Gears
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Monday, August 19, 2019 10:45:06 AM
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Gear Wheel Designer,
Deadbeat Escapement,
Involute Gears,
Mach3, Gearotic Motion
Involute Gear Cutters,
Range of Cutters,
Basic
Gear Formulae,
Module Tooth
Dimensions,
Common Clock Trains
Gear Wheel Designer
Cycloidal gear. Gear Wheel Designer software creates a
variety of clock gear types & generates the 2.5D g-code.
The units can be metric or imperial, the sequence of operations can be
specified, & it will also cut spokes.
It only cuts flat stock so you are limited by the size of the end mill (for
small detail) & the depth of the cut.
Used a 1/32" carbide end mill to cut a deadbeat escapement, below. This limited
the speed & depth of the cut.
This software is 2.5D only. Gearotic Motion is a
far more sophisticated 2.5D & 3D (4th-axis) solution.
Three curves
are used above & below
a gear's base circle to design cycloidal gears.
Cycloid. A rack would use true cycloid profiles.
Epicycloid, the shape above the base circle.
Hypocycloid, the shape below the base circle.
Deadbeat Escapement
Deadbeat escapement.
Click on linked thumbnail
1/32" carbide end mill.
A CNC-made deadbeat escapement wheel
that has 30-teeth.
Recoil escapement.
Ratchet.
Involute Gears
Involute of a circle.
The path is depicted by a virtual marker at the end of a taut string as it unwinds off
a cylinder (the gear's base circle).
Spur gears incorporate the involute shape.
A
simple
gear can be defined in terms of its pitch,
pressure angle,
& number of
teeth.
|
Gear Definitions |
|
Module
(M) |
Length,
in mm, of the pitch circle diameter per tooth |
|
Diametral
Pitch
(DP) |
Number of teeth per one-inch of pitch
circle diameter |
|
Circular
Pitch
(CP) |
Distance
along the pitch circle or pitch line between corresponding profiles of
adjacent teeth |
|
Addendum |
Height
of the tooth above the pitch circle diameter |
|
Center Distance |
Distance
between the axes of two gears in mesh |
|
Circular
Tooth Thickness |
Width of a tooth measured along the are
at the pitch circle diameter |
|
Dedendum |
Depth
of the tooth below the pitch circle diameter |
|
Outside Diameter
(OD) |
Outside
diameter of the gear |
|
Base Circle
Diameter |
Diameter
on which the involute teeth profile is based |
|
Pitch
Circle
Diameter (PCD) |
Diameter of the pitch circle |
|
Pitch
Point |
Point
at which the pitch circle diameters of two gears in mesh coincide |
|
Pitch to Back |
Distance
on a rack between the pitch circle diameter line & the rear face of the
rack |
|
Pressure
Angle (PA) |
Angle between the tooth profile at the
pitch circle diameter & a radial line passing through the same point |
|
Whole Depth |
Total depth of the space between
adjacent teeth |
Gear Wheel Designer generates G-code
for CNC applications, like Mach3. An involute gear example.
The outer dashed circle is the pitch circle & the inner one is the base circle.
The involute shape is calculated from the base circle.
The ratio between the two circles is used to derive the pressure angle.
Mach3
Mach3 CNC software.
Low-profile fixture (0.1225"). Note the slotted
holes in the back for quick, slide-in/slide-out mounting.
After degreasing, the brass plate is mounted using
double-sided tape.
The end mill is set to 4.0000" above the brass plate's top
surface in the Mach3 Z-axis DRO.
Click on linked thumbnails
The clear, 3M tape is 0.0025" thick so the final cut is set to 0.002"
below the 0.025" thick, brass plate.
Click on linked thumbnails
The gears have no burrs if the last cut ends in the tape
layer. These are module = 1 (25.4 DP) gears.
The fixture returns to the
same position using four 1/4" indexing pins.
A larger, thicker (0.497"), flatter tooling plate was
fabricated using MIC6.
The 3/8-16 button-head bolts are
below the top surface. Lightly scribed alignment lines mark the plate's center. The outer edges have
radii.
Involute gear animation. Not for a clock but another example of
Mach3 controlled CNC produced gears.
Gearotic
Motion
Gearotic Motion (GM)
is a CAD/CAM application that is integrated with Mach3. GM
is a
sophisticated 2.5D & 3D (4th-axis)
solution that can
design & mill many gear types including: involute, lantern, pinion,
elliptical, bevel, helical, knuckle, timing, &
imaginary. It can make short AVI movies of the gear train in motion; the master
(first) gear speed & direction can be controlled.
Periodic reversing motion can be specified over a defined angle. Different spoke
designs plus hand cranks & clock hands are available.
Version 4.xxx program designs the escapement wheel plus the pendulum with
matching pawl for
clock gear trains.
GM Manual
Spur gear window used to create wheels & pinions using metric
module or imperial diametral pitch specifications.
Lantern wheel & pinion.
GM can design & cut elliptical gears.
A ratchet shape in the ratchets/gadgets window.
A recoil shape in the ratchets/gadgets window.
Graham escapement.
Grasshopper escapement.
Latest Gearotic Motion version (2015).
Escapement wheels made of ABS plastic & brass using CNC
mill.
Gearotic Motion Output Manager.
Involute Gear Cutters
A complete set of eight, M = 0.5 (50.8 DP) involute gears cutters: high speed
tool steel, hardness
RC60,
form-relieved cutting teeth, 20 deg pressure angle, 16mm bore with keyway, nominal
40mm OD (Hong Kong).
