Mixing
Can someone explain this formula to me. It is a tapered hole
$begingroup$
I could not figure out how to do a couple of the symbols so I am inserting an image.
I am trying to figure out how to use this formula. It does involve machining a tapered hole but I am at a loss on how to use it.picture of formula
Transcription of formula:
$$
Delta H = 0.1 - frac{0.025}{tan frac{theta}{2}}.
$$
Here is some more information.
more information
geometry
asked Jan 31 at 13:31
JohnBurrJohnBurr
62
$endgroup$
|
show 1 more comment
$begingroup$
I could not figure out how to do a couple of the symbols so I am inserting an image.
I am trying to figure out how to use this formula. It does involve machining a tapered hole but I am at a loss on how to use it.picture of formula
Transcription of formula:
$$
Delta H = 0.1 - frac{0.025}{tan frac{theta}{2}}.
$$
Here is some more information.
more information
geometry
asked Jan 31 at 13:31
JohnBurrJohnBurr
62
$endgroup$
$begingroup$
Welcome to MSE. I've transcribed your formula to MathJax (which we use here for formatting math), because folks don't usually like pictures in questions. Let me know if you think I've transcribed it incorrectly.
$endgroup$
– John Hughes
Jan 31 at 13:34
$begingroup$
It's a pretty straightforward formula. You input the angle $theta$ (I don't know what it is exacly, but maybe it's explained in the book) and the outcome is the value $Delta H$. Which aspect is confusing to you?
$endgroup$
– Matti P.
Jan 31 at 13:37
$begingroup$
It is not in a book. This from a blueprint of a part to be made but I am not sure how how to use it.
$endgroup$
– JohnBurr
Jan 31 at 13:44
$begingroup$
And thanks for transcribing it.
$endgroup$
– JohnBurr
Jan 31 at 13:44
$begingroup$
The definition of $theta$ can be seen in the second picture (written sideways). Is it still confusing?
$endgroup$
– Matti P.
Jan 31 at 13:46
|
show 1 more comment
$begingroup$
I could not figure out how to do a couple of the symbols so I am inserting an image.
I am trying to figure out how to use this formula. It does involve machining a tapered hole but I am at a loss on how to use it.picture of formula
Transcription of formula:
$$
Delta H = 0.1 - frac{0.025}{tan frac{theta}{2}}.
$$
Here is some more information.
more information
geometry
asked Jan 31 at 13:31
JohnBurrJohnBurr
62
$endgroup$
I could not figure out how to do a couple of the symbols so I am inserting an image.
I am trying to figure out how to use this formula. It does involve machining a tapered hole but I am at a loss on how to use it.picture of formula
Transcription of formula:
$$
Delta H = 0.1 - frac{0.025}{tan frac{theta}{2}}.
$$
Here is some more information.
more information
geometry
geometry
asked Jan 31 at 13:31
JohnBurrJohnBurr
62
asked Jan 31 at 13:31
JohnBurrJohnBurr
62
edited Jan 31 at 13:41
JohnBurr
asked Jan 31 at 13:31
JohnBurrJohnBurr
62
asked Jan 31 at 13:31
JohnBurrJohnBurr
62
asked Jan 31 at 13:31
JohnBurrJohnBurr
62
62
$begingroup$
Welcome to MSE. I've transcribed your formula to MathJax (which we use here for formatting math), because folks don't usually like pictures in questions. Let me know if you think I've transcribed it incorrectly.
$endgroup$
– John Hughes
Jan 31 at 13:34
$begingroup$
It's a pretty straightforward formula. You input the angle $theta$ (I don't know what it is exacly, but maybe it's explained in the book) and the outcome is the value $Delta H$. Which aspect is confusing to you?
$endgroup$
– Matti P.
Jan 31 at 13:37
$begingroup$
It is not in a book. This from a blueprint of a part to be made but I am not sure how how to use it.
