16. Gear Profile Function¶
The gear_profile() function generates a format-B outline of a gear profile with the following features:
- the gear-tooth-profile ensures a constant line of action and a constant speed ratio
- the gear-profile (including the gear hollow) is makable by a 3-axis CNC
- a gear system with two parts can be simulated with the Tkinter GUI
- very configurable: asymmetrical teeth are possible
- active tooth profile made out of arcs and with a continuous tangent inclination
- optional portion of gear to make split gearwheel
To get an overview of the possible gear_profiles that can be generated by gear_profile(), run:
> python gear_profile.py --run_self_test
16.1. Gear high-level parameters¶
The gear high-level parameters let describe with a reduce number of integers and floats a complete gear system. Some of these high-level are depending on each others.
16.1.1. Gear types¶
16.1.3. Gearbar high-level parameters¶
16.2. gear_profile() function arguments list¶
The arguments of the function gear_profile() are not directly the high-level gear parameters but constraints used to deduce the high-level gear parameters.
The switches of the module gear_profile.py are directly connected to the function gear_profile(). Use the module gear_profile.py to experiment the gear_profile() arguments. Notice that -h and –run_self_test are not arguments of gear_profile().
usage: gear_profile.py [-h] [--gear_type SW_GEAR_TYPE]
[--gear_tooth_nb SW_GEAR_TOOTH_NB]
[--gear_module SW_GEAR_MODULE]
[--gear_primitive_diameter SW_GEAR_PRIMITIVE_DIAMETER]
[--gear_addendum_dedendum_parity SW_GEAR_ADDENDUM_DEDENDUM_PARITY]
[--gear_tooth_half_height SW_GEAR_TOOTH_HALF_HEIGHT]
[--gear_addendum_height_pourcentage SW_GEAR_ADDENDUM_HEIGHT_POURCENTAGE]
[--gear_dedendum_height_pourcentage SW_GEAR_DEDENDUM_HEIGHT_POURCENTAGE]
[--gear_hollow_height_pourcentage SW_GEAR_HOLLOW_HEIGHT_POURCENTAGE]
[--gear_router_bit_radius SW_GEAR_ROUTER_BIT_RADIUS]
[--gear_base_diameter SW_GEAR_BASE_DIAMETER]
[--gear_force_angle SW_GEAR_FORCE_ANGLE]
[--gear_tooth_resolution SW_GEAR_TOOTH_RESOLUTION]
[--gear_skin_thickness SW_GEAR_SKIN_THICKNESS]
[--gear_base_diameter_n SW_GEAR_BASE_DIAMETER_N]
[--gear_force_angle_n SW_GEAR_FORCE_ANGLE_N]
[--gear_tooth_resolution_n SW_GEAR_TOOTH_RESOLUTION_N]
[--gear_skin_thickness_n SW_GEAR_SKIN_THICKNESS_N]
[--second_gear_type SW_SECOND_GEAR_TYPE]
[--second_gear_tooth_nb SW_SECOND_GEAR_TOOTH_NB]
[--second_gear_primitive_diameter SW_SECOND_GEAR_PRIMITIVE_DIAMETER]
[--second_gear_addendum_dedendum_parity SW_SECOND_GEAR_ADDENDUM_DEDENDUM_PARITY]
[--second_gear_tooth_half_height SW_SECOND_GEAR_TOOTH_HALF_HEIGHT]
[--second_gear_addendum_height_pourcentage SW_SECOND_GEAR_ADDENDUM_HEIGHT_POURCENTAGE]
[--second_gear_dedendum_height_pourcentage SW_SECOND_GEAR_DEDENDUM_HEIGHT_POURCENTAGE]
[--second_gear_hollow_height_pourcentage SW_SECOND_GEAR_HOLLOW_HEIGHT_POURCENTAGE]
[--second_gear_router_bit_radius SW_SECOND_GEAR_ROUTER_BIT_RADIUS]
[--second_gear_base_diameter SW_SECOND_GEAR_BASE_DIAMETER]
[--second_gear_tooth_resolution SW_SECOND_GEAR_TOOTH_RESOLUTION]
[--second_gear_skin_thickness SW_SECOND_GEAR_SKIN_THICKNESS]
[--second_gear_base_diameter_n SW_SECOND_GEAR_BASE_DIAMETER_N]
[--second_gear_tooth_resolution_n SW_SECOND_GEAR_TOOTH_RESOLUTION_N]
[--second_gear_skin_thickness_n SW_SECOND_GEAR_SKIN_THICKNESS_N]
[--gearbar_slope SW_GEARBAR_SLOPE]
[--gearbar_slope_n SW_GEARBAR_SLOPE_N]
[--center_position_x SW_CENTER_POSITION_X]
[--center_position_y SW_CENTER_POSITION_Y]
[--gear_initial_angle SW_GEAR_INITIAL_ANGLE]
[--second_gear_position_angle SW_SECOND_GEAR_POSITION_ANGLE]
[--second_gear_additional_axis_length SW_SECOND_GEAR_ADDITIONAL_AXIS_LENGTH]
[--cut_portion SW_CUT_PORTION SW_CUT_PORTION SW_CUT_PORTION]
[--gear_profile_height SW_GEAR_PROFILE_HEIGHT]
[--simulation_enable]
[--output_file_basename SW_OUTPUT_FILE_BASENAME]
[--run_self_test]
Command line interface for the function gear_profile().
