Need a help in solving an equation (probably differentiation)

Hi,


I am trying to find out the interference condition between tool and a part. The below attached snapshot is the equation between interference and machine feed. At dy/dx = 0, I will have max. interference, which I intend to find. Except x and y every alphanumeric character in the following equations is a constant.

I tried to get it in y = f(x) format, however because the constants and y are so complexly attached, I failed. It would be of great help, if someone can help me find out an equation that gives me the dy/dx = 0 condition. Thanks.

k.udhaya said:

I am trying to find out the interference condition between tool and a part. The below attached snapshot is the equation between interference and machine feed. At dy/dx = 0, I will have max. interference, which I intend to find. Except x and y every alphanumeric character in the following equations is a constant.

I tried to get it in y = f(x) format, however because the constants and y are so complexly attached, I failed. It would be of great help, if someone can help me find out an equation that gives me the dy/dx = 0 condition. Thanks.
https://www.physicsforums.com/attac...4/?temp_hash=ca9901b07c967b8f522e5fad7c37d873

Click to expand...

The hotlink to the other forum isn't displaying here. (Hotlinking is often forbidden, or at least hindered, for very good reasons.) From another of your posts of this question, it appears that you are asking the following:

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The relationship between interference and machine feed is given by the following:

. . . . .\(\displaystyle x\, =\, M\, -\, \left(G_{10}\, +\, T\, +\, G_6\right)\)

...where:

. . . . .\(\displaystyle G_{10}\, =\, \dfrac{ \sqrt{ \left[ 1\, -\, \left( \dfrac{ 4\, \times\, \left( D_{12}\, +\, R_{tip}\, -\, \sqrt{R_{tip}^2\, -\, y^2\,} \right)^2 }{ H^2 } \right) \right]\, \times\, D_9^2 \quad } }{ 2 }\)

. . . . .\(\displaystyle G_6\, =\, \tan(\theta)\, \times\, y\)

Maximum interference occurs when \(\displaystyle \frac{dy}{dx}\, =\, 0.\)

Determine the conditions for which this maximum occurs.

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Is this what the original exercise was? (If not, please provide corrections.) Either way, what are the definitions of all of the various variables? How are they related, if at all? Which are constants?

When you reply, please include all of your efforts so far, including the nearly-solution that you were given at the above-linked website. Thank you!

(For other viewers, this question has also been posted here.)