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Work on intro, changed parameters for gear_dist, etc, fixed examples,
fixed rack to behave like gears
This commit is contained in:
Adrian Mariano
parent
cfcf72258a
commit
bf038ae032
1 changed files with 220 additions and 130 deletions
350
gears.scad
350
gears.scad
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@ -66,22 +66,35 @@ function _inherit_gear_thickness(thickness) =
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_inherit_gear_param("thickness", thickness, $parent_gear_thickness, dflt=10);
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// Section: Terminology
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// The outline of a gear is a smooth circle (the "pitch circle") which has
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// mountains and valleys added so it is toothed. There is an inner
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// circle (the "root circle") that touches the base of all the teeth, an
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// outer circle that touches the tips of all the teeth, and the invisible
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// pitch circle in between them. There is also a "base circle", which can
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// be smaller than all three of the others, which controls the shape of
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// the teeth. The side of each tooth lies on the path that the end of a
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// string would follow if it were wrapped tightly around the base circle,
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// then slowly unwound. That shape is an "involute", which gives this
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// type of gear its name.
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//// Section: Terminology
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//// The outline of a gear is a smooth circle (the "pitch circle") which has
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//// mountains and valleys added so it is toothed. There is an inner
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//// circle (the "root circle") that touches the base of all the teeth, an
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//// outer circle that touches the tips of all the teeth, and the invisible
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//// pitch circle in between them. There is also a "base circle", which can
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//// be smaller than all three of the others, which controls the shape of
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//// the teeth. The side of each tooth lies on the path that the end of a
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//// string would follow if it were wrapped tightly around the base circle,
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//// then slowly unwound. That shape is an "involute", which gives this
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//// type of gear its name.
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// Section: Involute Spur Gears
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// Section: Quick Introduction to Gears
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// This section gives a quick overview of gears with a focus on the information you need
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// to know to understand the gear parameters and create some gears. The topic of gears is very complex and highly technical and
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// this section provides the minimal information needed for gear making. If you want more information about the
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// details of gears, consult the references below, which are the ones that we consulted when writing the library code.
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// - Tec Science
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// * [Gear engagement](https://www.tec-science.com/mechanical-power-transmission/involute-gear/meshing-line-action-contact-pitch-circle-law/)
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// * [Gears meshing with racks](https://www.tec-science.com/mechanical-power-transmission/involute-gear/rack-meshing/)
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// * [Gear undercutting](https://www.tec-science.com/mechanical-power-transmission/involute-gear/undercut/)
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// * [Profile shifting](https://www.tec-science.com/mechanical-power-transmission/involute-gear/profile-shift/)
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// * [Detailed gear calculations](https://www.tec-science.com/mechanical-power-transmission/involute-gear/calculation-of-involute-gears/)
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// - SDPSI
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// * [Elements of Gear Technology](https://www.sdp-si.com/resources/elements-of-metric-gear-technology/index.php)
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// Subsection: Involute Spur Gears
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// The simplest gear form is the involute spur gear, which is an extrusion of a two dimensional form.
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// Figure(3D,Med,NoAxes): Involute Spur Gear
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// Figure(3D,Med,NoAxes,VPT=[-8.01632,15.2012,0],VPR=[0,0,0],VPD=237): Involute Spur Gear
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// spur_gear(mod=5,teeth=18,pressure_angle=20,thickness=25,shaft_diam=15);
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// Continues:
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// The term "involute" refers to the shape of the teeth: the curves of the teeth involutes of circles,
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@ -174,11 +187,13 @@ function _inherit_gear_thickness(thickness) =
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// A solution to the problem of undercutting is to use profile shifting. Profile shifting uses a different portion of the
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// involute curve to form the gear teeth, and this adjustment to the tooth form can eliminate undercutting, while
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// still allowing the gear to mesh with unmodified gears. Profile shifting
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// changes the diameter at which the gear meshes so it no longer meshes at the pitch circle. A profile shift of `x`
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// will increase the mesh distance by approximately `x*m` where `m` is the gear module. The exact adjustment is
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// a complex calculation that depends on the profile shifts of both meshing gears. This means that profile shifting
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// changes the diameter at which the gear meshes so it no longer meshes at the pitch circle.
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// A profile shift of `x`
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// will increase the mesh distance by approximately `x*m` where `m` is the gear module. The exact adjustment
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// which you compute with {{gear_dist()}} is a complex calculation that depends on the profile shifts of both meshing gears. This means that profile shifting
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// can also be used to fine tune the spacing between gears. When the gear has many teeth a negative profile shift may
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// be able to bring the gears slightly closer together, while still avoiding undercutting.
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// be able to bring the gears slightly closer together, while still avoiding undercutting.
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// Profile shifting also changes the effective pressure angle of the gear engagement.
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// .
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// The minimum number of teeth to avoid undercutting is 17 for a pressure angle of 20, but it is 32 for a pressure
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// angle of 14.5 degrees. It can be computed as `2/(sin(alpha))^2` where `alpha` is the pressure angle.
