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add backlash section
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Adrian Mariano
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1 changed files with 76 additions and 1 deletions
77
gears.scad
77
gears.scad
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@ -409,6 +409,73 @@ function _inherit_gear_thickness(thickness) =
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// color("lightblue")
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// fwd(d)
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// spur_gear(mod=mod, teeth=teeth1, profile_shift=ps1,gear_spin=-ang*360/teeth1,helical=-30,thickness=15);
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// Subsection: Backlash (Fitting Real Gears Together)
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// You may have noticed that the example gears shown fit together perfectly, making contact on both sides of
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// the teeth. Real gears need space between the teeth to prevent the gears from jamming, to provide space
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// for lubricant, and to provide allowance for fabrication error. This space is called backlash. Excessive backlash
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// is undesirable, especially if the drive reverses frequently.
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// .
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// Backlash can be introduced in two ways. One is to make the teeth narrower, so the gaps between the teeth are
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// larger than the teeth. Alternatively, you can move the gears farther apart than their ideal spacing.
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// Backlash can be measured in several different ways. The gear modules in this library accept a backlash
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// parameter which specifies backlash as a circular distance at the pitch circle. The modules narrow
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// the teeth by the amount specified, which means the spaces between the teeth grow larger. Of course, if you apply
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// backlash to both gears then the total backlash in the system is the combined amount from both gears.
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// Usually it is best to apply backlash symmetrically to both gears, but if one gear is very small it may
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// be better to place the backlash entirely on the larger gear to avoid weakening the teeth of the small gear.
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// Figure(2D,Big,VPT=[4.5244,64.112,0.0383045],VPR=[0,0,0],VPD=48.517,NoAxes): Backlash narrows the teeth by the specified length along the pitch circle. Below a very large backlash appears, with half of the backlash on either side of the tooth.
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// teeth1=20;
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// mod=5;
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// r1 = pitch_radius(mod=mod,teeth=teeth1,helical=40);
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// bang=4/(2*PI*r1) * 360 ;
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// zrot(-180/teeth1*.5){
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// color("white")
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// dashed_stroke(arc(r=r1, n=30, angle=[80,110]), width=.05);
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// spur_gear2d(mod=mod, teeth=teeth1,backlash=0+.5*0,profile_shift="auto",gear_spin=180/teeth1*.5,helical=40);
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// %spur_gear2d(mod=mod, teeth=teeth1,backlash=4+.5*0,profile_shift="auto",gear_spin=180/teeth1*.5,helical=40);
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// color("black")stroke(arc(n=32,r=r1,angle=[90+bang/2,90]),width=.1,endcaps="arrow2");
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// }
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// color("black")back(r1+.25)right(5.5)text("backlash/2",size=1);
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// Figure(2D,Med,VPT=[0.532987,50.0891,0.0383045],VPR=[0,0,0],VPD=53.9078): Here two gears appear together with a more reasonable backlash applied to both gears.
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// teeth1=20;teeth2=33;
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// mod=5;
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// ha=0;
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// r1 = pitch_radius(mod=mod,teeth=teeth1,helical=ha);
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// r2=pitch_radius(mod=mod,teeth=teeth2,helical=ha);
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// bang=4/(2*PI*r1) * 360 ;
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//
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// back(r1+pitch_radius(mod=mod,teeth=teeth2,helical=ha)){
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// spur_gear2d(mod=mod, teeth=teeth2,backlash=.5*0,helical=ha,gear_spin=-180/teeth2/2);
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// %spur_gear2d(mod=mod, teeth=teeth2,backlash=1,helical=ha,gear_spin=-180/teeth2/2);
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// }
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// {
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// spur_gear2d(mod=mod, teeth=teeth1,backlash=0+.5*0,profile_shift=0,gear_spin=180/teeth1*.5,helical=ha);
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// %spur_gear2d(mod=mod, teeth=teeth1,backlash=1+.5*0,profile_shift=0,gear_spin=180/teeth1*.5,helical=ha);
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// *color("white"){
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// dashed_stroke(arc(r=r1, n=30, angle=[80,110]), width=.05);
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// back(r1+r2)
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// dashed_stroke(arc(r=r2, n=30, angle=[-80,-110]), width=.05);
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// }
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// //color("black")stroke(arc(n=32,r=r1,angle=[90+bang/2,90]),width=.1,endcaps="arrow2");
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// }
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// Figure(2D,Med,VPT=[0.532987,50.0891,0.0383045],VPR=[0,0,0],VPD=53.9078): Here the same gears appear with backlash applied using the `backlash` parameter to {{gear_dist()}} to shift them apart.
