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Involute splines ISO 4156 (metric module, 30° side fit): pitch, major and minor diameter by module and tooth count + example shaft STEP/STL

Name: Involute splines ISO 4156 (metric module, 30° side fit): pitch, major and minor diameter by module and tooth count + example shaft STEP/STL dimension sheet
Creator: Xem Studio
License: https://creativecommons.org/licenses/by/4.0/

What are the pitch, major and minor diameters of an ISO 4156 involute spline for module 2 and 24 teeth? · Standard part · basis: ISO 4156:1981 Table 2 formulas (sample pages) and Roymech's transcription of the same table; basic dimensions, esv = 0, no tolerance; true involute shaft sections drawn from them

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Exact dimensions. Every file is drawn at true size with no tolerance added. The holes and pins that meet another part are listed below under Mating features, with the fit each joint needs; open those by your process's clearance before making the part. Mating features

sizes: 112 in table

Notes

ISO 4156 (straight cylindrical involute splines, metric module, side fit) names a spline by module m and tooth count z. Pressure angles 30°, 37.5° and 45°; this page tabulates the 30° forms. Basic formulas (ISO 4156:1981 Table 2 sample pages, confirmed by Roymech's transcription): pitch Ø D = m z; circular pitch π m; basic tooth thickness π m / 2; external major Ø 30° m (z + 1); external minor Ø 30° flat root m (z − 1.5) and fillet root m (z − 1.8); internal major Ø minimum 30° flat root m (z + 1.5) and fillet root m (z + 1.8); 37.5° fillet root: external major m (z + 0.9), external minor m (z − 1.4), internal major m (z + 1.4); 45° fillet root: external major m (z + 0.8), external minor m (z − 1.2), internal major m (z + 1.2); form radius cF = 0.1 m.
The standard's major / minor diameters carry an effective-variation term (esv / tan αD, with esv the effective tooth thickness deviation, and the machining allowance (T + λ) / tan αD for the maximum internal major diameter); the table lists the basic values, esv = 0. The modules are 0.25 to 10 (ISO 4156 scope; Machinery's Handbook lists the preferred series 0.25, 0.5, 0.75, 1, 1.25, 1.5, 1.75, 2, 2.5, 3, 4, 5, 6, 8, 10). Tolerance classes H/h, H/f, H/e, H/d (side fit) apply tooth thickness deviations from ISO 286-type fundamental deviations; those are not in the table.
Compare ANSI B92.1 (inch pitch): the ANSI flat-root external minor is (N − 1.35) / P (or − 1.2 for 16/32 and finer) against ISO's m (z − 1.5); the two systems are not identical even at the same pitch diameter. Files: 10 external spline shaft sections, 25 mm long, one extruded solid with the basic 30° flat-root tooth: pitch, major and minor diameters from the table, true involute flanks, tooth thickness half the circular pitch. The 25 mm length is an example; the root fillet is not modelled (the flank is carried down to the root circle). Fillet-root and 37.5° / 45° shafts and internal splines are not drawn.
The standard (ISO 4156-1 to -3) is sold by ISO and linked, not reproduced; tooth counts are not limited by the sample pages read, so any z follows from the formulas.