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@ -202,23 +217,25 @@ function _inherit_gear_thickness(thickness) =
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// zrot(ang2)
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// spur_gear2d(mod=5, teeth=5, pressure_angle=14.5, shaft_diam=2);
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// rack2d(teeth=4, height=15, mod=5, pressure_angle=14.5);
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// Section: Helical Gears
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// Subsection: Helical Gears
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// Helicals gears are a modification of spur gears. They can replace spur gears in any application. The teeth are cut
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// following a slanted, helical path. The angled teeth engage more gradually than spur gear teeth, so they run more smoothly
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// and quietly. A disadvantage of helical gears is that they have thrust along the axis of the gear that must be
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// accomodated. Helical gears also have more sliding friction between the meshing teeth compared to spur gears.
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// Figure(3D,Med,NoAxes): A Helical Gear
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// spur_gear(mod=5,teeth=18,pressure_angle=20,thickness=25,helical=-29,shaft_diam=15);
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// Figure(3D,Med,NoAxes,VPT=[3.5641,-7.03148,4.86523],VPR=[62.7,0,29.2],VPD=263.285): A Helical Gear
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// spur_gear(mod=5,teeth=18,pressure_angle=20,thickness=35,helical=-29,shaft_diam=15);
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// Continues:
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// Helical gears have the same compatibility requirements as spur gears, with the additional requirement that
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// the helical angles must be opposite each other, so a gear with a helical angle of 25 must mesh with one
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// that has an angle of -25. The separation between gears also has an additional correction that depends on the cosine of
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// the helical angle, so it will be different from a spur gear with the same parameters. This can allow you to
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// that has an angle of −25. The pitch circle of a helical gear differs is larger compared to a spur gear
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// by the cosine of the helical angle, so you cannot simply drop helical gears in to replace spur gears without
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// making other adjustments. This dependence does allow you to make
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// make much bigger spacing adjustments than are possible with profile shifting---without changing the tooth count.
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// The {{gear_dist()}} function will also compute the appropriate gear spacing for these gears.
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// The effective pressure angle of helical gears is larger than the nominal pressure angle. This can make it possible
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// to avoid undercutting without having to use profile shifting, so smaller tooth count gears can be more effective
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// using the helical form.
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// Figure(Anim,Frames=10,VPT=[43.8006,15.9214,3.52727],VPR=[62.3,0,20.3],VPD=446.129): Meshing compatible helical gears
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// Figure(Anim,Med,Frames=10,NoAxes,VPT=[43.8006,15.9214,3.52727],VPR=[62.3,0,20.3],VPD=446.129): Meshing compatible helical gears
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// zrot($t*360/18)
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// spur_gear(mod=5, teeth=18, pressure_angle=20, thickness=25, helical=-29, shaft_diam=15);
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// right(gear_dist(mod=5, teeth1=18, teeth2=18, helical=29))
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@ -227,25 +244,28 @@ function _inherit_gear_thickness(thickness) =
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// spur_gear(mod=5, teeth=18, pressure_angle=20, thickness=25, helical=29, shaft_diam=15);
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// Continues:
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// Helical gears can mesh in a second manner that is different from spur gears at skew, or crossed axis. These are also
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// sometimes called "screw gears". In fact, the general requirement for two helical gears to mesh is that the angle
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// sometimes called "screw gears". The general requirement for two non-profile-shifted helical gears to mesh is that the angle
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// between the gears' axes must equal the sum of the helical angles of the two gears, thus for parallel axes, the helical
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// angles must sum to zero.
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// Figure(Anim,Frames=10,VPT=[46,0,0],VPR=[55,0,25],VPD=713):
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// dist = gear_dist(mod=5, teeth1=18, teeth2=18, helical=22.5);
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// color("lightblue")
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// angles must sum to zero. If helical gears are profile shifted, then in addition to adjusting the distance between the
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// gears, a small adjustment in the angle is needed, so profile shifted gears won't mesh exactly at the sum of their angles.
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// The calculation for gear spacing is different for skew axis gears than for parallel gears, so you do this using {{gear_dist_skew()}},
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// and if you use profile shifting, then you can compute the angle using {{gear_skew_angle()}}.
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// Figure(Anim,Med,NoAxes,Frames=10,VPT=[44.765,6.09492,-3.01199],VPR=[55.7,0,33.2],VPD=401.289): Two helical gears meshing with axes at a 45 degree angle
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// dist = gear_dist_skew(mod=5, teeth1=18, teeth2=18, helical1=22.5,helical2=22.5);
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// axiscolor="darkgray";
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// down(10)color(axiscolor) cyl(d=15, l=145);
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// zrot($t*360/18)
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// spur_gear(mod=5,teeth=18,pressure_angle=20,thickness=25,helical=22.5,shaft_diam=15);
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// color("lightblue")spur_gear(mod=5,teeth=18,pressure_angle=20,thickness=25,helical=22.5,shaft_diam=15);
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// right(dist)
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// xrot(45)
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// xrot(45) {color(axiscolor)cyl(d=15,l=85);
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// zrot(360/18/2)
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// zrot(-$t*360/18)
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// spur_gear(mod=5,teeth=18,pressure_angle=20,thickness=25,helical=22.5,shaft_diam=15);
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// Section: Herringbone Gears
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// The herringbone gear addresses the problem of axial forces that afflict helical gears by having one section that slopes to the
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// spur_gear(mod=5,teeth=18,pressure_angle=20,thickness=25,helical=22.5,shaft_diam=15);}
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// Subsection: Herringbone Gears
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// The herringbone gear is made from two stacked helical gears with opposite angles. This design addresses the problem
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// of axial forces that afflict helical gears by having one section that slopes to the
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// right and another that slopes to the left. Herringbone gears also have the advantage of being self-aligning.
