Since this is a fairly long post, I'm going post the first part and the remainder as an attached PDF file.
Gear Cutting – Home Engineering Style.
It is possible using AutoCad or similar drafting package to develop you own custom (as well as standard) gear profiles.
From this you can also make your own cutters and make the necessary compromises to suit.
Involute Gear Profiles.
I am only going to deal with metric (Module) involute gears and I’ll leave it up to you to figure out that diameteral and circular pitch are merely variations of the same theme (metric or imperial).
A basic gear profile represents the circular tooth profile that would be generated from a “Rack” vis :-
A MAAG gear shaper in fact planes gears by using a rack shaped cutter – with each cut the “rack” is advanced and the gear rotated – in so doing it generates a true involute curve.
In my diagram above the green and red lines indicate the position of the cutter flanks as viewed from the perspective of the rotating gear in 2° rotation increments.
(A real MAAG cutter would have slightly taller teeth and corner radii to cut the clearance at the tooth root.)
The involute curvature is a constantly changing radius and is therefore difficult to make accurately (other than by generating using a MAAG or FELLOWS gear shaper – or using appropriately profiled cutters or hobs.
However in most cases a simple radius does very well – but there are limits.
The greater the number of teeth – the better the fit of a simple radius.
Typically for 16 teeth and over you will have no problem, 12 and lower tends to be problematical.
For smaller numbers of teeth you will find increasing incidence of interference and the need to use multiple radii which is somewhat outside the realm of home machining.
That said, for this tutorial I am going to make a pair of Module 1.5mm with the pinion being only 8 teeth and spur wheel 16 teeth. So the 8T is going to be problematical.
This was to repair a ride-on toy for my grandson who was delighted with the result (regardless of the slightly “grumbly” fit up of the gear. (Just to prove Grandad can fix anything.)
Basic Metric Gear Nomenclature.
For a standard Module gear the module is the height of the tooth above and below the centerline or pitch circle diameter – in this case 1.5mm so a tooth is approximately 2xM or 3mm in this case – there is also clearance which in almost all gear calculations is 0.138M or in this case ±0.2mm.
The pitch circle diameter is the module times the number of teeth (in this case Ø24.0) to which must be added a further two modules for the outside diameter (in this case Ø27.0)
The pressure angle for most gears is 20° (prior to WWII 14½° was commonly used – the greater the angle the greater the thrust between axles as the gears try to drive themselves apart – so in an attempt to limit this they tried to stay below the friction angle to eliminate this thrust – but with ballbearings and better lubrication and bearing materials this became less of an issue and 20° was adopted for its greater tooth strength and lesser interference problems with small tooth counts.)
What I Intend To Show.
I am going to show how to develop the tooth profiles using AutoCad (or similar).
Firstly I am going to approximate the spur wheel profile to the nearest cutter radius we might have to hand in order to make a cutter.
Then I am going to use the resultant compromised tooth profile of the spur wheel to generate the pinion gear profile and once again choose an approximate and convenient radius to make the cutter for the pinion.
Whilst I have done this to demonstrate home engineering capability, the method can be used to accurately determine wire cutting paths for wire cut EDM and the method can also be used for generating non-standard gears – for example for matching centerlines that do not equate to the normal pitch or making a gear with a deliberately oversized PCD vis :-
The above small pinion gear used in Slotcar racing – leaves far too little material to the Ø2.0mm driveshaft bore so the pitch circle is made larger – results in a non-standard tooth profile – but it does work.
Note: True involute gears “roll” over each other – there is no “sliding” of the gear faces.
When you deviate as above you do introduce sliding and therefore friction and wear problems – but it does work (see later).
First Step – Generate Spur Wheel Profile.
The illustration below demonstrates how to develop the tooth profiles using any CAD package.
Firstly draw the circular outlines of your gear and draw the rack adjacent to it vis:-
Copy a single flank (without clearance) from the middle of the rack crest to the centerline of your circular gear (In blue above).
Since this is a 16T gear, each tooth is going to occupy 22½°
We need to array rectangularly left and right at a pitch commensurate with a convenient angle.
I chose 2° of gear rotation which equates to 0.41887902mm of rack movement.
Next array a number of these lines to left and right (at this pitch) – I change the colour to keep track.
You could of course choose to array the flanks in say 0.5mm increments but then the rotation of each will be 2.387324° - you don’t want to have to type that in at each rotate command – so stick to single digit degrees and let the array command take care of the horrible divisions.
Next rotate each of these lines individually about the gear center - the first green line 2°, the second 4° the third 6° and so on- Repeat with the red lines -2° and so on.
Repeat until you have sufficient lines defining the profile.
Sooner or later the lines start to disappear away from the profile indicating where the tooth starts to disengage.
So now you have this :-
Next draw a three point arc – typically starting at the outer diameter intersect, the pitch line intersect and ending at the nearest inside line termination (black line above) vis:-
On measuring this radius I get R4.33mm – note gap – radius does not perfectly emulate involute – don’t worry at this stage we will (attempt to) fix that with the pinion.
Since I don’t have a R4.33 cutter (although I could spin one down in a tool and cutter grinder) I go for R4.5 or Ø9.0 milling cutter that I will use to form my hob (see later).
Next I redraw the arc using a SER (start, end, radius) method to draw the curve starting at the OD intersect plus any point you fancy and add the radius – this sounds a bit hit and miss – but play with it until you like the look of the fit – don’t worry if at this stage that it crosses some of our projected rack lines (interference) we will deal with that problem with the pinion.
Next add root and tip radii (if you want to) and complete the spur gear drawing.
