This is a ‘beginners guide’ to gear cutting and it concerns imperial gears not metric, as the numbers are slightly different when it comes to modules, as seen later.

The 1943 Machinery’s Handbook (11th edition) has approx. 250 pages on gears, gear drives and chains etc. so it is quite a deep subject. Here we concentrate on straight spur gears, as seen on the periphery of the two traction engine gears seen below. The smaller gear has a 12 DP, and the larger 8 DP.

DP is shorthand for Diametrical Pitch and is the number of teeth that will fit on 1" of the circumference of the PCD or Pitch Circle Diameter.

Gears are used to give a positive and uniform drive from one shaft to another. With alternative methods such as V-belts, there is always the possibility of slip. Also, by having different sizes of interlocking gears, shaft speeds can be different.

‘Non-Round’ Gears

There are various ‘non round’ gears, but they are rare and are only used in special cases. There are:

1. •Square Gears.
   

2. •Oval Gears.
   

3. •Gears with gaps in them.
   

Here we concentrate on round gears.

The Involute Gears

Two involute gears, the left driving the right: Blue arrows show the contact forces between them (1) downward force applied by the left gear and (2) upward resistance by the right gear. The force line (or line of action) runs along the long leg of dashed blue line which is a tangent common to both base circles.

Animation at this link:

https://en.wikipedia.org/wiki/Involute_gear#/media/File:Involute_wheel.gif

On pre-Second World War machinery gears, the pressure angle was 14.5°, whereas after that time, the pressure angle is 20°.

The base diameter is the diameter of the base cylinder from which the involute portion of a tooth profile is generated.

Gears Of Infinite Radius

A gear of infinite radius is called a rack. If a piece of string is taken off a rack it would come off at an angle of 14.5° to the vertical. The talk continued referring to 14.5° angles (20° angles gave slightly different measurements).

A 14.5° gear can usually be identified as it is a fairly ‘stubby’ gear. A 20° gear is thicker at the base and thinner at the tip. Nowadays it’s best to assume the gears are 20°.

Other Types Of Gears.

Other than Spur Gears there are:

1. • Bevel Gears.
   

2. • Worm Gears.
   

3. • Hypoid Gears.
   

Making Gears ~ Determination Of Tip Diameter

There are a number of equations that are required to find out what diameter, and what root depth is required for the gear teeth. To cut an Imperial gear, one of the first of the formulae required is:

Number Of Teeth + 2/DP = Tip Diameter Of Gear

The 2 is added to the number of teeth to allow for the fact that the teeth are above the base diameter of the gear.

The base diameter is the diameter of the base cylinder from which the involute portion of a tooth profile is generated. The formula is relevant for both imperial and metric gears.

If the gear to be cut is metric, the formula is:

(Number Of Teeth + 2) x pitch/π  = Tip Diameter Of Gear 

Where the Module = pitch/π The bigger the module the bigger the tooth.

Making Gears ~ Why Was The Pressure (Pitch) Angle Changed From 14.5° to 20° ?

The change was made in Pressure Angle when gear teeth started failing under high loads, such as in aero engines during the Second World War. By changing the angle from 14.5° to 20°, the tooth tips were made slightly thinner in width while the tooth root widths were made slightly thicker.

As machined gears have been made for at least the last 150 years, things have been modified over time. During the Second World War, Rolls Royce found that the gear teeth were wearing quickly on their Merlin engines. They did a few tests and found that the teeth were flexing under load. So, rather than changing the shape, they took about two or three thou off the tips, and that stopped the flexing and wear on the teeth. A Merlin engine normally operated for about 500 to 600 hours before overhaul. Before the modification they were failing around 200 hours.

Making gears - cutters

Involute Imperial gear cutters are normally about 4 DP up to 100 DP (or more). For Imperial gears, the lower the DP number, the bigger the gear and the thicker the teeth.

Below is an Imperial No. 4 12 DP cutter, a Metric No.3 M2 cutter (where M is the module ~ see previous page) and some smaller cutters, one of which is 8 DP and homemade:

As mentioned before, DP numbers vary from about 4 DP up to 100 DP, but a 4 DP would be rarely used except for some massive machinery. For normal workshop use, DPs will range from about 16 DP to about 64 DP.

The gear cutters are expensive to buy, for example, the 12 DP cutter above is well over £100, and eight are required for a full set. These go from 12 teeth up to 135. That also only applies to a single DP, so if the gears needing to be cut have different tooth thickness, this is all adding up in cost. Hence  some of the HOBS are home made. The HOB cutters will cut any number of gear teeth required.

If metric gears are required, then the same number of cutters may be required (with the same expense).

Making Gears ~ Tools Required

1. •A Lathe to Turn A Blank On.
   

2. •A Milling Machine To Use The Cutter.
   

3. •A Dividing Head.
   

4. •Cutter.
   

