679 lines
17 KiB
OpenSCAD
679 lines
17 KiB
OpenSCAD
// Parametric Involute Bevel and Spur Gears by GregFrost
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// It is licensed under the Creative Commons - GNU GPL license.
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// © 2010 by GregFrost
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// http://www.thingiverse.com/thing:3575
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// Simple Test:
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//gear (circular_pitch=700,
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// gear_thickness = 12,
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// rim_thickness = 15,
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// hub_thickness = 17,
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// circles=8);
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//Complex Spur Gear Test:
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//test_gears ();
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// Meshing Double Helix:
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//test_meshing_double_helix ();
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module test_meshing_double_helix(){
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test_meshing_double_helix ();
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}
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// Demonstrate the backlash option for Spur gears.
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//test_backlash ();
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// Demonstrate how to make meshing bevel gears.
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//test_bevel_gear_pair();
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module test_bevel_gear_pair(){
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bevel_gear_pair ();
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}
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pi=3.1415926535897932384626433832795;
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//==================================================
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// Bevel Gears:
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// Two gears with the same cone distance, circular pitch (measured at the cone distance)
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// and pressure angle will mesh.
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module bevel_gear_pair (
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gear1_teeth = 41,
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gear2_teeth = 7,
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axis_angle = 90,
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outside_circular_pitch=1000)
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{
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outside_pitch_radius1 = gear1_teeth * outside_circular_pitch / 360;
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outside_pitch_radius2 = gear2_teeth * outside_circular_pitch / 360;
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pitch_apex1=outside_pitch_radius2 * sin (axis_angle) +
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(outside_pitch_radius2 * cos (axis_angle) + outside_pitch_radius1) / tan (axis_angle);
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cone_distance = sqrt (pow (pitch_apex1, 2) + pow (outside_pitch_radius1, 2));
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pitch_apex2 = sqrt (pow (cone_distance, 2) - pow (outside_pitch_radius2, 2));
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echo ("cone_distance", cone_distance);
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pitch_angle1 = asin (outside_pitch_radius1 / cone_distance);
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pitch_angle2 = asin (outside_pitch_radius2 / cone_distance);
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echo ("pitch_angle1, pitch_angle2", pitch_angle1, pitch_angle2);
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echo ("pitch_angle1 + pitch_angle2", pitch_angle1 + pitch_angle2);
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rotate([0,0,90])
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translate ([0,0,pitch_apex1+20])
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{
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translate([0,0,-pitch_apex1])
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bevel_gear (
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number_of_teeth=gear1_teeth,
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cone_distance=cone_distance,
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pressure_angle=30,
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outside_circular_pitch=outside_circular_pitch);
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rotate([0,-(pitch_angle1+pitch_angle2),0])
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translate([0,0,-pitch_apex2])
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bevel_gear (
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number_of_teeth=gear2_teeth,
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cone_distance=cone_distance,
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pressure_angle=30,
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outside_circular_pitch=outside_circular_pitch);
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}
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}
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//Bevel Gear Finishing Options:
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bevel_gear_flat = 0;
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bevel_gear_back_cone = 1;
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module bevel_gear (
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number_of_teeth=11,
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cone_distance=100,
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face_width=20,
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outside_circular_pitch=1000,
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pressure_angle=30,
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clearance = 0.2,
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bore_diameter=5,
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gear_thickness = 15,
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backlash = 0,
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involute_facets=0,
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finish = -1)
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{
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echo ("bevel_gear",
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"teeth", number_of_teeth,
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"cone distance", cone_distance,
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face_width,
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outside_circular_pitch,
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pressure_angle,
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clearance,
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bore_diameter,
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involute_facets,
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finish);
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// Pitch diameter: Diameter of pitch circle at the fat end of the gear.
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outside_pitch_diameter = number_of_teeth * outside_circular_pitch / 180;
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outside_pitch_radius = outside_pitch_diameter / 2;
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// The height of the pitch apex.
