Resources and Software For High-Performance CNC Machinists
In Stores

Get it on Google Play

Subscribe to Blog
Email Address
 
Home >>Basic Machining Math >>Calculating Tool Engagement Angle, Radial Depth of Cut

Calculating Tool Engagement Angle, Radial Depth of Cut

August 18, 2012, 11:14 am

Article Summary

Eldar Gerfanov (Admin)

August 18, 2012, 11:14 am

August 20, 2012, 11:52 am

39667

Public

by Eldar Gerfanov (Admin)

Author Summary

Sat December 28, 2024, 10:37 am

Sat December 28, 2024, 10:37 am

Here i will show you how to calculate Tool Engagement Angle using tool diameter and Width Of Cut (radial deopth of cut)

Lets first draw a pretty image that shows us everything we need.

Where:

  • r: Radius of the cutter = Diamater /2
  • a: TEA - Enagagement angle we are trying to find here
  • WOC: Width of cut or RADIAL Depth of Cut
  • r2: The difference between r and WOC, r=r2+WOC

 

Below we develop 2 formulas that allow us to find TEA and WOC

Task 1: Find WOC (Radial Depth of Cut) knowing tool engagement angle and diameter of the tool

Solution:

WOC=r-r2

r2=COS(a) * r

COS(a)=r2 / r

r2=COS(a) * R


 Diamater

Diameter
WOC =
 -
COS(a) *

2

2

or if we move Diameter/2 outside of brackets:


 Diamater
   |

|
WOC =
 *
|
 1-
 COS(a) |

2
   |

|

or if we replace Diameter/2 with radius:

WOC=r * (1-COS(a))


Task 2: Find engagement angle knowing WOC (Radial Depth of Cut) and diameter of the tool

Solution:

WOC =  r - r2

r2 = COS(a) * r

COS(a)= r2 / r

a = COS-1( r2 / r )

a = COS-1( ( r - WOC) / r )

a = COS-1( 1 - WOC / r )

or

a = COS-1( 1 - WOC / Dia/2 )

 

Thats it folks

You shall be surprised but those two formulas work also for TEA bigger than 90 Degree


Comments:
Pages:(1) [1]
avatar

Divyang

April 9, 2015, 10:30 pm

Nice, Thanks. Could you please show how to  calculate cutter engagement angle when a tool is performing pocket machining using a curvilinear or spiral like tool path.

avatar

Eldar Gerfanov (Admin)

April 10, 2015, 11:39 pm
Updated by: Eldar Gerfanov (Admin)April 10, 2015, 11:43 pm

Quote:
Nice, Thanks. Could you please show how to  calculate cutter engagement angle when a tool is performing pocket machining using a curvilinear or spiral like tool path.
   hi, That is a hard task because your effective with of cut will change with the radius of the toolapth. It is easy to calculate, but the radius of the toolpath will be constanlty increasing, so your calculations will be off. Basically the same formulae will apply, but you have to multiply by factor Fx=(D_Toolpath-D_Cutter)/D_Toolpath Since your D_Toolpath will be constantly increasing, effect of the spiral radius will be anywhere from about 0.1 to 1

avatar

Divyang

May 2, 2015, 4:46 am

Hi,  Thank you very much Eldar Gerfanov for the reply. But still it is very difficult for me to comprehend what you exactly want to say.  My question is very simple. Say, I want to machine a circular pocket (with diameter, D) and tool (diameter, d) with spiral toolpath toolpath (R,theta), where R is the radius for corresponding theta. For one convolution theta varies from 0 to 230 degrees. and step over is kept as say 'S'.  How to calculate the cutter engagement angle in this case. I have tried but things are getting complicated for me as for each pass the surface generated by the preceding convolution has to be taken into account. If possible, a rough sketch would be helpful.  once again thanks.

avatar

Eldar Gerfanov (Admin)

May 3, 2015, 2:03 pm
Updated by: Eldar Gerfanov (Admin)May 3, 2015, 2:06 pm

Quote:
Hi,  Thank you very much Eldar Gerfanov for the reply. But still it is very difficult for me to comprehend what you exactly want to say.  My question is very simple. Say, I want to machine a circular pocket (with diameter, D) and tool (diameter, d) with spiral toolpath toolpath (R,theta), where R is the radius for corresponding theta. For one convolution theta varies from 0 to 230 degrees. and step over is kept as say 'S'.  How to calculate the cutter engagement angle in this case. I have tried but things are getting complicated for me as for each pass the surface generated by the preceding convolution has to be taken into account. If possible, a rough sketch would be helpful.  once again thanks.
    That is exactly what i tried to tell you in my previous post. You engagement angle will be changing as your toolpath radius grows

avatar

Jim

September 15, 2015, 10:41 pm

I'm sure this is not where I'm supposed to post, but I hope somone can help me.  I'm having problems opening/installing HSM Advisor in 64 bit vista.  Comapatibility mode is un usefull. Any help is much appreciated.

avatar

Eldar Gerfanov (Admin)

September 16, 2015, 5:12 am

Quote:
I'm sure this is not where I'm supposed to post, but I hope somone can help me.  I'm having problems opening/installing HSM Advisor in 64 bit vista.  Comapatibility mode is un usefull. Any help is much appreciated.
 what kind of trouble? Does it install and then don't run? Try downloading the version for another .NET framework

avatar

Hank

January 31, 2020, 9:46 am

Is there an app to calculate Tool Engagement Angle?

New Comment to: Calculating Tool Engagement Angle, Radial Depth of Cut

Name: *
Solve Capcha:
*
Sing In

© 2009-2022 Eldar Gerfanov. All Rights Reserved.
© 2009 Eldar Gerfanov. Materials on this site are presented as is and are mostly for educational use.

You may freely reproduce information presented herein without any consent from me, provided you include link to this site.
In case when i am not the copyright holder, you may want to contact proper owner of material. Anyway, they are freely available on the Internet.
If you hold the copyright right for any of the materials on this site and want them removed, please contact me here