Inside Radius given Workpiece Radius Ratio Solution

STEP 0: Pre-Calculation Summary
Formula Used
Inner Radius of Workpiece = Workpiece Radius Ratio*Outside Radius of the Workpiece
ri = ar*ro
This formula uses 3 Variables
Variables Used
Inner Radius of Workpiece - (Measured in Meter) - The Inner Radius of Workpiece is the radius of the innermost surface of the workpiece.
Workpiece Radius Ratio - Workpiece Radius Ratio is the ratio of the inner radius of the workpiece to its outer radius.
Outside Radius of the Workpiece - (Measured in Meter) - Outside Radius of the Workpiece is the radius of the outermost surface of the workpiece, away from the machining tool.
STEP 1: Convert Input(s) to Base Unit
Workpiece Radius Ratio: 0.45 --> No Conversion Required
Outside Radius of the Workpiece: 1000 Millimeter --> 1 Meter (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
ri = ar*ro --> 0.45*1
Evaluating ... ...
ri = 0.45
STEP 3: Convert Result to Output's Unit
0.45 Meter -->450 Millimeter (Check conversion here)
FINAL ANSWER
450 Millimeter <-- Inner Radius of Workpiece
(Calculation completed in 00.004 seconds)

Credits

Created by Kumar Siddhant
Indian Institute of Information Technology, Design and Manufacturing (IIITDM), Jabalpur
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19 Facing Operation Calculators

Optimum Spindle Speed
Go Rotational Frequency of Spindle = (Reference Cutting Velocity/(2*pi*Outside Radius of the Workpiece))*((((1+Taylor's Tool Life Exponent)*Cost of a Tool*Reference Tool Life*(1-Workpiece Radius Ratio))/((1-Taylor's Tool Life Exponent)*(Cost of a Tool*Time to Change One Tool+Cost of a Tool)*(1-(Workpiece Radius Ratio^((1+Taylor's Tool Life Exponent)/Taylor's Tool Life Exponent)))))^Taylor's Tool Life Exponent)
Machining and Operating Rate given Optimum Spindle Speed
Go Machining and Operating Rate = (Cost of a Tool/(((((((Reference Cutting Velocity/(2*pi*Outside Radius of the Workpiece)))/Rotational Frequency of Spindle)^(1/Taylor's Tool Life Exponent))*((((1+Taylor's Tool Life Exponent)/(1-Taylor's Tool Life Exponent)))*((1-Workpiece Radius Ratio)/(1-((Workpiece Radius Ratio)^((Taylor's Tool Life Exponent+1)/Taylor's Tool Life Exponent))))*Reference Tool Life))))-Time to Change One Tool)
Cost of 1 Tool given Optimum Spindle Speed
Go Cost of a Tool = (Machining and Operating Rate*(((((((Reference Cutting Velocity/(2*pi*Outside Radius of the Workpiece)))/Rotational Frequency of Spindle)^(1/Taylor's Tool Life Exponent))*((((1+Taylor's Tool Life Exponent)/(1-Taylor's Tool Life Exponent)))*((1-Workpiece Radius Ratio)/(1-((Workpiece Radius Ratio)^((Taylor's Tool Life Exponent+1)/Taylor's Tool Life Exponent))))*Maximum Tool Life))))-Time to Change One Tool)
Optimum Spindle Speed given Tool Changing Cost
Go Rotational Frequency of Spindle = (Reference Cutting Velocity/(2*pi*Outside Radius of the Workpiece))*((((1+Taylor's Tool Life Exponent)*Cost of a Tool*Reference Tool Life*(1-Workpiece Radius Ratio))/((1-Taylor's Tool Life Exponent)*(Cost of changing each Tool+Cost of a Tool)*(1-(Workpiece Radius Ratio^((1+Taylor's Tool Life Exponent)/Taylor's Tool Life Exponent)))))^Taylor's Tool Life Exponent)
Tool Changing Time given Optimum Spindle Speed
Go Time to Change One Tool = Reference 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/Machining and Operating Rate
Tool Changing Cost given Optimum Spindle Speed
Go Cost of changing each Tool = (Cost of a Tool*Maximum Tool Life/(((Rotational Frequency of Spindle*2*pi*Outside Radius of the 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
Machining Time given Rate of Increase of Wear-Land Width
Go Machining Time = Tool Life/(Rate of Increase of Wear Land Width*Reference Tool Life*((Reference Cutting Velocity/Cutting Velocity)^(1/Taylor's Tool Life Exponent))/Increase in Wear Land Width per Component)
Taylor's Exponent given Cutting Speed for Constant-Cutting-Speed Operation
Go Taylor's Tool Life Exponent = ln(Cutting Velocity/Reference Cutting Velocity)/ln(Maximum Tool Life/(Tool Life*Time Proportion of Cutting Edge Engagement))
Time for Facing given Instantaneous Cutting Speed
Go Process Time = (Outside Radius of the Workpiece-(Cutting Velocity/(2*pi*Rotational Frequency of Spindle)))/(Rotational Frequency of Spindle*Feed)
Feed given Instantaneous Cutting Speed
Go Feed = (Outside Radius of the Workpiece-(Cutting Velocity/(2*pi*Rotational Frequency of Spindle)))/(Rotational Frequency of Spindle*Process Time)
Time Proportion of Edge Engagement given Cutting Speed for Constant-Cutting-Speed Operation
Go Time Proportion of Cutting Edge Engagement = Reference Tool Life*((Reference Cutting Velocity/Cutting Velocity)^(1/Taylor's Tool Life Exponent))/Tool Life
Feed of Workpiece given Machining Time for Facing
Go Feed = (Outside Radius of the Workpiece-Inner Radius of Workpiece)/(Rotational Frequency of Spindle*Machining Time)
Total Machining Time for single Facing Operation
Go Machining Time = (Outside Radius of the Workpiece-Inner Radius of Workpiece)/(Rotational Frequency of Spindle*Feed)
Feed given Instantaneous Radius for Cut
Go Feed = (Outside Radius of the Workpiece-Instantaneous Radius for Cut)/(Rotational Frequency of Spindle*Process Time)
Time for Facing
Go Process Time = (Outside Radius of the Workpiece-Instantaneous Radius for Cut)/(Rotational Frequency of Spindle*Feed)
Inner Radius of Workpiece given Machining Time for Facing
Go Inner Radius of Workpiece = Outside Radius of the Workpiece-Rotational Frequency of Spindle*Feed*Machining Time
Machining Time given Maximum Wear-Land Width
Go Machining Time = Increase in Wear Land Width per Component*Tool Life/Maximum Wear Land Width
Inside Radius given Workpiece Radius Ratio
Go Inner Radius of Workpiece = Workpiece Radius Ratio*Outside Radius of the Workpiece
Workpiece Radius Ratio
Go Workpiece Radius Ratio = Inner Radius of Workpiece/Outside Radius of the Workpiece