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pitch_apex = sqrt (pow (cone_distance, 2) - pow (outside_pitch_radius, 2));
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pitch_angle = asin (outside_pitch_radius/cone_distance);
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echo ("Num Teeth:", number_of_teeth, " Pitch Angle:", pitch_angle);
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finish = (finish != -1) ? finish : (pitch_angle < 45) ? bevel_gear_flat : bevel_gear_back_cone;
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apex_to_apex=cone_distance / cos (pitch_angle);
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back_cone_radius = apex_to_apex * sin (pitch_angle);
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// Calculate and display the pitch angle. This is needed to determine the angle to mount two meshing cone gears.
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// Base Circle for forming the involute teeth shape.
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base_radius = back_cone_radius * cos (pressure_angle);
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// Diametrial pitch: Number of teeth per unit length.
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pitch_diametrial = number_of_teeth / outside_pitch_diameter;
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// Addendum: Radial distance from pitch circle to outside circle.
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addendum = 1 / pitch_diametrial;
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// Outer Circle
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outer_radius = back_cone_radius + addendum;
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// Dedendum: Radial distance from pitch circle to root diameter
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dedendum = addendum + clearance;
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dedendum_angle = atan (dedendum / cone_distance);
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root_angle = pitch_angle - dedendum_angle;
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root_cone_full_radius = tan (root_angle)*apex_to_apex;
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back_cone_full_radius=apex_to_apex / tan (pitch_angle);
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back_cone_end_radius =
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outside_pitch_radius -
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dedendum * cos (pitch_angle) -
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gear_thickness / tan (pitch_angle);
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back_cone_descent = dedendum * sin (pitch_angle) + gear_thickness;
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// Root diameter: Diameter of bottom of tooth spaces.
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root_radius = back_cone_radius - dedendum;
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half_tooth_thickness = outside_pitch_radius * sin (360 / (4 * number_of_teeth)) - backlash / 4;
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half_thick_angle = asin (half_tooth_thickness / back_cone_radius);
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face_cone_height = apex_to_apex-face_width / cos (pitch_angle);
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face_cone_full_radius = face_cone_height / tan (pitch_angle);
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face_cone_descent = dedendum * sin (pitch_angle);
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face_cone_end_radius =
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outside_pitch_radius -
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face_width / sin (pitch_angle) -
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face_cone_descent / tan (pitch_angle);
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// For the bevel_gear_flat finish option, calculate the height of a cube to select the portion of the gear that includes the full pitch face.
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bevel_gear_flat_height = pitch_apex - (cone_distance - face_width) * cos (pitch_angle);
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// translate([0,0,-pitch_apex])
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difference ()
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{
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intersection ()
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{
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union()
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{
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rotate (half_thick_angle)
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translate ([0,0,pitch_apex-apex_to_apex])
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cylinder ($fn=number_of_teeth*2, r1=root_cone_full_radius,r2=0,h=apex_to_apex);
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for (i = [1:number_of_teeth])
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// for (i = [1:1])
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{
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rotate ([0,0,i*360/number_of_teeth])
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{
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involute_bevel_gear_tooth (
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back_cone_radius = back_cone_radius,
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root_radius = root_radius,
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base_radius = base_radius,
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outer_radius = outer_radius,
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pitch_apex = pitch_apex,
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cone_distance = cone_distance,
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half_thick_angle = half_thick_angle,
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involute_facets = involute_facets);
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}
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}
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}
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if (finish == bevel_gear_back_cone)
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{
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translate ([0,0,-back_cone_descent])
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cylinder (
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$fn=number_of_teeth*2,
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r1=back_cone_end_radius,
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r2=back_cone_full_radius*2,
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h=apex_to_apex + back_cone_descent);
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}
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else
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{
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translate ([-1.5*outside_pitch_radius,-1.5*outside_pitch_radius,0])
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cube ([3*outside_pitch_radius,
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3*outside_pitch_radius,
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bevel_gear_flat_height]);
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}
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}
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if (finish == bevel_gear_back_cone)
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{
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translate ([0,0,-face_cone_descent])
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cylinder (