$endgroup$
– JohnBurr
Jan 31 at 13:44
$begingroup$
And thanks for transcribing it.
$endgroup$
– JohnBurr
Jan 31 at 13:44
$begingroup$
The definition of $theta$ can be seen in the second picture (written sideways). Is it still confusing?
$endgroup$
– Matti P.
Jan 31 at 13:46
|
show 1 more comment
$begingroup$
Welcome to MSE. I've transcribed your formula to MathJax (which we use here for formatting math), because folks don't usually like pictures in questions. Let me know if you think I've transcribed it incorrectly.
$endgroup$
– John Hughes
Jan 31 at 13:34
$begingroup$
It's a pretty straightforward formula. You input the angle $theta$ (I don't know what it is exacly, but maybe it's explained in the book) and the outcome is the value $Delta H$. Which aspect is confusing to you?
$endgroup$
– Matti P.
Jan 31 at 13:37
$begingroup$
It is not in a book. This from a blueprint of a part to be made but I am not sure how how to use it.
$endgroup$
– JohnBurr
Jan 31 at 13:44
$begingroup$
And thanks for transcribing it.
$endgroup$
– JohnBurr
Jan 31 at 13:44
$begingroup$
The definition of $theta$ can be seen in the second picture (written sideways). Is it still confusing?
$endgroup$
– Matti P.
Jan 31 at 13:46
$begingroup$
Welcome to MSE. I've transcribed your formula to MathJax (which we use here for formatting math), because folks don't usually like pictures in questions. Let me know if you think I've transcribed it incorrectly.
$endgroup$
– John Hughes
Jan 31 at 13:34
$begingroup$
Welcome to MSE. I've transcribed your formula to MathJax (which we use here for formatting math), because folks don't usually like pictures in questions. Let me know if you think I've transcribed it incorrectly.
$endgroup$
– John Hughes
Jan 31 at 13:34
$begingroup$
It's a pretty straightforward formula. You input the angle $theta$ (I don't know what it is exacly, but maybe it's explained in the book) and the outcome is the value $Delta H$. Which aspect is confusing to you?
$endgroup$
– Matti P.
Jan 31 at 13:37
$begingroup$
It's a pretty straightforward formula. You input the angle $theta$ (I don't know what it is exacly, but maybe it's explained in the book) and the outcome is the value $Delta H$. Which aspect is confusing to you?
$endgroup$
– Matti P.
Jan 31 at 13:37
$begingroup$
It is not in a book. This from a blueprint of a part to be made but I am not sure how how to use it.
$endgroup$
– JohnBurr
Jan 31 at 13:44
$begingroup$
It is not in a book. This from a blueprint of a part to be made but I am not sure how how to use it.
$endgroup$
– JohnBurr
Jan 31 at 13:44
$begingroup$
And thanks for transcribing it.
$endgroup$
– JohnBurr
Jan 31 at 13:44
$begingroup$
And thanks for transcribing it.
$endgroup$
– JohnBurr
Jan 31 at 13:44
$begingroup$
The definition of $theta$ can be seen in the second picture (written sideways). Is it still confusing?
$endgroup$
– Matti P.
Jan 31 at 13:46
$begingroup$
The definition of $theta$ can be seen in the second picture (written sideways). Is it still confusing?
$endgroup$
– Matti P.
Jan 31 at 13:46
|
show 1 more comment
1 Answer
1
active
oldest
votes
$begingroup$
John.
I assume that this is for some sort of machining process, and I haven't much experience with machining. But let me try to make a guess or two.
If your "tapered" hole had no taper, it'd be a cylinder, right? In that case, we'd say that the angle of taper is $theta = 0$. If the sides tilted in just a little bit, we might say that the taper was $theta = 1$ degree. If it looked like a "90 degree) countersink, we might say that the taper was $theta = 45$ degrees (i.e., the taper is the slope of one side of the hole, compared to vertical). I could easily be wrong here: the taper might be the angle between the two opposite sides, so that for a 90-degree countersink, the taper would be $90$ degrees. The use of $theta/2$ in your formula suggests to me that this latter interpretation might be the correct one, but without more information, I can't say.
