Cutting Speed Angle using Resultant Cutting Speed Solution

STEP 0: Pre-Calculation Summary
Formula Used
Cutting Speed Angle = acos(Cutting Velocity/Resultant Cutting Velocity)
η = acos(V/Vr)
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
Cutting Speed Angle - (Measured in Radian) - Cutting Speed Angle is the angle between the direction of Primary Motion of the Tool and Resultant Cutting direction.
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).
Resultant Cutting Velocity - (Measured in Meter per Second) - Resultant Cutting Velocity is the result from simultaneous Primary Tool Velocity and Feed Velocity, given to the Tool during Machining.
STEP 1: Convert Input(s) to Base Unit
Cutting Velocity: 120 Meter per Minute --> 2 Meter per Second (Check conversion here)
Resultant Cutting Velocity: 11 Meter per Second --> 11 Meter per Second No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
η = acos(V/Vr) --> acos(2/11)
Evaluating ... ...
η = 1.38796118980199
STEP 3: Convert Result to Output's Unit
1.38796118980199 Radian -->79.5243183036251 Degree (Check conversion here)
FINAL ANSWER
79.5243183036251 79.52432 Degree <-- Cutting Speed Angle
(Calculation completed in 00.004 seconds)

Credits

Created by Kumar Siddhant
Indian Institute of Information Technology, Design and Manufacturing (IIITDM), Jabalpur
Kumar Siddhant has created this Calculator and 400+ more calculators!
Verified by Anshika Arya
National Institute Of Technology (NIT), Hamirpur
Anshika Arya has verified this Calculator and 2500+ more calculators!

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

Cutting Speed Angle using Resultant Cutting Speed Formula

Cutting Speed Angle = acos(Cutting Velocity/Resultant Cutting Velocity)
η = acos(V/Vr)

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 Cutting Speed Angle = acos(Cutting Velocity/Resultant Cutting Velocity) to calculate the Cutting Speed Angle, Cutting Speed Angle using Resultant Cutting Speed is a method to determine the angle between the Resultant and applied Cutting Velocity. Under ideal conditions, it is considered to be equal to zero. 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 (Vr) and hit the calculate button. Here is how the Cutting Speed Angle using Resultant Cutting Speed calculation can be explained with given input values -> 1410.621 = acos(2/11).

FAQ

What is Cutting Speed Angle using Resultant Cutting Speed?
Cutting Speed Angle using Resultant Cutting Speed is a method to determine the angle between the Resultant and applied Cutting Velocity. Under ideal conditions, it is considered to be equal to zero and is represented as η = acos(V/Vr) or Cutting Speed Angle = acos(Cutting Velocity/Resultant Cutting Velocity). The Cutting Velocity is the tangential velocity at the periphery of the cutter or workpiece (whichever is rotating) & Resultant Cutting Velocity is the result from simultaneous Primary Tool Velocity and Feed Velocity, given to the Tool during Machining.
How to calculate Cutting Speed Angle using Resultant Cutting Speed?
Cutting Speed Angle using Resultant Cutting Speed is a method to determine the angle between the Resultant and applied Cutting Velocity. Under ideal conditions, it is considered to be equal to zero is calculated using 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 (Vr). 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.
Let Others Know
Facebook
Twitter
Reddit
LinkedIn
Email
WhatsApp
Copied!