Tool Engagement Angle in Slab Milling using Depth of Cut Solution

STEP 0: Pre-Calculation Summary
Formula Used
Tool Engagement Angle = acos(1-(2*Depth of Cut/Diameter of Cutting Tool))
θ = acos(1-(2*dcut/Dt))
This formula uses 2 Functions, 3 Variables
Functions Used
cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)
acos - The inverse cosine function, is the inverse function of the cosine function. It is the function that takes a ratio as an input and returns the angle whose cosine is equal to that ratio., acos(Number)
Variables Used
Tool Engagement Angle - (Measured in Radian) - Tool Engagement Angle is the angle made by the portion of the tool that engages with the workpiece during machining process.
Depth of Cut - (Measured in Meter) - Depth of Cut is the tertiary cutting motion that provides a necessary depth of material that is required to remove by machining. It is usually given in the third perpendicular direction.
Diameter of Cutting Tool - (Measured in Meter) - The Diameter of Cutting Tool is the outer diameter of the cutting part of the tool.
STEP 1: Convert Input(s) to Base Unit
Depth of Cut: 13 Millimeter --> 0.013 Meter (Check conversion here)
Diameter of Cutting Tool: 45 Millimeter --> 0.045 Meter (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
θ = acos(1-(2*dcut/Dt)) --> acos(1-(2*0.013/0.045))
Evaluating ... ...
θ = 1.13490095055767
STEP 3: Convert Result to Output's Unit
1.13490095055767 Radian -->65.0250346323523 Degree (Check conversion here)
FINAL ANSWER
65.0250346323523 65.02503 Degree <-- Tool Engagement Angle
(Calculation completed in 00.004 seconds)

Credits

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Indian Institute of Information Technology, Design and Manufacturing (IIITDM), Jabalpur
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17 Machine tools and machine operations Calculators

Mean Cutting Speed
Go Mean Cutting Speed = Angular Velocity of Job or Workpiece*pi*(Work Surface Diameter+Machine Surface Diameter)/2
Energy per Unit Material Removal given Efficiency of Motor Drive System
Go Rate of Energy Consumption during Machining = Electrical Power Available for Machining*Overall Machining Efficiency/Metal removal rate
Diameter of Drill Bit given Length of Approach
Go Diameter of drill bit = 2*Length of Approach/tan((pi/2)-(Drill Point Angle/2))
Minimum Length of Approach required in Slab Milling
Go Length of Approach = sqrt(Depth of Cut*(Diameter of Cutting Tool-Depth of Cut))
Length of Cut using Machining Time
Go Length of Cut = Feed Rate*Machining Time*Angular Velocity of Job or Workpiece
Tool Engagement Angle in Slab Milling using Depth of Cut
Go Tool Engagement Angle = acos(1-(2*Depth of Cut/Diameter of Cutting Tool))
Depth of Cut in Slab Milling using Tool Engagement Angle
Go Depth of Cut = (1-cos(Tool Engagement Angle))*Diameter of Cutting Tool/2
Drill Point Angle for given Length of Approach
Go Drill Point Angle = 2*atan(0.5*Diameter of drill bit/Length of Approach)
Resultant Cutting Velocity
Go Resultant Cutting Velocity = Cutting Velocity/cos((Cutting Speed Angle))
Cutting Speed Angle using Resultant Cutting Speed
Go Cutting Speed Angle = acos(Cutting Velocity/Resultant Cutting Velocity)
Length of Approach for Drilling Operation
Go Length of Approach = 0.5*Diameter of drill bit*cot(Drill Point Angle/2)
Overall Efficiency of Machine Tool and Motor Drive System
Go Overall Machining Efficiency = Machining Power/Electrical Power Available for Machining
Machining Power using Overall Efficiency
Go Machining Power = Overall Machining Efficiency*Electrical Power Available for Machining
Cutting Speed in Turning
Go Cutting Speed = pi*Diameter of Workpiece*Spindle Speed
Power required for Machining Operation
Go Machining Power = Metal removal rate*Rate of Energy Consumption during Machining
Cross sectional Area of Uncut Chip
Go Cross-sectional Area of Uncut Chip = Feed Rate*Depth of Cut
Minimum Length of Approach required in Face Milling
Go Length of Approach = Diameter of Cutting Tool/2

Tool Engagement Angle in Slab Milling using Depth of Cut Formula

Tool Engagement Angle = acos(1-(2*Depth of Cut/Diameter of Cutting Tool))
θ = acos(1-(2*dcut/Dt))

Optimal Cutting During Milling

To cut optimally means to create chips with the optimal geometry for the particular tool being used and the particular material being cut. This requires controlling the feed rate, spindle speed, depth-of-cut, and the tool’s engagement with the material.

How to Calculate Tool Engagement Angle in Slab Milling using Depth of Cut?

Tool Engagement Angle in Slab Milling using Depth of Cut calculator uses Tool Engagement Angle = acos(1-(2*Depth of Cut/Diameter of Cutting Tool)) to calculate the Tool Engagement Angle, The Tool Engagement Angle in Slab Milling using Depth of Cut is defined as the angle made by the portion of the tool that engages with the workpiece during the Machining Process, the Depth of Cut is given. Tool Engagement Angle is denoted by θ symbol.

How to calculate Tool Engagement Angle in Slab Milling using Depth of Cut using this online calculator? To use this online calculator for Tool Engagement Angle in Slab Milling using Depth of Cut, enter Depth of Cut (dcut) & Diameter of Cutting Tool (Dt) and hit the calculate button. Here is how the Tool Engagement Angle in Slab Milling using Depth of Cut calculation can be explained with given input values -> 3725.66 = acos(1-(2*0.013/0.045)).

FAQ

What is Tool Engagement Angle in Slab Milling using Depth of Cut?
The Tool Engagement Angle in Slab Milling using Depth of Cut is defined as the angle made by the portion of the tool that engages with the workpiece during the Machining Process, the Depth of Cut is given and is represented as θ = acos(1-(2*dcut/Dt)) or Tool Engagement Angle = acos(1-(2*Depth of Cut/Diameter of Cutting Tool)). Depth of Cut is the tertiary cutting motion that provides a necessary depth of material that is required to remove by machining. It is usually given in the third perpendicular direction & The Diameter of Cutting Tool is the outer diameter of the cutting part of the tool.
How to calculate Tool Engagement Angle in Slab Milling using Depth of Cut?
The Tool Engagement Angle in Slab Milling using Depth of Cut is defined as the angle made by the portion of the tool that engages with the workpiece during the Machining Process, the Depth of Cut is given is calculated using Tool Engagement Angle = acos(1-(2*Depth of Cut/Diameter of Cutting Tool)). To calculate Tool Engagement Angle in Slab Milling using Depth of Cut, you need Depth of Cut (dcut) & Diameter of Cutting Tool (Dt). With our tool, you need to enter the respective value for Depth of Cut & Diameter of Cutting Tool and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
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