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r1=face_cone_end_radius,
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r2=face_cone_full_radius * 2,
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h=face_cone_height + face_cone_descent+pitch_apex);
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}
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translate ([0,0,pitch_apex - apex_to_apex])
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cylinder (r=bore_diameter/2,h=apex_to_apex);
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}
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}
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module involute_bevel_gear_tooth (
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back_cone_radius,
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root_radius,
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base_radius,
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outer_radius,
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pitch_apex,
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cone_distance,
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half_thick_angle,
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involute_facets)
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{
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// echo ("involute_bevel_gear_tooth",
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// back_cone_radius,
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// root_radius,
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// base_radius,
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// outer_radius,
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// pitch_apex,
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// cone_distance,
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// half_thick_angle);
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min_radius = max (base_radius*2,root_radius*2);
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pitch_point =
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involute (
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base_radius*2,
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involute_intersect_angle (base_radius*2, back_cone_radius*2));
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pitch_angle = atan2 (pitch_point[1], pitch_point[0]);
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centre_angle = pitch_angle + half_thick_angle;
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start_angle = involute_intersect_angle (base_radius*2, min_radius);
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stop_angle = involute_intersect_angle (base_radius*2, outer_radius*2);
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res=(involute_facets!=0)?involute_facets:($fn==0)?5:$fn/4;
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translate ([0,0,pitch_apex])
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rotate ([0,-atan(back_cone_radius/cone_distance),0])
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translate ([-back_cone_radius*2,0,-cone_distance*2])
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union ()
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{
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for (i=[1:res])
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{
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assign (
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point1=
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involute (base_radius*2,start_angle+(stop_angle - start_angle)*(i-1)/res),
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point2=
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involute (base_radius*2,start_angle+(stop_angle - start_angle)*(i)/res))
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{
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assign (
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side1_point1 = rotate_point (centre_angle, point1),
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side1_point2 = rotate_point (centre_angle, point2),
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side2_point1 = mirror_point (rotate_point (centre_angle, point1)),
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side2_point2 = mirror_point (rotate_point (centre_angle, point2)))
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{
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polyhedron (
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points=[
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[back_cone_radius*2+0.1,0,cone_distance*2],
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[side1_point1[0],side1_point1[1],0],
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[side1_point2[0],side1_point2[1],0],
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[side2_point2[0],side2_point2[1],0],
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[side2_point1[0],side2_point1[1],0],
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[0.1,0,0]],
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triangles=[[0,1,2],[0,2,3],[0,3,4],[0,5,1],[1,5,2],[2,5,3],[3,5,4],[0,4,5]]);
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}
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}
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}
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}
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}
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module gear (
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number_of_teeth=15,
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circular_pitch=false, diametral_pitch=false,
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pressure_angle=28,
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clearance = 0.2,
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gear_thickness=5,
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rim_thickness=8,
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rim_width=5,
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hub_thickness=10,
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hub_diameter=15,
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bore_diameter=5,
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circles=0,
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backlash=0,
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twist=0,
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involute_facets=0)
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{
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if (circular_pitch==false && diametral_pitch==false)
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echo("MCAD ERROR: gear module needs either a diametral_pitch or circular_pitch");
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//Convert diametrial pitch to our native circular pitch
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circular_pitch = (circular_pitch!=false?circular_pitch:180/diametral_pitch);
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// Pitch diameter: Diameter of pitch circle.
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pitch_diameter = number_of_teeth * circular_pitch / 180;
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pitch_radius = pitch_diameter/2;
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echo ("Teeth:", number_of_teeth, " Pitch radius:", pitch_radius);
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// Base Circle
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base_radius = pitch_radius*cos(pressure_angle);
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// Diametrial pitch: Number of teeth per unit length.