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// Figure(3D,Med,NoAxes): A herringbone gear
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// Figure(3D,Med,NoAxes,VPT=[3.5641,-7.03148,4.86523],VPR=[62.7,0,29.2],VPD=263.285): A herringbone gear
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// spur_gear(mod=5, teeth=16, pressure_angle=20, thickness=35, helical=-20, herringbone=true, shaft_diam=15);
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@ -338,9 +358,9 @@ function _inherit_gear_thickness(thickness) =
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// pr = pitch_radius(circ_pitch, teeth);
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// left(10) {
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// profile_shift = 0;
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// d = gear_dist(circ_pitch,teeth,0,profile_shift1=profile_shift);
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// d = gear_dist(circ_pitch=circ_pitch,teeth,0,profile_shift1=profile_shift);
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// back(d) spur_gear(circ_pitch, teeth, thick, shaft, profile_shift=profile_shift);
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// rack(circ_pitch, teeth=3, thickness=thick, height=5, orient=BACK);
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// rack(circ_pitch, teeth=3, thickness=thick, height=5);
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// color("black") up(thick/2) linear_extrude(height=0.1) {
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// back(d) dashed_stroke(circle(r=pr), width=strokewidth, closed=true);
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// dashed_stroke([[-7.5,0],[7.5,0]], width=strokewidth);
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@ -348,9 +368,9 @@ function _inherit_gear_thickness(thickness) =
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// }
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// right(10) {
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// profile_shift = 0.59;
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// d = gear_dist(circ_pitch,teeth,0,profile_shift1=profile_shift);
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// d = gear_dist(circ_pitch=circ_pitch,teeth,0,profile_shift1=profile_shift);
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// back(d) spur_gear(circ_pitch, teeth, thick, shaft, profile_shift=profile_shift);
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// rack(circ_pitch, teeth=3, thickness=thick, height=5, orient=BACK);
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// rack(circ_pitch, teeth=3, thickness=thick, height=5);
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// color("black") up(thick/2) linear_extrude(height=0.1) {
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// back(d)
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// dashed_stroke(circle(r=pr), width=strokewidth, closed=true);
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@ -368,10 +388,10 @@ function _inherit_gear_thickness(thickness) =
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// thickness = 6;
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// hole = 3;
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// rack_base = 12;
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// d12 = gear_dist(circ_pitch,teeth1=n1,teeth2=n2);
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// d13 = gear_dist(circ_pitch,teeth1=n1,teeth2=n3);
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// d14 = gear_dist(circ_pitch,teeth1=n1,teeth2=n4);
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// d1r = gear_dist(circ_pitch,teeth1=n1,teeth2=0);
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// d12 = gear_dist(circ_pitch=circ_pitch,teeth1=n1,teeth2=n2);
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// d13 = gear_dist(circ_pitch=circ_pitch,teeth1=n1,teeth2=n3);
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// d14 = gear_dist(circ_pitch=circ_pitch,teeth1=n1,teeth2=n4);
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// d1r = gear_dist(circ_pitch=circ_pitch,teeth1=n1,teeth2=0);
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// a1 = $t * 360 / n1;
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// a2 = -$t * 360 / n2 + 180/n2;
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// a3 = -$t * 360 / n3 - 3*90/n3;
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@ -381,7 +401,7 @@ function _inherit_gear_thickness(thickness) =
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// color("#77f") right(d13) zrot(a3) spur_gear(circ_pitch,n3,thickness,hole);
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// color("#fc7") left(d14) zrot(a4) spur_gear(circ_pitch,n4,thickness,hole,hide=n4-3);
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// color("#ccc") fwd(d1r) right(circ_pitch*$t)
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// rack(pitch=circ_pitch,teeth=n5,thickness=thickness,height=rack_base,anchor=CENTER,orient=BACK);
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// rack(pitch=circ_pitch,teeth=n5,thickness=thickness,height=rack_base,anchor=CENTER);
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// Example: Helical gears meshing with non-parallel shafts BROKEN
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// ang1 = 30;
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// ang2 = 10;
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@ -406,7 +426,7 @@ function _inherit_gear_thickness(thickness) =
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// Example(Anim,Frames=36,VPT=[0,0,0],VPR=[55,0,25],VPD=375): Planetary Gear Assembly
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// rteeth=56; pteeth=16; cteeth=24;
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// circ_pitch=5; thick=10; pa=20;
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// gd = gear_dist(circ_pitch, cteeth, pteeth);
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// gd = gear_dist(circ_pitch=circ_pitch, cteeth, pteeth);
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// ring_gear(
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// circ_pitch=circ_pitch,
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// teeth=rteeth,
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@ -662,7 +682,7 @@ module spur_gear(
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// module the_gear(profile_shift=0) {
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// $fn=72;
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// pr = pitch_radius(circ_pitch,teeth);
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// mr = gear_dist(circ_pitch,teeth,profile_shift1=profile_shift,teeth2=0);
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// mr = gear_dist(circ_pitch=circ_pitch,teeth,profile_shift1=profile_shift,teeth2=0);
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// back(mr) {
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// spur_gear2d(circ_pitch, teeth, shaft_diam=shaft, profile_shift=profile_shift);
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// up(0.1) color("black")
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@ -680,7 +700,7 @@ module spur_gear(
