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Tool Changing Cost given Optimum Spindle Speed Formula

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The cost of changing each Tool is the cost that arises due to the time taken by the operator to change one tool when he is paid by the hour. Check FAQs

C ct = (\frac{C t \cdot T max}{{(ω s \cdot 2 \cdot π \cdot \frac{R o}{V ref})}^{\frac{1}{n}} \cdot (1 - {R w}^{\frac{1 + n}{n}}) \cdot \frac{1 - n}{(1 + n) \cdot (1 - R w)}}) - C t

C_ct - Cost of Changing Each Tool?C_t - Cost of a Tool?T_max - Maximum Tool Life?ω_s - Rotational Frequency of Spindle?R_o - Outer Radius of Workpiece?V_ref - Reference Cutting Velocity?n - Taylor's Tool Life Exponent?R_w - Workpiece Radius Ratio?π - Archimedes' constant?

Tool Changing Cost given Optimum Spindle Speed Example

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Here is how the Tool Changing Cost given Optimum Spindle Speed equation looks like with Values.

Here is how the Tool Changing Cost given Optimum Spindle Speed equation looks like with Units.

Here is how the Tool Changing Cost given Optimum Spindle Speed equation looks like.

150.5757 = (\frac{158.8131 \cdot 7000}{{(600 \cdot 2 \cdot 3.1416 \cdot \frac{1000}{5000})}^{\frac{1}{0.5129}} \cdot (1 - {0.45}^{\frac{1 + 0.5129}{0.5129}}) \cdot \frac{1 - 0.5129}{(1 + 0.5129) \cdot (1 - 0.45)}}) - 158.8131

150.5757 = (\frac{158.8131 \cdot 7000min}{{(600rev/min \cdot 2 \cdot 3.1416 \cdot \frac{1000mm}{5000mm/min})}^{\frac{1}{0.5129}} \cdot (1 - {0.45}^{\frac{1 + 0.5129}{0.5129}}) \cdot \frac{1 - 0.5129}{(1 + 0.5129) \cdot (1 - 0.45)}}) - 158.8131

150.5757 = (\frac{158.8131 \cdot 7000}{{(600 \cdot 2 \cdot 3.1416 \cdot \frac{1000}{5000})}^{\frac{1}{0.5129}} \cdot (1 - {0.45}^{\frac{1 + 0.5129}{0.5129}}) \cdot \frac{1 - 0.5129}{(1 + 0.5129) \cdot (1 - 0.45)}}) - 158.8131

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Tool Changing Cost given Optimum Spindle Speed Solution

Follow our step by step solution on how to calculate Tool Changing Cost given Optimum Spindle Speed?

FIRST Step Consider the formula

C ct = (\frac{C t \cdot T max}{{(ω s \cdot 2 \cdot π \cdot \frac{R o}{V ref})}^{\frac{1}{n}} \cdot (1 - {R w}^{\frac{1 + n}{n}}) \cdot \frac{1 - n}{(1 + n) \cdot (1 - R w)}}) - C t

Next Step Substitute values of Variables

∴

C ct = (\frac{158.8131 \cdot 7000min}{{(600rev/min \cdot 2 \cdot π \cdot \frac{1000mm}{5000mm/min})}^{\frac{1}{0.5129}} \cdot (1 - {0.45}^{\frac{1 + 0.5129}{0.5129}}) \cdot \frac{1 - 0.5129}{(1 + 0.5129) \cdot (1 - 0.45)}}) - 158.8131

Next Step Substitute values of Constants

∴

C ct = (\frac{158.8131 \cdot 7000min}{{(600rev/min \cdot 2 \cdot 3.1416 \cdot \frac{1000mm}{5000mm/min})}^{\frac{1}{0.5129}} \cdot (1 - {0.45}^{\frac{1 + 0.5129}{0.5129}}) \cdot \frac{1 - 0.5129}{(1 + 0.5129) \cdot (1 - 0.45)}}) - 158.8131

