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How to Replicate and 3D Print Gears

Hello Machine Bros!
Do you want to know How to Replicate and 3D Print Gears? In this article, we will show you everything about copying, replicating and 3D printing spur and helical gears using SolidWorks.

So Machine Bros, let’s get started!

Note: This article is designed to show you how to copy or replicate gears already created. If what you want is to create or design a gear from scratch, we recommend you to check out Easy Way of How to Design Gears.
How to Replicate and 3D Print Gears
How to Replicate and 3D Print Gears

What is a Gear?

The first thing you should be clear about is that a gear according to Wikipedia is “… a rotating machine part having cut teeth or, in the case of a cogwheel, inserted teeth (called cogs), which mesh with another toothed part to transmit torque.”

Gears are mechanisms that we can find in all kinds of devices and machines, there are as small as those used in personal mechanical watches and as large as those used in industrial machines.

Spur Gear and Helical Gear

How to replicate gears
Helical gears
How to 3D print gears
Spur Gears

The spur and helical gears are the two most common types of gears.

Why choose one or the other? There are generally three salient factors that are taken into account in making this decision:

  • Axial load is the most important factor, helical gears produce axial load and spur gears do not.

  • The second factor is noise, spur gears at high speeds are much louder than helical gears.

  • The third and final factor is the way the gear teeth come into contact, spur gears do not come into contact “smoothly and gradually” while helical gears do come into contact “smoothly and gradually”, allowing the helical gears to be better to transmit force and speed gradually. In addition, it should be noted that, if we had a spur gear and a helical gear of the same dimensions and similar characteristics, the teeth of the helical gear would have a greater contact area due to their inclination, therefore, its teeth would be more resistant. It is also necessary to take into account that a spur gear is cheaper and easier to manufacture than a helical gear.

For the reasons mentioned above, helical gears are often chosen for private vehicles and spur gears for racing vehicles.

In a racing vehicle, noise does not matter so much, in addition, it is better not to have axial loads since it reduces the need to use mechanical devices that reduce axial friction (for example, thrust bearings), therefore, simple bearings can be used, reducing overall weight, an important issue in racing vehicles.

In private vehicles, it is preferable to reduce noise and obtain a more “gradual and smooth” power transmission, thus gaining more comfort. For this reason, it is that helical gears are usually used in vehicles intended for “common” driving.

Gear's ecuations

In applications where large loads are required to be moved or transmitted, helical gears are also often used, since they allow a smoother power transmission, this added to the point mentioned before, that if we had a spur gear and a helical gear of the same dimensions and similar characteristics, the teeth of the helical gear would have a greater contact area due to their inclination, therefore, its teeth would be more resistant.

IMPORTANT NOTE: In the formulas and calculations we will work with the following units, the units of length in millimeters (mm) and the angles in sexagesimal degree (deg) (°)

Spur Gear Measurement (Data Collection)

For the videos, remember to activate the subtitles.
Spur Gear Measurement

The first thing you should keep in mind is that for two spur gears to mesh well, it is necessary that both have the same Module (M).

Taking this into account, you must think that the gear was designed by a person, that most likely used some CAD software, and in most CAD software there are already standard modules.

So, we have to redesign the gears thinking about discovering which module they used to design it. In addition, we must bear in mind that the gear will be 3D printed, a factor that we will take into account.

In our case, we will use SolidWorks CAD software, which will ask us for:

  • Module (M)
  • The number of teeth (N)
  • Gear width (W)
  • Hole diameter (Hole)
  • The pressure angle that in general, we will always select 20° since it is the most used.

Spur Gear Calculation

Calculations and Formulas for Spur Gears

For the calculation of spur gears, we will only need a formula with which we will obtain the approximate module (Ma).

Later in SolidWorks we will choose the module that most closely resembles this value, the module in SolidWorks will be our real module (M).

Gear Modulus Formula

Approximate Value = Ma

Number of teeth = N

Outside Diameter (Measured on the gear) = De

Gear width (Measured on gear) = W

The formula allows a certain margin of error. It is always possible that there are errors in the measurement, for this reason, we recommend measuring several times.

Also, you should keep in mind that the gear teeth may be worn, therefore, the measurement of the external diameter (De) may not be very accurate.

Spur Gear Design

Spur Gear Design in Solidworks

The only thing that remains is to enter in SolidWorks the measured and calculated values to obtain our gear.

After having created the gear we can carry out extra operations that the CAD software allows, for example, extrusions, cuts, among others.