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// teeth1=20;teeth2=33;
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// mod=5;
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// ha=0;
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// r1 = pitch_radius(mod=mod,teeth=teeth1,helical=ha);
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// r2 = pitch_radius(mod=mod,teeth=teeth2,helical=ha);
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// bang=4/(2*PI*r1) * 360 ;
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// shift = 1 * cos(ha)/2/tan(20);
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// back(r1+pitch_radius(mod=mod,teeth=teeth2,helical=ha)){
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// zrot(-180/teeth2/2){
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// %back(shift)spur_gear2d(mod=mod, teeth=teeth2,backlash=0,helical=ha);
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// spur_gear2d(mod=mod, teeth=teeth2,backlash=0,helical=ha);
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// }
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// }
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// zrot(180/teeth1*.5){
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// %fwd(shift)spur_gear2d(mod=mod, teeth=teeth1,backlash=0+.5*0,profile_shift=0,helical=ha);
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// spur_gear2d(mod=mod, teeth=teeth1,backlash=0,profile_shift=0,helical=ha);
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// }
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// Section: Gears
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@ -2869,6 +2936,8 @@ function pitch_radius(
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pitch
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) =
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let( circ_pitch = circular_pitch(pitch, mod, circ_pitch, diam_pitch) )
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assert(is_finite(helical))
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assert(is_finite(circ_pitch))
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circ_pitch * teeth / PI / 2 / cos(helical);
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@ -3108,6 +3177,7 @@ function worm_gear_thickness(circ_pitch, teeth, worm_diam, worm_arc=60, crowning
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// internal1 = first gear is an internal (ring) gear. Default: false
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// internal2 = second gear is an internal (ring) gear. Default: false
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// pressure_angle = The pressure angle of the gear.
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// backlash = Add extra space to produce the specified backlash
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// Example(2D,NoAxes): Spur gears (with automatic profile shifting on both)
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// circ_pitch=5; teeth1=7; teeth2=24;
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// d = gear_dist(circ_pitch=circ_pitch, teeth1, teeth2);
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@ -3147,6 +3217,7 @@ function gear_dist(
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profile_shift2,
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internal1=false,
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internal2=false,
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backlash = 0,
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pressure_angle=20,
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diam_pitch,
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circ_pitch,
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@ -3177,7 +3248,7 @@ function gear_dist(
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pa_eff = _working_pressure_angle(teeth1,profile_shift1,teeth2,profile_shift2,pressure_angle,helical),
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pa_transv = atan(tan(pressure_angle)/cos(helical))
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)
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mod*(teeth1+teeth2)*cos(pa_transv)/cos(pa_eff)/cos(helical)/2;
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mod*(teeth1+teeth2)*cos(pa_transv)/cos(pa_eff)/cos(helical)/2 + backlash*cos(helical)/2/tan(pressure_angle);
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function _invol(a) = tan(a) - a*PI/180;
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@ -3253,6 +3324,7 @@ function _working_normal_pressure_angle_skew(teeth1,profile_shift1,helical1, tee
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// Function: gear_skew_angle()
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// Usage:
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// ang = gear_skew_angle(teeth1, teeth2, helical1, helical2, [profile_shift1], [profile_shift2], [pressure_angle=]
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// Synopsis: Returns corrected skew angle between two profile shifted helical gears.
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// Description:
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// Compute the correct skew angle between the axes of two profile shifted helical gears. When profile shifting is zero, or when one of
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// the gears is a rack, this angle is simply the sum of the helical angles of the two gears. But with profile shifted gears, a small
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@ -3301,6 +3373,7 @@ function gear_skew_angle(teeth1,teeth2,helical1,helical2,profile_shift1,profile_
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// Function: get_profile_shift()
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// Usage:
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// total_shift = get_profile_shift(mod=|diam_pitch=|circ_pitch=, desired, teeth1, teeth2, [helical], [pressure_angle=],
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// Synopsis: Returns total profile shift needed to achieve a desired spacing between two gears
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// Description:
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// Compute the total profile shift, split between two gears, needed to place those gears with a specified separation.
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// If the requested separation is too small, returns NaN. Note that the profile shift returned may also be impractically
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@ -3395,6 +3468,7 @@ function auto_profile_shift(teeth, pressure_angle=20, helical=0, min_teeth, prof
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// Function: gear_shorten()
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// Usage:
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// shorten = gear_shorten(teeth1, teeth2, [helical], [profile_shift1], [profile_shift2], [pressure_angle=]);
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// Synopsis: Returns the tip shortening parameter for profile shifted parallel axis gears.
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// Description:
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// Compute the gear tip shortening factor for gears that have profile shifts. This factor depends on both
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// gears in a pair and when applied, will results in teeth that meet the specified clearance distance.
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@ -3446,6 +3520,7 @@ function gear_shorten(teeth1,teeth2,helical=0,profile_shift1="auto",profile_shif
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// Function: gear_shorten_skew()
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// Usage:
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// shorten = gear_shorten(teeth1, teeth2, helical1, helical2, [profile_shift1], [profile_shift2], [pressure_angle=]);
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// Synopsis: Returns the tip shortening parameter for profile shifted skew axis helical gears.
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// Description:
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// Compute the gear tip shortening factor for skew axis helical gears that have profile shifts. This factor depends on both
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// gears in a pair and when applied, will results in teeth that meet the specified clearance distance.
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