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// Example(2D): Planetary Gear Assembly
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// rteeth=56; pteeth=16; cteeth=24;
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// circ_pitch=5; pa=20;
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// gd = gear_dist(circ_pitch, cteeth,pteeth);
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// gd = gear_dist(circ_pitch=circ_pitch, cteeth,pteeth);
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// ring_gear2d(
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// circ_pitch=circ_pitch,
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// teeth=rteeth,
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@ -1144,21 +1164,21 @@ module rack(
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d = _dedendum(pitch, clearance, profile_shift);
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l = teeth * trans_pitch;
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anchors = [
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named_anchor("adendum", [0,0,a], BACK),
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named_anchor("adendum-left", [-l/2,0,a], LEFT),
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named_anchor("adendum-right", [ l/2,0,a], RIGHT),
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named_anchor("adendum-front", [0,-thickness/2,a], DOWN),
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named_anchor("adendum-back", [0, thickness/2,a], UP),
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named_anchor("dedendum", [0,0,-d], BACK),
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named_anchor("dedendum-left", [-l/2,0,-d], LEFT),
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named_anchor("dedendum-right", [ l/2,0,-d], RIGHT),
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named_anchor("dedendum-front", [0,-thickness/2,-d], DOWN),
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named_anchor("dedendum-back", [0, thickness/2,-d], UP),
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named_anchor("adendum", [0,a,0], UP),
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named_anchor("adendum-left", [-l/2,a,0], LEFT),
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named_anchor("adendum-right", [ l/2,a,0], RIGHT),
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named_anchor("adendum-front", [0,a,-thickness/2], BACK),
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named_anchor("adendum-back", [0, a, thickness/2], FRONT),
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named_anchor("dedendum", [0,-d,0], UP),
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named_anchor("dedendum-left", [-l/2,-d,0], LEFT),
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named_anchor("dedendum-right", [ l/2,-d,0], RIGHT),
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named_anchor("dedendum-front", [0,-d,-thickness/2], BACK),
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named_anchor("dedendum-back", [0,-d, thickness/2,], FRONT),
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];
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size = [l, thickness, 2*height];
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size = [l, 2*height, thickness];
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attachable(anchor,spin,orient, size=size, anchors=anchors) {
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right(gear_travel)
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skew(sxy=tan(helical)) xrot(90) {
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skew(sxz=tan(helical)) {
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linear_extrude(height=thickness, center=true, convexity=teeth*2) {
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rack2d(
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pitch = pitch,
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@ -1229,21 +1249,21 @@ function rack(
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vnf = linear_sweep(path, height=thickness, anchor="origin", orient=FWD),
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m = product([
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right(gear_travel),
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if (helical) skew(sxy=tan(helical)),
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if (helical) skew(sxz=tan(helical)),
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]),
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out = apply(m, vnf),
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size = [l, thickness, 2*height],
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size = [l, 2*height, thickness],
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anchors = [
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named_anchor("adendum", [0,0,a], BACK),
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named_anchor("adendum-left", [-l/2,0,a], LEFT),
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named_anchor("adendum-right", [ l/2,0,a], RIGHT),
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named_anchor("adendum-front", [0,-thickness/2,a], DOWN),
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named_anchor("adendum-back", [0, thickness/2,a], UP),
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named_anchor("dedendum", [0,0,-d], BACK),
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named_anchor("dedendum-left", [-l/2,0,-d], LEFT),
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named_anchor("dedendum-right", [ l/2,0,-d], RIGHT),
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named_anchor("dedendum-front", [0,-thickness/2,-d], DOWN),
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named_anchor("dedendum-back", [0, thickness/2,-d], UP),
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named_anchor("adendum", [0,a,0], UP),
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named_anchor("adendum-left", [-l/2,a,0], LEFT),
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named_anchor("adendum-right", [ l/2,a,0], RIGHT),
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named_anchor("adendum-front", [0,a,-thickness/2], BACK),
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named_anchor("adendum-back", [0, a, thickness/2], FRONT),
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named_anchor("dedendum", [0,-d,0], UP),
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named_anchor("dedendum-left", [-l/2,-d,0], LEFT),
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named_anchor("dedendum-right", [ l/2,-d,0], RIGHT),
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named_anchor("dedendum-front", [0,-d,-thickness/2], BACK),
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named_anchor("dedendum-back", [0,-d, thickness/2,], FRONT),
|
||||
]
|
||||
) reorient(anchor,spin,orient, size=size, anchors=anchors, p=out);
|
||||
|
||||
|
|
@ -2778,50 +2798,57 @@ function worm_gear_thickness(circ_pitch, teeth, worm_diam, worm_arc=60, crowning
|
|||
|
||||
|
||||
// Function: gear_dist()
|
||||
// Synopsis: Returns the distance between two gear centers.
|
||||
// Synopsis: Returns the distance between two gear centers for spur gears or parallel axis helical gears.
