Need a help in solving an equation (probably differentiation

In summary, the equation between interference and machine feed is dy/dx=0 when x and y are each constant alphanumeric characters.
  • #1
k.udhay
160
10
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.
cpu8N.jpg


https://i.stack.imgur.com/cpu8N.jpg
 

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  • #2
k.udhay 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.
View attachment 215316

https://i.stack.imgur.com/cpu8N.jpg

If ##y=f(x)## you have ##x=f^{-1}(y)##, if the inverse ##f^{-1}## exist. As is shown at the Wikipedia page, you then have
$$f'(x)=\frac{1}{x'(y)}$$.
 
  • #3
k.udhay 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.
View attachment 215316

https://i.stack.imgur.com/cpu8N.jpg
Let's see...
I would go for x=f(y)
So dx/dy = -d(G10+G6)/dy = -tan - d(G10)/dy
Since we are going to be looking for a denominator that goes toh zero, we can drop the tangent term.
So we are looking for 1/(d(G10)/dy)=0.

Attacking the G10 equation:
Let A = D9/H; So G10 = A sqrt( (H/2)^2 - (D12 + Rtip -Sqrt(Rtip^2-y^2) )^2 )
Let B = (H/2)^2 - (D12 + Rtip -Sqrt(Rtip^2-y^2) )^2; So G10 = A sqrt(B)
the derivative of that is:
d(G10)/dy = (A/(2 sqrt(B)) ) (dB/dy) = (A/(2 sqrt(B)) ) ( -(D12+Rtip-sqrt(Rtip^2-y^2))^2 /dy)
Since we are looking for excursions to infinity, the factors "A" and (-(D12+Rtip-sqrt(Rtip^2-y^2))^2) will not assist and can be dropped.
So we are looking for 2sqrt(B) = 0; thus B = 0
So (H/2)^2 = (D12 + Rtip -Sqrt(Rtip^2-y^2) )^2
H = +/-2(D12 + Rtip - sqrt(Rtip^2-y^2) )

Specific information about what's positive and negative helps here.
So I'll leave the rest to you.

BTW: Check everything - I can make mistakes.
 

1. How do I solve a differentiation equation?

To solve a differentiation equation, you must first determine the derivative of the given equation. This can be done by using the power rule, product rule, quotient rule, or chain rule. Once you have found the derivative, set it equal to the given value and solve for the variable.

2. What is the purpose of differentiation?

Differentiation is a mathematical concept used to find the rate of change of a function. It is commonly used in physics, engineering, and economics to model and analyze various systems. It can also be used to find the maximum and minimum values of a function.

3. How do I know when to use differentiation?

You can use differentiation when you need to find the slope or rate of change of a function, or if you need to find the maximum or minimum values of a function. It is also commonly used to solve optimization problems in various fields.

4. What are some common strategies for solving differentiation equations?

Some common strategies for solving differentiation equations include using the power rule, product rule, quotient rule, and chain rule. It is also helpful to simplify the equation before attempting to find the derivative, and to check your answer by plugging it back into the original equation.

5. Are there any tools or resources available to help with solving differentiation equations?

Yes, there are many online calculators and software programs that can help with solving differentiation equations. Additionally, there are many textbooks, videos, and online tutorials available to provide step-by-step instructions and practice problems for differentiation. It can also be helpful to consult with a math tutor or instructor for additional guidance and support.

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