optional arguments:
-h, --help show this help message and exit
--gear_type SW_GEAR_TYPE, --gt SW_GEAR_TYPE
Select the type of gear. Possible values: 'e', 'i',
'l'. Default: 'e'
--gear_tooth_nb SW_GEAR_TOOTH_NB, --gtn SW_GEAR_TOOTH_NB
Set the number of teeth of the first gear_profile.
--gear_module SW_GEAR_MODULE, --gm SW_GEAR_MODULE
Set the module of the gear. It influences the
gear_profile diameters.
--gear_primitive_diameter SW_GEAR_PRIMITIVE_DIAMETER, --gpd SW_GEAR_PRIMITIVE_DIAMETER
If not zero, redefine the gear module to get this
primitive diameter of the first gear_profile. Default:
0. If gearbar, it redefines the length.
--gear_addendum_dedendum_parity SW_GEAR_ADDENDUM_DEDENDUM_PARITY, --gadp SW_GEAR_ADDENDUM_DEDENDUM_PARITY
Set the addendum / dedendum parity of the first
gear_profile. Default: 50.0%
--gear_tooth_half_height SW_GEAR_TOOTH_HALF_HEIGHT, --gthh SW_GEAR_TOOTH_HALF_HEIGHT
If not zero, redefine the tooth half height of the
first gear_profile. Default: 0.0
--gear_addendum_height_pourcentage SW_GEAR_ADDENDUM_HEIGHT_POURCENTAGE, --gahp SW_GEAR_ADDENDUM_HEIGHT_POURCENTAGE
Set the addendum height of the first gear_profile in
pourcentage of the tooth half height. Default: 100.0%
--gear_dedendum_height_pourcentage SW_GEAR_DEDENDUM_HEIGHT_POURCENTAGE, --gdhp SW_GEAR_DEDENDUM_HEIGHT_POURCENTAGE
Set the dedendum height of the first gear_profile in
pourcentage of the tooth half height. Default: 100.0%
--gear_hollow_height_pourcentage SW_GEAR_HOLLOW_HEIGHT_POURCENTAGE, --ghhp SW_GEAR_HOLLOW_HEIGHT_POURCENTAGE
Set the hollow height of the first gear_profile in
pourcentage of the tooth half height. The hollow is a
clear space for the top of the teeth of the other
gearwheel. Default: 25.0%
--gear_router_bit_radius SW_GEAR_ROUTER_BIT_RADIUS, --grr SW_GEAR_ROUTER_BIT_RADIUS
Set the router_bit radius used to create the gear
hollow of the first gear_profile. Default: 0.1
--gear_base_diameter SW_GEAR_BASE_DIAMETER, --gbd SW_GEAR_BASE_DIAMETER
If not zero, redefine the base diameter of the first
gear involute. Default: 0
--gear_force_angle SW_GEAR_FORCE_ANGLE, --gfa SW_GEAR_FORCE_ANGLE
If not zero, redefine the gear_base_diameter to get
this force angle at the gear contact. Default: 0.0
--gear_tooth_resolution SW_GEAR_TOOTH_RESOLUTION, --gtr SW_GEAR_TOOTH_RESOLUTION
It sets the number of segments of the gear involute.
Default: 2
--gear_skin_thickness SW_GEAR_SKIN_THICKNESS, --gst SW_GEAR_SKIN_THICKNESS
Add or remove radial thickness on the gear involute.