|
||||
// Topics: Gears, Parts
|
||||
// See Also: worm(), worm_gear(), pitch_radius(), outer_radius()
|
||||
// Usage:
|
||||
// dist = gear_dist(pitch, teeth1, teeth2, [helical=], [profile_shift=], [pressure_angle=]);
|
||||
// dist = gear_dist(mod=, teeth=, [helical=], [profile_shift=], [pressure_angle=]);
|
||||
// dist = gear_dist([mod=|diam_pitch=|circ_pitch=], teeth1, teeth2, [helical], [profile_shift1], [profile_shift2], [pressure_angle=]);
|
||||
// Description:
|
||||
// Calculate the distance between the centers of two gears with parallel axes, taking into account
|
||||
// profile shifting and helical angles.
|
||||
// Calculate the distance between the centers of two spur gears gears or helical gears with parallel axes,
|
||||
// taking into account profile shifting and helical angle. You can give the helical angle as either positive or negative.
|
||||
// Set the tooth count to zero to use a rack.
|
||||
// Arguments:
|
||||
// pitch = The circular pitch, or distance between teeth around the pitch circle, in mm. Default: 5
|
||||
// teeth1 = Total number of teeth in the first gear. If given 0, we assume this is a rack or worm.
|
||||
// teeth2 = Total number of teeth in the second gear. If given 0, we assume this is a rack or worm.
|
||||
// ---
|
||||
// helical = The absolute value of the helical angle (from vertical) of the teeth on the gears. Default: 0
|
||||
// helical = The value of the helical angle (from vertical) of the teeth on the two gears (either sign). Default: 0
|
||||
// profile_shift1 = Profile shift factor x for the first gear. Default: 0
|
||||
// profile_shift2 = Profile shift factor x for the second gear. Default: 0
|
||||
// pressure_angle = The pressure angle of the gear.
|
||||
// --
|
||||
// diam_pitch = The diametral pitch, or number of teeth per inch of pitch diameter. Note that the diametral pitch is a completely different thing than the pitch diameter.
|
||||
// mod = The metric module/modulus of the gear, or mm of pitch diameter per tooth.
|
||||
// Example(2D):
|
||||
// pitch=5; teeth1=7; teeth2=24;
|
||||
// d = gear_dist(pitch, teeth1, teeth2);
|
||||
// spur_gear2d(pitch, teeth1, gear_spin=-90);
|
||||
// right(d) spur_gear2d(pitch, teeth2, gear_spin=90-180/teeth2);
|
||||
// Example: Non-parallel Helical Gears BROKEN
|
||||
// //pitch=5; teeth1=15; teeth2=24; ha1=45; ha2=30; thick=10;
|
||||
// //d = mesh_radius(pitch, teeth1, teeth2, helical=ha1);
|
||||
// //mr2 = mesh_radius(pitch, teeth2, helical=ha2);
|
||||
// //left(mr1) spur_gear(pitch, teeth1, helical=ha1, thickness=thick, gear_spin=-90);
|
||||
// //right(mr2) xrot(ha1+ha2) spur_gear(pitch, teeth2, helical=ha2, thickness=thick, gear_spin=90-180/teeth2);
|
||||
// Example(2D): Disable Auto Profile Shifting on the Small Gear
|
||||
// pitch=5; teeth1=7; teeth2=24;
|
||||
// d = gear_dist(pitch, teeth1, teeth2, profile_shift1=0);
|
||||
// spur_gear2d(pitch, teeth1, profile_shift=0, gear_spin=-90);
|
||||
// right(d) spur_gear2d(pitch, teeth2, gear_spin=90-180/teeth2);
|
||||
// circ_pitch = distance between teeth around the pitch circle.
|
||||
// pressure_angle = The pressure angle of the gear.
