Number of Tools Used given Machining Time and Conditions Solution

STEP 0: Pre-Calculation Summary
Formula Used
Number of Tools Used = Machining Time*Batch Size/(Reference Tool Life*((Reference Cutting Velocity/Cutting Velocity)^(1/Taylor's Tool Life Exponent)))
Nt = tm*Nb/(Tref*((Vref/V)^(1/n)))
This formula uses 7 Variables
Variables Used
Number of Tools Used - The Number of Tools Used is the total number of tools used for manufacturing a batch of products.
Machining Time - (Measured in Second) - Machining Time is the time when a machine is actually processing something. Generally, machining time is the term used when there is a removal of unwanted material.
Batch Size - Batch Size is the count of similar kinds of products to be manufactured.
Reference Tool Life - (Measured in Second) - Reference Tool Life is the Tool Life of the tool obtained in the reference Machining Condition.
Reference Cutting Velocity - (Measured in Meter per Second) - Reference Cutting Velocity is the Cutting Velocity of the tool used in the reference Machining Condition.
Cutting Velocity - (Measured in Meter per Second) - The Cutting Velocity is the tangential velocity at the periphery of the cutter or workpiece (whichever is rotating).
Taylor's Tool Life Exponent - Taylor's Tool Life Exponent is an experimental exponent that helps in quantifying the rate of Tool Wear.
STEP 1: Convert Input(s) to Base Unit
Machining Time: 0.5 Minute --> 30 Second (Check conversion here)
Batch Size: 2 --> No Conversion Required
Reference Tool Life: 1200 Minute --> 72000 Second (Check conversion here)
Reference Cutting Velocity: 5 Meter per Minute --> 0.0833333333333333 Meter per Second (Check conversion here)
Cutting Velocity: 550 Meter per Minute --> 9.16666666666667 Meter per Second (Check conversion here)
Taylor's Tool Life Exponent: 0.55 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Nt = tm*Nb/(Tref*((Vref/V)^(1/n))) --> 30*2/(72000*((0.0833333333333333/9.16666666666667)^(1/0.55)))
Evaluating ... ...
Nt = 4.28984714611231
STEP 3: Convert Result to Output's Unit
4.28984714611231 --> No Conversion Required
FINAL ANSWER
4.28984714611231 4.289847 <-- Number of Tools Used
(Calculation completed in 00.020 seconds)

Credits

Created by Kumar Siddhant
Indian Institute of Information Technology, Design and Manufacturing (IIITDM), Jabalpur
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Verified by Parul Keshav
National Institute of Technology (NIT), Srinagar
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18 Tool Life and Production Batch Calculators

Taylor's Tool Life Exponent given Production Batch and Machining Conditions
Go Taylor's Tool Life Exponent = ln(Cutting Velocity/Reference Cutting Velocity)/ln((Reference Tool Life*Number of Tools Used)/(Batch Size*Machining Time))
Machining Time of one product given Production Batch and Machining Conditions
Go Machining Time = Number of Tools Used*(Reference Tool Life*((Reference Cutting Velocity/Cutting Velocity)^(1/Taylor's Tool Life Exponent)))/Batch Size
Number of Tools Used given Machining Time and Conditions
Go Number of Tools Used = Machining Time*Batch Size/(Reference Tool Life*((Reference Cutting Velocity/Cutting Velocity)^(1/Taylor's Tool Life Exponent)))
Batch Size given Machining Time and Conditions
Go Batch Size = Number of Tools Used*(Reference Tool Life*((Reference Cutting Velocity/Cutting Velocity)^(1/Taylor's Tool Life Exponent)))/Machining Time
Reference Cutting Velocity given Production Batch and Machining Conditions
Go Reference Cutting Velocity = Cutting Velocity*(((Batch Size*Machining Time)/(Reference Tool Life*Number of Tools Used))^Taylor's Tool Life Exponent)
Reference Tool Life given Production Batch and Machining Conditions
Go Reference Tool Life = Machining Time*Batch Size*((Cutting Velocity/Reference Cutting Velocity)^(1/Taylor's Tool Life Exponent))/Number of Tools Used
Cutting Velocity given Production Batch and Machining Conditions
Go Cutting Velocity = Reference Cutting Velocity*(((Reference Tool Life*Number of Tools Used)/(Batch Size*Machining Time))^Taylor's Tool Life Exponent)
Diameter of workpiece given Constant for Cylindrical Turning
Go Diameter of Workpiece = Constant For Machining Condition*Feed/(pi*Length of Cut)
Turning Length given Constant for Cylindrical Turning
Go Length of Cut = Constant For Machining Condition*Feed/(pi*Diameter of Workpiece)
Feed given Constant for Cylindrical Turning
Go Feed = pi*Diameter of Workpiece*Length of Cut/Constant For Machining Condition
Constant for given Cylindrical Turning
Go Constant For Machining Condition = pi*Diameter of Workpiece*Length of Cut/Feed
Tool Life given Batch Size and Number of Tools
Go Tool Life = Machining Time*Batch Size/Number of Tools Used
Machining Time of One Product using Tool Life
Go Machining Time = Number of Tools Used*Tool Life/Batch Size
Batch Size using Tool Life and Machining Time
Go Batch Size = Number of Tools Used*Tool Life/Machining Time
Number of Tools Used given Tool Life
Go Number of Tools Used = Machining Time*Batch Size/Tool Life
Cutting Velocity of one product given Constant for Machining Operation
Go Cutting Velocity = Constant For Machining Condition/Machining Time
Constant for Machining Operation of one product given Machining Condition
Go Constant For Machining Condition = Machining Time*Cutting Velocity
Machining Time of one product given Constant for Machining Operation
Go Machining Time = Constant For Machining Condition/Cutting Velocity