Default: 0.0
--gear_base_diameter_n SW_GEAR_BASE_DIAMETER_N, --gbdn SW_GEAR_BASE_DIAMETER_N
If not zero, redefine the base diameter of the first
gear negative involute. Default: 0
--gear_force_angle_n SW_GEAR_FORCE_ANGLE_N, --gfan SW_GEAR_FORCE_ANGLE_N
If not zero, redefine the negative_gear_base_diameter
to get this force angle at the gear contact. Default:
0.0
--gear_tooth_resolution_n SW_GEAR_TOOTH_RESOLUTION_N, --gtrn SW_GEAR_TOOTH_RESOLUTION_N
If not zero, it sets the number of segments of the
gear negative involute. Default: 0
--gear_skin_thickness_n SW_GEAR_SKIN_THICKNESS_N, --gstn SW_GEAR_SKIN_THICKNESS_N
If not zero, add or remove radial thickness on the
gear negative involute. Default: 0.0
--second_gear_type SW_SECOND_GEAR_TYPE, --sgt SW_SECOND_GEAR_TYPE
Select the type of gear. Possible values: 'e', 'i',
'l'. Default: 'e'
--second_gear_tooth_nb SW_SECOND_GEAR_TOOTH_NB, --sgtn SW_SECOND_GEAR_TOOTH_NB
Set the number of teeth of the second gear_profile.
--second_gear_primitive_diameter SW_SECOND_GEAR_PRIMITIVE_DIAMETER, --sgpd SW_SECOND_GEAR_PRIMITIVE_DIAMETER
If not zero, redefine the gear module to get this
primitive diameter of the second gear_profile.
Default: 0.0. If gearbar, it redefines the length.
--second_gear_addendum_dedendum_parity SW_SECOND_GEAR_ADDENDUM_DEDENDUM_PARITY, --sgadp SW_SECOND_GEAR_ADDENDUM_DEDENDUM_PARITY
Overwrite the addendum / dedendum parity of the second
gear_profile if different from 0.0. Default: 0.0%
--second_gear_tooth_half_height SW_SECOND_GEAR_TOOTH_HALF_HEIGHT, --sgthh SW_SECOND_GEAR_TOOTH_HALF_HEIGHT
If not zero, redefine the tooth half height of the
second gear_profile. Default: 0.0
--second_gear_addendum_height_pourcentage SW_SECOND_GEAR_ADDENDUM_HEIGHT_POURCENTAGE, --sgahp SW_SECOND_GEAR_ADDENDUM_HEIGHT_POURCENTAGE
Set the addendum height of the second gear_profile in
pourcentage of the tooth half height. Default: 100.0%
--second_gear_dedendum_height_pourcentage SW_SECOND_GEAR_DEDENDUM_HEIGHT_POURCENTAGE, --sgdhp SW_SECOND_GEAR_DEDENDUM_HEIGHT_POURCENTAGE
Set the dedendum height of the second gear_profile in
pourcentage of the tooth half height. Default: 100.0%
--second_gear_hollow_height_pourcentage SW_SECOND_GEAR_HOLLOW_HEIGHT_POURCENTAGE, --sghhp SW_SECOND_GEAR_HOLLOW_HEIGHT_POURCENTAGE
Set the hollow height of the second gear_profile in
pourcentage of the tooth half height. The hollow is a
clear space for the top of the teeth of the other
gearwheel. Default: 25.0%
--second_gear_router_bit_radius SW_SECOND_GEAR_ROUTER_BIT_RADIUS, --sgrr SW_SECOND_GEAR_ROUTER_BIT_RADIUS
If not zero, overwrite the router_bit radius used to
create the gear hollow of the second gear_profile.
Default: 0.0
--second_gear_base_diameter SW_SECOND_GEAR_BASE_DIAMETER, --sgbd SW_SECOND_GEAR_BASE_DIAMETER
If not zero, redefine the base diameter of the second
gear involute. Default: 0.0
--second_gear_tooth_resolution SW_SECOND_GEAR_TOOTH_RESOLUTION, --sgtr SW_SECOND_GEAR_TOOTH_RESOLUTION
If not zero, it sets the number of segments of the
second gear involute. Default: 0
--second_gear_skin_thickness SW_SECOND_GEAR_SKIN_THICKNESS, --sgst SW_SECOND_GEAR_SKIN_THICKNESS
Add or remove radial thickness on the gear involute.