Involute splines ISO 4156 (metric module, 30° side fit): pitch… size chart

module m, mm	teeth z	pitch Ø D = m z, mm	major Ø external (30°) m (z + 1)	minor Ø external, flat root m (z − 1.5)	minor Ø external, fillet root m (z − 1.8)	major Ø internal min, flat root m (z + 1.5)	major Ø internal min, fillet root m (z + 1.8)
0.5	10	5	5.5	4.25	4.1	5.75	5.9
0.5	12	6	6.5	5.25	5.1	6.75	6.9
0.5	16	8	8.5	7.25	7.1	8.75	8.9
0.5	20	10	10.5	9.25	9.1	10.75	10.9
0.5	24	12	12.5	11.25	11.1	12.75	12.9
0.5	30	15	15.5	14.25	14.1	15.75	15.9
0.5	36	18	18.5	17.25	17.1	18.75	18.9
0.5	48	24	24.5	23.25	23.1	24.75	24.9
0.75	10	7.5	8.25	6.375	6.15	8.625	8.85
0.75	12	9	9.75	7.875	7.65	10.125	10.35
0.75	16	12	12.75	10.875	10.65	13.125	13.35
0.75	20	15	15.75	13.875	13.65	16.125	16.35
0.75	24	18	18.75	16.875	16.65	19.125	19.35
0.75	30	22.5	23.25	21.375	21.15	23.625	23.85
0.75	36	27	27.75	25.875	25.65	28.125	28.35
0.75	48	36	36.75	34.875	34.65	37.125	37.35
1	10	10	11	8.5	8.2	11.5	11.8
1	12	12	13	10.5	10.2	13.5	13.8
1	16	16	17	14.5	14.2	17.5	17.8
1	20	20	21	18.5	18.2	21.5	21.8
1	24	24	25	22.5	22.2	25.5	25.8
1	30	30	31	28.5	28.2	31.5	31.8
1	36	36	37	34.5	34.2	37.5	37.8
1	48	48	49	46.5	46.2	49.5	49.8
1.25	10	12.5	13.75	10.625	10.25	14.375	14.75
1.25	12	15	16.25	13.125	12.75	16.875	17.25
1.25	16	20	21.25	18.125	17.75	21.875	22.25
1.25	20	25	26.25	23.125	22.75	26.875	27.25
1.25	24	30	31.25	28.125	27.75	31.875	32.25
1.25	30	37.5	38.75	35.625	35.25	39.375	39.75
1.25	36	45	46.25	43.125	42.75	46.875	47.25
1.25	48	60	61.25	58.125	57.75	61.875	62.25
1.5	10	15	16.5	12.75	12.3	17.25	17.7
1.5	12	18	19.5	15.75	15.3	20.25	20.7
1.5	16	24	25.5	21.75	21.3	26.25	26.7
1.5	20	30	31.5	27.75	27.3	32.25	32.7
1.5	24	36	37.5	33.75	33.3	38.25	38.7
1.5	30	45	46.5	42.75	42.3	47.25	47.7
1.5	36	54	55.5	51.75	51.3	56.25	56.7
1.5	48	72	73.5	69.75	69.3	74.25	74.7
1.75	10	17.5	19.25	14.875	14.35	20.125	20.65
1.75	12	21	22.75	18.375	17.85	23.625	24.15
1.75	16	28	29.75	25.375	24.85	30.625	31.15
1.75	20	35	36.75	32.375	31.85	37.625	38.15
1.75	24	42	43.75	39.375	38.85	44.625	45.15
1.75	30	52.5	54.25	49.875	49.35	55.125	55.65
1.75	36	63	64.75	60.375	59.85	65.625	66.15
1.75	48	84	85.75	81.375	80.85	86.625	87.15
2	10	20	22	17	16.4	23	23.6
2	12	24	26	21	20.4	27	27.6
2	16	32	34	29	28.4	35	35.6
2	20	40	42	37	36.4	43	43.6
2	24	48	50	45	44.4	51	51.6
2	30	60	62	57	56.4	63	63.6
2	36	72	74	69	68.4	75	75.6
2	48	96	98	93	92.4	99	99.6
2.5	10	25	27.5	21.25	20.5	28.75	29.5
2.5	12	30	32.5	26.25	25.5	33.75	34.5
2.5	16	40	42.5	36.25	35.5	43.75	44.5
2.5	20	50	52.5	46.25	45.5	53.75	54.5
2.5	24	60	62.5	56.25	55.5	63.75	64.5
2.5	30	75	77.5	71.25	70.5	78.75	79.5
2.5	36	90	92.5	86.25	85.5	93.75	94.5
2.5	48	120	122.5	116.25	115.5	123.75	124.5
3	10	30	33	25.5	24.6	34.5	35.4
3	12	36	39	31.5	30.6	40.5	41.4
3	16	48	51	43.5	42.6	52.5	53.4
3	20	60	63	55.5	54.6	64.5	65.4
3	24	72	75	67.5	66.6	76.5	77.4
3	30	90	93	85.5	84.6	94.5	95.4
3	36	108	111	103.5	102.6	112.5	113.4
3	48	144	147	139.5	138.6	148.5	149.4
4	10	40	44	34	32.8	46	47.2
4	12	48	52	42	40.8	54	55.2
4	16	64	68	58	56.8	70	71.2
4	20	80	84	74	72.8	86	87.2
4	24	96	100	90	88.8	102	103.2
4	30	120	124	114	112.8	126	127.2
4	36	144	148	138	136.8	150	151.2
4	48	192	196	186	184.8	198	199.2
5	10	50	55	42.5	41	57.5	59
5	12	60	65	52.5	51	67.5	69
5	16	80	85	72.5	71	87.5	89
5	20	100	105	92.5	91	107.5	109
5	24	120	125	112.5	111	127.5	129
5	30	150	155	142.5	141	157.5	159
5	36	180	185	172.5	171	187.5	189
5	48	240	245	232.5	231	247.5	249
6	10	60	66	51	49.2	69	70.8
6	12	72	78	63	61.2	81	82.8
6	16	96	102	87	85.2	105	106.8
6	20	120	126	111	109.2	129	130.8
6	24	144	150	135	133.2	153	154.8
6	30	180	186	171	169.2	189	190.8
6	36	216	222	207	205.2	225	226.8
6	48	288	294	279	277.2	297	298.8
8	10	80	88	68	65.6	92	94.4
8	12	96	104	84	81.6	108	110.4
8	16	128	136	116	113.6	140	142.4
8	20	160	168	148	145.6	172	174.4
8	24	192	200	180	177.6	204	206.4
8	30	240	248	228	225.6	252	254.4
8	36	288	296	276	273.6	300	302.4
8	48	384	392	372	369.6	396	398.4
10	10	100	110	85	82	115	118
10	12	120	130	105	102	135	138
10	16	160	170	145	142	175	178
10	20	200	210	185	182	215	218
10	24	240	250	225	222	255	258
10	30	300	310	285	282	315	318
10	36	360	370	345	342	375	378
10	48	480	490	465	462	495	498