It is important that after creating the gear you evaluate and compare the measurements provided by SolidWorks with the measurements made physically.

IMPORTANT NOTE: Replicating the helical gear of this set of gears will be a more complicated job, this is because the approximate modulus (Ma) calculated does not resemble the pre-established modules by SolidWorks, for this reason we will begin by explaining how to replicate a simpler helical gear, which its module is quite close to one of the modules preset by SolidWorks. In this way it will be easier for you to understand the procedure used to replicate the helical gears, once this is understood, we will proceed to replicate the more complex helical gear.

Spur Gear 3D Printing

3D printing of a Spur Gear
Spur Gear 3D Printing

The spur gear is 3D printed together with the helical gear.

To see the video of how we print the combination of both gears, continue reading the article, you will find the video in the section “3D printing of the complex helical gear + the spur gear

Helical Gear Measurement (Data Collection)

Helical Gear Measurement

The first thing that you should keep in mind is that for two helical gears to mesh well, it is necessary that both have:

  • The same Modulus (M)
  • Helix angle (A)
  • And helix directions (one gear must have a “right” helix direction and the other “left”).And

Taking all this into account, you must think that the gear was designed by a person, that person most likely has used some CAD software, and in most CAD software there are already standard modules.

That is why we have to redesign the gears thinking about discovering which module they used to design it and we must also bear in mind that the gear will be printed in 3D, so when redesigning it is a factor that we will take into account.

In our case we will use SolidWorks CAD software, which will ask us for:

  • Module (M)
  • Number of teeth (N)
  • Gear width (W)
  • Hole diameter (Hole)
  • Helix angle (A )
  • The direction of the propeller (“Right” or “Left”)
  • Pressure angle that we will generally always select 20° since it is the most used.

Another thing you should keep in mind is that the helix angles (A) most used in this type of gears range from 15 degrees to 30 degrees, the reasonable limit being 45 degrees (integer values, that is, without decimals).

The auxiliary verification value (Vi) is only an extra measure that will help us later to have more ways to verify that our replica is as close as possible to the original gear, dimensionally speaking.

Helical Gear Calculation

Calculations and Formulas for Helical Gears

For the calculation of this type of gears it is necessary to use more formulas.

The first one will help us to calculate the measured helix angle (Am), which will give us an approximation of the real helix angle (A).

MEasure Helix Angle Ecuation of a Gear
How to calculate the helix angle of a gear

Helix angle measured = Am

Length or tooth length (It is measured in the gear) = L

Gear width (Measured on gear) = W

Small variations in the value of the length or length of the tooth (L) considerably affect the result, usually, it is not so easy or accurate to measure (L).

The following formula to use is to calculate the approximate module (Ma), later in SolidWorks, we will choose the module that most closely resembles this value, the module in SolidWorks will be our real module (M).

Approximate module calculation of a gear

Approximate Module = Ma

Number of teeth = N

Helix angle measured = Am

Outside Diameter (Measured on the gear) = De

The formula allows a certain margin of error, it is always possible that there are errors in the measurement, for this reason, we advise measuring several times, also that you must bear in mind that the gear teeth could be worn. For this reason, the measurement of the external diameter (De) may not be very accurate.

Remember that the measured helix angle (Am) is an approximation since small variations in the value of the length or length of the tooth (L) considerably affect the result, normally it is not so easy or accurate to measure (L).

Finally, the next step is a little more complex to understand, in the following formula we will enter angle values in (A) until we obtain the (De) (External diameter) result closest to the (De) measured.

The value of (A) that gives us the closest (De) value to the measured (De) will be our Real Helix Angle (A) value. Remember to use the value of the Real Modulus (M) obtained in SolidWorks in the formula.

In other words, we will test by entering several helix angles (A) into the formula, the helix angle that results in the closest value to the external diameter that we measure (De), this will be our final helix angle (A).

In the video, you can understand it more easily.

The most commonly used helix angles in this type of gear range from 15 degrees to 30 degrees, the reasonable limit being 45 degrees (integer values, that is, without decimals).

Test with values close to the measured Angle (Am) using integer values (without decimals), for example, 15°, 16°, 17°, etc.

Outside diameter calculation of a gear

Real Module (Obtained from SolidWorks) = M

Number of teeth = N

Real helix angle = A

Outside Diameter (Measured on the gear) = De

Helical Gear Design

The only thing that remains is to enter in SolidWorks the measured and calculated values to obtain our gear.

After having created the gear, we could carry out extra operations that the CAD software allows, for example, extrusions, cuts, among others.