|
||||
// Example(2D): Spur gears (with automatic profile shifting on both)
|
||||
// circ_pitch=5; teeth1=7; teeth2=24;
|
||||
// d = gear_dist(circ_pitch=circ_pitch, teeth1, teeth2);
|
||||
// spur_gear2d(circ_pitch, teeth1, gear_spin=-90);
|
||||
// right(d) spur_gear2d(circ_pitch, teeth2, gear_spin=90-180/teeth2);
|
||||
// Example: Helical gears (with auto profile shifting on one of the gears)
|
||||
// circ_pitch=5; teeth1=7; teeth2=24; helical=37;
|
||||
// d = gear_dist(circ_pitch=circ_pitch, teeth1, teeth2, helical);
|
||||
// spur_gear(circ_pitch, teeth1, helical=helical, gear_spin=-90);
|
||||
// right(d) spur_gear(circ_pitch, teeth2, helical=-helical, gear_spin=-90-180/teeth2);
|
||||
// Example(2D): Disable Auto Profile Shifting on the smaller gear
|
||||
// circ_pitch=5; teeth1=7; teeth2=24;
|
||||
// d = gear_dist(circ_pitch=circ_pitch, teeth1, teeth2, profile_shift1=0);
|
||||
// spur_gear2d(circ_pitch, teeth1, profile_shift=0, gear_spin=-90);
|
||||
// right(d) spur_gear2d(circ_pitch, teeth2, gear_spin=90-180/teeth2);
|
||||
// Example(2D): Manual Profile Shifting
|
||||
// pitch=5; teeth1=7; teeth2=24; ps1 = 0.5; ps2 = -0.2;
|
||||
// d = gear_dist(pitch, teeth1, teeth2, profile_shift1=ps1, profile_shift2=ps2);
|
||||
// spur_gear2d(pitch, teeth1, profile_shift=ps1, gear_spin=-90);
|
||||
// right(d) spur_gear2d(pitch, teeth2, profile_shift=ps2, gear_spin=90-180/teeth2);
|
||||
|
||||
// circ_pitch=5; teeth1=7; teeth2=24; ps1 = 0.5; ps2 = -0.2;
|
||||
// d = gear_dist(circ_pitch=circ_pitch, teeth1, teeth2, profile_shift1=ps1, profile_shift2=ps2);
|
||||
// spur_gear2d(circ_pitch, teeth1, profile_shift=ps1, gear_spin=-90);
|
||||
// right(d) spur_gear2d(circ_pitch, teeth2, profile_shift=ps2, gear_spin=90-180/teeth2);
|
||||
// Example(2D): Profile shifted gear and a rack
|
||||
// mod=3; teeth=8;
|
||||
// d = gear_dist(mod=mod, teeth, 0);
|
||||
// rack2d(mod=mod, teeth=5, height=9);
|
||||
// back(d) spur_gear2d(mod=mod, teeth=teeth, gear_spin=180/teeth);
|
||||
// Example(VPT=[-3.47556,6.39564,2.5111],VPR=[64.8,0,214.7],VPD=113.336): Profile shifted helical gear and rack
|
||||
// mod=3; teeth=8; helical=29;
|
||||
// d = gear_dist(mod=mod, teeth, 0, helical);
|
||||
// rack(mod=mod, teeth=5, height=9, helical=helical);
|
||||
// back(d) spur_gear(mod=mod, teeth=teeth, helical=-helical, gear_spin=180/teeth);
|
||||
function gear_dist(
|
||||
circ_pitch,
|
||||
teeth1,
|
||||
teeth2,
|
||||
helical=0,
|
||||
|
|
@ -2829,12 +2856,13 @@ function gear_dist(
|
|||
profile_shift2,
|
||||
pressure_angle=20,
|
||||
diam_pitch,
|
||||
mod,
|
||||
pitch
|
||||
circ_pitch,
|
||||
mod
|
||||
) =
|
||||
|
||||
assert(all_nonnegative([teeth1,teeth2]),"Must give nonnegative values for teeth")
|
||||
assert(teeth1>0 || teeth2>0, "One of the teeth counts must be nonzero")
|
||||
let(
|
||||
mod = circular_pitch(pitch, mod, circ_pitch, diam_pitch)/PI,
|
||||
mod = module_value(mod=mod,circ_pitch= circ_pitch, diam_pitch=diam_pitch),
|
||||
profile_shift1 = default(profile_shift1, teeth1>0? auto_profile_shift(teeth1,pressure_angle,helical) : 0),
|
||||
profile_shift2 = default(profile_shift2, teeth2>0? auto_profile_shift(teeth2,pressure_angle,helical) : 0)
|
||||
)
|
||||
|
|
@ -2842,8 +2870,7 @@ function gear_dist(
|
|||
:
|
||||
let(
|
||||
pa_eff = _working_pressure_angle(teeth1,profile_shift1,teeth2,profile_shift2,pressure_angle,helical),
|
||||
pa_transv = atan(tan(pressure_angle)/cos(helical)),
|
||||
fda= echo(pa_eff=pa_eff,pa_transv=pa_transv,mod*(teeth1+teeth2)*cos(pa_transv)/cos(pa_eff)/cos(helical)/2)
|
||||
pa_transv = atan(tan(pressure_angle)/cos(helical))
|
||||
)
|
||||
mod*(teeth1+teeth2)*cos(pa_transv)/cos(pa_eff)/cos(helical)/2;
|
||||
|
||||
|
|
@ -2863,46 +2890,111 @@ function _working_pressure_angle(teeth1,profile_shift1, teeth2, profile_shift2,
|
|||
|
||||
|
||||
// Function: gear_dist_skew()
|
||||
// Synopsis: Returns the distance between two helical gear centers.
|
||||
// Usage:
|
||||
// Synopsis: Returns the distance between two helical gear centers with skew axes.
|
||||
// Topics: Gears, Parts
|
||||
// See Also: gear_dist(), worm(), worm_gear(), pitch_radius(), outer_radius()
|
||||
// Usage:
|
||||
// dist = gear_dist_skew(mod, teeth1, profile_shift1, helical1, teeth2, profile_shift2, helical2, [pressure_angle=]);
|
||||
// dist = gear_dist_skew(diam_pitch=, teeth1=, [profile_shift1=], [helical1=], teeth2=, [profile_shift2=], [helical2=], [pressure_angle=]);
|
||||
// dist = gear_dist_skew(circ_pitch=, teeth1=, [profile_shift1=], [helical1=], teeth2=, [profile_shift2=], [helical2=], [pressure_angle=]);
|
||||
// dist = gear_dist_skew(mod=|diam_pitch=|circ_pitch=, teeth1, teeth2, helical1, helical2, [profile_shift1], [profile_shift2], [pressure_angle=]
|
||||
// Description:
|
||||
// Calculate the distance between two helical gears that mesh with non-parallel axes, taking into account
|
||||
// profile shift and the helical angles.