Default: 0.0
--second_gear_base_diameter_n SW_SECOND_GEAR_BASE_DIAMETER_N, --sgbdn SW_SECOND_GEAR_BASE_DIAMETER_N
If not zero, redefine the base diameter of the second
gear negative involute. Default: 0.0
--second_gear_tooth_resolution_n SW_SECOND_GEAR_TOOTH_RESOLUTION_N, --sgtrn SW_SECOND_GEAR_TOOTH_RESOLUTION_N
If not zero, it sets the number of segments of the
second gear negative involute. Default: 0
--second_gear_skin_thickness_n SW_SECOND_GEAR_SKIN_THICKNESS_N, --sgstn SW_SECOND_GEAR_SKIN_THICKNESS_N
If not zero, add or remove radial thickness on the
gear negative involute. Default: 0.0
--gearbar_slope SW_GEARBAR_SLOPE, --gbs SW_GEARBAR_SLOPE
if not zero, set the tooth slope angle for the
gearbar. Default 0.0
--gearbar_slope_n SW_GEARBAR_SLOPE_N, --gbsn SW_GEARBAR_SLOPE_N
if not zero, set the tooth negative slope angle for
the gearbar. Default 0.0
--center_position_x SW_CENTER_POSITION_X, --cpx SW_CENTER_POSITION_X
Set the x-position of the first gear_profile center.
Default: 0.0
--center_position_y SW_CENTER_POSITION_Y, --cpy SW_CENTER_POSITION_Y
Set the y-position of the first gear_profile center.
Default: 0.0
--gear_initial_angle SW_GEAR_INITIAL_ANGLE, --gia SW_GEAR_INITIAL_ANGLE
Set the gear reference angle (in Radian). Default: 0.0
--second_gear_position_angle SW_SECOND_GEAR_POSITION_ANGLE, --sgpa SW_SECOND_GEAR_POSITION_ANGLE
Angle in Radian that sets the postion on the second
gear_profile. Default: 0.0
--second_gear_additional_axis_length SW_SECOND_GEAR_ADDITIONAL_AXIS_LENGTH, --sgaal SW_SECOND_GEAR_ADDITIONAL_AXIS_LENGTH
Set an additional value for the inter-axis length
between the first and the second gear_profiles.
Default: 0.0
--cut_portion SW_CUT_PORTION SW_CUT_PORTION SW_CUT_PORTION, --cp SW_CUT_PORTION SW_CUT_PORTION SW_CUT_PORTION
(N, first_end, last_end) If N>1, cut a portion of N
tooth ofthe gear_profile. first_end and last_end
defines in details where the profile stop (0: slope-
top, 1: top-middle, 2: slope-bottom, 3: hollow-
middle). Default: (0,0,0)
--gear_profile_height SW_GEAR_PROFILE_HEIGHT, --gwh SW_GEAR_PROFILE_HEIGHT
Set the height of the linear extrusion of the first
gear_profile. Default: 1.0
--simulation_enable, --se
It display a Tk window where you can observe the gear
running. Check with your eyes if the geometry is
working.
--output_file_basename SW_OUTPUT_FILE_BASENAME, --ofb SW_OUTPUT_FILE_BASENAME
If not the empty_string (the default value), it
outputs the (first) gear in file(s) depending on your
argument file_extension: .dxf uses mozman dxfwrite,
.svg uses mozman svgwrite, no-extension uses FreeCAD
and you get .brep and .dxf
--run_self_test, --rst
Generate several corner cases of parameter sets and
display the Tk window where you should check the gear
running.
16.3. From gear_profile() arguments to high-level parameters¶
16.3.1. Gear type¶
Gear type possible values:
- e : external (a.k.a. gearwheel)
- i : internal (a.k.a. gearring)
- l : linear (a.k.a. gearbar)
16.3.2. Gear tooth number (N)¶
N > 2
16.3.3. Gear module (m)¶
Set after those priorities:
1. gear-module parameter
2. primitive diameter parameter (m=pd/N)
3. second primitive diameter parameter (m=pd2/N2)
4. the default value (m=1)
16.3.4. Gear base diameter (bd)¶
Set after those priorities:
1. gear base diameter parameter
2. second gear base diameter parameter (bd=bd2*N1/N2)
3. gearbar slope angle (bd=pd*cos(sa))
4. force angle parameter (bd=pd*cos(fa))
5. the default value (bd=[dedendum diameter of the smallest gear])
When two gears are specified (by setting second_gear_tooth_nb), and the gear base diameter is not constrainted, the dedendum diameter of the smallest gear is used to calculate the gear base diameter.
16.3.5. Gearbar slope angle (sa)¶
It is only applicable with a gearbar. Because gearbar-gearbar system doesn’t exist, the first and the second gear share the parameters gearbar_slope and gearbar_slope_n.
Set after those priorities:
1. gearbar_slope parameter
2. force angle parameter (sa=fa)
3. second gear base diameter parameter (sa=acos(bd/pd))
The Gearbar slope has no default value and must be constraint by one of those three possibilities.
