Formula & Calculator
Material Removal Rate (Turning)
Estimates how quickly material is removed during a turning operation from the cutting speed, feed rate, and depth of cut.
Interpretation
Material removal rate (MRR) in turning is the volume of material removed per unit time: MRR = V·f·d. It is a measure of machining productivity, combining cutting speed, feed, and depth of cut.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| MRR | Material removal rate | mm3/min |
| V | Cutting speed | mm/min |
| f | Feed rate per revolution | mm/rev (used as mm here for rate calc) |
| d | Depth of cut | mm |
What it means
The material removal rate (MRR) is the volume of workpiece material removed by the cutting tool per unit time. For turning, MRR = V × f × d, where V is the cutting speed (m/min), f is the feed rate (mm/rev), and d is the depth of cut (mm). This product yields mm³/min. MRR directly affects machining time and productivity: higher MRR means faster production, but it also increases tool wear and power consumption. The MRR is used to estimate machining costs and to select appropriate cutting parameters. In process planning, the aim is to maximise MRR while maintaining tool life and surface quality. The power required for cutting is roughly proportional to MRR times the specific cutting energy. MRR can also be expressed for other operations like milling, drilling, and grinding, with appropriate formulas. It is a fundamental metric in manufacturing engineering, and it guides the selection of machine tools and cutting fluids.
Worked example
Material Removal Rate – Two Examples
Real‑World| Parameter | Value |
|---|---|
| V | 100 m/min = 100,000 mm/min |
| f | 0.2 mm |
| d | 1.5 mm |
| Parameter | Value |
|---|---|
| V | 150,000 mm/min |
| f | 0.3 mm |
| d | 2 mm |
Common mistakes
- Cutting speed V: In m/min (as calculated from ID 828).
- Feed f: In mm/rev (for turning).
- Depth of cut d: In mm (radial depth).
- Units: V (m/min) × f (mm/rev) × d (mm) gives mm³/min – ensure unit conversions if needed.
- MRR vs. material removal rate: This is the theoretical rate; actual rate may be lower due to tool wear.
Applications
Material removal rate (MRR) in turning is the volume of material removed per unit time, calculated from cutting speed, feed, and depth of cut. It is a measure of machining productivity, directly affecting manufacturing time and cost. Engineers use MRR to compare different cutting strategies and to optimise machining parameters. Higher MRR can reduce cycle times, but it may accelerate tool wear. Therefore, MRR is balanced against tool life and surface quality. The formula is also used in process planning and cost estimation. By maximising MRR within safe limits, manufacturers can achieve efficient production while maintaining quality standards.
- Process planning and optimisation in machining
- Tool life and cost‑benefit analysis
- Comparison of different cutting tools and coatings
- Automation and CNC machining productivity
- Material removal simulation and CAM programming
Frequently Asked Questions
Material removal rate is the volume of material removed per unit time. For turning, the formula is MRR = V · f · d, where V is the cutting speed (m/min), f is the feed rate (mm/rev), and d is the depth of cut (mm). The result is in mm³/min.
- MRR – material removal rate (mm³/min or in³/min).
- V – cutting speed (m/min, ft/min).
- f – feed per revolution (mm/rev, in/rev).
- d – depth of cut (mm, in).
- Using feed per minute instead of feed per revolution – the formula requires feed per revolution. If you have feed rate (mm/min), divide by spindle speed (RPM) to get feed per revolution.
- Mixing units – ensure V is in the same unit system as f and d.
- Forgetting to convert diameter to circumference – the formula uses V (which already includes π·D·N), so no need to multiply by π again.
- Ignoring the radial and axial components – MRR is based on the volume swept; the formula is a simplification assuming a straight cut.
The machining time for a turning operation (face or longitudinal) is: t = (L × A) / (MRR), where L is the length of cut and A is the cross‑sectional area of the removed material. In practice, t = (length of cut) / (feed rate in mm/min). Higher MRR means faster machining.
MRR is directly proportional to depth of cut (d). Doubling d doubles the MRR, but it also increases the cutting forces and power consumption. There is a maximum d limited by tool strength and machine rigidity.
Higher feed rate increases MRR, but it also increases the roughness of the surface (the feed marks). There is a trade‑off: roughing cuts use high feeds for productivity, finishing cuts use low feeds for good surface quality.
MRR is directly proportional to V. However, increasing V reduces tool life (Taylor's equation). Therefore, the optimal V is chosen to balance MRR and tool life economics (minimum cost or maximum production rate).
The required power is P = MRR × (specific cutting energy). Specific cutting energy (J/mm³) depends on the material (e.g., aluminium: 0.5‑1 J/mm³, steel: 2‑4 J/mm³). This is used to select the machine tool motor size.
For boring (internal turning), the formula is the same: MRR = V·f·d, but V is based on the bore diameter. However, if the bore is small, the effective diameter may change; the MRR is based on the instantaneous diameter.
MRR is the actual volume removal rate. Cutting efficiency is the ratio of MRR to the maximum theoretical MRR based on the machine's power and the material's specific cutting energy. It indicates how well the machine is utilised.