|
||||
function gear_dist_skew(mod,teeth1,profile_shift1=0, helical1, teeth2, profile_shift2=0, helical2, pressure_angle=20, circ_pitch, diam_pitch) =
|
||||
// profile shift and the helical angles.
|
||||
// Arguments:
|
||||
// teeth1 = Total number of teeth in the first gear. If given 0, we assume this is a rack or worm.
|
||||
// teeth2 = Total number of teeth in the second gear. If given 0, we assume this is a rack or worm.
|
||||
// helical1 = The helical angle (from vertical) of the teeth on the first gear.
|
||||
// helical1 = The helical angle (from vertical) of the teeth on the second gear.
|
||||
// profile_shift1 = Profile shift factor x for the first gear. Default: 0
|
||||
// profile_shift2 = Profile shift factor x for the second gear. Default: 0
|
||||
// --
|
||||
// diam_pitch = The diametral pitch, or number of teeth per inch of pitch diameter. Note that the diametral pitch is a completely different thing than the pitch diameter.
|
||||
// mod = The metric module/modulus of the gear, or mm of pitch diameter per tooth.
|
||||
// circ_pitch = distance between teeth around the pitch circle.
|
||||
// pressure_angle = The pressure angle of the gear.
|
||||
// Example: Non-parallel Helical Gears (without any profile shifting)
|
||||
// circ_pitch=5; teeth1=15; teeth2=24; ha1=45; ha2=30; thick=10;
|
||||
// d = gear_dist_skew(circ_pitch=circ_pitch, teeth1, teeth2, helical1=ha1, helical2=ha2);
|
||||
// left(d/2) spur_gear(circ_pitch, teeth1, helical=ha1, thickness=thick, gear_spin=-90);
|
||||
// right(d/2) xrot(ha1+ha2) spur_gear(circ_pitch, teeth2, helical=ha2, thickness=thick, gear_spin=90-180/teeth2);
|
||||
function gear_dist_skew(teeth1,teeth2,helical1,helical2,profile_shift1,profile_shift2,pressure_angle=20, mod, circ_pitch, diam_pitch) =
|
||||
assert(all_nonnegative([teeth1,teeth2]),"Must give nonnegative values for teeth")
|
||||
assert(teeth1>0 || teeth2>0, "One of the teeth counts must be nonzero")
|
||||
let(
|
||||
profile_shift1 = default(profile_shift1, auto_profile_shift(teeth1,pressure_angle,helical1)),
|
||||
profile_shift2 = default(profile_shift2, auto_profile_shift(teeth2,pressure_angle,helical2)),
|
||||
mod = module_value(circ_pitch=circ_pitch, diam_pitch=diam_pitch, mod=mod),
|
||||
pa_normal_eff = _working_normal_pressure_angle_skew(teeth1,profile_shift1,helical1,teeth2,profile_shift2,helical2,pressure_angle),
|
||||
dist_adj = 0.5*(teeth1/cos(helical1)^3+teeth2/cos(helical2)^3)*(cos(pressure_angle)/cos(pa_normal_eff)-1),
|
||||
ff=echo(y=dist_adj,pa_normal_eff)
|
||||
dist_adj = 0.5*(teeth1/cos(helical1)^3+teeth2/cos(helical2)^3)*(cos(pressure_angle)/cos(pa_normal_eff)-1)
|
||||
)
|
||||
mod*(teeth1/2/cos(helical1)+teeth2/2/cos(helical2)+dist_adj);
|
||||
|
||||
|
||||
function _working_normal_pressure_angle_skew(teeth1,profile_shift1,helical1, teeth2, profile_shift2, helical2, pressure_angle) =
|
||||
let(
|
||||
inv = function(a) tan(a) + a*PI/180,
|
||||
rhs = 2*(profile_shift1+profile_shift2)/(teeth1/cos(helical1)^3+teeth2/cos(helical2)^3)*tan(pressure_angle) + inv(pressure_angle),
|
||||
pa_eff_normal = root_find(function (x) inv(x)-rhs, 5, 75)
|
||||
inv = function(a) tan(a) + a*PI/180,
|
||||
rhs = 2*(profile_shift1+profile_shift2)/(teeth1/cos(helical1)^3+teeth2/cos(helical2)^3)*tan(pressure_angle) + _invol(pressure_angle),
|
||||
pa_eff_normal = root_find(function (x) _invol(x)-rhs, 5, 75)
|
||||
)
|
||||
pa_eff_normal;
|
||||
|
||||
|
||||
// Function: gear_skew_angle()
|
||||
// Usage:
|
||||
// ang = gear_skew_angle(....
|
||||
// ang = gear_skew_angle(mod=|diam_pitch=|circ_pitch=, teeth1, teeth2, helical1, helical2, [profile_shift1], [profile_shift2], [pressure_angle=]
|
||||
// Description:
|
||||
// Compute the correct skew angle between the axes of two helical gears.
