moodyjs

An implementation of the "Moody Method" for surface plate flatness.

Try It. Click "Create Tables" and then "Fill Test Data" if you don't have any real values to put in.

Overall Flatness Grades

Two different grading standards for the overall measured flatness of a surface plate are defined by ISO and ASME. Both standards provide a list of standard table sizes and their associated flatness tolerances for the different grades as well as an equation for calculating the flatness tolerance when the size is ±5% outside the range of a standard size. The ISO equation is linear, whereas the ASME equation is a second degree polynomial (both are a function of the plate's diagonal length). An important difference between the two standards is that the equation provided by the ISO standard matches the values in the standard sizes table. This is not the case for the ASME standard.

ASME (B89.3.7-2013)

ASME B89.3.7-2013:

4.3.4 Flatness Tolerance (Entire Work Surface)

All points of the work surface shall be contained between two parallel planes. For sizes not listed in Table 1 (more specifically, for sizes that are outside +-5% of the sizes listed in Table 1) the "AA" grade flatness tolerance can be calculated by the following second degree polynomial (D = diagonal of the plate):

Overall flatness tolerance (µm) = 1.6D² + 1 Overall flatness tolerance (µinch) = D² / 25 + 40

The tolerance for grades "A" and "B" are calculated by multiplying the "AA" tolerance grade by 2 and 4 respectively:

tolerance(A) = tolerance(AA) * 2 tolerance(B) = tolerance(AA) * 4

The specification states that the calculated flatness tolerance for grade "AA" is rounded up to the nearest 0.5 micrometer or 25 µinch increments. However, this makes the calculated values even farther off than the tabulated values.

The table values do not match the calculated values. For example:

For a 12" x 12" standard size surface plate the table lists an overall flatness tolerance of 50 µinch:

((sqrt(12² + 12²))² / 25) + 40 = ((12² + 12²) / 25) + 40 = 51.52

Rounded up to nearest 25 µinch increment = 75

This doesn't match (the calculated value is 1.52 µinches more than the table value). The rounding makes matters worse.

For a 18" x 24" standard size surface plate the table lists an overall flatness tolerance of 80 µinch:

40 + ((sqrt(18² + 24²))² / 25) = 76

Rounded up to nearest 25 µinch increment = 100

This doesn't match (the calculated value is 4 µinches less than the table value). The rounding again makes matters worse.

Here is a table that shows the difference between the tabulated and calculated values for ASME (and a comparison between ISO grade 0 and ASME grade "AA"):

Plate Length	Plate Width	Diagonal	Diagonal (µm)	AA Overall Flatness Calc (µinch)	AA Overall Flatness Table (µinch)	Diff(Calc - Table)	ISO Equation Grade 0 (µm)	ISO Grade 0 (µinch)	A Overall Flatness Calc (µinch)	B Overall Flatness Calc (µinch)	A Overall Flatness Table (µinch)	B Overall Flatness Table (µinch)
12	12	16.97056275	431.0522938	51.52	50	1.52	4	157.480315	103.04	206.08	100	200
12	18	21.63330765	549.4860144	58.72	50	8.72	4.3	169.2913386	117.44	234.88	100	200
18	18	25.45584412	646.5784407	65.92	50	15.92	4.6	181.1023622	131.84	263.68	100	200
18	24	30	762	76	80	-4	4.9	192.9133858	152	304	160	320
24	24	33.9411255	862.1045876	86.08	80	6.08	5.2	204.7244094	172.16	344.32	160	320
24	36	43.26661531	1098.972029	114.88	100	14.88	5.8	228.3464567	229.76	459.52	200	400
24	48	53.66563146	1363.107039	155.2	150	5.2	6.7	263.7795276	310.4	620.8	300	600
30	48	56.60388679	1437.738725	168.16	180	-11.84	7	275.5905512	336.32	672.64	360	720
36	36	50.91168825	1293.156881	143.68	150	-6.32	6.4	251.9685039	287.36	574.72	300	600
36	48	60	1524	184	200	-16	7.3	287.4015748	368	736	400	800
36	60	69.97142274	1777.274138	235.84	250	-14.16	7.9	311.023622	471.68	943.36	500	1000
36	72	80.49844719	2044.660559	299.2	300	-0.8	8.8	346.4566929	598.4	1196.8	600	1200
48	48	67.88225099	1724.209175	224.32	200	24.32	7.9	311.023622	448.64	897.28	400	800
48	60	76.83749085	1951.672268	276.16	300	-23.84	8.5	334.6456693	552.32	1104.64	600	1200
48	72	86.53323061	2197.944058	339.52	350	-10.48	9.1	358.2677165	679.04	1358.08	700	1400
48	96	107.3312629	2726.214078	500.8	500	0.8	10.9	429.1338583	1001.6	2003.2	1000	2000
48	120	129.2439554	3282.796466	708.16	700	8.16	12.4	488.1889764	1416.32	2832.64	1400	2800
60	120	134.1640786	3407.767598	760	750	10	13	511.8110236	1520	3040	1500	3000
72	96	120	3048	616	600	16	11.8	464.5669291	1232	2464	1200	2400
72	144	160.9968944	4089.321117	1076.8	1100	-23.2	14.8	582.6771654	2153.6	4307.2	2200	4400

We believe that the table values should be changed to match the calculated values from the second degree polynomial and that the advice on rounding up to the nearest 25 µinches for calculated values should be abandoned.

ISO 8512-2

TODO

Add a way to show a semi-transparent plane that corresponds to grade "AA", "A", and "B" flatness. tolerance(AA) = (40 + diagonal squared/25) x .000001″, A = tolerance(AA) * 2, B=tolerance(AA) * 4
Show a scale for the z-axis height values or add axes to the 3D scene.
Add a thickness for the table slab (add manufacturer's label).
Allow for "importing" a number set (maybe from a CSV file or a textarea with a simple format).
Fix the way that some measuring lines are cut off on the 3D representation (this happens because the vertices are located at the first foot location).
Make zooming relative to where the mouse cursor is (keep the mouse centered on zoom).

Developer Notes

You can just open index.html to run MoodyJS but because external resources are used (textures) these assets need to be served via http:// (and not file://) for the browser not to complain. This can be done by running npm run serve in the root project directory.

Thanks To

Bruce Allen - Published a very useful paper that corrects some mistakes from Moody's original magazine article and provides some useful citations.