For the rest, open the PDF.........
Gear Cutting – Home Engineering Style.
It is possible using AutoCad or similar drafting package to develop you own custom (as well as standard) gear profiles.
From this you can also make your own cutters and make the necessary compromises to suit.
Involute Gear Profiles.
I am only going to deal with metric (Module) involute gears and I’ll leave it up to you to figure out that diameteral and circular pitch are merely variations of the same theme (metric or imperial).
A basic gear profile represents the circular tooth profile that would be generated from a “Rack” vis :-
A MAAG gear shaper in fact planes gears by using a rack shaped cutter – with each cut the “rack” is advanced and the gear rotated – in so doing it generates a true involute curve.
In my diagram above the green and red lines indicate the position of the cutter flanks as viewed from the perspective of the rotating gear in 2° rotation increments.
(A real MAAG cutter would have slightly taller teeth and corner radii to cut the clearance at the tooth root.)
The involute curvature is a constantly changing radius and is therefore difficult to make accurately (other than by generating using a MAAG or FELLOWS gear shaper – or using appropriately profiled cutters or hobs.
However in most cases a simple radius does very well – but there are limits.
The greater the number of teeth – the better the fit of a simple radius.
Typically for 16 teeth and over you will have no problem, 12 and lower tends to be problematical.
For smaller numbers of teeth you will find increasing incidence of interference and the need to use multiple radii which is somewhat outside the realm of home machining.
That said, for this tutorial I am going to make a pair of Module 1.5mm with the pinion being only 8 teeth and spur wheel 16 teeth. So the 8T is going to be problematical.
This was to repair a ride-on toy for my grandson who was delighted with the result (regardless of the slightly “grumbly” fit up of the gear. (Just to prove Grandad can fix anything.)
Basic Metric Gear Nomenclature.
For a standard Module gear the module is the height of the tooth above and below the centerline or pitch circle diameter – in this case 1.5mm so a tooth is approximately 2xM or 3mm in this case – there is also clearance which in almost all gear calculations is 0.138M or in this case ±0.2mm.
The pitch circle diameter is the module times the number of teeth (in this case Ø24.0) to which must be added a further two modules for the outside diameter (in this case Ø27.0)
The pressure angle for most gears is 20° (prior to WWII 14½° was commonly used – the greater the angle the greater the thrust between axles as the gears try to drive themselves apart – so in an attempt to limit this they tried to stay below the friction angle to eliminate this thrust – but with ballbearings and better lubrication and bearing materials this became less of an issue and 20° was adopted for its greater tooth strength and lesser interference problems with small tooth counts.)
What I Intend To Show.
I am going to show how to develop the tooth profiles using AutoCad (or similar).
Firstly I am going to approximate the spur wheel profile to the nearest cutter radius we might have to hand in order to make a cutter.
Then I am going to use the resultant compromised tooth profile of the spur wheel to generate the pinion gear profile and once again choose an approximate and convenient radius to make the cutter for the pinion.
Whilst I have done this to demonstrate home engineering capability, the method can be used to accurately determine wire cutting paths for wire cut EDM and the method can also be used for generating non-standard gears – for example for matching centerlines that do not equate to the normal pitch or making a gear with a deliberately oversized PCD vis :-
The above small pinion gear used in Slotcar racing – leaves far too little material to the Ø2.0mm driveshaft bore so the pitch circle is made larger – results in a non-standard tooth profile – but it does work.
Note: True involute gears “roll” over each other – there is no “sliding” of the gear faces.
When you deviate as above you do introduce sliding and therefore friction and wear problems – but it does work (see later).
First Step – Generate Spur Wheel Profile.
The illustration below demonstrates how to develop the tooth profiles using any CAD package.
Firstly draw the circular outlines of your gear and draw the rack adjacent to it vis:-
Copy a single flank (without clearance) from the middle of the rack crest to the centerline of your circular gear (In blue above).
Since this is a 16T gear, each tooth is going to occupy 22½°
We need to array rectangularly left and right at a pitch commensurate with a convenient angle.
I chose 2° of gear rotation which equates to 0.41887902mm of rack movement.
Next array a number of these lines to left and right (at this pitch) – I change the colour to keep track.
You could of course choose to array the flanks in say 0.5mm increments but then the rotation of each will be 2.387324° - you don’t want to have to type that in at each rotate command – so stick to single digit degrees and let the array command take care of the horrible divisions.
Next rotate each of these lines individually about the gear center - the first green line 2°, the second 4° the third 6° and so on- Repeat with the red lines -2° and so on.
Repeat until you have sufficient lines defining the profile.
Sooner or later the lines start to disappear away from the profile indicating where the tooth starts to disengage.
So now you have this :-
Next draw a three point arc – typically starting at the outer diameter intersect, the pitch line intersect and ending at the nearest inside line termination (black line above) vis:-
On measuring this radius I get R4.33mm – note gap – radius does not perfectly emulate involute – don’t worry at this stage we will (attempt to) fix that with the pinion.
Since I don’t have a R4.33 cutter (although I could spin one down in a tool and cutter grinder) I go for R4.5 or Ø9.0 milling cutter that I will use to form my hob (see later).
Next I redraw the arc using a SER (start, end, radius) method to draw the curve starting at the OD intersect plus any point you fancy and add the radius – this sounds a bit hit and miss – but play with it until you like the look of the fit – don’t worry if at this stage that it crosses some of our projected rack lines (interference) we will deal with that problem with the pinion.
Next add root and tip radii (if you want to) and complete the spur gear drawing.
For the rest, open the PDF.........
