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Cutting Speed from Tool Temperature Formula

GoCutting Speed given Spindle Speed Formula

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Cutting velocity, cutting speed, it is the speed at which the cutting tool engages the workpiece material, directly impacting the efficiency, quality, and economics of the machining process. Check FAQs

V = {(\frac{θ \cdot k^{0.44} \cdot c^{0.56}}{C 0 \cdot U s \cdot A^{0.22}})}^{\frac{100}{44}}

V - Cutting Velocity?θ - Tool Temperature?k - Thermal Conductivity?c - Specific Heat Capacity?C₀ - Tool Temperature Constant?U_s - Specific Cutting Energy?A - Cutting Area?

Cutting Speed from Tool Temperature Example

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With units

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Here is how the Cutting Speed from Tool Temperature equation looks like with Values.

Here is how the Cutting Speed from Tool Temperature equation looks like with Units.

Here is how the Cutting Speed from Tool Temperature equation looks like.

2 = {(\frac{273 \cdot {10.18}^{0.44} \cdot {4.184}^{0.56}}{0.29 \cdot 200 \cdot {26.4493}^{0.22}})}^{\frac{100}{44}}

2m/s = {(\frac{273°C \cdot {10.18W/(m*K)}^{0.44} \cdot {4.184kJ/kg*K}^{0.56}}{0.29 \cdot 200kJ/kg \cdot {26.4493m²}^{0.22}})}^{\frac{100}{44}}

2 = {(\frac{273 \cdot {10.18}^{0.44} \cdot {4.184}^{0.56}}{0.29 \cdot 200 \cdot {26.4493}^{0.22}})}^{\frac{100}{44}}

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Home » Engineering » Production Engineering » Metal Cutting » Cutting Speed from Tool Temperature

Cutting Speed from Tool Temperature Solution

Follow our step by step solution on how to calculate Cutting Speed from Tool Temperature?

FIRST Step Consider the formula

V = {(\frac{θ \cdot k^{0.44} \cdot c^{0.56}}{C 0 \cdot U s \cdot A^{0.22}})}^{\frac{100}{44}}

Next Step Substitute values of Variables

∴

V = {(\frac{273°C \cdot {10.18W/(m*K)}^{0.44} \cdot {4.184kJ/kg*K}^{0.56}}{0.29 \cdot 200kJ/kg \cdot {26.4493m²}^{0.22}})}^{\frac{100}{44}}

Next Step Convert Units

∴

V = {(\frac{546.15K \cdot {10.18W/(m*K)}^{0.44} \cdot {4184J/(kg*K)}^{0.56}}{0.29 \cdot 200000J/kg \cdot {26.4493m²}^{0.22}})}^{\frac{100}{44}}

Next Step Prepare to Evaluate

∴

V = {(\frac{546.15 \cdot {10.18}^{0.44} \cdot 4184^{0.56}}{0.29 \cdot 200000 \cdot {26.4493}^{0.22}})}^{\frac{100}{44}}

Next Step Evaluate

∴

V = 1.99999986355394m/s

LAST Step Rounding Answer

∴

V = 2m/s

Cutting Speed from Tool Temperature Formula Elements

Variables

Cutting Velocity

Cutting velocity, cutting speed, it is the speed at which the cutting tool engages the workpiece material, directly impacting the efficiency, quality, and economics of the machining process.

Symbol: V

Measurement: SpeedUnit: m/s

Note: Value should be greater than 0.

Tool Temperature

Tool Temperature is the temperature reached during cutting for tool.

Symbol: θ

Measurement: TemperatureUnit: °C

Note: Value should be greater than 0.

Thermal Conductivity

Thermal Conductivity is rate of heat passes through specified material, expressed as amount of heat flows 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.

Specific Heat Capacity

Specific Heat Capacity 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: kJ/kg*K

Note: Value can be positive or negative.

Tool Temperature Constant

Tool Temperature Constant is a Constant for tool temperature determination.

Symbol: C₀

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Specific Cutting Energy

Specific cutting energy, often denoted as "specific cutting energy per unit cutting force"is a measure of the amount of energy required to remove a unit volume of material during a cutting process.

Symbol: U_s

Measurement: Specific EnergyUnit: kJ/kg

Note: Value should be greater than 0.

Cutting Area

Cutting area is a key parameter that represents the cross-sectional area of the material being removed by the cutting tool during machining.

Symbol: A

Measurement: AreaUnit: m²

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 Sai Venkata Phanindra Chary Arendra

Vallurupalli Nageswara Rao Vignana Jyothi Institute of Engineering and Technology (VNRVJIET), Hyderabad

Sai Venkata Phanindra Chary Arendra has verified this Formula and 300+ more formulas!

Other Formulas to find Cutting Velocity

Go Cutting Speed given Spindle Speed

V = π \cdot D \cdot N

Other formulas in Mechanics of Orthogonal Cutting category

Go Machining Time given Spindle Speed

t = \frac{L}{f \cdot N}

Go Machining Time given Cutting Speed

t = \frac{π \cdot D \cdot L}{f \cdot V}

How to Evaluate Cutting Speed from Tool Temperature?

Cutting Speed from Tool Temperature evaluator uses Cutting Velocity = ((Tool Temperature*Thermal Conductivity^0.44*Specific Heat Capacity^0.56)/(Tool Temperature Constant*Specific Cutting Energy*Cutting Area^0.22))^(100/44) to evaluate the Cutting Velocity, The Cutting speed from tool temperature formula is defined as the speed employed for cutting a particular material using tool. Cutting Velocity is denoted by V symbol.

How to evaluate Cutting Speed from Tool Temperature using this online evaluator? To use this online evaluator for Cutting Speed from Tool Temperature, enter Tool Temperature (θ), Thermal Conductivity (k), Specific Heat Capacity (c), Tool Temperature Constant (C₀), Specific Cutting Energy (U_s) & Cutting Area (A) and hit the calculate button.

FAQs on Cutting Speed from Tool Temperature

What is the formula to find Cutting Speed from Tool Temperature?

The formula of Cutting Speed from Tool Temperature is expressed as Cutting Velocity = ((Tool Temperature*Thermal Conductivity^0.44*Specific Heat Capacity^0.56)/(Tool Temperature Constant*Specific Cutting Energy*Cutting Area^0.22))^(100/44). Here is an example- 7200 = ((546.15*10.18^0.44*4184^0.56)/(0.29*200000*26.4493^0.22))^(100/44).

How to calculate Cutting Speed from Tool Temperature?

With Tool Temperature (θ), Thermal Conductivity (k), Specific Heat Capacity (c), Tool Temperature Constant (C₀), Specific Cutting Energy (U_s) & Cutting Area (A) we can find Cutting Speed from Tool Temperature using the formula - Cutting Velocity = ((Tool Temperature*Thermal Conductivity^0.44*Specific Heat Capacity^0.56)/(Tool Temperature Constant*Specific Cutting Energy*Cutting Area^0.22))^(100/44).

What are the other ways to Calculate Cutting Velocity?

Here are the different ways to Calculate Cutting Velocity-

Cutting Velocity=pi*Workpiece Diameter*Spindle Speed

Can the Cutting Speed from Tool Temperature be negative?

No, the Cutting Speed from Tool Temperature, measured in Speed cannot be negative.

Which unit is used to measure Cutting Speed from Tool Temperature?

Cutting Speed from Tool Temperature is usually measured using the Meter per Second[m/s] for Speed. Meter per Minute[m/s], Meter per Hour[m/s], Kilometer per Hour[m/s] are the few other units in which Cutting Speed from Tool Temperature can be measured.