Number of Tools Used given Machining Time and Conditions Formula

Number of Tools Used = Machining Time*Batch Size/(Reference Tool Life*((Reference Cutting Velocity/Cutting Velocity)^(1/Taylor's Tool Life Exponent)))
Nt = tm*Nb/(Tref*((Vref/V)^(1/n)))

Tool Failure and Need to change the Tool

The tool generally undergoes the following failure:
1. Fracture failure - Cutting force becomes excessive, leading to brittle fracture
2. Temperature failure - The cutting temperature is too high for the tool material
3. Gradual wear Due to Wear, the sharpness of the Cutting edge of the tool is lost
which leads to roughness and tolerances at the surface. To tackle this, the tool is
usually sharpened rather than completely changed.

How to Calculate Number of Tools Used given Machining Time and Conditions?

Number of Tools Used given Machining Time and Conditions calculator uses Number of Tools Used = Machining Time*Batch Size/(Reference Tool Life*((Reference Cutting Velocity/Cutting Velocity)^(1/Taylor's Tool Life Exponent))) to calculate the Number of Tools Used, Number of Tools Used given Machining Time and Conditions is a method to determine the maximum number of tools that might be required to manufacture a batch of components when the conditions under which the tool is being used are known. Number of Tools Used is denoted by Nt symbol.

How to calculate Number of Tools Used given Machining Time and Conditions using this online calculator? To use this online calculator for Number of Tools Used given Machining Time and Conditions, enter Machining Time (tm), Batch Size (Nb), Reference Tool Life (Tref), Reference Cutting Velocity (Vref), Cutting Velocity (V) & Taylor's Tool Life Exponent (n) and hit the calculate button. Here is how the Number of Tools Used given Machining Time and Conditions calculation can be explained with given input values -> 4.289847 = 30*2/(72000*((0.0833333333333333/9.16666666666667)^(1/0.55))) .

FAQ

What is Number of Tools Used given Machining Time and Conditions?
Number of Tools Used given Machining Time and Conditions is a method to determine the maximum number of tools that might be required to manufacture a batch of components when the conditions under which the tool is being used are known and is represented as Nt = tm*Nb/(Tref*((Vref/V)^(1/n))) or Number of Tools Used = Machining Time*Batch Size/(Reference Tool Life*((Reference Cutting Velocity/Cutting Velocity)^(1/Taylor's Tool Life Exponent))). Machining Time is the time when a machine is actually processing something. Generally, machining time is the term used when there is a removal of unwanted material, Batch Size is the count of similar kinds of products to be manufactured, Reference Tool Life is the Tool Life of the tool obtained in the reference Machining Condition, Reference Cutting Velocity is the Cutting Velocity of the tool used in the reference Machining Condition, The Cutting Velocity is the tangential velocity at the periphery of the cutter or workpiece (whichever is rotating) & Taylor's Tool Life Exponent is an experimental exponent that helps in quantifying the rate of Tool Wear.
How to calculate Number of Tools Used given Machining Time and Conditions?
Number of Tools Used given Machining Time and Conditions is a method to determine the maximum number of tools that might be required to manufacture a batch of components when the conditions under which the tool is being used are known is calculated using Number of Tools Used = Machining Time*Batch Size/(Reference Tool Life*((Reference Cutting Velocity/Cutting Velocity)^(1/Taylor's Tool Life Exponent))). To calculate Number of Tools Used given Machining Time and Conditions, you need Machining Time (tm), Batch Size (Nb), Reference Tool Life (Tref), Reference Cutting Velocity (Vref), Cutting Velocity (V) & Taylor's Tool Life Exponent (n). With our tool, you need to enter the respective value for Machining Time, Batch Size, Reference Tool Life, Reference Cutting Velocity, Cutting Velocity & Taylor's Tool Life Exponent 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 Number of Tools Used?
In this formula, Number of Tools Used uses Machining Time, Batch Size, Reference Tool Life, Reference Cutting Velocity, Cutting Velocity & Taylor's Tool Life Exponent. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • Number of Tools Used = Machining Time*Batch Size/Tool Life
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