Material Removal Rate (MRR), often denoted as Q, is a critical parameter in machining operations, particularly in turning. It represents the volume of material removed from the workpiece per unit of time. Understanding MRR is essential for estimating machining time, calculating power requirements, and optimizing production efficiency.
The Turning MRR Formula
The calculation for MRR in a turning operation on a lathe is derived from three primary cutting parameters: Cutting Speed, Feed Rate, and Depth of Cut. The formula varies slightly depending on whether you are using Metric or Imperial units.
Metric Formula:
Q = Vc × fn × ap
Where:
Q = Material Removal Rate (cm³/min)
Vc = Cutting Speed (m/min)
fn = Feed Rate (mm/rev)
ap = Depth of Cut (mm)
Imperial Formula:
Q = 12 × Vc × fn × ap
Where:
Q = Material Removal Rate (in³/min)
Vc = Surface Speed (ft/min)
fn = Feed Rate (in/rev)
ap = Depth of Cut (in) (The constant 12 converts feet to inches)
Key Parameters Explained
Cutting Speed (Vc): This is the speed at which the workpiece surface moves past the cutting tool edge. In metric, it is measured in meters per minute (m/min), and in imperial, it is surface feet per minute (sfm).
Feed Rate (fn): The distance the tool advances along the workpiece for each revolution of the spindle. Higher feed rates increase MRR but may degrade surface finish.
Depth of Cut (ap): The perpendicular distance the tool penetrates into the workpiece. This is usually the difference between the initial radius and the final radius of the part.
Example Calculation (Metric)
Suppose you are turning a steel shaft with the following parameters:
Cutting Speed (Vc) = 180 m/min
Feed Rate (fn) = 0.3 mm/rev
Depth of Cut (ap) = 2.0 mm
Using the formula:
Q = 180 × 0.3 × 2.0 = 108 cm³/min
Why MRR Matters
Maximizing MRR is often a goal in roughing operations to remove material as quickly as possible. However, high MRR requires significant machine power and torque. If the MRR exceeds the machine's capability, it can lead to tool breakage, chatter, or motor stall. Machinists use this calculation to balance productivity with tool life and machine health.
function updateLabels() {
var system = document.getElementById("unitSystem").value;
var speedUnit = document.getElementById("speedUnit");
var feedUnit = document.getElementById("feedUnit");
var depthUnit = document.getElementById("depthUnit");
var mrrUnit = document.getElementById("mrrUnit");
var speedInput = document.getElementById("cuttingSpeed");
var feedInput = document.getElementById("feedRate");
var depthInput = document.getElementById("depthOfCut");
if (system === "metric") {
speedUnit.innerHTML = "Unit: Meters per Minute (m/min)";
feedUnit.innerHTML = "Unit: Millimeters per Revolution (mm/rev)";
depthUnit.innerHTML = "Unit: Millimeters (mm)";
mrrUnit.innerHTML = "cm³/min";
// Set placeholders to metric examples
speedInput.placeholder = "e.g., 200";
feedInput.placeholder = "e.g., 0.25";
depthInput.placeholder = "e.g., 2.5";
} else {
speedUnit.innerHTML = "Unit: Surface Feet per Minute (sfm)";
feedUnit.innerHTML = "Unit: Inches per Revolution (ipr)";
depthUnit.innerHTML = "Unit: Inches (in)";
mrrUnit.innerHTML = "in³/min";
// Set placeholders to imperial examples
speedInput.placeholder = "e.g., 600";
feedInput.placeholder = "e.g., 0.010";
depthInput.placeholder = "e.g., 0.100";
}
// Hide result when switching units until calculated again
document.getElementById("resultBox").style.display = "none";
}
function calculateMRR() {
// Get Inputs
var system = document.getElementById("unitSystem").value;
var vc = parseFloat(document.getElementById("cuttingSpeed").value);
var fn = parseFloat(document.getElementById("feedRate").value);
var ap = parseFloat(document.getElementById("depthOfCut").value);
var resultElement = document.getElementById("mrrResult");
var resultBox = document.getElementById("resultBox");
// Validation
if (isNaN(vc) || isNaN(fn) || isNaN(ap)) {
alert("Please enter valid numerical values for all fields.");
return;
}
if (vc < 0 || fn < 0 || ap cm^3/min).
mrr = vc * fn * ap;
} else {
// Formula: Q = 12 * Vc * fn * ap
// Vc is ft/min. fn is in/rev. ap is in.
// 1 ft = 12 inches.
// Result in in^3/min.
mrr = 12 * vc * fn * ap;
}
// Display Result
resultElement.innerHTML = mrr.toFixed(2);
resultBox.style.display = "block";
}