Depth of Cut given Average Temperature Rise of Material under Primary Shear Zone Calculator

✖Fraction of Heat Conducted into the workpiece, a portion of Ps which is conducted to the workpiece, so, this portion will not cause a temperature increase in the chip.ⓘ Fraction of Heat Conducted into the workpiece [Γ]			+10% -10%
✖The Rate of Heat Generation in Primary Shear Zone is the heat transfer rate in the narrow zone surrounding the shear plane in machining.ⓘ Rate of Heat Generation in Primary Shear Zone [P_s]			+10% -10%
✖The Density of work piece is the mass per unit volume ratio of the material of workpiece.ⓘ Density of work piece [ρ_{work piece}]			+10% -10%
✖The Specific Heat Capacity of Workpiece is the amount of heat per unit mass required to raise the temperature by one degree Celsius.ⓘ Specific Heat Capacity of Workpiece [C]			+10% -10%
✖Cutting Speed is defined as the speed at which the work moves with respect to the tool (usually measured in feet per minute).ⓘ Cutting Speed [V_cutting]			+10% -10%
✖Undeformed Chip Thickness in milling is defined as the distance between two consecutive cut surfaces.ⓘ Undeformed Chip Thickness [a_c]			+10% -10%
✖Average Temperature Rise is defined as the actual amount of increase in the temperature.ⓘ Average Temperature Rise [θ_{avg rise}]			+10% -10%

✖Depth of Cut 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.ⓘ Depth of Cut given Average Temperature Rise of Material under Primary Shear Zone [d_cut]

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Formula

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Depth of Cut given Average Temperature Rise of Material under Primary Shear Zone

Formula

`"d"_{"cut"} = ((1-"Γ")*"P"_{"s"})/("ρ"_{"work piece"}*"C"*"V"_{"cutting"}*"a"_{"c"}*"θ"_{"avg rise"})`

Example

`"2.500004mm"=((1-"0.1")*"1380W")/("7200kg/m³"*"502J/(kg*K)"*"2m/s"*"0.25mm"*"274.9°C")`

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Depth of Cut given Average Temperature Rise of Material under Primary Shear Zone Solution

STEP 0: Pre-Calculation Summary

Formula Used

Depth of Cut = ((1-Fraction of Heat Conducted into the workpiece)*Rate of Heat Generation in Primary Shear Zone)/(Density of work piece*Specific Heat Capacity of Workpiece*Cutting Speed*Undeformed Chip Thickness*Average Temperature Rise)
d_cut = ((1-Γ)*P_s)/(ρ_{work piece}*C*V_cutting*a_c*θ_{avg rise})
This formula uses 8 Variables

Variables Used

Depth of Cut - (Measured in Meter) - Depth of Cut 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.
Fraction of Heat Conducted into the workpiece - Fraction of Heat Conducted into the workpiece, a portion of Ps which is conducted to the workpiece, so, this portion will not cause a temperature increase in the chip.
Rate of Heat Generation in Primary Shear Zone - (Measured in Watt) - The Rate of Heat Generation in Primary Shear Zone is the heat transfer rate in the narrow zone surrounding the shear plane in machining.
Density of work piece - (Measured in Kilogram per Cubic Meter) - The Density of work piece is the mass per unit volume ratio of the material of workpiece.
Specific Heat Capacity of Workpiece - (Measured in Joule per Kilogram per K) - The Specific Heat Capacity of Workpiece is the amount of heat per unit mass required to raise the temperature by one degree Celsius.
Cutting Speed - (Measured in Meter per Second) - Cutting Speed is defined as the speed at which the work moves with respect to the tool (usually measured in feet per minute).
Undeformed Chip Thickness - (Measured in Meter) - Undeformed Chip Thickness in milling is defined as the distance between two consecutive cut surfaces.
Average Temperature Rise - (Measured in Kelvin) - Average Temperature Rise is defined as the actual amount of increase in the temperature.