Mating features

Drawn at the exact size. Open press, slide, run and socket features by your process's clearance (tolerances by process); leave designed gaps and clamp fits as drawn.

feature	exact	mates with	fit	files
external spline	D = m z, major m (z + 1), flat-root minor m (z − 1.5), fillet-root minor m (z − 1.8) (basic)	internal spline of the same module and z (internal major m (z + 1.5) flat root, m (z + 1.8) fillet root, minimum)	designed	spline-shaft*
tooth form	30°, basic tooth thickness π m / 2 on the pitch circle	internal spline of the same module, z and 30° pressure angle	designed	spline-shaft*

Where the files are

Other publishers' files are linked, not hosted. "verify" = check the license at the link before commercial use.

iTeh Standards	ISO 4156:1981 sample pages: Table 2 basic formulas (m z, m (z + 1), m (z - 1.5), m (z + 1.5)), modules 0.25 to 10	web	Publisher's page; dimensions are facts
Roymech	Involute splines (ISO 4156): module formulas for 30 degree flat and fillet root, 37.5 and 45 degrees	web	Publisher's page; dimensions are facts
ISO	ISO 4156-1:2005 Straight cylindrical involute splines, metric module, side fit (standard; sold, not reproduced)	standard	ISO; dimensions are facts verify
Machinery's Handbook, 31st ed. (online edition)	Table 3: basic dimensions for involute splines ANSI B92.1-1996: pitch series 2.5/5 to 128/256, 6 to 60 teeth at 30 degrees	web	Publisher's page; dimensions are facts