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pitch_diametrial = number_of_teeth / pitch_diameter;
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// Addendum: Radial distance from pitch circle to outside circle.
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addendum = 1/pitch_diametrial;
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//Outer Circle
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outer_radius = pitch_radius+addendum;
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// Dedendum: Radial distance from pitch circle to root diameter
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dedendum = addendum + clearance;
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// Root diameter: Diameter of bottom of tooth spaces.
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root_radius = pitch_radius-dedendum;
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backlash_angle = backlash / pitch_radius * 180 / pi;
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half_thick_angle = (360 / number_of_teeth - backlash_angle) / 4;
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// Variables controlling the rim.
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rim_radius = root_radius - rim_width;
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// Variables controlling the circular holes in the gear.
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circle_orbit_diameter=hub_diameter/2+rim_radius;
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circle_orbit_curcumference=pi*circle_orbit_diameter;
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// Limit the circle size to 90% of the gear face.
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circle_diameter=
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min (
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0.70*circle_orbit_curcumference/circles,
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(rim_radius-hub_diameter/2)*0.9);
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difference ()
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{
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union ()
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{
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difference ()
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{
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linear_extrude (height=rim_thickness, convexity=10, twist=twist)
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gear_shape (
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number_of_teeth,
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pitch_radius = pitch_radius,
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root_radius = root_radius,
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base_radius = base_radius,
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outer_radius = outer_radius,
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half_thick_angle = half_thick_angle,
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involute_facets=involute_facets);
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if (gear_thickness < rim_thickness)
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translate ([0,0,gear_thickness])
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cylinder (r=rim_radius,h=rim_thickness-gear_thickness+1);
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}
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if (gear_thickness > rim_thickness)
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cylinder (r=rim_radius,h=gear_thickness);
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if (hub_thickness > gear_thickness)
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translate ([0,0,gear_thickness])
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cylinder (r=hub_diameter/2,h=hub_thickness-gear_thickness);
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}
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translate ([0,0,-1])
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cylinder (
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r=bore_diameter/2,
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h=2+max(rim_thickness,hub_thickness,gear_thickness));
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if (circles>0)
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{
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for(i=[0:circles-1])
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rotate([0,0,i*360/circles])
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translate([circle_orbit_diameter/2,0,-1])
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cylinder(r=circle_diameter/2,h=max(gear_thickness,rim_thickness)+3);
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}
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}
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}
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module gear_shape (
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number_of_teeth,
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pitch_radius,
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root_radius,
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base_radius,
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outer_radius,
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half_thick_angle,
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involute_facets)
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{
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union()
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{
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rotate (half_thick_angle) circle ($fn=number_of_teeth*2, r=root_radius);
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for (i = [1:number_of_teeth])
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{
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rotate ([0,0,i*360/number_of_teeth])
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{
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involute_gear_tooth (
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pitch_radius = pitch_radius,
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root_radius = root_radius,
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base_radius = base_radius,
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outer_radius = outer_radius,
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half_thick_angle = half_thick_angle,
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involute_facets=involute_facets);
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}
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}
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}
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}
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module involute_gear_tooth (
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pitch_radius,
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root_radius,
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base_radius,
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outer_radius,
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half_thick_angle,
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involute_facets)
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{
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min_radius = max (base_radius,root_radius);
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pitch_point = involute (base_radius, involute_intersect_angle (base_radius, pitch_radius));
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pitch_angle = atan2 (pitch_point[1], pitch_point[0]);
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centre_angle = pitch_angle + half_thick_angle;
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start_angle = involute_intersect_angle (base_radius, min_radius);
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stop_angle = involute_intersect_angle (base_radius, outer_radius);
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res=(involute_facets!=0)?involute_facets:($fn==0)?5:$fn/4;
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union ()
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{
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for (i=[1:res])
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assign (
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point1=involute (base_radius,start_angle+(stop_angle - start_angle)*(i-1)/res),
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point2=involute (base_radius,start_angle+(stop_angle - start_angle)*i/res))
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{
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assign (
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side1_point1=rotate_point (centre_angle, point1),
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side1_point2=rotate_point (centre_angle, point2),
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side2_point1=mirror_point (rotate_point (centre_angle, point1)),
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side2_point2=mirror_point (rotate_point (centre_angle, point2)))
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{
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polygon (
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points=[[0,0],side1_point1,side1_point2,side2_point2,side2_point1],
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paths=[[0,1,2,3,4,0]]);
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}
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}
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}
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}
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// Mathematical Functions
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//===============
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// Finds the angle of the involute about the base radius at the given distance (radius) from it's center.