STEP 1: Convert Input(s) to Base Unit

Fraction of Heat Conducted into the workpiece: 0.1 --> No Conversion Required
Rate of Heat Generation in Primary Shear Zone: 1380 Watt --> 1380 Watt No Conversion Required
Density of work piece: 7200 Kilogram per Cubic Meter --> 7200 Kilogram per Cubic Meter No Conversion Required
Specific Heat Capacity of Workpiece: 502 Joule per Kilogram per K --> 502 Joule per Kilogram per K No Conversion Required
Cutting Speed: 2 Meter per Second --> 2 Meter per Second No Conversion Required
Undeformed Chip Thickness: 0.25 Millimeter --> 0.00025 Meter (Check conversion here)
Average Temperature Rise: 274.9 Degree Celsius --> 274.9 Kelvin (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

d_cut = ((1-Γ)*P_s)/(ρ_{work piece}*C*V_cutting*a_c*θ_{avg rise}) --> ((1-0.1)*1380)/(7200*502*2*0.00025*274.9)

Evaluating ... ...

d_cut = 0.00250000362319366

STEP 3: Convert Result to Output's Unit

0.00250000362319366 Meter -->2.50000362319366 Millimeter (Check conversion here)

FINAL ANSWER

2.50000362319366 ≈ 2.500004 Millimeter <-- Depth of Cut

(Calculation completed in 00.004 seconds)

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Home » Engineering » Production Engineering » Metal Machining » Metal Machining Dynamics » Temperatures in Metal Cutting » Temperature Rise » Depth of Cut given Average Temperature Rise of Material under Primary Shear Zone

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Created by Parul Keshav

National Institute of Technology (NIT), Srinagar

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Indian Institute of Information Technology, Design and Manufacturing (IIITDM), Jabalpur

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< 20 Temperature Rise Calculators

Undeformed Chip Thickness given Average Temperature Rise of Material under Primary Shear Zone

Go Undeformed Chip Thickness = ((1-Fraction of Heat Conducted into the workpiece)*Rate of Heat Generation in Primary Shear Zone)/(Density of work piece*Specific Heat Capacity of Workpiece*Cutting Speed*Average Temperature Rise*Depth of Cut)

Density of Material using Average Temperature Rise of material under Primary Shear Zone

Go Density of work piece = ((1-Fraction of Heat Conducted into the workpiece)*Rate of Heat Generation in Primary Shear Zone)/(Average Temperature Rise*Specific Heat Capacity of Workpiece*Cutting Speed*Undeformed Chip Thickness*Depth of Cut)

Specific Heat given Average Temperature Rise of Material under Primary Shear Zone

Go Specific Heat Capacity of Workpiece = ((1-Fraction of Heat Conducted into the workpiece)*Rate of Heat Generation in Primary Shear Zone)/(Density of work piece*Average Temperature Rise*Cutting Speed*Undeformed Chip Thickness*Depth of Cut)

Cutting Speed given Average Temperature Rise of Material under Primary Shear Zone

Go Cutting Speed = ((1-Fraction of Heat Conducted into the workpiece)*Rate of Heat Generation in Primary Shear Zone)/(Density of work piece*Specific Heat Capacity of Workpiece*Average Temperature Rise*Undeformed Chip Thickness*Depth of Cut)

Depth of Cut given Average Temperature Rise of Material under Primary Shear Zone

Go Depth of Cut = ((1-Fraction of Heat Conducted into the workpiece)*Rate of Heat Generation in Primary Shear Zone)/(Density of work piece*Specific Heat Capacity of Workpiece*Cutting Speed*Undeformed Chip Thickness*Average Temperature Rise)

Average Temperature Rise of Material under Primary Deformation Zone

Go Average Temperature Rise = ((1-Fraction of Heat Conducted into the workpiece)*Rate of Heat Generation in Primary Shear Zone)/(Density of work piece*Specific Heat Capacity of Workpiece*Cutting Speed*Undeformed Chip Thickness*Depth of Cut)

Un-deformed Chip Thickness using Average Temperature Rise of Chip from Secondary Deformation

Go Undeformed Chip Thickness = Rate of Heat Gen in Secondary Shear Zone/(Specific Heat Capacity of Workpiece*Density of work piece*Cutting Speed*Average Temp Rise of Chip in Secondary Shear Zone*Depth of Cut)

Density of Material using Average Temperature rise of Chip from Secondary Deformation

