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To do this we need to calculate the diameter of a nut ACROSS THE POINTS .........d = 2*rw = 2*aFrom the diagram, we have,a = r * cos(x)so:2*a = w = 2*r*cos(x) = d * cos(x)Solving for d,d = w/cos(x)For a hexagonal nut, x will be 30 degrees so,cos(x) = sqrt(3)/2 = 0.866Finally,d = w/0.866 = 1.1547 * w
I favour the 'guess it and whack it' approach.
To do this we need to calculate the diameter of a nut ACROSS THE POINTS given the conventional width of the nut measured ACROSS THE FLATS. That diameter, suitably adjusted for an interference fit, will be the size of the recess into which the nut is driven.Take a look at the canonical circular arc diagram shown below. In this diagram the desired diameter, d, will be twice the radius, r. Similarly, the width of the nut, w, will be twice the apothem, a, shown in the diagram.d = 2*rw = 2*aFrom the diagram, we have,a = r * cos(x)so:2*a = w = 2*r*cos(x) = d * cos(x)Solving for d,d = w/cos(x)For a hexagonal nut, x will be 30 degrees so,cos(x) = sqrt(3)/2 = 0.866Finally,d = w/0.866 = 1.1547 * wRemember to drill slightly smaller than d so the points of the nut have something to bite into.
Quote from: mklotz on April 13, 2015, 11:15:54 AMTo do this we need to calculate the diameter of a nut ACROSS THE POINTS given the conventional width of the nut measured ACROSS THE FLATS. That diameter, suitably adjusted for an interference fit, will be the size of the recess into which the nut is driven.Take a look at the canonical circular arc diagram shown below. In this diagram the desired diameter, d, will be twice the radius, r. Similarly, the width of the nut, w, will be twice the apothem, a, shown in the diagram.d = 2*rw = 2*aFrom the diagram, we have,a = r * cos(x)so:2*a = w = 2*r*cos(x) = d * cos(x)Solving for d,d = w/cos(x)For a hexagonal nut, x will be 30 degrees so,cos(x) = sqrt(3)/2 = 0.866Finally,d = w/0.866 = 1.1547 * wRemember to drill slightly smaller than d so the points of the nut have something to bite into.Could you not just measure the nut??
And then of course apply the technical term "slightly smaller than" to arrive at an exact value.