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//source: http://www.mathhelpforum.com/math-help/geometry/136011-circle-involute-solving-y-any-given-x.html
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function involute_intersect_angle (base_radius, radius) = sqrt (pow (radius/base_radius, 2) - 1) * 180 / pi;
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// Calculate the involute position for a given base radius and involute angle.
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function rotated_involute (rotate, base_radius, involute_angle) =
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[
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cos (rotate) * involute (base_radius, involute_angle)[0] + sin (rotate) * involute (base_radius, involute_angle)[1],
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cos (rotate) * involute (base_radius, involute_angle)[1] - sin (rotate) * involute (base_radius, involute_angle)[0]
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];
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function mirror_point (coord) =
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[
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coord[0],
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-coord[1]
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];
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|
|
|
function rotate_point (rotate, coord) =
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|
[
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|
cos (rotate) * coord[0] + sin (rotate) * coord[1],
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|
cos (rotate) * coord[1] - sin (rotate) * coord[0]
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|
];
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|
|
|
function involute (base_radius, involute_angle) =
|
|
[
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|
base_radius*(cos (involute_angle) + involute_angle*pi/180*sin (involute_angle)),
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|
base_radius*(sin (involute_angle) - involute_angle*pi/180*cos (involute_angle)),
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|
];
|
|
|
|
|
|
// Test Cases
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|
//===============
|
|
|
|
module test_gears()
|
|
{
|
|
translate([17,-15])
|
|
{
|
|
gear (number_of_teeth=17,
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|
circular_pitch=500,
|
|
circles=8);
|
|
|
|
rotate ([0,0,360*4/17])
|
|
translate ([39.088888,0,0])
|
|
{
|
|
gear (number_of_teeth=11,
|
|
circular_pitch=500,
|
|
hub_diameter=0,
|
|
rim_width=65);
|
|
translate ([0,0,8])
|
|
{
|
|
gear (number_of_teeth=6,
|
|
circular_pitch=300,
|
|
hub_diameter=0,
|
|
rim_width=5,
|
|
rim_thickness=6,
|
|
pressure_angle=31);
|
|
rotate ([0,0,360*5/6])
|
|
translate ([22.5,0,1])
|
|
gear (number_of_teeth=21,
|
|
circular_pitch=300,
|
|
bore_diameter=2,
|
|
hub_diameter=4,
|
|
rim_width=1,
|
|
hub_thickness=4,