Let's suppose that the taper is $theta = 10$ degrees. Then $theta/2$ is $5$ degrees, and $tan frac{theta}{2} approx 0.0875$ (I got this answer using a calculator set to "degrees" mode!)
Then your formula says that
$$
Delta H
= 0.1 - frac{0.025}{tan frac{theta}{2}}
approx 0.1 - frac{0.025}{0.0875}
approx 0.1 - 0.2857 approx -0.1857
$$
where $approx$ means "is approximately equal to," because I suspect you don't want more than a few decimal digits of accuracy for machining.
The symbol $Delta$ is often used to mean "the change in", so this seems to say that the "change in H" should be $-0.1857$. I don't know what $H$ is in your setup, but this suggests reducing it by a modest amount.
I'm sorry not to be able to be more confident in my answer, but to do so, I'd need a bit more context.
answered Jan 31 at 13:46
John HughesJohn Hughes
65.2k24293
$endgroup$
$begingroup$
And now I see (from your added picture) that my second interpretation was correct: $theta$ is the angle between the two sides, not the angle from one side to the centerline. I can't make sense in your picture of what $Delta H$ is -- it looks like the thickness of a single line -- but presumably you can make sense of that.
$endgroup$
– John Hughes
Jan 31 at 13:48
$begingroup$
Thanks, I think I can do this now. What is the symbol of the o with a line threw it called?
$endgroup$
– JohnBurr
Jan 31 at 13:50
$begingroup$
That's called "theta" (rhymes with "hate, uh"). It's the 8th letter in the Greek alphabet. I think that in modern greek it might be pronounced to rhyme with "heat, uh" ... just in case you ever get a Greek mechanic in your shop. :)
$endgroup$
– John Hughes
Jan 31 at 13:52
$begingroup$
Thanks for all of the help.
$endgroup$
– JohnBurr
Jan 31 at 13:54
add a comment |
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$begingroup$
John.
I assume that this is for some sort of machining process, and I haven't much experience with machining. But let me try to make a guess or two.
If your "tapered" hole had no taper, it'd be a cylinder, right? In that case, we'd say that the angle of taper is $theta = 0$. If the sides tilted in just a little bit, we might say that the taper was $theta = 1$ degree. If it looked like a "90 degree) countersink, we might say that the taper was $theta = 45$ degrees (i.e., the taper is the slope of one side of the hole, compared to vertical). I could easily be wrong here: the taper might be the angle between the two opposite sides, so that for a 90-degree countersink, the taper would be $90$ degrees. The use of $theta/2$ in your formula suggests to me that this latter interpretation might be the correct one, but without more information, I can't say.
Let's suppose that the taper is $theta = 10$ degrees. Then $theta/2$ is $5$ degrees, and $tan frac{theta}{2} approx 0.0875$ (I got this answer using a calculator set to "degrees" mode!)
Then your formula says that
$$
Delta H
= 0.1 - frac{0.025}{tan frac{theta}{2}}
approx 0.1 - frac{0.025}{0.0875}
approx 0.1 - 0.2857 approx -0.1857
$$
where $approx$ means "is approximately equal to," because I suspect you don't want more than a few decimal digits of accuracy for machining.
The symbol $Delta$ is often used to mean "the change in", so this seems to say that the "change in H" should be $-0.1857$. I don't know what $H$ is in your setup, but this suggests reducing it by a modest amount.
I'm sorry not to be able to be more confident in my answer, but to do so, I'd need a bit more context.
answered Jan 31 at 13:46
John HughesJohn Hughes
65.2k24293
$endgroup$
$begingroup$
And now I see (from your added picture) that my second interpretation was correct: $theta$ is the angle between the two sides, not the angle from one side to the centerline. I can't make sense in your picture of what $Delta H$ is -- it looks like the thickness of a single line -- but presumably you can make sense of that.
