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

STEP 0: Pre-Calculation Summary
Formula Used
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)
ac = ((1-Γ)*Ps)/(ρwork piece*C*Vcutting*θavg rise*dcut)
This formula uses 8 Variables
Variables Used
Undeformed Chip Thickness - (Measured in Meter) - Undeformed Chip Thickness in milling is defined as the distance between two consecutive cut surfaces.
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).
Average Temperature Rise - (Measured in Kelvin) - Average Temperature Rise is defined as the actual amount of increase in the temperature.
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.
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
Average Temperature Rise: 274.9 Degree Celsius --> 274.9 Kelvin (Check conversion here)
Depth of Cut: 2.5 Millimeter --> 0.0025 Meter (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
ac = ((1-Γ)*Ps)/(ρwork piece*C*Vcuttingavg rise*dcut) --> ((1-0.1)*1380)/(7200*502*2*274.9*0.0025)
Evaluating ... ...
ac = 0.000250000362319366
STEP 3: Convert Result to Output's Unit
0.000250000362319366 Meter -->0.250000362319366 Millimeter (Check conversion here)
FINAL ANSWER
0.250000362319366 0.25 Millimeter <-- Undeformed Chip Thickness
(Calculation completed in 00.004 seconds)

Credits

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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18 Temperatures in Metal Cutting 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)
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)
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)
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)
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)
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)
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)
Rate of Heat Conduction into Workpiece given Total Rate of Heat Generation
Go Rate of Heat Conduction into the Workpiece = Total Rate of Heat Generation in Metal Cutting-Rate of Heat Transportation by Chip-Rate of Heat Conduction into the Tool
Rate of Heat Transportation by Chip given Total Rate of Heat Generation
Go Rate of Heat Transportation by Chip = Total Rate of Heat Generation in Metal Cutting-Rate of Heat Conduction into the Workpiece-Rate of Heat Conduction into the Tool
Rate of Heat Conduction into Tool given Total Rate of Heat Generation
Go Rate of Heat Conduction into the Tool = Total Rate of Heat Generation in Metal Cutting-Rate of Heat Transportation by Chip-Rate of Heat Conduction into the Workpiece
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
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
Rate of Energy Consumption using Rate of Heat Generation during Machining
Go Rate of Energy Consumption during Machining = Rate of Heat Generation in Primary Shear Zone+Rate of Heat Gen in Secondary Shear Zone

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

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)
ac = ((1-Γ)*Ps)/(ρwork piece*C*Vcutting*θavg rise*dcut)

What is Undeformed Chip Thickness?

The undeformed chip thickness in milling is defined as the distance between two consecutive cut surfaces. It varies during cutting and is measured in the direction perpendicular to the preceding cut surface.

How to Calculate Undeformed Chip Thickness given Average Temperature Rise of Material under Primary Shear Zone?

Undeformed Chip Thickness given Average Temperature Rise of Material under Primary Shear Zone calculator uses 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) to calculate the Undeformed Chip Thickness, The Undeformed Chip Thickness given Average Temperature rise of material under Primary Shear Zone is defined as the distance between two consecutive cut surfaces. Undeformed Chip Thickness is denoted by ac symbol.

How to calculate Undeformed Chip Thickness given Average Temperature Rise of Material under Primary Shear Zone using this online calculator? To use this online calculator for Undeformed Chip Thickness 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 (Ps), Density of work piece work piece), Specific Heat Capacity of Workpiece (C), Cutting Speed (Vcutting), Average Temperature Rise avg rise) & Depth of Cut (dcut) and hit the calculate button. Here is how the Undeformed Chip Thickness given Average Temperature Rise of Material under Primary Shear Zone calculation can be explained with given input values -> 250.0004 = ((1-0.1)*1380)/(7200*502*2*274.9*0.0025).

FAQ

What is Undeformed Chip Thickness given Average Temperature Rise of Material under Primary Shear Zone?
The Undeformed Chip Thickness given Average Temperature rise of material under Primary Shear Zone is defined as the distance between two consecutive cut surfaces and is represented as ac = ((1-Γ)*Ps)/(ρwork piece*C*Vcuttingavg rise*dcut) or 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). 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), Average Temperature Rise is defined as the actual amount of increase in the temperature & 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.
How to calculate Undeformed Chip Thickness given Average Temperature Rise of Material under Primary Shear Zone?
The Undeformed Chip Thickness given Average Temperature rise of material under Primary Shear Zone is defined as the distance between two consecutive cut surfaces is calculated using 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). To calculate Undeformed Chip Thickness 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 (Ps), Density of work piece work piece), Specific Heat Capacity of Workpiece (C), Cutting Speed (Vcutting), Average Temperature Rise avg rise) & Depth of Cut (dcut). 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, Average Temperature Rise & Depth of Cut 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 Undeformed Chip Thickness?
In this formula, Undeformed Chip Thickness 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, Average Temperature Rise & Depth of Cut. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • 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)
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