|
|
rim_thickness=4,
|
|
gear_thickness=3,
|
|
pressure_angle=31);
|
|
}
|
|
}
|
|
|
|
translate ([-61.1111111,0,0])
|
|
{
|
|
gear (number_of_teeth=27,
|
|
circular_pitch=500,
|
|
circles=5,
|
|
hub_diameter=2*8.88888889);
|
|
|
|
translate ([0,0,10])
|
|
{
|
|
gear (
|
|
number_of_teeth=14,
|
|
circular_pitch=200,
|
|
pressure_angle=5,
|
|
clearance = 0.2,
|
|
gear_thickness = 10,
|
|
rim_thickness = 10,
|
|
rim_width = 15,
|
|
bore_diameter=5,
|
|
circles=0);
|
|
translate ([13.8888888,0,1])
|
|
gear (
|
|
number_of_teeth=11,
|
|
circular_pitch=200,
|
|
pressure_angle=5,
|
|
clearance = 0.2,
|
|
gear_thickness = 10,
|
|
rim_thickness = 10,
|
|
rim_width = 15,
|
|
hub_thickness = 20,
|
|
hub_diameter=2*7.222222,
|
|
bore_diameter=5,
|
|
circles=0);
|
|
}
|
|
}
|
|
|
|
rotate ([0,0,360*-5/17])
|
|
translate ([44.444444444,0,0])
|
|
gear (number_of_teeth=15,
|
|
circular_pitch=500,
|
|
hub_diameter=10,
|
|
rim_width=5,
|
|
rim_thickness=5,
|
|
gear_thickness=4,
|
|
hub_thickness=6,
|
|
circles=9);
|
|
|
|
rotate ([0,0,360*-1/17])
|
|
translate ([30.5555555,0,-1])
|
|
gear (number_of_teeth=5,
|
|
circular_pitch=500,
|
|
hub_diameter=0,
|
|
rim_width=5,
|
|
rim_thickness=10);
|
|
}
|
|
}
|
|
|
|
module meshing_double_helix ()
|
|
{
|
|
test_double_helix_gear ();
|
|
|
|
mirror ([0,1,0])
|
|
translate ([58.33333333,0,0])
|
|
test_double_helix_gear (teeth=13,circles=6);
|
|
}
|
|
|
|
module test_double_helix_gear (
|
|
teeth=17,
|
|
circles=8)
|
|
{
|
|
//double helical gear
|
|
{
|
|
twist=200;
|
|
height=20;
|
|
pressure_angle=30;
|
|
|
|
gear (number_of_teeth=teeth,
|
|
circular_pitch=700,
|
|
pressure_angle=pressure_angle,
|
|
clearance = 0.2,
|
|
gear_thickness = height/2*0.5,
|
|
rim_thickness = height/2,
|
|
rim_width = 5,
|
|
hub_thickness = height/2*1.2,
|
|
hub_diameter=15,
|
|
bore_diameter=5,
|
|
circles=circles,
|
|
twist=twist/teeth);
|
|
mirror([0,0,1])
|
|
gear (number_of_teeth=teeth,
|
|
circular_pitch=700,
|
|
pressure_angle=pressure_angle,
|
|
clearance = 0.2,
|
|
gear_thickness = height/2,
|
|
rim_thickness = height/2,
|
|
rim_width = 5,
|
|
hub_thickness = height/2,
|
|
hub_diameter=15,
|
|
bore_diameter=5,
|
|
circles=circles,
|
|
twist=twist/teeth);
|
|
}
|
|
}
|
|
|
|
module test_backlash ()
|
|
{
|
|
backlash = 2;
|
|
teeth = 15;
|
|
|
|
translate ([-29.166666,0,0])
|
|
{
|
|
translate ([58.3333333,0,0])
|
|
rotate ([0,0,-360/teeth/4])
|
|
gear (
|
|
number_of_teeth = teeth,
|
|
circular_pitch=700,
|
|
gear_thickness = 12,
|
|
rim_thickness = 15,
|
|
rim_width = 5,
|
|
hub_thickness = 17,
|
|
hub_diameter=15,
|
|
bore_diameter=5,
|
|
backlash = 2,
|
|
circles=8);
|
|
|
|
rotate ([0,0,360/teeth/4])
|
|
gear (
|
|
number_of_teeth = teeth,
|
|
circular_pitch=700,
|
|
gear_thickness = 12,
|
|
rim_thickness = 15,
|
|
rim_width = 5,
|
|
hub_thickness = 17,
|
|
hub_diameter=15,
|
|
bore_diameter=5,
|
|
backlash = 2,
|
|
circles=8);
|
|
}
|
|
|
|
color([0,0,128,0.5])
|
|
translate([0,0,-5])
|
|
cylinder ($fn=20,r=backlash / 4,h=25);
|
|
}
|
|
|