Josh Glenn’s Blog

A few CAMaster CNC Router owners have recently asked for an article on how to go about calculating the step resolution, as they are modifying their older machines with different drivers, gears, etc. There are two methods: (1) The Absolute Method; and (2.) the Relative Method.

Comparison of the Two Calculation Methods
The absolute method is by far the most accurate of the two methods. It is also the most technically challenging and time consuming. Once you have a full understanding of the concepts and principles involved, it’s not so bad. But it can be taxing for someone who doesn’t want to fool with highly technical scientific stuff. If you’re reading this, though, chances are you like that type of thing.

The relative method is by far the easiest for the average Joe. But, it is subject to the accuracy with which a person is able to measure the size of an object cut on the machine or the distance the machine has moved. Despite that, it is generally a good way to go about things unless you are milling aerospace components that require extreme precision.

How to Calculate CNC Step Resolution Using the Absolute Method

1. Calculate the ratio of your driven pulley to your driving pulley. For example, Figure 1 on the right shows an example with a 15 tooth motor pulley and a 72 tooth driven pulley. So, if we divide 72 by 15, what do we get? We come up with 4.8. That means our ratio is 4.8 to 1, written as 4.8:1 .
2. Calculate the Linear Distance Traveled per Revolution of your Output Shaft. The method used for this depends on the type of system you are using. If it is a rack-and-pinion system, you do this by calculating the  Pitch Circumference of your output spur gear. Otherwise, if your system is a ball-screw or lead-screw driven system, you must use the screw lead.
3. Calculate the Number of Motor Turns Per Inch (TPI).
4. Calculate the Number of Inches Per Motor Revolution (IPR). Divide the Number of Motor Turns Per Inch by the left side of the gear ratio (4.8:1)
5. Calculate the Number of Steps Per Motor Revolution. This value is dependent on the drive and the motor you are using.
6. Multiply the Number of Inches Per Motor Revolution by the Number of Steps per motor revolution.Congratulations, this number is your Resolution value for that axis.

An Example: Calculating Step Resolution for a Rack and Pinion System with a Gear Reduction

Let’s use an example to figure this:

Let’s say we have a cnc router with a 4.8 to 1 gear reduction and a spur gear (rack-and-pinion drive). That means 4.8 turns of the motor will turn the output shaft one revolution.

This system has a 1.2″ pitch diameter. If we multiply 1.2 * pi, we get 3.7699. This is how many inches the machine moves for each revolution of the output shaft.

Next, we divide that number (3.7699) by the number of motor turns (4.8) to get the number of motor turns per inch. Like so: 3.7699 divided by 4.8 eguals .78539 . This number is the actual linear distance the machine moves for every revolution of the motor. If we are running a 10 microstep pulse, our step size will be .78539 / 2000 = .000392695″ . Finally, divide 0.78539 by .00039 to get your resolution. In this case, the resolution of this machine axis’ configuration is: 2013.821 steps per inch.

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Q: What does the term resolution mean when talking about cnc machines?
A: The answer can be found on CAMaster’s Glossary of CNC Terms and Definitions.

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How to Calculate CNC Step Resolution Using the Relative Method

1. Find your current axis resolution. For this example lets say it is 2354.6 steps per inch.
2. Command your machine to move a specific distance. For this example, let’s tell the machine to move 50 inches.
3. Measure the actual distance the machine moved, and write this number down. For this example, let’s say the machine moved 53.25″.
4. Use CAMaster’s VisualCNC Toolkit (free download)  to calculate the new resolution.
   Visit the CAMaster WIki for Installation Tips, Features, and Instructional Videos on the CAMaster VisualCNC Toolkit.
5. Divide the commanded distance traveled (from step 2) by the actual distance traveled (from step 3), then multiply that number by the current resolution to get the new resolution. In our example we divide 50 by 53.25 and get .93897 (plus about 50 numbers after that). Then we multiply .93897 by 2354.6 to get our new resolution, which is 2210.8920 .