Formula & Calculator
Feed Rate (Machining)
Calculates the linear feed rate of a cutting tool from the feed per revolution and the spindle rotational speed.
Interpretation
Feed rate in machining is the linear speed at which the tool advances into the workpiece. It equals the product of feed per revolution and spindle speed: f_r = f·N. It affects surface finish, tool wear, and chip thickness.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| f_r | Feed rate | mm/min |
| f | Feed per revolution | mm/rev |
| N | Spindle rotational speed | RPM |
What it means
Feed rate (f_r) is the speed at which the cutting tool moves relative to the workpiece along the direction of feed. In turning and milling, it is often expressed in mm/min. For rotating workpieces, feed rate is calculated as f_r = f · N, where f is the feed per revolution (mm/rev) and N is the spindle speed (rpm). This parameter determines the rate of material removal and influences surface roughness, chip formation, and tool life. Higher feed rates improve productivity but may compromise surface finish and increase cutting forces. The feed per tooth in milling is similar. In CNC programming, feed rate is one of the main cutting parameters to be set. It must be optimised along with cutting speed and depth of cut. Feed rate also affects the power required and the quality of the machined surface. Understanding feed rate is essential for process planning and tool path generation. Proper selection balances productivity and quality.
Worked example
Feed Rate – Two Examples
Real‑World| Parameter | Value |
|---|---|
| f | 0.2 mm/rev |
| N | 500 RPM |
| Parameter | Value |
|---|---|
| f_z | 0.1 mm/tooth |
| z | 4 |
| N | 800 RPM |
Common mistakes
- Feed per revolution f: In mm/rev.
- Spindle speed N: In rpm.
- Units: f (mm/rev) × N (rev/min) = mm/min – correct.
- Feed rate vs. cutting speed: These are different – feed rate is the tool’s linear advance, cutting speed is surface speed.
- For milling: Feed rate may be per tooth; adjust accordingly.
Applications
Feed rate in machining is the linear speed at which the tool advances into the workpiece, calculated as feed per revolution times spindle speed. It directly affects surface roughness, tool life, and machining time. Proper feed rate selection is essential for achieving desired surface finish and dimensional accuracy while minimising tool wear. In CNC programming, feed rates are optimised based on material, tool geometry, and cutting conditions. The formula is used in process planning to calculate cycle times and to balance productivity with tool life. By carefully controlling feed rate, manufacturers can achieve high‑quality parts efficiently.
- CNC machining process planning and programming
- Surface finish and dimensional accuracy control
- Tool wear and tool life optimisation
- Cycle time estimation and productivity improvement
- Selection of machining parameters for different materials
Frequently Asked Questions
Feed rate is the linear speed at which the cutting tool moves relative to the workpiece, typically expressed as distance per minute. In turning, it is f_r = f · N, where f is the feed per revolution (mm/rev) and N is the spindle speed (RPM). The result is in mm/min.
- f = feed per revolution (mm/rev, in/rev) – the advance of the tool per one complete turn of the workpiece.
- N = spindle speed (RPM).
- Confusing feed per revolution with feed per minute – if you use the feed rate directly without multiplying by N, you get a very low value (by a factor of N).
- Using the wrong unit for f – if f is in mm/rev and N is in RPM, the result is in mm/min.
- Not accounting for the number of teeth in milling – for milling, feed rate is f_z × z × N, where f_z is feed per tooth and z is the number of teeth.
- Ignoring the lead of the workpiece (in thread cutting) – for threading, the feed rate is equal to the lead per revolution, not a separate parameter.
The feed rate determines the chip thickness and the surface finish. Higher feed rates increase MRR (material removal rate) but produce rougher surfaces. Lower feed rates give finer finishes but reduce productivity. The feed rate is a key adjustable parameter.
Cutting speed (V) is the relative tangential speed at the cutting edge (m/min). Feed rate (f_r) is the axial speed of the tool (mm/min). They are perpendicular: V is along the direction of rotation; feed rate is along the tool feed direction.
The machining time is t = L / f_r, where L is the length of the cut (mm) and f_r is the feed rate (mm/min). This is a simple and widely used formula for estimating production times.
A higher feed rate increases the mechanical load on the tool, leading to faster flank wear and higher temperatures. However, increasing feed (rather than cutting speed) can improve tool life because it reduces the contact time per revolution. The optimal feed rate balances tool life and productivity.
Manufacturers provide recommended feed ranges for different materials and insert types. For roughing, a high feed (e.g., 0.2‑0.5 mm/rev) is used. For finishing, a low feed (e.g., 0.05‑0.1 mm/rev) is used. Also, machine rigidity and power limit the maximum feed.
In milling, the feed rate is usually given as table feed (mm/min) or feed per tooth (mm/tooth). The formula is: f_table = f_z × z × N, where f_z is the feed per tooth, z is the number of teeth, and N is the spindle speed. This accounts for the multiple cutting edges.
The theoretical surface roughness in turning is given by R_a ≈ (f² / (8·R)) (for a rounded tool nose radius R). Therefore, increasing the feed increases roughness (R_a ∝ f²). For a good surface finish, you must use a low feed and a large nose radius.