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Tool temperature Formula

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Tool Temperature is the temperature reached during cutting for tool. Check FAQs

θ = \frac{C 0 \cdot U s \cdot V^{0.44} \cdot A^{0.22}}{k^{0.44} \cdot c^{0.56}}

θ - Tool Temperature?C₀ - Constant For Tool Temperature?U_s - Specific Cutting Energy Per Unit Cutting Force?V - Cutting Velocity in Tool Life?A - Area of Cut?k - Thermal Conductivity?c - Specific Heat Capacity of Work?

Tool temperature Example

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With units

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Here is how the Tool temperature equation looks like with Values.

Here is how the Tool temperature equation looks like with Units.

Here is how the Tool temperature equation looks like.

412.8269 = \frac{0.29 \cdot 200 \cdot {0.8333}^{0.44} \cdot 45^{0.22}}{48^{0.44} \cdot 510^{0.56}}

412.8269°C = \frac{0.29 \cdot 200kJ/kg \cdot {0.8333m/s}^{0.44} \cdot {45m²}^{0.22}}{{48W/(m*K)}^{0.44} \cdot {510J/(kg*K)}^{0.56}}

412.8269 = \frac{0.29 \cdot 200 \cdot {0.8333}^{0.44} \cdot 45^{0.22}}{48^{0.44} \cdot 510^{0.56}}

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Tool temperature Solution

Follow our step by step solution on how to calculate Tool temperature?

FIRST Step Consider the formula

θ = \frac{C 0 \cdot U s \cdot V^{0.44} \cdot A^{0.22}}{k^{0.44} \cdot c^{0.56}}

Next Step Substitute values of Variables

∴

θ = \frac{0.29 \cdot 200kJ/kg \cdot {0.8333m/s}^{0.44} \cdot {45m²}^{0.22}}{{48W/(m*K)}^{0.44} \cdot {510J/(kg*K)}^{0.56}}

Next Step Convert Units

∴

θ = \frac{0.29 \cdot 200000J/kg \cdot {0.8333m/s}^{0.44} \cdot {45m²}^{0.22}}{{48W/(m*K)}^{0.44} \cdot {510J/(kg*K)}^{0.56}}

Next Step Prepare to Evaluate

∴

θ = \frac{0.29 \cdot 200000 \cdot {0.8333}^{0.44} \cdot 45^{0.22}}{48^{0.44} \cdot 510^{0.56}}

Next Step Evaluate

∴

θ = 685.976880379248K

Next Step Convert to Output's Unit

∴

θ = 412.826880379248°C

LAST Step Rounding Answer

∴

θ = 412.8269°C

Tool temperature Formula Elements

Variables

Tool Temperature

Tool Temperature is the temperature reached during cutting for tool.

Symbol: θ

Measurement: TemperatureUnit: °C

Note: Value should be greater than 0.

Formulas to find Tool Temperature

Constant For Tool Temperature

Constant For Tool Temperature is a constant for the tool temperature determination.

Symbol: C₀

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Constant For Tool Temperature

Specific Cutting Energy Per Unit Cutting Force

Specific Cutting Energy Per Unit Cutting Force is a crucial parameter in machining processes. It quantifies the energy required to remove a unit volume of material during cutting operations.

Symbol: U_s

Measurement: Specific EnergyUnit: kJ/kg

Note: Value should be greater than 0.

Formulas to find Specific Cutting Energy Per Unit Cutting Force

Cutting Velocity in Tool Life

The Cutting Velocity in Tool Life is the tangential velocity at the periphery of the cutter or workpiece (whichever is rotating).

Symbol: V

Measurement: SpeedUnit: m/s

Note: Value should be greater than 0.

Formulas to find Cutting Velocity in Tool Life

Area of Cut

Area of Cut is the area which is to be cut using cutting tool.

Symbol: A

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Area of Cut

Thermal Conductivity

Thermal Conductivity is the rate of heat flow through a material, expressed as the amount of heat flow per unit time through a unit area with a temperature gradient of one degree per unit distance.

Symbol: k

Measurement: Thermal ConductivityUnit: W/(m*K)

Note: Value should be greater than 0.

Formulas to find Thermal Conductivity

Specific Heat Capacity of Work

Specific Heat Capacity of Work is the heat required to raise the temperature of the unit mass of a given substance by a given amount.

Symbol: c

Measurement: Specific Heat CapacityUnit: J/(kg*K)

Note: Value should be greater than 0.

Formulas to find Specific Heat Capacity of Work

Other formulas in Tool Life category

Go Volume of Metal removed given Cutting Velocity and Tool Life

vol = TL \cdot V \cdot f \cdot d' cut

Go Feed given Cutting Velocity, Tool Life, and Volume of Metal Removed

f = \frac{vol}{TL \cdot V \cdot d' cut}

How to Evaluate Tool temperature?

Tool temperature evaluator uses Tool Temperature = (Constant For Tool Temperature*Specific Cutting Energy Per Unit Cutting Force*Cutting Velocity in Tool Life^0.44*Area of Cut^0.22)/(Thermal Conductivity^0.44*Specific Heat Capacity of Work^0.56) to evaluate the Tool Temperature, The Tool temperature formula is defined as the increase in temperature because of machining heat. This is calculated using specific energy per unit of cutting force used. Tool Temperature is denoted by θ symbol.

How to evaluate Tool temperature using this online evaluator? To use this online evaluator for Tool temperature, enter Constant For Tool Temperature (C₀), Specific Cutting Energy Per Unit Cutting Force (U_s), Cutting Velocity in Tool Life (V), Area of Cut (A), Thermal Conductivity (k) & Specific Heat Capacity of Work (c) and hit the calculate button.

FAQs on Tool temperature

What is the formula to find Tool temperature?

The formula of Tool temperature is expressed as Tool Temperature = (Constant For Tool Temperature*Specific Cutting Energy Per Unit Cutting Force*Cutting Velocity in Tool Life^0.44*Area of Cut^0.22)/(Thermal Conductivity^0.44*Specific Heat Capacity of Work^0.56). Here is an example- 139.677 = (0.29*200000*0.833333^0.44*45^0.22)/(48^0.44*510^0.56).

How to calculate Tool temperature?

With Constant For Tool Temperature (C₀), Specific Cutting Energy Per Unit Cutting Force (U_s), Cutting Velocity in Tool Life (V), Area of Cut (A), Thermal Conductivity (k) & Specific Heat Capacity of Work (c) we can find Tool temperature using the formula - Tool Temperature = (Constant For Tool Temperature*Specific Cutting Energy Per Unit Cutting Force*Cutting Velocity in Tool Life^0.44*Area of Cut^0.22)/(Thermal Conductivity^0.44*Specific Heat Capacity of Work^0.56).

Can the Tool temperature be negative?

No, the Tool temperature, measured in Temperature cannot be negative.

Which unit is used to measure Tool temperature?

Tool temperature is usually measured using the Celsius[°C] for Temperature. Kelvin[°C], Fahrenheit[°C], Rankine[°C] are the few other units in which Tool temperature can be measured.

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Tool temperature Formula

Tool temperature Example

Tool temperature Solution

Tool temperature Formula Elements

Other formulas in Tool Life category

How to Evaluate Tool temperature?

FAQs on Tool temperature

Variable Name