If a 20 DP gear (or below) is being cut, fairly robust machinery is required. For example, the full depth of each tooth on the traction engine gear shown above was cut through in one operation**. As can be seen, there is quite a distance from the centre of the gear (where the blank was held) and the outer edge of the tooth. For this reason, the outer periphery of the gear wheel was supported while the gear was cut. In this case Peter rounded metal ball was used to take the thrust from the cutter. Such was the force that the ball created small indents in the wheel. This is further illustration of how robust the machinery has to be.

** Some people cut through half the depth of each tooth on the first revolution of the gear wheel, and then the other half when the gear wheel is rotated again. This can lead to errors.

Making Gears ~ Operations

The first operation is to turn the blank to size. The outside diameter of the blank is determined by the formula for Imperial gears.

The bore of the blank must be concentric with the outside circumference. If a chuck is used in turning the blank, there is always the chance that when the blank is transferred to the dividing head, there may be a small eccentricity. There are two ways to avoid that:

1.The Dividing Head with a ‘Myford Nose’, so if a Myford lathe is being used to turn the blank, then the chuck can be screwed off the lathe and screwed on the ‘nose’ with no problem.

2.if a blank is being turned in a collet on the lathe, a mandrel can be made which screws on to the Dividing Head as shown below, and the blank will remain concentric.

When the smallest gear is being cut, if the blank is on the mandrel or in a chuck, then you have to make sure there is plenty of space between the chuck or the arbor of the mandrel and the Dividing Head so that the cutter doesn’t cut into the mandrel or even the Dividing Head itself.

Making Gears ~ The Dividing Head.

This is the most important tool used for cutting gears. The Dividing Head consists of a base and a head ideally an all-purpose tool that can be used to cut bevel gears by swiveling the head.

To make this dividing head a 40:1 worm gear (with 40 teeth on the wheel) was bought. The worm wheel goes on the Mandrel shaft, and the worm itself is on the rotation axis of the Sliding Arm. When the Arm is turned, the spindle rotates in the ratio of the worm wheel. Most commercial worm gears, especially second-hand ones will be 40:1 ratio. Most model engineering worm gears are 60:1 and some are actually 90:1.

For this Dividing Head, to find out how far to rotate the Arm for each gear tooth cut, 40 is divided by the number of teeth on the gear.

If the Arm is rotated once on this Dividing Head, the spindle turns 1/40th or 9°. Rarely is a number of teeth required on a gear not divisible into 40.

Making Gears ~ Setting Up The Dividing Head On The Bed Of The Vertical Milling Machine

Before the Dividing Head is attached to the bed of the vertical milling machine, the machine must be cleaned down, lubricated and a check made that all adjustments are as minimal as possible. This is all to prevent the cutter ‘grabbing’ the work and twisting the Dividing Head.

The spindle must also must be horizontal and parallel with the table movement. To check this, a 2MT test bar was made which is a tight fit in the Dividing Head as shown:

This helps with the positioning of the cutter which also needs to be at the centre of the mandrel

Making Gears ~ How Does The Dividing Head Operate?

For most gears cut, the Sliding Arm will either be turned once, or two turns and a bit, or a part turn.

Some Examples:

1. •If 20 teeth are being cut 40 / 20 = 2. This means the Arm is turned two full turns for each tooth (18° mandrel spindle rotation).
   

2. •The detent on the end of the arm attached to the central worm gear locates into the same hole in the plate each time a gear tooth is cut. It’s rare to have that few teeth on a gear, though.
   

3. •If 30 teeth are cut on a gear 40 / 30 = 1turn + 1/3rd turn.
   

4. •If 45 teeth are cut on a gear 40 / 45 = 8/9th turn
   

5. •For 64 Teeth 40 / 64 = 5/8th turn.
   

To use all these numbers, there are a number of rows of holes in the Dividing Plate. On the plate on the previous page there are 13 rows. Each row has a different number of holes in it.

To use the plate, this table was made.

The first column shows the number of teeth on the gear. The calculations are then done to work out the fractions of the Arm turns required. The bigger the fraction, it is expedient to make sure that there are three or four gears to be cut that can use the same row of holes.

As mentioned before, attached to the worm gear spindle at the centre of the plate is an Arm, at the end of which is the detent. At the back end of the detent is a small rod which goes into the holes. It is a fairly good fit. When rotating the Arm, it is easy to determine if the right hole is located; if the Arm approaches close to the required hole, it can be slightly tapped and it will drop in. The sliding arm allows the detent to operate across the available holes.

When making the next cut, the starting point is always the hole for the cut just made. To make this easier to reference, there are two sector arms which are movable of themselves. A sector arm is moved so it touches the detent in its current hole position. The hole needed for the next cut is then counted to (not including the current hole position), and the Arm is rotated so that the detent almost locates into it. It is then gently tapped into the hole.

The sector arm is then moved around until it touches the detent in its new hole position. This makes sure that the position of the detent is known at any one time. It’s a good idea to mark the plate at the current sector arm position with a piece of chalk so there is a good reference to go back to. There are a lot of precautions that are needed to be taken when cutting a gear.