$endgroup$
– John Hughes
Jan 31 at 13:48
$begingroup$
Thanks, I think I can do this now. What is the symbol of the o with a line threw it called?
$endgroup$
– JohnBurr
Jan 31 at 13:50
$begingroup$
That's called "theta" (rhymes with "hate, uh"). It's the 8th letter in the Greek alphabet. I think that in modern greek it might be pronounced to rhyme with "heat, uh" ... just in case you ever get a Greek mechanic in your shop. :)
$endgroup$
– John Hughes
Jan 31 at 13:52
$begingroup$
Thanks for all of the help.
$endgroup$
– JohnBurr
Jan 31 at 13:54
add a comment |
$begingroup$
John.
I assume that this is for some sort of machining process, and I haven't much experience with machining. But let me try to make a guess or two.
If your "tapered" hole had no taper, it'd be a cylinder, right? In that case, we'd say that the angle of taper is $theta = 0$. If the sides tilted in just a little bit, we might say that the taper was $theta = 1$ degree. If it looked like a "90 degree) countersink, we might say that the taper was $theta = 45$ degrees (i.e., the taper is the slope of one side of the hole, compared to vertical). I could easily be wrong here: the taper might be the angle between the two opposite sides, so that for a 90-degree countersink, the taper would be $90$ degrees. The use of $theta/2$ in your formula suggests to me that this latter interpretation might be the correct one, but without more information, I can't say.
Let's suppose that the taper is $theta = 10$ degrees. Then $theta/2$ is $5$ degrees, and $tan frac{theta}{2} approx 0.0875$ (I got this answer using a calculator set to "degrees" mode!)
Then your formula says that
$$
Delta H
= 0.1 - frac{0.025}{tan frac{theta}{2}}
approx 0.1 - frac{0.025}{0.0875}
approx 0.1 - 0.2857 approx -0.1857
$$
where $approx$ means "is approximately equal to," because I suspect you don't want more than a few decimal digits of accuracy for machining.
The symbol $Delta$ is often used to mean "the change in", so this seems to say that the "change in H" should be $-0.1857$. I don't know what $H$ is in your setup, but this suggests reducing it by a modest amount.
I'm sorry not to be able to be more confident in my answer, but to do so, I'd need a bit more context.
answered Jan 31 at 13:46
John HughesJohn Hughes
65.2k24293
$endgroup$
$begingroup$
And now I see (from your added picture) that my second interpretation was correct: $theta$ is the angle between the two sides, not the angle from one side to the centerline. I can't make sense in your picture of what $Delta H$ is -- it looks like the thickness of a single line -- but presumably you can make sense of that.
$endgroup$
– John Hughes
Jan 31 at 13:48
$begingroup$
Thanks, I think I can do this now. What is the symbol of the o with a line threw it called?
$endgroup$
– JohnBurr
Jan 31 at 13:50
$begingroup$
That's called "theta" (rhymes with "hate, uh"). It's the 8th letter in the Greek alphabet. I think that in modern greek it might be pronounced to rhyme with "heat, uh" ... just in case you ever get a Greek mechanic in your shop. :)
$endgroup$
– John Hughes
Jan 31 at 13:52
$begingroup$
Thanks for all of the help.
$endgroup$
– JohnBurr
Jan 31 at 13:54
add a comment |
$begingroup$
John.
I assume that this is for some sort of machining process, and I haven't much experience with machining. But let me try to make a guess or two.
