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Average Material Removal Rate given Depth of Cut Formula

GoAverage Material Removal Rate using Uncut Chip Cross-Section Area Formula

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Material removal rate in turning operation (MRR) is the volume of material removed per unit time from workpiece while performing turning operations. Check FAQs

Z t = π \cdot f \cdot d c \cdot n w \cdot (d' m + d c)

Z_t - Material Removal Rate in Turning Operation?f - Feed Rate in Machining?d_c - Depth of Cut in Machining?n_w - Rotational Frequency of The Workpiece?d'_m - Machined Surface Diameter?π - Archimedes' constant?

Average Material Removal Rate given Depth of Cut Example

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Here is how the Average Material Removal Rate given Depth of Cut equation looks like with Values.

Here is how the Average Material Removal Rate given Depth of Cut equation looks like with Units.

Here is how the Average Material Removal Rate given Depth of Cut equation looks like.

0.0043 = 3.1416 \cdot 2.7 \cdot 13 \cdot 750 \cdot (480 + 13)

0.0043m³/s = 3.1416 \cdot 2.7mm/rev \cdot 13mm \cdot 750rev/min \cdot (480mm + 13mm)

0.0043 = 3.1416 \cdot 2.7 \cdot 13 \cdot 750 \cdot (480 + 13)

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Average Material Removal Rate given Depth of Cut Solution

Follow our step by step solution on how to calculate Average Material Removal Rate given Depth of Cut?

FIRST Step Consider the formula

Z t = π \cdot f \cdot d c \cdot n w \cdot (d' m + d c)

Next Step Substitute values of Variables

∴

Z t = π \cdot 2.7mm/rev \cdot 13mm \cdot 750rev/min \cdot (480mm + 13mm)

Next Step Substitute values of Constants

∴

Z t = 3.1416 \cdot 2.7mm/rev \cdot 13mm \cdot 750rev/min \cdot (480mm + 13mm)

Next Step Convert Units

∴

Z t = 3.1416 \cdot 0.0027m/rev \cdot 0.013m \cdot 78.5398rad/s \cdot (0.48m + 0.013m)

Next Step Prepare to Evaluate

∴

Z t = 3.1416 \cdot 0.0027 \cdot 0.013 \cdot 78.5398 \cdot (0.48 + 0.013)

Next Step Evaluate

∴

Z t = 0.00426966488572684m³/s

LAST Step Rounding Answer

∴

Z t = 0.0043m³/s

Average Material Removal Rate given Depth of Cut Formula Elements

Variables

Constants

Material Removal Rate in Turning Operation

Material removal rate in turning operation (MRR) is the volume of material removed per unit time from workpiece while performing turning operations.

Symbol: Z_t

Measurement: Volumetric Flow RateUnit: m³/s

Note: Value should be greater than 0.

Formulas to find Material Removal Rate in Turning Operation

Feed Rate in Machining

Feed Rate in Machining refers to the speed at which the cutting tool advances against the workpiece. It essentially controls how much material is removed with each pass of the tool.

Symbol: f

Measurement: FeedUnit: mm/rev

Note: Value should be greater than 0.

Formulas to find Feed Rate in Machining

Depth of Cut in Machining

Depth of Cut in Machining is the tertiary cutting motion that provides a necessary depth of material that is required to remove by machining. It is usually given in the third perpendicular direction.

Symbol: d_c

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Depth of Cut in Machining

Rotational Frequency of The Workpiece

Rotational frequency of the workpiece is defined as the number of rotations the workpiece around the tip of single point cutting tool makes in a specified time frame.

Symbol: n_w

Measurement: Angular VelocityUnit: rev/min

Note: Value should be greater than 0.

Formulas to find Rotational Frequency of The Workpiece

Machined Surface Diameter

Machined Surface Diameter is the diameter of the machined surface refers to the final diameter of a feature created by machining, specifically focusing on the measurement across the machined area.