Go Density of work piece = Rate of Heat Gen in Secondary Shear Zone/(Specific Heat Capacity of Workpiece*Average Temp Rise of Chip in Secondary Shear Zone*Cutting Speed*Undeformed Chip Thickness*Depth of Cut)

Specific Heat using Average Temperature Rise of Chip from Secondary Deformation

Go Specific Heat Capacity of Workpiece = Rate of Heat Gen in Secondary Shear Zone/(Average Temp Rise of Chip in Secondary Shear Zone*Density of work piece*Cutting Speed*Undeformed Chip Thickness*Depth of Cut)

Cutting Speed using Average Temperature Rise of Chip from Secondary Deformation

Go Cutting Speed = Rate of Heat Gen in Secondary Shear Zone/(Specific Heat Capacity of Workpiece*Density of work piece*Average Temp Rise of Chip in Secondary Shear Zone*Undeformed Chip Thickness*Depth of Cut)

Depth of Cut using Average Temperature Rise of Chip from Secondary Deformation

Go Depth of Cut = Rate of Heat Gen in Secondary Shear Zone/(Specific Heat Capacity of Workpiece*Density of work piece*Cutting Speed*Undeformed Chip Thickness*Average Temp Rise of Chip in Secondary Shear Zone)

Average Temperature rise of chip from Secondary Deformation

Go Average Temp Rise of Chip in Secondary Shear Zone = Rate of Heat Gen in Secondary Shear Zone/(Specific Heat Capacity of Workpiece*Density of work piece*Cutting Speed*Undeformed Chip Thickness*Depth of Cut)

Average Temperature rise of chip from Secondary Deformation within boundary condition

Go Average Temp Rise of Chip in Secondary Shear Zone = Max Temp in Chip in Secondary Deformation Zone/(1.13*sqrt(Thermal Number/Length of Heat Source per Chip Thickness))

Maximum Temperature rise in Chip in Secondary deformation zone

Go Max Temp in Chip in Secondary Deformation Zone = Average Temp Rise of Chip in Secondary Shear Zone*1.13*sqrt(Thermal Number/Length of Heat Source per Chip Thickness)

Length of Heat Source per Chip Thickness using Max Temperature Rise in Secondary Shear Zone

Go Length of Heat Source per Chip Thickness = Thermal Number/((Max Temp in Chip in Secondary Deformation Zone/(Average Temp Rise of Chip in Secondary Shear Zone*1.13))^2)

Thermal Number using Maximum Temperature Rise in Chip in Secondary Deformation Zone

Go Thermal Number = Length of Heat Source per Chip Thickness*((Max Temp in Chip in Secondary Deformation Zone/(Average Temp Rise of Chip in Secondary Shear Zone*1.13))^2)

Initial Workpiece Temperature using Maximum Temperature in Secondary Deformation Zone

Go Initial Workpiece Temperature = Max Temp in Chip in Secondary Deformation Zone-Temperature Rise in Secondary Deformation-Temperature Rise in Primary Deformation

Temperature Rise of Material in Secondary Deformation Zone

Go Temperature Rise in Secondary Deformation = Max Temp in Chip in Secondary Deformation Zone-Temperature Rise in Primary Deformation-Initial Workpiece Temperature

Temperature rise of material in primary deformation zone

Go Temperature Rise in Primary Deformation = Max Temp in Chip in Secondary Deformation Zone-Temperature Rise in Secondary Deformation-Initial Workpiece Temperature

Maximum temperature in secondary deformation zone

Go Max Temp in Chip in Secondary Deformation Zone = Temperature Rise in Secondary Deformation+Temperature Rise in Primary Deformation+Initial Workpiece Temperature

Depth of Cut given Average Temperature Rise of Material under Primary Shear Zone Formula

What is Depth of Cut?

It is the total amount of metal removed per pass of the cutting tool. It is expressed in mm. It can vary and depend upon the type of tool and work material.

How to Calculate Depth of Cut given Average Temperature Rise of Material under Primary Shear Zone?

Depth of Cut given Average Temperature Rise of Material under Primary Shear Zone calculator uses Depth of Cut = ((1-Fraction of Heat Conducted into the workpiece)*Rate of Heat Generation in Primary Shear Zone)/(Density of work piece*Specific Heat Capacity of Workpiece*Cutting Speed*Undeformed Chip Thickness*Average Temperature Rise) to calculate the Depth of Cut, The Depth of cut given Average Temperature rise of material under Primary Shear Zone is the total amount of metal removed per pass of the cutting tool. Depth of Cut is denoted by d_cut symbol.