If your "tapered" hole had no taper, it'd be a cylinder, right? In that case, we'd say that the angle of taper is $theta = 0$. If the sides tilted in just a little bit, we might say that the taper was $theta = 1$ degree. If it looked like a "90 degree) countersink, we might say that the taper was $theta = 45$ degrees (i.e., the taper is the slope of one side of the hole, compared to vertical). I could easily be wrong here: the taper might be the angle between the two opposite sides, so that for a 90-degree countersink, the taper would be $90$ degrees. The use of $theta/2$ in your formula suggests to me that this latter interpretation might be the correct one, but without more information, I can't say.
Let's suppose that the taper is $theta = 10$ degrees. Then $theta/2$ is $5$ degrees, and $tan frac{theta}{2} approx 0.0875$ (I got this answer using a calculator set to "degrees" mode!)
Then your formula says that
$$
Delta H
= 0.1 - frac{0.025}{tan frac{theta}{2}}
approx 0.1 - frac{0.025}{0.0875}
approx 0.1 - 0.2857 approx -0.1857
$$
where $approx$ means "is approximately equal to," because I suspect you don't want more than a few decimal digits of accuracy for machining.
The symbol $Delta$ is often used to mean "the change in", so this seems to say that the "change in H" should be $-0.1857$. I don't know what $H$ is in your setup, but this suggests reducing it by a modest amount.
I'm sorry not to be able to be more confident in my answer, but to do so, I'd need a bit more context.
answered Jan 31 at 13:46
John HughesJohn Hughes
65.2k24293
$endgroup$
John.
I assume that this is for some sort of machining process, and I haven't much experience with machining. But let me try to make a guess or two.
If your "tapered" hole had no taper, it'd be a cylinder, right? In that case, we'd say that the angle of taper is $theta = 0$. If the sides tilted in just a little bit, we might say that the taper was $theta = 1$ degree. If it looked like a "90 degree) countersink, we might say that the taper was $theta = 45$ degrees (i.e., the taper is the slope of one side of the hole, compared to vertical). I could easily be wrong here: the taper might be the angle between the two opposite sides, so that for a 90-degree countersink, the taper would be $90$ degrees. The use of $theta/2$ in your formula suggests to me that this latter interpretation might be the correct one, but without more information, I can't say.
Let's suppose that the taper is $theta = 10$ degrees. Then $theta/2$ is $5$ degrees, and $tan frac{theta}{2} approx 0.0875$ (I got this answer using a calculator set to "degrees" mode!)
Then your formula says that
$$
Delta H
= 0.1 - frac{0.025}{tan frac{theta}{2}}
approx 0.1 - frac{0.025}{0.0875}
approx 0.1 - 0.2857 approx -0.1857
$$
where $approx$ means "is approximately equal to," because I suspect you don't want more than a few decimal digits of accuracy for machining.
The symbol $Delta$ is often used to mean "the change in", so this seems to say that the "change in H" should be $-0.1857$. I don't know what $H$ is in your setup, but this suggests reducing it by a modest amount.
I'm sorry not to be able to be more confident in my answer, but to do so, I'd need a bit more context.
answered Jan 31 at 13:46
John HughesJohn Hughes
65.2k24293
answered Jan 31 at 13:46
John HughesJohn Hughes
65.2k24293
answered Jan 31 at 13:46
John HughesJohn Hughes
65.2k24293
answered Jan 31 at 13:46
John HughesJohn Hughes
65.2k24293
65.2k24293
$begingroup$
And now I see (from your added picture) that my second interpretation was correct: $theta$ is the angle between the two sides, not the angle from one side to the centerline. I can't make sense in your picture of what $Delta H$ is -- it looks like the thickness of a single line -- but presumably you can make sense of that.
$endgroup$
– John Hughes
Jan 31 at 13:48
$begingroup$
Thanks, I think I can do this now. What is the symbol of the o with a line threw it called?
$endgroup$
– JohnBurr
Jan 31 at 13:50
$begingroup$
That's called "theta" (rhymes with "hate, uh"). It's the 8th letter in the Greek alphabet. I think that in modern greek it might be pronounced to rhyme with "heat, uh" ... just in case you ever get a Greek mechanic in your shop. :)
$endgroup$
– John Hughes
Jan 31 at 13:52
$begingroup$
Thanks for all of the help.