Symbol: d'_m

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Machined Surface Diameter

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

Other Formulas to find Material Removal Rate in Turning Operation

Go Average Material Removal Rate using Uncut Chip Cross-Section Area

Z t = A cs \cdot V

Other formulas in Cutting Operation category

Go Cutting Speed Angle using Resultant Cutting Speed

η = a \cos (\frac{v}{v e})

Go Cross sectional Area of Uncut Chip

A c = F \cdot D c

Go Mean Cutting Speed

V t = n \cdot π \cdot \frac{d w + d m}{2}

Go Power required for Machining Operation

P m = Z w \cdot P s

How to Evaluate Average Material Removal Rate given Depth of Cut?

Average Material Removal Rate given Depth of Cut evaluator uses Material Removal Rate in Turning Operation = pi*Feed Rate in Machining*Depth of Cut in Machining*Rotational Frequency of The Workpiece*(Machined Surface Diameter+Depth of Cut in Machining) to evaluate the Material Removal Rate in Turning Operation, The Average Material Removal Rate given Depth of Cut is a method to determine the time average of rate of material volume removed from workpiece when depth of cut is known. It is an approximation method based on the assumption that the workpiece is uniform throughout. Material Removal Rate in Turning Operation is denoted by Z_t symbol.

How to evaluate Average Material Removal Rate given Depth of Cut using this online evaluator? To use this online evaluator for Average Material Removal Rate given Depth of Cut, enter Feed Rate in Machining (f), Depth of Cut in Machining (d_c), Rotational Frequency of The Workpiece (n_w) & Machined Surface Diameter (d'_m) and hit the calculate button.

FAQs on Average Material Removal Rate given Depth of Cut

What is the formula to find Average Material Removal Rate given Depth of Cut?

The formula of Average Material Removal Rate given Depth of Cut is expressed as Material Removal Rate in Turning Operation = pi*Feed Rate in Machining*Depth of Cut in Machining*Rotational Frequency of The Workpiece*(Machined Surface Diameter+Depth of Cut in Machining). Here is an example- 0.00427 = pi*0.0027*0.013*78.5398163357453*(0.48+0.013).

How to calculate Average Material Removal Rate given Depth of Cut?

With Feed Rate in Machining (f), Depth of Cut in Machining (d_c), Rotational Frequency of The Workpiece (n_w) & Machined Surface Diameter (d'_m) we can find Average Material Removal Rate given Depth of Cut using the formula - Material Removal Rate in Turning Operation = pi*Feed Rate in Machining*Depth of Cut in Machining*Rotational Frequency of The Workpiece*(Machined Surface Diameter+Depth of Cut in Machining). This formula also uses Archimedes' constant .

What are the other ways to Calculate Material Removal Rate in Turning Operation?

Here are the different ways to Calculate Material Removal Rate in Turning Operation-

Material Removal Rate in Turning Operation=Cross-Sectional Area of The Uncut Chip*Mean Cutting Speed

Can the Average Material Removal Rate given Depth of Cut be negative?

No, the Average Material Removal Rate given Depth of Cut, measured in Volumetric Flow Rate cannot be negative.

Which unit is used to measure Average Material Removal Rate given Depth of Cut?

Average Material Removal Rate given Depth of Cut 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 Average Material Removal Rate given Depth of Cut can be measured.

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Average Material Removal Rate given Depth of Cut Formula

​GoAverage Material Removal Rate using Uncut Chip Cross-Section Area Formula

Average Material Removal Rate given Depth of Cut Example

Average Material Removal Rate given Depth of Cut Solution

Average Material Removal Rate given Depth of Cut Formula Elements

Other Formulas to find Material Removal Rate in Turning Operation

Other formulas in Cutting Operation category

How to Evaluate Average Material Removal Rate given Depth of Cut?

FAQs on Average Material Removal Rate given Depth of Cut

Variable Name

GoAverage Material Removal Rate using Uncut Chip Cross-Section Area Formula