Watch Gear Calculator

A Gear Calculator App for Watchmakers by Margolis Watch Co.

“A particularly useful tool for watch restorers. A great idea!”

Dr Rebecca Struthers

Stuck and in need of help? Please follow the below instructions. If you're still having issues, please email david@margoliswatch.co.uk.

Watch Gear Calculator helps watchmakers diagnose watch gear train issues. It should be used in conjunction with a Timegrapher with a Trace function.

If a trace analysis shows a significant change in amplitude at a regular frequency, Watch Gear Calculator will help you identify the likely cause. You have to input the number of teeth for each wheel and leaves for each pinion and press calculate. Whichever result matches the frequency of issues seen on the trace will reveal where the problem is.

For example, your trace shows a reduction in amplitude every five minutes. This matches a 00:05:00 result for the Great Wheel Tooth Passage. Meaning the issue is caused by the meshing of the Great Wheel teeth with the Second Wheel pinion.

Instructions for Use

Step 1 - Open Watch Gear Calculator

Open the app (or press and hold “start over” if a calculation is already open). This is the initial setup screen.

Step 2 - Check Existing Calculations

Tap “Manage Saved” and check to see if your movement has already been calculated. See if it’s listed under “Shared Calculations” on the right. It’s early days for this feature so you may not find many calculations listed yet. But if it is there, you can just hit the triangle button next to it and it will load up. You can then skip to Interpreting Calculations below.

If it’s not there, just hit the back button to get back to the initial setup screen.

Watch Gear Calculator Share Calculations

Step 3 - Prepare the Calculator

You are presented with 3 questions.

2nd Wheel rotation rate. If you know what it is (it’s usually 1 turn per hour) set to “Yes”. Only answer yes if you are 100% sure what it is. If you’re not sure, set to “Unknown”.

4th Wheel rotation rate. As the 2nd wheel, set to “Yes” if you know the rotation rate. (It’s often 1 turn per minute). Only set to yes if you are 100% sure. Otherwise, set to “Unknown”.

Movement’s overall BPH. Set the frequency of the watch movement. You will most likely know this. But if you’re not sure, you can set it to unknown and it will be calculated. However, you will need to know at least one of the RPMs in order to proceed.

Once everything is set you can tap the “Create New” button.

TIP - Giving the calculator more information will mean fewer teeth to count and it will allow the calculator to validate your inputs and check for mistakes.

Step 4 - Enter Required Information

You will now see the main calculator screen. It has been set up according to your answers in the previous step.

You now need to fill in all the white boxes. Carefully count the required teeth and pinion leaves.

TIP 1 - If your phone has a macro lens, take a close-up picture of the wheel. Then you can zoom in and count teeth more easily.

TIP 2 - Research your movement on Google. You might find information on tooth counts is already out there. Check service manuals as they might have drawings which you can zoom in on and count teeth.

If you told the calculator you knew RPMs for 2nd and / or 4th wheels, you will see they have been filled in with their default values used for most watch movements. If they are wrong, you can change them. It’s important these are correct. If you are not sure, touch and hold “start over” and go back to Step 3.

If some boxes are dark grey and say “will calculate”, you can skip these. They will be automatically filled in.

Watch Gear Calculator Enter Details Screen

Step 5 - Calculate and Interpret

Simply hit calculate to get your results. If any boxes turn red, they contain errors. You can correct them and try again. See below how to interpret your results.

Step 6 - Save

Enter the name of the movement at the top of the calculator and hit save to save your calculation.

Step 7 - Share

Please share your calculation to help others! Tap “My Calcs”. On the left you will see all your own calculations. On the right, you will see the public repository of calculations shared by others. To share your calculation, tap the share button next to it. You will be prompted to read and agree to our Terms and Conditions. Then, you can enter your name if you would like to be credited. Just leave this blank if you want to be anonymous.

Once submitted, all calculations are moderated before being added to the public repository. So it may take a while before your calculation appears. Thank you in advance to everyone that shares their calculations!

How To Interpret Calculations

You will mostly be relying on Turn Time, Tooth Passage and Hunting Tooth Frequency to diagnose issues. These are all displayed in hours, minutes, seconds and milliseconds. Gear Ratio and RPM are also provided for completeness.

Turn Time - The time it takes for a wheel to complete a full turn. An abrupt drop in amplitude matching this frequency indicates a damaged tooth or pinion leaf. A gradual wave matching this frequency indicates a bent pivot or an out-of-true wheel.

Tooth passage - The time it takes for a given tooth to engage and disengage with a pinion leaf. If this shows on the trace, the problem is likely to be caused by incorrectly meshing teeth. This is very common between the Great Wheel and the Second Wheel and often indicates worn bushes causing the barrel to not be fully upright.

FHT - This is the "Hunting Tooth Frequency" of the wheel and its meshing pinion. This is an unusual calculation not well known in horology. It is commonly used in gear vibration analysis for cars. But it is extremely useful in watchmaking too. If both a tooth and a pinion leaf were damaged, this is the frequency at which they will make contact. This might be seen on a trace as a seemingly random drop in amplitude every so often. Or even a watch that stops for no obvious reason. If the time between stopping matches a hunting tooth frequency, then you have identified the cause.

HCF - A close relation of FHT, this is the "Highest Common Factor" between a gear and the pinion it meshes with. It can offer valuable insights into the design and characteristics of a gear train. It is the largest possible integer that can divide both gear-tooth-count and meshing pinion-leaf-count without leaving a remainder.

To understand why this is useful, first consider the notion of a “gear cycle”. This is the routine the gears perform with various leaves meshing with various teeth until all possible combinations are completed. Then the cycle repeats from the beginning.

Consider a wheel meshing with a pinion, where one of the pinion leaves is inked and will always leave a mark on the gear tooth it meshes with.

If the HCF is 1, every single wheel tooth will be marked by the ink after a cycle.

If the HCF is 5, every fifth tooth will be marked after a cycle.

If the HCF is 10, every tenth tooth will be marked… And so on.

A low HCF indicates a long and complex gear cycle but more evenly distributed wear. A higher HCF indicates a shorter and simpler cycle but with some tooth and leaf pairs meshing more frequently than others thus creating uneven wear.

An HCF of 1 implies perfect wear distribution, which is more commonly found between Great and Second gears, which are under heavier loads and more prone to wear. This helps extend the wheel and meshing pinion’s lifespan. However, the cycles can last for 100 hours or more making it difficult to find potential issues or use regulation to compensate for imperfections.

In areas with lower forces and reduced wear concerns, you’re more likely to find an HCF that matches the pinion leaf count (which is the highest HCF possible). For instance, a wheel with 90 teeth turning at 1 RPM and engaging with a pinion with 9 leaves would have an HCF of 9. This means the gear set’s cycle also lasts for 1 RPM. The advantage is that it minimizes variables. Or to put it another way, there is as little as possible to go wrong. The wheels only need to engage perfectly for their 1 minute cycle to know they will remain perfect always.

HCF in watch gear trains can provide interesting insights into the design of the gear train and any compromises that may have been made. It’s also interesting to observe how HCF values vary between manufacturers and over time.

by David Margolis