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# Formula to calculate actual positional tolerance error

## Formula to calculate actual positional tolerance error

(OP)
Hello all.
I have a question regarding ASME GD& T and I will be thankful to all who respond.

The question is

Mathematically, in Cartesian Co-ordinate system, the formula to calculate the actual positional error is given is 2 sqrt delta x^2 + dlta y^. We find actual values of x and y, then find the difference from relative basic dimensions and calculate positional error.

Does any formula exists when we talk about polar coordinates having basic PCD and angle for locating a perfect position of a pattern of holes wrt appropriate datum feature references.

Thank you all

Best regards

### RE: Formula to calculate actual positional tolerance error

Aren't the mathematics behind GD&T defined and/or explained in ASME Y14.5.1?

"Wildfires are dangerous, hard to control, and economically catastrophic."

Ben Loosli

### RE: Formula to calculate actual positional tolerance error

I'm sure an equation could be found if you have an example diagram of what a PCD is.

### RE: Formula to calculate actual positional tolerance error

(OP)
I believe that same formula can be used for calculating the actual positional error of hole located by basic PCD and basic angle if we use the concept of datum axis as an intersection of two datum planes and assign the basic x and y dimensions from these two planes from CAD software. Then the actual values of x and y can be checked instead of finding actual PCD and actual angle.

Am i right in my understanding?

### RE: Formula to calculate actual positional tolerance error

PCD = Peripheral Control Device? Post Congressional Decrement?

### RE: Formula to calculate actual positional tolerance error

I believe it's Pitch Circle Diameter. The diameter of the imaginary circle going through the centers of the holes in a circular pattern.

Evan Janeshewski

Axymetrix Quality Engineering Inc.
www.axymetrix.ca

### RE: Formula to calculate actual positional tolerance error

I was hoping to get the OP to cough up his own definition. Tired, tired, tired, of people tossing in abbreviations. Certainly not mentioned in Y14.5 in either form.

Still have no idea what they want and suddenly no longer care.

### RE: Formula to calculate actual positional tolerance error

Aside from utilizing a standard formula to convert cartesian/rectangular coordinates to polar [r = sqrt( x^2 + y^2 ) and θ = arctan( y / x ) ], I'm not quite sure what you're looking for or asking.

I would suggest providing a figure or example which displays what you're inquiring about, otherwise I'm not sure what more help can be provided. Though perhaps someone better than I can decipher your question.

### RE: Formula to calculate actual positional tolerance error

Are you just looking for simple conversion of polar basic coordinates (R, alpha) to rectangular basic coordinates (x, y):

Assuming alpha is the angle between Y axis and the line passing through the true position of particular hole and the datum axis, and R is the radius of the "pitch" circle, then:
x = R*sin(alpha)
y = R*cos(alpha)

### RE: Formula to calculate actual positional tolerance error

pmarc,

You may be right, the way I initially read it I thought the question was how to convert rectangular to polar - now that I re-read it may be the other way around.

Beyond that I'm with 3DDave I'm not really clear on whats being asked.

### RE: Formula to calculate actual positional tolerance error

(OP)
Thank you all members for their responses. I am grateful to all.

My question was does the formula to calculate the actual positional error of the considered holes in Cartesian coordinates is also applicable to cylindrical flange having a pattern of holes at basic Bolt circle and basic angle wrt to DRF. If yes then how to find actual x and actual y?

### RE: Formula to calculate actual positional tolerance error

(OP)
Consider this figure from the standard. The positional tolerance applied to dia 7.9-8.1

### RE: Formula to calculate actual positional tolerance error

I assume on that second post you were trying to attach a figure - there is nothing attached. If you're referencing ASME Y14.5 then maybe just refer to a figure number so we can look it up.

In regards to cartesian vs. polar they are just methods of referencing coordinates in two different systems - they are interchangeable and can be converted from one to another. Their use usually depends on what is most useful/intuitive to utilize for the referenced shape, pattern, or mathematical function.

You have referred to basic dimensions - this is just a means of defining true position (or true profile), it does not somehow fix the coordinate system to be utilized. If these dimensions have been specified as a pitch circle and angle they can be easily converted to (x,y) rectangular coordinates and back again using the standard equations previously provided. A formula for calculating position tolerance in either coordinate system can then be used.

### RE: Formula to calculate actual positional tolerance error

(OP)
Fig 3-29 in ASME Y14.5-2009

### RE: Formula to calculate actual positional tolerance error

#### Quote (AM Engineer 7 Mar 19 13:45)

The positional tolerance applied to dia 7.9-8.1
The position tolerance is exactly as specified - 8x cylinders of size 0.14@MMC (and of size 0.14+0.2=0.34@LMC due to bonus tolerance).

#### Quote (AM Engineer 7 Mar 19 13:51)

formula to calculate the actual positional error
This suggests a measured feature or pattern of features, which your referenced figure 3-29 does not have (not sure than any do - perhaps you'd have to draw from an external reference/textbook example or create your own). Unless the DRF is fully constrained, this will require some sort of fitting method, this was discussed not too long ago in a thread https://www.eng-tips.com/viewthread.cfm?qid=445857 perhaps that would be an interesting read.

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