How to calculate Depth of Cut given Average Temperature Rise of Material under Primary Shear Zone using this online calculator? To use this online calculator for Depth of Cut given Average Temperature Rise of Material under Primary Shear Zone, enter Fraction of Heat Conducted into the workpiece (Γ), Rate of Heat Generation in Primary Shear Zone (P_s), Density of work piece (ρ_{work piece}), Specific Heat Capacity of Workpiece (C), Cutting Speed (V_cutting), Undeformed Chip Thickness (a_c) & Average Temperature Rise (θ_{avg rise}) and hit the calculate button. Here is how the Depth of Cut given Average Temperature Rise of Material under Primary Shear Zone calculation can be explained with given input values -> 2500.004 = ((1-0.1)*1380)/(7200*502*2*0.00025*274.9).

FAQ

What is Depth of Cut given Average Temperature Rise of Material under Primary Shear Zone?

The Depth of cut given Average Temperature rise of material under Primary Shear Zone is the total amount of metal removed per pass of the cutting tool and is represented as d_cut = ((1-Γ)*P_s)/(ρ_{work piece}*C*V_cutting*a_c*θ_{avg rise}) or Depth of Cut = ((1-Fraction of Heat Conducted into the workpiece)*Rate of Heat Generation in Primary Shear Zone)/(Density of work piece*Specific Heat Capacity of Workpiece*Cutting Speed*Undeformed Chip Thickness*Average Temperature Rise). Fraction of Heat Conducted into the workpiece, a portion of Ps which is conducted to the workpiece, so, this portion will not cause a temperature increase in the chip, The Rate of Heat Generation in Primary Shear Zone is the heat transfer rate in the narrow zone surrounding the shear plane in machining, The Density of work piece is the mass per unit volume ratio of the material of workpiece, The Specific Heat Capacity of Workpiece is the amount of heat per unit mass required to raise the temperature by one degree Celsius, Cutting Speed is defined as the speed at which the work moves with respect to the tool (usually measured in feet per minute), Undeformed Chip Thickness in milling is defined as the distance between two consecutive cut surfaces & Average Temperature Rise is defined as the actual amount of increase in the temperature.

How to calculate Depth of Cut given Average Temperature Rise of Material under Primary Shear Zone?

The Depth of cut given Average Temperature rise of material under Primary Shear Zone is the total amount of metal removed per pass of the cutting tool is calculated using Depth of Cut = ((1-Fraction of Heat Conducted into the workpiece)*Rate of Heat Generation in Primary Shear Zone)/(Density of work piece*Specific Heat Capacity of Workpiece*Cutting Speed*Undeformed Chip Thickness*Average Temperature Rise). To calculate Depth of Cut given Average Temperature Rise of Material under Primary Shear Zone, you need Fraction of Heat Conducted into the workpiece (Γ), Rate of Heat Generation in Primary Shear Zone (P_s), Density of work piece (ρ_{work piece}), Specific Heat Capacity of Workpiece (C), Cutting Speed (V_cutting), Undeformed Chip Thickness (a_c) & Average Temperature Rise (θ_{avg rise}). With our tool, you need to enter the respective value for Fraction of Heat Conducted into the workpiece, Rate of Heat Generation in Primary Shear Zone, Density of work piece, Specific Heat Capacity of Workpiece, Cutting Speed, Undeformed Chip Thickness & Average Temperature Rise and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Depth of Cut?

In this formula, Depth of Cut uses Fraction of Heat Conducted into the workpiece, Rate of Heat Generation in Primary Shear Zone, Density of work piece, Specific Heat Capacity of Workpiece, Cutting Speed, Undeformed Chip Thickness & Average Temperature Rise. We can use 1 other way(s) to calculate the same, which is/are as follows -

Depth of Cut = Rate of Heat Gen in Secondary Shear Zone/(Specific Heat Capacity of Workpiece*Density of work piece*Cutting Speed*Undeformed Chip Thickness*Average Temp Rise of Chip in Secondary Shear Zone)

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