Free files

★ Free files 10 parts. Generated by Xem Studio from the standard; threads are plain cylinders at major diameter. CC BY 4.0. index.json

spline-shaft-iso-4156-m0-5-z30	ISO 4156 30° flat-root external spline shaft section, module 0.5, 30 teeth: pitch Ø15 mm, major Ø15.5 mm, minor (root) Ø14.25 mm; basic tooth (thickness half the circular pitch, no tolerance, effective-variation shift esv = 0), true involute flank carried down to the root circle (root fillet not modelled); the 25 mm length is an example, no chamfer, no bore	STEP · STL
spline-shaft-iso-4156-m1-z20	ISO 4156 30° flat-root external spline shaft section, module 1, 20 teeth: pitch Ø20 mm, major Ø21 mm, minor (root) Ø18.5 mm; basic tooth (thickness half the circular pitch, no tolerance, effective-variation shift esv = 0), true involute flank carried down to the root circle (root fillet not modelled); the 25 mm length is an example, no chamfer, no bore	STEP · STL
spline-shaft-iso-4156-m1-z30	ISO 4156 30° flat-root external spline shaft section, module 1, 30 teeth: pitch Ø30 mm, major Ø31 mm, minor (root) Ø28.5 mm; basic tooth (thickness half the circular pitch, no tolerance, effective-variation shift esv = 0), true involute flank carried down to the root circle (root fillet not modelled); the 25 mm length is an example, no chamfer, no bore	STEP · STL
spline-shaft-iso-4156-m1-5-z16	ISO 4156 30° flat-root external spline shaft section, module 1.5, 16 teeth: pitch Ø24 mm, major Ø25.5 mm, minor (root) Ø21.75 mm; basic tooth (thickness half the circular pitch, no tolerance, effective-variation shift esv = 0), true involute flank carried down to the root circle (root fillet not modelled); the 25 mm length is an example, no chamfer, no bore	STEP · STL
spline-shaft-iso-4156-m1-5-z24	ISO 4156 30° flat-root external spline shaft section, module 1.5, 24 teeth: pitch Ø36 mm, major Ø37.5 mm, minor (root) Ø33.75 mm; basic tooth (thickness half the circular pitch, no tolerance, effective-variation shift esv = 0), true involute flank carried down to the root circle (root fillet not modelled); the 25 mm length is an example, no chamfer, no bore	STEP · STL
spline-shaft-iso-4156-m2-z16	ISO 4156 30° flat-root external spline shaft section, module 2, 16 teeth: pitch Ø32 mm, major Ø34 mm, minor (root) Ø29 mm; basic tooth (thickness half the circular pitch, no tolerance, effective-variation shift esv = 0), true involute flank carried down to the root circle (root fillet not modelled); the 25 mm length is an example, no chamfer, no bore	STEP · STL
spline-shaft-iso-4156-m2-z24	ISO 4156 30° flat-root external spline shaft section, module 2, 24 teeth: pitch Ø48 mm, major Ø50 mm, minor (root) Ø45 mm; basic tooth (thickness half the circular pitch, no tolerance, effective-variation shift esv = 0), true involute flank carried down to the root circle (root fillet not modelled); the 25 mm length is an example, no chamfer, no bore	STEP · STL
spline-shaft-iso-4156-m2-5-z18	ISO 4156 30° flat-root external spline shaft section, module 2.5, 18 teeth: pitch Ø45 mm, major Ø47.5 mm, minor (root) Ø41.25 mm; basic tooth (thickness half the circular pitch, no tolerance, effective-variation shift esv = 0), true involute flank carried down to the root circle (root fillet not modelled); the 25 mm length is an example, no chamfer, no bore	STEP · STL
spline-shaft-iso-4156-m3-z14	ISO 4156 30° flat-root external spline shaft section, module 3, 14 teeth: pitch Ø42 mm, major Ø45 mm, minor (root) Ø37.5 mm; basic tooth (thickness half the circular pitch, no tolerance, effective-variation shift esv = 0), true involute flank carried down to the root circle (root fillet not modelled); the 25 mm length is an example, no chamfer, no bore	STEP · STL
spline-shaft-iso-4156-m3-z20	ISO 4156 30° flat-root external spline shaft section, module 3, 20 teeth: pitch Ø60 mm, major Ø63 mm, minor (root) Ø55.5 mm; basic tooth (thickness half the circular pitch, no tolerance, effective-variation shift esv = 0), true involute flank carried down to the root circle (root fillet not modelled); the 25 mm length is an example, no chamfer, no bore	STEP · STL

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Plain text: sheet.txt · JSON: /api/geometry?object=involute-splines-iso-4156-metric-module