Cutting Speed Angle using Resultant Cutting Speed Calculator

✖The Cutting Velocity refers to the speed of the material being removed at the point of contact between the cutting tool and the workpiece.ⓘ Cutting Velocity [v]			+10% -10%
✖Resultant Cutting Velocity is the instantaneous velocity of the resultant cutting motion of the selected point on the cutting edge relative to the workpiece.ⓘ Resultant Cutting Velocity [v_e]			+10% -10%

✖Resultant Cutting Speed Angle is the angle between cutting tool primary motion vector and resultant cutting motion vector. For most of the practical operations this parameter is very small.ⓘ Cutting Speed Angle using Resultant Cutting Speed [η]

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Cutting Speed Angle using Resultant Cutting Speed Solution

STEP 0: Pre-Calculation Summary

Formula Used

Resultant Cutting Speed Angle = acos(Cutting Velocity/Resultant Cutting Velocity)
η = acos(v/v_e)
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

Resultant Cutting Speed Angle - (Measured in Radian) - Resultant Cutting Speed Angle is the angle between cutting tool primary motion vector and resultant cutting motion vector. For most of the practical operations this parameter is very small.
Cutting Velocity - (Measured in Meter per Second) - The Cutting Velocity refers to the speed of the material being removed at the point of contact between the cutting tool and the workpiece.
Resultant Cutting Velocity - (Measured in Meter per Second) - Resultant Cutting Velocity is the instantaneous velocity of the resultant cutting motion of the selected point on the cutting edge relative to the workpiece.

STEP 1: Convert Input(s) to Base Unit

Cutting Velocity: 4.3489 Meter per Second --> 4.3489 Meter per Second No Conversion Required
Resultant Cutting Velocity: 4.3503 Meter per Second --> 4.3503 Meter per Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

η = acos(v/v_e) --> acos(4.3489/4.3503)

Evaluating ... ...

η = 0.025370618782012

STEP 3: Convert Result to Output's Unit

0.025370618782012 Radian -->1.4536293798449 Degree (Check conversion here)

FINAL ANSWER

1.4536293798449 ≈ 1.453629 Degree <-- Resultant Cutting Speed Angle

(Calculation completed in 00.004 seconds)

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Created by Kumar Siddhant

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

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National Institute Of Technology (NIT), Hamirpur

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< Cutting Operation Calculators

Mean Cutting Speed

LaTeX Go Mean Cutting Speed in Turning = Workpiece Revolution*pi*(Work Surface Diameter+Diameter of Machined Surface)/2

Cutting Speed Angle using Resultant Cutting Speed

LaTeX Go Resultant Cutting Speed Angle = acos(Cutting Velocity/Resultant Cutting Velocity)

Average Material Removal Rate using Uncut Chip Cross-Section Area

LaTeX Go Material Removal Rate in Turning Operation = Cross-Sectional Area of The Uncut Chip*Mean Cutting Speed

Cross sectional Area of Uncut Chip

LaTeX Go Cross-Sectional Area of Uncut Chip = Feed Rate*Depth of Cut

Cutting Speed Angle using Resultant Cutting Speed Formula

LaTeX Go

Resultant Cutting Speed Angle = acos(Cutting Velocity/Resultant Cutting Velocity)
η = acos(v/v_e)

Variation in Cutting Speed Angle

The Cutting Speed Angle changes with variation in Feed Rate (caused due to variation in cross-sectional area of the workpiece) and Cutting Velocity (due to variation in temperatures, hardness, and wear resistance of tool-workpiece interface).

How to Calculate Cutting Speed Angle using Resultant Cutting Speed?

Cutting Speed Angle using Resultant Cutting Speed calculator uses Resultant Cutting Speed Angle = acos(Cutting Velocity/Resultant Cutting Velocity) to calculate the Resultant Cutting Speed Angle, Cutting Speed Angle using Resultant Cutting Speed calculates the angle between Tool primary motion vector and Resultant cutting motion vector. For most the practical operations this angle is very small, therefore negligible. Resultant Cutting Speed Angle is denoted by η symbol.

How to calculate Cutting Speed Angle using Resultant Cutting Speed using this online calculator? To use this online calculator for Cutting Speed Angle using Resultant Cutting Speed, enter Cutting Velocity (v) & Resultant Cutting Velocity (v_e) and hit the calculate button. Here is how the Cutting Speed Angle using Resultant Cutting Speed calculation can be explained with given input values -> 4367.813 = acos(4.3489/4.3503).

FAQ

What is Cutting Speed Angle using Resultant Cutting Speed?

Cutting Speed Angle using Resultant Cutting Speed calculates the angle between Tool primary motion vector and Resultant cutting motion vector. For most the practical operations this angle is very small, therefore negligible and is represented as η = acos(v/v_e) or Resultant Cutting Speed Angle = acos(Cutting Velocity/Resultant Cutting Velocity). The Cutting Velocity refers to the speed of the material being removed at the point of contact between the cutting tool and the workpiece & Resultant Cutting Velocity is the instantaneous velocity of the resultant cutting motion of the selected point on the cutting edge relative to the workpiece.

How to calculate Cutting Speed Angle using Resultant Cutting Speed?

Cutting Speed Angle using Resultant Cutting Speed calculates the angle between Tool primary motion vector and Resultant cutting motion vector. For most the practical operations this angle is very small, therefore negligible is calculated using Resultant Cutting Speed Angle = acos(Cutting Velocity/Resultant Cutting Velocity). To calculate Cutting Speed Angle using Resultant Cutting Speed, you need Cutting Velocity (v) & Resultant Cutting Velocity (v_e). With our tool, you need to enter the respective value for Cutting Velocity & Resultant Cutting Velocity 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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