Common Woodworking Equations

Let’s take a closer look at the different woodworking equations and calculations used with a CNC router.

Router tools have small diameters and compact precise features and operate at very high RPMs in order to achieve the effective rim speeds. The daily requirements for performance make the router tools the hardest worked tools in the woodworking industry. The following table identifies the key for the different woodworking equations and shows how several of the routing elements correspond.

Operators will often select an ideal feed speed without regard to the diameter, RPM, available horsepower, and material being cut by the tool. Feeding too slowly elevates tool temperatures dangerously, and feeding too quickly places enormous work loads on the tool. Operators should always be cautious about the depth of cut, feed speed, RPM, and tool diameter and how those parameters relate during the cutting sequence.

Mark Cutter Depth

The Cutter Mark Depth identifies the cupped appearance prevalent especially when using smaller diameter cutting tools. For tools above 125mm in diameter, the cupper surface essentially disappears as the radius arc sections of the cutting process more closely blend together unless the feedrate/tooth/knife is very high. This calculation is usually a diagnostic tool for identifying a subsequent finishing process to remove the effect. There is no specific range of normal for this figure as it is a relationship that changes with the tool diameter, tooth/knife progression, and feedrate.

Mean Chip Thickness

Whether stated as a mean or average chip thickness, the mean chip thickness formula is important especially when cutting hard, dense, or brittle materials. The calculation relates to achieving a particular work load on the cutting tool or seeking a desired finish quality when cutting a particular material and is primarily used as a diagnostic tool. There is np specific normal s the figure expresses a relationship between the tool diameter, depth of cut, and tooth/knife progression.

Rim/ Peripheral Speed

The Rim/Peripheral speed is the velocity, measured at the largest diameter of any cutting tool. Different rim speed velocities are required for cutting different materials by different types of cutting tools. The formula identifies the tool circumference and converts the RPM figure to M/sec.

Feedrate

Feedrate and Tooth/Knife Progression formulas can be either implemented before-the-fact to seek a particular outcome or sought after-the-fact to diagnose the outcome. Both formulas can be worked either forward or backward. The feddrate is the forward movement of the material being cut and includes the incremental movement by each cutter tooth/knife, the number of cutting teeth/knives present, and the RPM of the tool body.

Tooth/Knife Progression

The Tooth/Knife Progression is expressed as the length of each cutter mark. The figure identifies the forward progress of each cutting tool knife/tooth. Such progression indicates finish quality and the amount of work performed by each tooth/knife segment of any cutting tool. The numerator equation U x 1000 converts the feedrate from M/min to mm/min, while the denominator equation N x Z converts the RPM multiplied by the number of teeth/knives into the sum per minute. The value of Sz equals the tooth/knife progression expressed in 0.010mm.

Horsepower Calculations

Horsepower consumption is difficult to calculate in all machining processes as it involves far too many factors and variables to place into a single formula or equation for all feedrates, tool types, and materials with any great precision. The chosen feedrate of 5M/min is the calculated maximum possible for manual feedrate operations. Operators should multiply the higher feedrate by 140% when estimating horsepower for higher feedrates. A machining process using 10hp at 5M/min would on average require 14hp for 10M/min if the other variables were held constant.
The calculations are based on laboratory findings only, assuming that all conditions are correct and ideal. Actual horsepower usage can therefore be significantly different from the values indicated. Operators are encouraged to use the slide calculator figures as a beginning point only and to refer to either electrical or mechanical force measurements for more specific accuracy.