It is important that after creating the gear you evaluate and compare the measurements provided by SolidWorks with the measurements made physically.

IMPORTANT NOTE: Remember that only this time will reverse the direction of the helix of the replica only to be able to demonstrate how the replica engages with the original gear, but to make a replica this step is not necessary, rather it is useless because the replica would not be capable of engaging with the rest of the original gears that made up the mechanism.

Helical Gear 3D Printing

Helical Gear 3D Printing

Complex Helical Gear Measurement (Data Collection)

Complex Helical Gear Measurement

For the moment, in the measurement of this helical gear we will apply everything we have learned and mentioned previously.

Complex Helical Gear Calculation

Calculations and Formulas of a Complex Helical Gear

This is where we will find the problem, the result of the approximate modulus (Ma) gives us 0.78. SolidWorks has default modules 0.75 and 0.8, meaning that we are far from both values.

If we design the gear by choosing a module (M) of 0.75, we will have a very small external diameter (De), approximately between 43mm and 44mm.

On the contrary, if we use 0.8 as module (M), we will have a large external diameter (De), approximately 46mm to 47mm, this compared to the outer diameter (De) measured at the gear (45.56mm). Later we will see the calculations made in a table.

But why does this happen? There are several hypotheses, these are perhaps the most probable:

  1. It could be that the gear was designed without using standardized values.
  2. It could be that after designing the gear it was scaled it using software.
  3. It could be that, during the gear manufacturing process, which in theory should have been by plastic injection, it has undergone dimensional changes.

Complex Helical Gear Calculation (Part 2)

Continuation of the calculations and formulas of a Complex Helical Gear

Really the only practical solution that remains is to try varying the number of teeth (N) and try with the two SolidWorks modules (M) (0.75 and 0.8) that approximate the calculated module (Ma) (0.78).

For this we will use the following formula:

Formula of the External Diameter of a gear

Real Module (Obtained from SolidWorks) = M

Number of teeth = N

Real helix angle = A

Outside Diameter (Measured on the gear) = De

In the formula, we are going to try various combinations, making use of the SolidWorks modules (M) that most closely approximate the calculated module (Ma) and helix angles close to the measured angle (Am), which in this case was 17.75°.

The result that is closest to the measured external diameter (De) will tell us what real modulus (M) and what real helix angle (A) we will use to replicate and design our helical gear.

Before starting there is something that you should take into account, the greater the modulus (M) and/or the greater the helix angle (A) and/or the greater number of teeth (N), the greater the outer diameter of the gear (De). In other words, if we want to increase the outer diameter (De) we only have to increase any of the three variables (M, N, A) and vice versa if we want to decrease (De).

Obviously, if what we want is to replicate a gear, we must always try not to vary much from the original values, in addition, you must remember the conditions already mentioned before so that two gears mesh or couple correctly (it is necessary that both have the same Module (M), it is also necessary that both gears have the same helix angle (A) and finally it is necessary that they have opposite helix directions, one gear must have a “right” helix direction and the other “left”).  

Next, we present a table with the different combinations achieved:

Guide to replicate a gear

In the table we can see that there are two combinations that are quite close to the measured outer diameter (De):

  • M = 0.75, N = 56, A = 18°
  • M = 0.8, N = 53, A = 15°

In this opportunity it is better to choose the second combination (M = 0.8, N = 53, A = 15 °) since it is the one that least alters the original number of teeth (N) of the gear.

Now, you must be wondering, how does varying the number of teeth (N) in a gear affect me?

To understand the influence of varying the number of teeth (N) you should know the following: If you divide the gear with the highest number of teeth (E) by the gear with the least number of teeth (e), you will know the ratio of turns and speed between both gears (E/e).

E = Gear with the largest number of teeth (N).

e = Gear with fewer teeth (N).

(E/e) = Turns and speed ratio between both gears.

For example, we have a gear with 50 teeth (E, N = 50), which is coupled to another gear with 25 teeth (e, N = 25).

To know the turning ratio between both gears we divide (E/e) -> (50/25) which results in 2.

What does this mean? That when the big gear (E) turns one turn, the small gear (e) will turn two turns, which is the same as saying that the small gear (e) will turn two times faster than the big gear (E).

Knowing this, let’s go back to the helical gear that we are designing.

The replicated gear will now have 53 teeth (E, N = 53).

