Previous | Next | G. D. & T.
Topic: PARALLELISM
Conf: G. D. & T., Msg: 5281
From: Karl-Johan Karlsson (karl-johan.karlsson@volvo.com)
Date: 6/18/2004 10:28 AM

Hi!
Could be like this, I don't know what machine You use.
Let's say that You have a datum surface as primary datum and have placed the opposite surface in Z+ direction in the machine. This opposite surface, we can call it surface 1, have a parallel tolerance. Surface 1 is quadratic with both sides 50 mm. Let's say You have rotated the co-ordinate system so that the X-axis follows one of the sides and the Y-axis the other. When You measure the machine calculate the least square surface and also the angel deviations in two directions, angel deviation in X-direction and in Y-direction. The parallelism deviation can then be calculated :
(Tan angel deviation in X-direction) • length in X-direction + (Tan angel deviation in Y-direction) • length in Y-direction = Parallel deviation for the least square feature.
In Your example 50 must be surface length in X- direction and 0,0140 angel deviation in X-direction. Tan 0,014 • 50 = 0,0122. (Angel deviation is 0,014° and 50 is 50 mm). To get the parallel deviation You must add 0,0122 + 0,0071 = 0,0193 mm.
Be aware of two things : This calculation does not follow the standard ISO 1101 because the calculation is of parallel deviation on a least square feature and that means that the flatness deviation is not included in the parallelism measurement! The distance between highest and lowest actual measuring point is the correct parallelism deviation. It's anyway an often used method.
Second : The formula gives a decent result for surfaces that are quadratic or rectangular. If it is round You must calculate :
Diameter of surface • (tan total angel deviation) = parallelism deviation.

Total angel deviation is calculated as the theorem of Pythagoras using the two angel deviations in X- and Y-directions as indata. Let's say that You have the angel deviations as in Your example, 0,014° and 0,0081°, and that the surface is round with diameter 50 mm.
Then parallel deviation should then be 0,0141 mm.

Best Regards
Karl-Johan Karlsson
Volvo CE Components
Eskilstuna SWEDEN