If you are looking at building a CNC router, one of the first questions you might ask yourself is what kind of lead screws you need – this is a critical part of the design, as these load-bearing screws ultimately will determine whether your machine cuts accurately or not.
The lead screw size for a CNC router is determined by a few factors – namely, the size of the router, the weight of the moving parts, and how quickly they are required to move along the lead screws.
Below we will explore these considerations to give you an idea of what size lead screws you will need for your application. Failure to choose an appropriate lead screw will result in a machine that will either cut inaccurately or, worse, cause the outright failure of the lead screws.
Choosing the Right Lead Screw Size for a CNC Router
Get your calculator ready – we’re about to get mathematical! An essential part of designing any machine is making sure that any given part can withstand the forces it will inevitably have to withstand.
To select the right lead screw for a CNC router, you must determine how quickly you want your CNC to work and factor in the critical speed and column strength required for your application.
Besides the weight of the moving parts and your target speed (we will discuss these later), you must also consider how the lead screw is going to be held in place since this also has a direct influence on its overall effectiveness.
Cutting Speed
The cutting speed of your CNC router is typically measured in Inches Per Minute (IPM), and this is determined by your motor speed and the thread size of the lead screw. The coarser the thread, the further it moves through each revolution – this value is known as screw lead.
For example, let’s say you want a cutting speed of 60 IPM – the lead screw will need to move the nut 1 inch every second (25.4 mm/s). If your desired lead screw has a pitch of 20 TPI (Threads Per Inch), it will have to go through that many revolutions every second to reach your desired cutting speed – that is, 1200 revolutions per minute (RPM).
Naturally, this means you will also need a stepper motor capable of producing 1200 RPM. If your motor can only produce 1000 RPM, you can compensate for this by selecting a lead screw with a coarser thread.
Bearing Support Types
There are a few ways you can support your lead screw, which ultimately has a massive impact on your column strength and critical speed.
The four bearing support types are as follows:
- Fixed/Free: One end of the lead screw is rigidly attached by using 2 bearing supports, while the other end is unsupported.
- Supported/Supported: Each end of the lead screw has a single bearing holding it in place.
- Fixed/Supported: One end of the lead screw has 2 bearing supports, while the other only has 1.
- Fixed/Fixed: Both sides of the lead screw have 2 bearing supports.
For a lead screw to bearing support to be considered fixed, the 2 bearing supports must be separated by a distance of 1.5 times the shaft diameter or more.
How Bearing Support Types Affect Critical Speed and Column Strength
Each bearing support type will have a quantifiable effect on both critical speed and column strength.
The table below will give you a figure for each, which you will need for these important calculations:
| Bearing Support Type | Critical Speed | Column Strength |
| Fixed/Free | 0.36 | 0.25 |
| Supported/Supported | 1 | 1 |
| Fixed/Supported | 1.47 | 2 |
| Fixed/Fixed | 2.23 | 4 |
Many CNC router designs use the supported/supported setup, but as you can probably tell you can get more speed out of your router by using the fixed/supported or fixed/fixed bearing support types. That said, there is no need to over-engineer your design.
Calculating Critical Speed
The important thing about the speed at which your lead screw operates is that at a point the rotation will resonate with the screw’s natural frequency. This leads to excessive vibration – it is a wave function, and the waves begin to amplify each other at this speed.
The formula for critical speed is as follows: CS = (4.76)(106)dN/l2. CS is your critical speed in revolutions per minute, d is the minor diameter of your lead screw, N is the fixity type (see the table above), and l is the unsupported length of your lead screw.
The important thing here is that the shaft speed you desire is below the critical speed. At or above the critical speed, the lead screw is likely to bend due to the rotational force. It is recommended that you do not exceed 80% of the critical speed to ensure you get the maximum service life out of your lead screw.
Calculating Column Strength
This is where the weight factor comes in – you need to determine whether the lead screw you have in mind is able to carry the weight of the components it is required to move. Meeting or exceeding the maximum column strength will likely bend or buckle your lead screw.
The formula for calculating column strength is as follows: Cl = (N x 14.03 x 106 x d4) / l2. Cl is your maximum load, N is your fixity type factor (refer to the above table), d is your lead screw’s minor diameter, and l is the unsupported length of your lead screw.
Once again, it’s best to err on the side of caution – do not treat the column strength as a target. Instead, aim for around 80% to be on the safe side. If you are not comfortable doing your own calculations, Roton Products has a nifty online calculator that you can use.
Is the Load or Speed Too High for Your Lead Screw? Here Is What You Can Do
Now that you know what your critical speed and column strength figures are, you can compare these to your desired cutting speed and the weight of the components your lead screw is intended to hold. If you are uncomfortably close to or exceeding these important values, not all is lost.
Do the following if your target load or cutting speed is too high for the lead screw you have in mind:
- Change the bearing support type. A fixed/supported or fixed/fixed support type will effectively increase both critical speed and column strength values.
- Increase the screw diameter. Thicker lead screws are inherently stronger, handling higher loads and speeds.
The only other alternative is to change your design entirely to use a rack and pinion for linear actuation. Rack and pinion setups offer higher load-bearing capacities but also have their own set of considerations and weaknesses that are beyond the scope of this article.
Conclusion
Choosing the right lead screw is one of the most critical steps when designing and building your own CNC router – you must be sure that it can handle the desired load and rotational forces, or you will risk bending them, and a bent lead screw cannot be saved.
The bearing support style is a critical factor that can improve the strength of a lead screw, but if it is not practical to change this or you are already using a fixed/fixed support style, then it is best to opt for a thicker screw.