|
||||
function gear_skew_angle(mod,teeth1,profile_shift1,helical1,teeth2, profile_shift2,helical2,pressure_angle=20)=
|
||||
profile_shift1==0 && profile_shift2==0 ? helical1+helical2
|
||||
:
|
||||
// Compute the correct skew angle between the axes of two profile shifted helical gears. When profile shifting is zero
|
||||
// this angle is simply the sum of the helical angles of the two gears.
|
||||
|
||||
// Example:
|
||||
// circ_pitch=5; teeth1=5; teeth2=7; ha1=45; ha2=30; thick=10;
|
||||
|
||||
|
||||
circ_pitch=5; teeth1=10; teeth2=14; ha1=45; ha2=30; thick=10;
|
||||
d = .4+gear_dist_skew(circ_pitch=circ_pitch, teeth1, teeth2, helical1=ha1, helical2=ha2);//,profile_shift1=0,profile_shift2=0)+2;
|
||||
d0 = gear_dist_skew(circ_pitch=circ_pitch, teeth1, teeth2, helical1=ha1, helical2=ha2,profile_shift1=0,profile_shift2=0);
|
||||
echo(d=d,d0);
|
||||
ang = gear_skew_angle(circ_pitch=circ_pitch, teeth1, teeth2, helical1=ha1, helical2=ha2);
|
||||
echo(ang=ang);
|
||||
color_overlaps()
|
||||
{
|
||||
// left(d/2) spur_gear(circ_pitch, teeth1, helical=ha1, thickness=thick, gear_spin=-90);
|
||||
// right(d/2) xrot(ang) spur_gear(circ_pitch, teeth2, helical=ha2, thickness=thick, gear_spin=90-180/teeth2);
|
||||
left(d/2) spur_gear(circ_pitch, teeth1, helical=ha1, thickness=thick);
|
||||
right(d/2) xrot(ang) spur_gear(circ_pitch, teeth2, helical=ha2, thickness=thick,gear_spin=180/teeth2);
|
||||
}
|
||||
|
||||
|
||||
|
||||
|
||||
/*
|
||||
mod=3; teeth1=15; ha1=20; ps1=0.4;
|
||||
teeth2=24; ha2=30; ps2=0.2;
|
||||
thick=20;
|
||||
|
||||
d = gear_dist_skew(mod=mod, teeth1, teeth2, ha1, ha2, ps1,ps2);
|
||||
echo(d=d);
|
||||
ang = gear_skew_angle(mod=mod, teeth1, teeth2, ha1, ha2, ps1, ps2);
|
||||
echo(ang=ang);
|
||||
color_overlaps(){
|
||||
left(d/2) spur_gear(mod=mod, teeth=teeth1, helical=ha1, thickness=thick, gear_spin=-90,profile_shift=ps1);
|
||||
right(d/2) xrot(ang) spur_gear(mod=mod, teeth=teeth2, helical=ha2, thickness=thick, gear_spin=90-180/teeth2,profile_shift=ps2);
|
||||
}
|
||||
*/
|
||||
|
||||
function gear_skew_angle(teeth1,teeth2,helical1,helical2,profile_shift1,profile_shift2,pressure_angle=20, mod, circ_pitch, diam_pitch) =
|
||||
assert(all_nonnegative([teeth1,teeth2]),"Must give nonnegative values for teeth")
|
||||
assert(teeth1>0 || teeth2>0, "One of the teeth counts must be nonzero")
|
||||
let(
|
||||
//mod = circular_pitch(pitch, mod, circ_pitch, diam_pitch)/PI,
|
||||
a = gear_dist_skew(mod,teeth1,profile_shift1,helical1,teeth2, profile_shift2,helical2,pressure_angle),
|
||||
profile_shift1 = default(profile_shift1, auto_profile_shift(teeth1,pressure_angle,helical1)),
|
||||
profile_shift2 = default(profile_shift2, auto_profile_shift(teeth2,pressure_angle,helical2))
|
||||
,fe=echo(ingsaps=profile_shift1,profile_shift2)
|
||||
)
|
||||
// profile_shift1==0 && profile_shift2==0 ? helical1+helical2
|
||||
// :
|
||||
let(
|
||||
mod = module_value(mod=mod, circ_pitch=circ_pitch, diam_pitch=diam_pitch),
|
||||
a = gear_dist_skew(mod=mod,teeth1,teeth2,helical1,helical2,profile_shift1,profile_shift2,pressure_angle=pressure_angle),
|
||||
b = gear_dist_skew(mod=mod,teeth1,teeth2,helical1,helical2,0,0,pressure_angle=pressure_angle),
|
||||
fdase= echo(a=a,b=b),
|
||||
d1 = 2*pitch_radius(mod=mod,teeth=teeth1,helical=helical1),
|
||||
d2 = 2*pitch_radius(mod=mod,teeth=teeth2,helical=helical2),
|
||||
dw1 = 2*a*d1/(d1+d2),
|
||||
|
|
@ -2913,8 +3005,6 @@ function gear_skew_angle(mod,teeth1,profile_shift1,helical1,teeth2, profile_shif
|
|||
beta1+beta2;
|
||||
|
||||
|
||||
|
||||
|
||||
// Function: get_profile_shift()
|
||||
// Usage:
|
||||
// total_shift = get_profile_shift(desired,....)
|
||||
|
|
|
|||
Loading…
Reference in a new issue