CNC
Gears
Last updated on
Thursday, March 24, 2011 05:51:48 AM
Eastern US Time Zone
Gear Wheel Designer,
Deadbeat Escapement,
Involute Gears,
Mach3, 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 gcode.
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.
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.
1/32" carbide end mill.
A CNC deadbeat escapement wheel
that has 30teeth.
Recoil escapement.
Ratchet.
Involute Gears
Animated 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 Wheel Designer generates Gcode
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 control software.
Lowprofile fixture (0.1225"). Note the slotted
holes in the back for quick, slidein/slideout mounting.
After degreasing, the brass plate is mounted using
doublesided tape.
The end mill is set to 4.0000" above the brass plate's top
surface in the Mach3 Zaxis DRO.
The tape is 0.0025" thick so the final cut is set to 0.002"
below the 0.025" thick, brass plate.
The gears have no burrs if the last cut ends in the
tape layer. These gears have a module = 1 (25.4T/inch).
The fixture returns to the
same position using four ¼" indexing pins.
A larger, thicker (0.497"), flatter tooling plate was
fabricated using MIC6.
The ⅜16 hex bolt heads 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.
A complete set of eight, M = 0.5 (50.8 DP) involute gears cutters: high speed
tool steel, hardness
RC60,
precision ground formrelieved cutting teeth, 20° pressure angle, 16mm bore with
keyway.
The best overall price in the world for involute gear cutter sets is
CTC Tools in Hong Kong.
Range of Cutters  
To cut gears from  use cutter number 
12 to 13 teeth  8 
14 to 16 teeth  7 
17 to 20 teeth  6 
21 to 25 teeth  5 
26 to 34 teeth  4 
35 to 54 teeth  3 
55 to 134 teeth  2 
135 teeth to a rack  1 
Proxxon 24 425 blackoxide HSS 16mm arbor for involute gear cutters
(Germany).
This arbor was designed for smallmodule 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  M81.25 x 12 
Shank Diameter  10 
Shank Length  30 
Body Diameter  24.7 
Body Length  25 
Overall Length  65 
Basic Gear Formulae  
Gear (G) Dimensions  Examples  
Imperial  Diametral Pitch (DP) = # teeth/inch  24 teeth/inch 
Outside Diameter (OD) inches = (G1+2)/DP  (40+2)/24 = 1.75 inches outside diameter  
Whole Tooth Depth inches = 2.157/DP  2.157/24 = 0.089875 inches depth  
Distance Between Gear Centers = (G1+G2)/(2*DP)  (30+20)/(2*24) = 1.0417" distance  
Metric  Metric Module (M) = 25.4/DP  25.4/28.222 = 0.9 
DP = 25.4/M  25.4/0.9 = 28.222 teeth per inch  
Circular Pitch (CP) mm = M*pi  1*3.142 = 3.142 mm  
M = (CP)/pi  2.827 mm / 3.142 = 0.9  
Outside Diameter (OD) mm = (G1+2)*M  (24+2)*0.9 = 23.4 mm outside diameter  
Whole Tooth Depth mm = 2.157*M  2.157*0.9 = 1.9413 mm depth 
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 onehalf 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°
Pressure Angle (PA) has a better tooth form for cutting pinions
than e.g., a 14½° 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 onesixth module.
‡
Total depth equivalent to
American standard fulldepth teeth where clearance =
0.157 x module.
Module
(M)  The length, in mm, of the pitch circle
diameter per tooth.
Diametral
Pitch
(DP)
 The number of teeth per one inch of pitch circle diameter.
Circular
Pitch (CP)  The
distance between adjacent teeth measured along the are at the pitch circle
diameter
Addendum  The height of the tooth above the pitch
circle diameter.
Center Distance

The distance between the axes of two gears in
mesh.
Circular Tooth Thickness
 The width of a tooth measured along the are at
the pitch circle diameter.
Dedendum  The depth of the tooth below the pitch
circle diameter.
Outside Diameter (OD)  The outside diameter of the
gear.
Base Circle Diameter

The diameter on which the involute teeth profile is based.
Pitch
Circle
Diameter
(PCD)  The diameter of the pitch circle.
Pitch
Point 
The point at which the pitch circle
diameters of two gears in mesh coincide.
Pitch to Back 
The distance on a rack between the
pitch circle diameter line & the rear face of the rack.
Pressure
Angle (PA)
 The
angle between the tooth profile at the pitch circle diameter & a radial line
passing through the same point.
Whole Depth  The total depth of the space between
adjacent teeth.
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.
Gear Theory Gear Module Data Spur Gears Gear Module Formulae See "Gears & Gear Cutting" by Ivan Law
Gear Wheel Designer,
Deadbeat Escapement,
Involute Gears,
Mach3, Involute Gear Cutters
Range of Cutters,
Basic
Gear Formulae, Module Tooth
Dimensions, Common Clock Trains