Tool Engagement Angle in Slab Milling using Depth of Cut Calculator

✖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.ⓘ Depth of Cut [d_cut]			+10% -10%
✖The Diameter of Cutting Tool is the outer diameter of the cutting part of the tool.ⓘ Diameter of Cutting Tool [D_t]			+10% -10%

✖Tool Engagement Angle is the angle made by the portion of the tool that engages with the workpiece during machining process.ⓘ Tool Engagement Angle in Slab Milling using Depth of Cut [θ]

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Formula

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Tool Engagement Angle in Slab Milling using Depth of Cut

Formula

`"θ" = acos(1-(2*"d"_{"cut"}/"D"_{"t"}))`

Example

`"65.02503°"=acos(1-(2*"13mm"/"45mm"))`

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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*d_cut/D_t))
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*d_cut/D_t)) --> 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 00.006 seconds)

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Created by Kumar Siddhant

Indian Institute of Information Technology, Design and Manufacturing (IIITDM), Jabalpur

Kumar Siddhant has created this Calculator and 400+ more calculators!

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Osmania University (OU), Hyderabad

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< 10+ Slab and Slide Milling Calculators

Maximum Chip Thickness obtained in Slab Milling using Depth of Cut

Go Maximum Chip Thickness = 2*Feed Speed*sqrt(Depth of Cut/Diameter of Cutting Tool)/(Number of Teeth on Cutting Tool*Rotational Frequency)

Maximum Chip Thickness obtained in Slab Milling using Tool Engagement Angle

Go Maximum Chip Thickness = Feed Speed*sin(Tool Engagement Angle)/(Number of Teeth on Cutting Tool*Rotational Frequency)

Diameter of Tool given Proportion of Edge Engagement for Slab and Side Milling

Go Diameter of A Cutting Tool For Slab = 2*Work Engagement/(sin((Time Proportion of Cutting Edge Engagement-0.25)*2*pi)+1)

Work Engagement given Proportion of Edge Engagement for Slab and Side Milling

Go Work Engagement = (sin((Time Proportion of Cutting Edge Engagement-0.25)*2*pi)+1)*Diameter of A Cutting Tool For Slab/2

Proportion of Cutting Edge Engagement for Slab and Side Milling

Go Time Proportion of Cutting Edge Engagement = 0.25+(asin((2*Work Engagement/Diameter of A Cutting Tool)-1)/(2*pi))

Minimum Length of Approach required in Slab Milling

Go Length of Approach = sqrt(Depth of Cut*(Diameter of Cutting Tool-Depth of Cut))

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

Feed Speed of Workpiece in Slab Milling

Go Feed Speed = Feed Rate*Frequency of Reciprocating Strokes

Feed in Slab Milling given Feed Speed

Go Feed Rate = Feed Speed/Frequency of Reciprocating Strokes

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*d_cut/D_t))

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 (d_cut) & Diameter of Cutting Tool (D_t) 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*d_cut/D_t)) 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 (d_cut) & Diameter of Cutting Tool (D_t). 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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