An example is given on how to count holes between cut positions: Referring to the table above, if a 64 teeth gear is being cut, each position is 15 holes along from the current position on row 24 on the plate. 15 holes are counted from the current position (which doesn’t include the current hole). It is also important not to accidentally move to an adjacent row.

When cutting gears, it always pays to cut the smallest gear first, because if the largest is started and there is a mistake, that’s a lot of time and material spent.

In Summary

o Before making the first cut, clean the milling machine thoroughly before mounting the Dividing Head.

o Check the Dividing Head and make sure it is clamped down firmly on the bed of the Milling Machine.

o Using a test bar, align the Dividing Head with the bed of Milling machine so the mandrel or chuck will be parallel with the bed.

o The mandrel used for holding the blank during cutting (or in the case of the Myford, the chuck holding the blank) is screwed firmly onto the Diving Head’s ‘nose’.

o A tightening screw is used to secure either onto the ‘nose’.

o In the case of the mandrel, put the blank on the mandrel, put the spacers on and then tighten it up. Make sure it is TIGHT, otherwise a ‘spiral gear’ may result.

o With short mandrels a free end support is not required. For longer mandrels a jack/prop can be made.

o The cutter is then adjusted in height so it’s horizontal centre line aligns with the horizontal centre line through the mandrel. The blank should be in a position on the mandrel to provide adequate clearance between the cutter edge and the Dividing Head ‘nose’ or chuck.

o The next thing to know is how far into the blank the cutter needs to move to make the cut. The depth of cut is normally marked on the cutters.

Modern cutters normally have four pieces of information on them:

i) The D.P.

ii) A number from 1 to 8.

iii) The number of teeth it’s supposed to cut.

iv) The depth of feed, (D+F) that is how far into the blank the cutter needs to

be fed. In the case of the cutter shown 0.18” = 4.6 mm.

Because they are modern cutters the angle (20°) is not notified on the cutter.

The only time this is important is when a replacement gear is being cut for a very old machine.

o Wind the Y-axis handle of the mill until the cutter almost touches the feeler gauge placed between the cutter and the blank. Move the cutter until it just ‘nips’ the feeler gauge. This is the start of the cut.

o Remove the feeler gauge. The operator should not start cutting until they are clear of the blank!

o Engage the cutter and wind it in the thickness of the feeler gauge plus the depth stated on the cutter.

o The latest gears are made so they give a little bit of clearance at the bottom of the tooth.

o There are two parts to a gear tooth:

The outer Addendum

The inner Dedendum

The Dedendum is normally slightly longer than the

Addendum. The two together give the depth of feed.

o TAKE A REST before making any more cuts!

o When restarting operations, lock the workshop door behind you, as you need all the concentration without disturbance.

Turn off the phone and turn on some music because cutting gears is the most tedious job you can do. For example, Making three traction engine gears as shown erlier. Each gear has 57 teeth. There’s a smaller gear that runs off it with 10 to 12 teeth. In all that’s 800 teeth cut all at once in the workshop for eight hours a day for three months!

o Before starting, everything is checked again, making sure everything is tightened and the depth is right for cutting.

o The coolant is then turned on.

o The cutter speed is then selected. With the cutters displayed on the evening, 200 rev/min is recommended for starting off. Depending on the direction of cut, make sure the cutter is cutting not ‘rubbing’. A simple thing that can easily be overlooked.

o Cutting towards the strongest part of the mandrel (not the tip) is recommmended.

o For a large gear like the traction engine gear, a support was required on the outer periphery, inside the teeth, especially as it had been thinned down and it had a tendency to flex.

o Whichever way the cutter turns, make sure the cutter is cutting ‘up-hill’. If it cuts ‘down-hill” the cutter will ‘grab the blank and pull everything apart. With ‘up-hill’ cutting a large piece is removed first then the pieces get thinner and thinner.

o Winding the cutter in can either be done manually or with the use of an auto-feed.

o As soon as cutting starts, listen to what is happening. If it doesn’t sound right, stop the machine immediately.

o Teeth aren’t being cut, just the space between them.

o With a horizontal cutter cutting into a blank, it is difficult to know what the space looks like until the cutter is pulled back.

o After making the first cut, the Dividing Head Arm is rotated to the next hole position. If the detent moves beyond the required hole, always wind back at least half a turn. This is why the previous advice to chalk mark the position of the sector arm is so important. Remember to remove the existing chalk mark when moving to the next hole position.

o The only way to tell if you’ve gone wrong with a lot of teeth already cut on the gear, is if a tooth is too thick or too thin.

o Say you’ve cut 30 teeth, and the Arm has gone round, the detent will not be at the starting point. Rotate the Arm until the detent is in the starting hole, and start cutting again. If you hear any cutting noise, you have got it wrong. That’s another way of checking.

A Practical Tip.

Do not worry if you cut too deep by 2 or 3 thou, the tooth will be slightly thinner, but practically it doesn’t matter, as the gear will run. If the teeth are slightly thicker, the gears will not run on the right centres.