Suppose that it couples in a gear with 20 teeth (e, N = 20), the relationship between both gears would be (E/e -> 53/20), so which results in 2.65, that is, when the gear we are replicating (E) makes one turn, the hypothetical gear (e) will make 2.65 turns.

Let’s do this same exercise using the number of teeth of the original gear (E, N = 54).

The operation would be (E/e -> 54/20), this results in 2.7.

As you can see, the result does not vary almost at all, we are talking about a variation of only 0.05, that is, in this example, the hypothetical small gear (e) would rotate 5% more if we use the original 54 tooth gear (N = 54), instead of using the replica we did where we reduced the number of teeth to 53 (N = 53).

The short answer to the question posed above is that for practical purposes in most cases a variety of one or two teeth will not affect practically at all the variation of the ratio of turns and speed.

Now, if you are replicating a gear of a complex system, which needs the speed ratio to remain intact, you cannot apply this technique. But the logical thing is that in a complex system of gears they should use the standard values for the design of gears.

An example of this is that the first gear that we replicate is from a crankshaft of the engine of a generator set.

We can see that it gave us an approximate modulus (Ma) very close to the real modulus (M), on the contrary, this helical gear with which the replication process was complicated is from a small appliance, which was used to chop and grind food.

What to do if we have this same problem, but with a spur gear?

We apply the same procedure mentioned above, from the following formula we clear (De)

Modulus of a gear calculation

Which we have left:

External diameter and modulus of a gear calculation

We know the modulus (M) in SolidWorks, we just need to vary the number of teeth (N) a bit to see if we get a result that is close enough to the measured outside diameter (De).

Complex Helical Gear Design

Spur+Helical Gear Design in SolidWorks

The only thing that remains is to enter in SolidWorks the measured and calculated values to obtain our gear.

After having created the gear, we can carry out extra operations that the CAD software allows, for example, extrusions, cuts, among others.

It is important that after creating the gear you evaluate and compare the measurements provided by SolidWorks with the measurements made physically.

Remember that for this gear we had two Ws, a “real” and a “fake”.

With the “real” we do all the calculations, the “false” is used to facilitate 3D printing, making the gear a little wider so as not to have to print support material under the gear, since under this gear there is originally a protruding.

In this case, we will also have to join the spur gear with the helical one to print everything in the same set.

IMPORTANT NOTE: Remember that only this time will reverse the direction of the helix of the replica only to be able to demonstrate how the replica engages with the original gear, but to make a replica this step is not necessary, rather it is useless, because the replica would not be capable of engaging with the rest of the original gears that made up the mechanism.

3D Printing Complex Helical Gear and Spur Gear

3D Printing of the Helical + Spur Gear

Frequently Asked Questions about 3D Printing Gears

Find next, some FAQ about 3D printing gears:

Can You 3D Print Gears?

Yes, of course you can! for this reason, we made this guide for you, one of the most complete guides you will find on the internet to be able to design, copy, replicate and 3D print gears.

The limitations that you will have when printing gears in 3D will be the same as those in 3D printing in general, very small teeth will be difficult to print by FDM, the resistance of the gear will depend on the percentage of filling used and the type of material.

Although ABS is a widely used material in the manufacture of plastic injection gears, in FDM printing with common machines it’s harder for the ABS to adhere to the layers. For this reason, 3D printed gears with ABS, if they have very long rods or shafts in the “Z” direction, they usually break (the rods or shafts).

3D printed gears
3D printed gear on ABS using FDM technology whose shaft or stem broke

How to Design a Gear in 3D?

In this guide we explain in detail how to replicate and design a gear in 3D.

Is PETG Good for 3D Printing Gears?

PETG is one of many options you have. You can 3D print gears with PETG, PLA, ABS, Nylon, ASA, PC, among others.

If you have a regular FDM printer, PETG is a good choice.

If you want to know more about how to choose materials for your 3D prints, we recommend our article “Guide to select 3D printing filaments” and this amazing infographic.

Guide of How to Make Gears in SolidWorks

We will provide you with a PDF in which there is a summary prepared by ourselves on how to replicate and design the gears in SolidWorks so that you can download and save it, take it on your smartphone, or wherever you want.

To download the guide, click here “How to Design Gears in SolidWorks“.

Conclusions About How to Replicate and 3D Print Gears

Gears are fundamental, they are everywhere and with this guide, you will be able to replicate them when for instance, one is damaged.

In the article, Easy Way of How to Design Gears, we teach you how to design gears from scratch, which satisfies a specific need for a project or prototype that you are developing.

Cheers.

See you soon Machine Bros!

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