Next Step Convert Units

∴

C ct = (\frac{158.8131 \cdot 420000s}{{(10Hz \cdot 2 \cdot 3.1416 \cdot \frac{1m}{0.0833m/s})}^{\frac{1}{0.5129}} \cdot (1 - {0.45}^{\frac{1 + 0.5129}{0.5129}}) \cdot \frac{1 - 0.5129}{(1 + 0.5129) \cdot (1 - 0.45)}}) - 158.8131

Next Step Prepare to Evaluate

∴

C ct = (\frac{158.8131 \cdot 420000}{{(10 \cdot 2 \cdot 3.1416 \cdot \frac{1}{0.0833})}^{\frac{1}{0.5129}} \cdot (1 - {0.45}^{\frac{1 + 0.5129}{0.5129}}) \cdot \frac{1 - 0.5129}{(1 + 0.5129) \cdot (1 - 0.45)}}) - 158.8131

Next Step Evaluate

∴

C ct = 150.575653136286

LAST Step Rounding Answer

∴

C ct = 150.5757

Tool Changing Cost given Optimum Spindle Speed Formula Elements

Variables

Constants

Cost of Changing Each Tool

The cost of changing each Tool is the cost that arises due to the time taken by the operator to change one tool when he is paid by the hour.

Symbol: C_ct

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Cost of Changing Each Tool

Cost of a Tool

The Cost of a Tool refers to the expenses associated with acquiring and using cutting tools used in various machining operations.

Symbol: C_t

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Cost of a Tool

Maximum Tool Life

Maximum Tool Life is the point at which a cutting tool reaches its limit in terms of usage before it becomes too worn, damaged, or otherwise unable to effectively perform its intended function.

Symbol: T_max

Measurement: TimeUnit: min

Note: Value should be greater than 0.

Formulas to find Maximum Tool Life

Rotational Frequency of Spindle

Rotational Frequency of Spindle is the speed at which the spindle of a machine tool rotates during machining operations. It is typically measured in revolutions per minute.

Symbol: ω_s

Measurement: FrequencyUnit: rev/min

Note: Value should be greater than 0.

Formulas to find Rotational Frequency of Spindle

Outer Radius of Workpiece

Outer Radius of Workpiece is the distance from the center of rotation to the outermost surface of the workpiece being machined.

Symbol: R_o

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Outer Radius of Workpiece

Reference Cutting Velocity

Reference Cutting Velocity refers to a standard cutting speed used as a baseline or reference point for selecting appropriate cutting speeds for specific machining operations.

Symbol: V_ref

Measurement: SpeedUnit: mm/min

Note: Value should be greater than 0.

Formulas to find Reference Cutting Velocity

Taylor's Tool Life Exponent

Taylor's Tool Life Exponent is a parameter used in tool life equations to describe the relationship between cutting speed and tool life in metal machining.

Symbol: n

Measurement: NAUnit: Unitless

Note: Value should be between 0 to 1.

Formulas to find Taylor's Tool Life Exponent

Workpiece Radius Ratio

Workpiece Radius Ratio refers to the ratio between the initial radius and the final radius of the workpiece being machined.

Symbol: R_w

Measurement: NAUnit: Unitless

Note: Value should be between 0 to 1.

Formulas to find Workpiece Radius Ratio

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 in Cutting Speed category

Go Reference Cutting Velocity given Rate of Increase of Wear-Land Width

V ref = \frac{V}{{(V r \cdot \frac{T ref}{w})}^{n}}

Go Cutting Velocity given Rate of Increase of Wear-Land Width

V = V ref \cdot {(V r \cdot \frac{T ref}{w})}^{n}

How to Evaluate Tool Changing Cost given Optimum Spindle Speed?