Inside Radius given Workpiece Radius Ratio Formula

Inner Radius of Workpiece = Workpiece Radius Ratio*Outside Radius of the Workpiece
ri = ar*ro

Significance of Workpiece Radius Ratio

Workpiece Radius Ratio helps in determining the optimum conditions for machining especially during Facing Operation. It happens as the Workpiece Radius Ratio for standard dimensions has been tabulated for different Optimality Conditions during machining as required and hence can be referenced.

How to Calculate Inside Radius given Workpiece Radius Ratio?

Inside Radius given Workpiece Radius Ratio calculator uses Inner Radius of Workpiece = Workpiece Radius Ratio*Outside Radius of the Workpiece to calculate the Inner Radius of Workpiece, The Inside Radius given Workpiece Radius Ratio is a method to determine the Outermost Radius of the Workpiece when Workpiece Radius Ratio is given. Inner Radius of Workpiece is denoted by ri symbol.

How to calculate Inside Radius given Workpiece Radius Ratio using this online calculator? To use this online calculator for Inside Radius given Workpiece Radius Ratio, enter Workpiece Radius Ratio (ar) & Outside Radius of the Workpiece (ro) and hit the calculate button. Here is how the Inside Radius given Workpiece Radius Ratio calculation can be explained with given input values -> 450000 = 0.45*1.

FAQ

What is Inside Radius given Workpiece Radius Ratio?
The Inside Radius given Workpiece Radius Ratio is a method to determine the Outermost Radius of the Workpiece when Workpiece Radius Ratio is given and is represented as ri = ar*ro or Inner Radius of Workpiece = Workpiece Radius Ratio*Outside Radius of the Workpiece. Workpiece Radius Ratio is the ratio of the inner radius of the workpiece to its outer radius & Outside Radius of the Workpiece is the radius of the outermost surface of the workpiece, away from the machining tool.
How to calculate Inside Radius given Workpiece Radius Ratio?
The Inside Radius given Workpiece Radius Ratio is a method to determine the Outermost Radius of the Workpiece when Workpiece Radius Ratio is given is calculated using Inner Radius of Workpiece = Workpiece Radius Ratio*Outside Radius of the Workpiece. To calculate Inside Radius given Workpiece Radius Ratio, you need Workpiece Radius Ratio (ar) & Outside Radius of the Workpiece (ro). With our tool, you need to enter the respective value for Workpiece Radius Ratio & Outside Radius of the Workpiece 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 Inner Radius of Workpiece?
In this formula, Inner Radius of Workpiece uses Workpiece Radius Ratio & Outside Radius of the Workpiece. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • Inner Radius of Workpiece = Outside Radius of the Workpiece-Rotational Frequency of Spindle*Feed*Machining Time
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