$endgroup$
– JohnBurr
Jan 31 at 13:54
add a comment |
$begingroup$
And now I see (from your added picture) that my second interpretation was correct: $theta$ is the angle between the two sides, not the angle from one side to the centerline. I can't make sense in your picture of what $Delta H$ is -- it looks like the thickness of a single line -- but presumably you can make sense of that.
$endgroup$
– John Hughes
Jan 31 at 13:48
$begingroup$
Thanks, I think I can do this now. What is the symbol of the o with a line threw it called?
$endgroup$
– JohnBurr
Jan 31 at 13:50
$begingroup$
That's called "theta" (rhymes with "hate, uh"). It's the 8th letter in the Greek alphabet. I think that in modern greek it might be pronounced to rhyme with "heat, uh" ... just in case you ever get a Greek mechanic in your shop. :)
$endgroup$
– John Hughes
Jan 31 at 13:52
$begingroup$
Thanks for all of the help.
$endgroup$
– JohnBurr
Jan 31 at 13:54
$begingroup$
And now I see (from your added picture) that my second interpretation was correct: $theta$ is the angle between the two sides, not the angle from one side to the centerline. I can't make sense in your picture of what $Delta H$ is -- it looks like the thickness of a single line -- but presumably you can make sense of that.
$endgroup$
– John Hughes
Jan 31 at 13:48
$begingroup$
And now I see (from your added picture) that my second interpretation was correct: $theta$ is the angle between the two sides, not the angle from one side to the centerline. I can't make sense in your picture of what $Delta H$ is -- it looks like the thickness of a single line -- but presumably you can make sense of that.
$endgroup$
– John Hughes
Jan 31 at 13:48
$begingroup$
Thanks, I think I can do this now. What is the symbol of the o with a line threw it called?
$endgroup$
– JohnBurr
Jan 31 at 13:50
$begingroup$
Thanks, I think I can do this now. What is the symbol of the o with a line threw it called?
$endgroup$
– JohnBurr
Jan 31 at 13:50
$begingroup$
That's called "theta" (rhymes with "hate, uh"). It's the 8th letter in the Greek alphabet. I think that in modern greek it might be pronounced to rhyme with "heat, uh" ... just in case you ever get a Greek mechanic in your shop. :)
$endgroup$
– John Hughes
Jan 31 at 13:52
$begingroup$
That's called "theta" (rhymes with "hate, uh"). It's the 8th letter in the Greek alphabet. I think that in modern greek it might be pronounced to rhyme with "heat, uh" ... just in case you ever get a Greek mechanic in your shop. :)
$endgroup$
– John Hughes
Jan 31 at 13:52
$begingroup$
Thanks for all of the help.
$endgroup$
– JohnBurr
Jan 31 at 13:54
$begingroup$
Thanks for all of the help.
$endgroup$
– JohnBurr
Jan 31 at 13:54
add a comment |
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Welcome to MSE. I've transcribed your formula to MathJax (which we use here for formatting math), because folks don't usually like pictures in questions. Let me know if you think I've transcribed it incorrectly.
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– John Hughes
Jan 31 at 13:34
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It's a pretty straightforward formula. You input the angle $theta$ (I don't know what it is exacly, but maybe it's explained in the book) and the outcome is the value $Delta H$. Which aspect is confusing to you?
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– Matti P.
Jan 31 at 13:37
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It is not in a book. This from a blueprint of a part to be made but I am not sure how how to use it.
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– JohnBurr
Jan 31 at 13:44
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And thanks for transcribing it.
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– JohnBurr
Jan 31 at 13:44
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The definition of $theta$ can be seen in the second picture (written sideways). Is it still confusing?
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– Matti P.
Jan 31 at 13:46