Tool Changing Cost given Optimum Spindle Speed evaluator uses Cost of Changing Each Tool = ((Cost of a Tool*Maximum Tool Life)/((Rotational Frequency of Spindle*2*pi*Outer Radius of Workpiece/Reference Cutting Velocity)^(1/Taylor's Tool Life Exponent)*(1-Workpiece Radius Ratio^((1+Taylor's Tool Life Exponent)/Taylor's Tool Life Exponent))*(1-Taylor's Tool Life Exponent)/((1+Taylor's Tool Life Exponent)*(1-Workpiece Radius Ratio))))-Cost of a Tool to evaluate the Cost of Changing Each Tool, The Tool Changing Cost given Optimum Spindle Speed refers to the expenses associated with changing or replacing cutting tools during the machining process. These costs include direct expenses such as the purchase cost of the tools, labor costs associated with tool changeovers, and indirect costs such as machine downtime and lost productivity. The optimum spindle speed, on the other hand, refers to the ideal rotational speed of the spindle that maximizes machining efficiency, tool life, and surface finish quality for a given machining operation. Cost of Changing Each Tool is denoted by C_ct symbol.

How to evaluate Tool Changing Cost given Optimum Spindle Speed using this online evaluator? To use this online evaluator for Tool Changing Cost given Optimum Spindle Speed, enter Cost of a Tool (C_t), Maximum Tool Life (T_max), Rotational Frequency of Spindle (ω_s), Outer Radius of Workpiece (R_o), Reference Cutting Velocity (V_ref), Taylor's Tool Life Exponent (n) & Workpiece Radius Ratio (R_w) and hit the calculate button.

FAQs on Tool Changing Cost given Optimum Spindle Speed

What is the formula to find Tool Changing Cost given Optimum Spindle Speed?

The formula of Tool Changing Cost given Optimum Spindle Speed is expressed as Cost of Changing Each Tool = ((Cost of a Tool*Maximum Tool Life)/((Rotational Frequency of Spindle*2*pi*Outer Radius of Workpiece/Reference Cutting Velocity)^(1/Taylor's Tool Life Exponent)*(1-Workpiece Radius Ratio^((1+Taylor's Tool Life Exponent)/Taylor's Tool Life Exponent))*(1-Taylor's Tool Life Exponent)/((1+Taylor's Tool Life Exponent)*(1-Workpiece Radius Ratio))))-Cost of a Tool. Here is an example- 150.5757 = ((158.8131*420000)/((10*2*pi*1/0.0833333333333333)^(1/0.512942)*(1-0.45^((1+0.512942)/0.512942))*(1-0.512942)/((1+0.512942)*(1-0.45))))-158.8131.

How to calculate Tool Changing Cost given Optimum Spindle Speed?

With Cost of a Tool (C_t), Maximum Tool Life (T_max), Rotational Frequency of Spindle (ω_s), Outer Radius of Workpiece (R_o), Reference Cutting Velocity (V_ref), Taylor's Tool Life Exponent (n) & Workpiece Radius Ratio (R_w) we can find Tool Changing Cost given Optimum Spindle Speed using the formula - Cost of Changing Each Tool = ((Cost of a Tool*Maximum Tool Life)/((Rotational Frequency of Spindle*2*pi*Outer Radius of Workpiece/Reference Cutting Velocity)^(1/Taylor's Tool Life Exponent)*(1-Workpiece Radius Ratio^((1+Taylor's Tool Life Exponent)/Taylor's Tool Life Exponent))*(1-Taylor's Tool Life Exponent)/((1+Taylor's Tool Life Exponent)*(1-Workpiece Radius Ratio))))-Cost of a Tool. This formula also uses Archimedes' constant .

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Tool Changing Cost given Optimum Spindle Speed Formula

Tool Changing Cost given Optimum Spindle Speed Example

Tool Changing Cost given Optimum Spindle Speed Solution

Tool Changing Cost given Optimum Spindle Speed Formula Elements

Other formulas in Cutting Speed category

How to Evaluate Tool Changing Cost given Optimum Spindle Speed?

FAQs on Tool Changing Cost given Optimum Spindle Speed

Variable Name