Modified the supplied packaging to safely hold the cutter set. The 5/8" wooden
dowel contacts the lid.
|
Range of
Cutters - Metric & Imperial |
|
To
cut gears from |
use
Module
cutter number |
use
DP
cutter number |
|
12 to
13 teeth |
1 |
8 |
|
14 to
16 teeth |
2 |
7 |
|
17 to
20 teeth |
3 |
6 |
|
21 to
25 teeth |
4 |
5 |
|
26 to
34 teeth |
5 |
4 |
|
35 to
54 teeth |
6 |
3 |
|
55 to
134 teeth |
7 |
2 |
|
135
teeth to a rack |
8 |
1 |
Note: metric module & diametral pitch
(DP) cutter numbers are inverted.
Proxxon 24 425 black-oxide HSS 16mm arbor for involute gear cutters
(Germany).
This arbor was designed for small-module cutters (e.g., M = 0.5, 0.6, 0.7,
0.8).
|
Proxxon 24 425 Arbor |
|
Attributes |
Dimensions (mm) |
|
Arbor Size |
16 x 5 |
|
Key Size |
4 (W) x 5 (L) |
|
Wrench Size |
17 |
|
Thread |
M8-1.25 x 12 |
|
Shank Diameter |
10 |
|
Shank Length |
30 |
|
Body Diameter |
24.7 |
|
Body Length |
25 |
|
Overall Length |
65 |
The cutters are not quite thick enough for secure clamping so a custom
0.0525" thick washer was made.
Click on linked thumbnails
Formulae
Table Notes
(a) Diametral Pitch
(DP) is measured at the Pitch Circle (PC), not the Outside Diameter (OD). G1 = # of teeth for Gear 1.
(b)
The metric standard measure
for
pitch
is the
Module (M).
(c) The distance between centers is determined by the
total
number of teeth
used for the mating pair of gears. Therefore, any G1+G2 combination that that sums to the same
value (in the
numerator) yields the same distance.
(d) The British
standardized the calculations by starting with a
diameter
of 1" making the
circumference equal to pi (3.1416).
This simplifies the calculations as pi is a constant on
both sides
of the
equation for calculating blank diameters & thus, cancel.
Adding 2 to the teeth number works
because gears contact each
other at
exactly one-half the distance from the top
of the gear to the bottom. There is
also a bottom clearance but it
is not
considered in simple calculations. (e) 2.157 is a constant. (f) 1 mm = 0.03937" &
1" = 25.4 mm. (g) A 20 deg
Pressure Angle (PA) has a better tooth form for cutting pinions
than e.g., a 14-1/2 deg PA.
To run
two
gears together,
their
pitches & pressure angles
must match.
(h)
The contact point/plane on a true
involute
generated on
& from the Pitch
Circle is between the addenda, only.
|
Module Pitch Tooth Dimensions |
|
M |
DP |
CP
(mm) |
CP
( inches) |
Addendum
(mm) |
Dedendum
(mm) |
Whole
Depth
(mm) |
Whole
Depth
(mm) |
|
0.5 |
50.800 |
1.571 |
0.0618 |
0.50 |
0.583 |
1.083 |
1.079 |
|
0.6 |
42.333 |
1.885 |
0.0742 |
0.60 |
0.700 |
1.300 |
1.294 |
|
0.7 |
36.286 |
2.199 |
0.0865 |
 0.70 |
0.817 |
1.517 |
1.510 |
|
0.8 |
31.750 |
2.513 |
0.0989 |
0.80 |
0.933 |
1.733 |
1.726 |
|
0.9 |
28.222 |
2.827 |
0.1113 |
0.90 |
1.050 |
1.950 |
1.941 |
|
1.0 |
25.400 |
pi |
0.1237 |
1 |
1.167 |
2.167 |
2.157 |
Dedendum & total depth when clearance = 0.1666 x
module or one-sixth module.
Total depth equivalent to
American standard full-depth teeth where clearance =
0.157 x module.
|
Common Clock Trains |
|
Center Wheel |
3rd Pinion |
3rd Wheel |
Escapement
Pinion |
Escapement
Wheel |
Vibrations per
Minute |
Pendulum
Length (inches) |
|
112 |
14 |
105 |
14 |
60 |
60 |
39.14 |
|
96 |
12 |
90 |
12 |
30 |
60 |
39.14 |
|
80 |
10 |
75 |
10 |
30 |
60 |
39.14 |
|
64 |
8 |
60 |
8 |
30 |
60 |
39.14 |
|
75 |
8 |
60 |
8 |
32 |
75 |
25.53 |
|
80 |
8 |
72 |
8 |
30 |
90 |
17.39 |
|
108 |
12 |
100 |
10 |
32 |
96 |
15.28 |
Drawing M = 0.5 (50.8 DP)
12T, 90T, 96T involute,
a 30T ratchet, & a
30T deadbeat clock
gears using a
pen on cardboard to visualize sizes. In clock
gear nomenclature small gears are
called pinions &
their
teeth are called pedals while the larger gears are termed wheels.
Indicating the rotary table face by performing adjustments both
horizontally & vertically.
Mounting the 4-jaw
chuck.
A
rotary table
alignment bracket
is used to
initially center the
part before
transferring to the
4th-axis for final
tramming.
Gear Theory
Gear Module Data Spur
Gears Gear Module
Formulae Gearotic Motion See "Gears & Gear Cutting" by Ivan Law
Gear Wheel Designer,
Deadbeat Escapement,
Involute Gears,
Mach3, Gearotic Motion
Involute Gear Cutters,
Range of Cutters,
Basic
Gear Formulae,
Module Tooth
Dimensions,
Common Clock Trains
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