0000 -0.5122 0.0538
176 175.0000 -0.5130 0.0449
177 176.0000 -0.5137 0.0359
178 177.0000 -0.5143 0.0270
179 178.0000 -0.5147 0.0180
180 179.0000 -0.5149 0.0090

Turn the OD of the stock to the desired radius. In this example that would be 1"
Touch on the end of the stock and set a zero. Then touch on the OD
of the stock and set a zero. For a 90° radius use coordinates 1 - 90.
For a half round use 1 - 180

You will end up with a perfect radius that has a whole bunch of tiny ridges that
are easily blended in with emery paper. If that is too many coordinates for you
the number of holes can be reduced. You will still wind up with a perfect radius
but it will take much more polishing to get the ridges out.

This system also works for an internal radius.
Just invert the X and Y coordinates.

Rick

 

[mklotz]

Rick,

Thanks for the endorsement but you're using the wrong program - although what you did is fairly clever.

BOLTCIRC, as the name suggests, is used for laying out coordinates for bolt circles.

I do lots of radii by the incremental method and wrote a program, ROUNDER, for just that purpose. I've appended the text file that accompanies the program below. While the description talks about the use of a ball end mill, one could just as easily use an ordinary end mill. Many other tricky radiused cuts are possible via the judicious use of the program's output. Those who are mystified by anything mathematical can contact me for help on their particular application.

	Let's say I have a 3" x 2" x 1/4" piece of metal and I want to round
off one of the 2" edges with a 1" radius. I can't do the job on the lathe for
obvious reasons. There can't be any holes in the finished product so I can't
conveniently pivot the workpiece against a cutter to form the radius.

	One approach is to rough out the radius on the milling machine using a
ball-ended mill.

	Assume:

		R = radius of desired profile (1" in the example)
		d = diameter of ball mill
		r = radius of ball mill = d/2
		theta = an angle (see below)

	Now assume the work is mounted in the vise with the 2" edge sticking up
and aligned with the x axis. Assume the end of the ball mill is just touching
the (center of) the 2" edge. Let theta be measured from the vertical about the
center of the radius to be cut. Thus theta = 0 corresponds to the starting
position just described. Now, it's easy to show that for some other value of
theta, the ball mill will just be tangent to the desired radius if its
position (i.e. the position of the center of the ball) is given by:

		x = (R+r) * sin(theta) [=0 when theta=0]
		z = (R+r) * (1 - cos(theta)) [=0 when theta=0]

where z is measured positive downward from the starting position and x is
measured +\- along the x axis from the starting position. So, if we step
theta by small amounts and make cuts with the tool positioned at the x,z
positions corresponding to each value of theta, we'll cut succesive "scallops"
into the workpiece, each of which is tangent to the required radius profile at
that angle. If the increments in theta are small enough, the resulting
scallops will often be small enough to ignore. If they're not, ten minutes
with a fine file will produce an acceptable finish.

	ROUNDER allows you to specify R, d, and the theta increment and
produces a file which contains a table of the values of:

		(R+r) * sin(theta) [x in the example]
		(R+r) * cos(theta)
		(R+r) * (1 - sin(theta))
		(R+r) * (1 - cos(theta)) [z in the example]

	The second and third values above may seem superfluous but not
everyone may want to set up the cut as in my example. As you try different
approaches, you'll find that being able to generate the other values is an
asset. If you don't need them, just cross out their columns on the printed
copy of the data file that you carry to the shop.

	A good suggestion is to rough out the profile of the radius with
hacksaw or whatever so the ball mill doesn't have to chew through a lot of
material. Just be sure to leave whatever starting reference point you're
going to use intact so you can accurately locate for the reference.

 

[starbolin]

That's an interesting re-purposing of a bolt-circle calculator. Another method for radii cutting which allows you to directly cut a radii is to follow a template.

FYI approximating a curved surface by multiple square cuts is called kellering.

 

[BobWarfield]

Rick, that's brilliant!

What a fine re-purposing of the bolt circle calculations. I love it.

In fact, I've got to add a little feature to my G-Wizard Calculator's bolt circle calculations to streamline it for just such occasions.

And, starbolin, thank you for reminding of a word I once knew, was on the tip of my tongue, but that I just have been unable to access for 3 or 4 months and too lazy to go look it up.

"Kellering"

Makes one wonder who this "Keller" might have been or where the name came from.

Cheers,

BW

 

[rake60]

The horizontal boring mills at work had DROs with bolt circle calculation software
built in to them. One night I was struggling with manually cutting a 3" radius in
the top 48" bore of a brass bushing.

I took my problem to a buddy who was running a horizontal mill and asked
him if he could work out a coordinate solution for me with his DROs bolt
circle calculator. It worked out perfectly, and I never even tried to free
hand a radius bigger than 1" after that. I'd just find an open DRO on a mill
and run the bolt circle program.

I no longer have access to those DROs but any bolt circle calculator works.

Rick