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Material removal rate Formula

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Metal Removal Rate(MRR) is the amount of material removed per time unit (usually per minute) when performing machining operations such as using a lathe or milling machine. Check FAQs

Z w = A 0 \cdot N \cdot {d mean}^{3} \cdot V^{\frac{3}{2}} \cdot {(\frac{ρ}{12 \cdot h b})}^{\frac{3}{4}}

Z_w - Metal Removal Rate?A₀ - Empirical Constant?N - Abrasive Particles Number Impacting Per Unit Time?d_mean - Mean Diameter of Abrasive Particles?V - Velocity?ρ - Density?h_b - Brinell Hardness?

Material removal rate Example

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With units

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Here is how the Material removal rate equation looks like with Values.

Here is how the Material removal rate equation looks like with Units.

Here is how the Material removal rate equation looks like.

0.16 = 100 \cdot 5 \cdot 4^{3} \cdot {1.4E+6}^{\frac{3}{2}} \cdot {(\frac{997}{12 \cdot 200})}^{\frac{3}{4}}

0.16m³/s = 100 \cdot 5 \cdot {4mm}^{3} \cdot {1.4E+6m/s}^{\frac{3}{2}} \cdot {(\frac{997kg/m³}{12 \cdot 200kgf/mm²})}^{\frac{3}{4}}

0.16 = 100 \cdot 5 \cdot 4^{3} \cdot {1.4E+6}^{\frac{3}{2}} \cdot {(\frac{997}{12 \cdot 200})}^{\frac{3}{4}}

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Material removal rate Solution

Follow our step by step solution on how to calculate Material removal rate?

FIRST Step Consider the formula

Z w = A 0 \cdot N \cdot {d mean}^{3} \cdot V^{\frac{3}{2}} \cdot {(\frac{ρ}{12 \cdot h b})}^{\frac{3}{4}}

Next Step Substitute values of Variables

∴

Z w = 100 \cdot 5 \cdot {4mm}^{3} \cdot {1.4E+6m/s}^{\frac{3}{2}} \cdot {(\frac{997kg/m³}{12 \cdot 200kgf/mm²})}^{\frac{3}{4}}

Next Step Convert Units

∴

Z w = 100 \cdot 5 \cdot {0.004m}^{3} \cdot {1.4E+6m/s}^{\frac{3}{2}} \cdot {(\frac{997kg/m³}{12 \cdot 2E+9Pa})}^{\frac{3}{4}}

Next Step Prepare to Evaluate

∴

Z w = 100 \cdot 5 \cdot {0.004}^{3} \cdot {1.4E+6}^{\frac{3}{2}} \cdot {(\frac{997}{12 \cdot 2E+9})}^{\frac{3}{4}}

LAST Step Evaluate

∴

Z w = 0.16m³/s

Material removal rate Formula Elements

Variables

Metal Removal Rate

Metal Removal Rate(MRR) is the amount of material removed per time unit (usually per minute) when performing machining operations such as using a lathe or milling machine.

Symbol: Z_w

Measurement: Volumetric Flow RateUnit: m³/s

Note: Value should be greater than 0.

Empirical Constant

The Empirical constant is a self determined constant whose value is accessible from table of such constants. This constant is used to calculate the intrinsic carrier concentration.

Symbol: A₀

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Abrasive Particles Number Impacting Per Unit Time

Abrasive Particles Number Impacting Per Unit Time is defined as the average number of particles impacting work surface to cut it during Abrasive Jet Machining.

Symbol: N

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Mean Diameter of Abrasive Particles

Mean diameter of Abrasive Particles is the mean calculated from sampling method.

Symbol: d_mean

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Velocity

Velocity is a vector quantity (it has both magnitude and direction) and is the rate of change of the position of an object with respect to time.

Symbol: V

Measurement: SpeedUnit: m/s

Note: Value can be positive or negative.

Density

The Density of a material shows the denseness of that material in a specific given area. This is taken as mass per unit volume of a given object.

Symbol: ρ

Measurement: DensityUnit: kg/m³

Note: Value should be greater than 0.

Brinell Hardness

Brinell Hardness uses a hard, spherical indenter which is forced into the surface of the metal to be tested.

Symbol: h_b

Measurement: PressureUnit: kgf/mm²

Note: Value should be greater than 0.

Credits

Created by Rajat Vishwakarma

University Institute of Technology RGPV (UIT - RGPV), Bhopal

Rajat Vishwakarma has created this Formula and 400+ more formulas!

Verified by Nishan Poojary

Shri Madhwa Vadiraja Institute of Technology and Management (SMVITM), Udupi

Nishan Poojary has verified this Formula and 400+ more formulas!

Other formulas in Abrasive Jet Machining (AJM) category

Go Empirical constant for AJM

A 0 = \frac{Z w}{N \cdot {d mean}^{3} \cdot V^{\frac{3}{2}} \cdot {(\frac{ρ}{12 \cdot h b})}^{\frac{3}{4}}}

Go Number of abrasive particles impacting per unit time

N = \frac{Z w}{A 0 \cdot {d mean}^{3} \cdot V^{\frac{3}{2}} \cdot {(\frac{ρ}{12 \cdot h b})}^{\frac{3}{4}}}

How to Evaluate Material removal rate?

Material removal rate evaluator uses Metal Removal Rate = Empirical Constant*Abrasive Particles Number Impacting Per Unit Time*Mean Diameter of Abrasive Particles^3*Velocity^(3/2)*(Density/(12*Brinell Hardness))^(3/4) to evaluate the Metal Removal Rate, The Material Removal Rate (MRR) represents the volume of material removed per unit of time during a machining process. It is a crucial parameter in manufacturing as it directly influences the efficiency and productivity of the machining operation. Metal Removal Rate is denoted by Z_w symbol.

How to evaluate Material removal rate using this online evaluator? To use this online evaluator for Material removal rate, enter Empirical Constant (A₀), Abrasive Particles Number Impacting Per Unit Time (N), Mean Diameter of Abrasive Particles (d_mean), Velocity (V), Density (ρ) & Brinell Hardness (h_b) and hit the calculate button.

FAQs on Material removal rate

What is the formula to find Material removal rate?

The formula of Material removal rate is expressed as Metal Removal Rate = Empirical Constant*Abrasive Particles Number Impacting Per Unit Time*Mean Diameter of Abrasive Particles^3*Velocity^(3/2)*(Density/(12*Brinell Hardness))^(3/4). Here is an example- 0.16 = 100*5*0.004^3*1420686.92120444^(3/2)*(997/(12*1961329999.99986))^(3/4).

How to calculate Material removal rate?

With Empirical Constant (A₀), Abrasive Particles Number Impacting Per Unit Time (N), Mean Diameter of Abrasive Particles (d_mean), Velocity (V), Density (ρ) & Brinell Hardness (h_b) we can find Material removal rate using the formula - Metal Removal Rate = Empirical Constant*Abrasive Particles Number Impacting Per Unit Time*Mean Diameter of Abrasive Particles^3*Velocity^(3/2)*(Density/(12*Brinell Hardness))^(3/4).

Can the Material removal rate be negative?

No, the Material removal rate, measured in Volumetric Flow Rate cannot be negative.

Which unit is used to measure Material removal rate?

Material removal rate is usually measured using the Cubic Meter per Second[m³/s] for Volumetric Flow Rate. Cubic Meter per Day[m³/s], Cubic Meter per Hour[m³/s], Cubic Meter per Minute[m³/s] are the few other units in which Material removal rate can be measured.

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Material removal rate Formula

Material removal rate Example

Material removal rate Solution

Material removal rate Formula Elements

Credits

Other formulas in Abrasive Jet Machining (AJM) category

How to Evaluate Material removal rate?

FAQs on Material removal rate

Variable Name