Machinery's Handbook 28th Edition
INVOLUTE SPLINES Page 36 of 38
c Values of (0.2m0.667 ? 0.01m?0.5) are as follows: for 10 module, 0.93; for 8 module, 0.80; for 6 mod- ule, 0.66; for 5 module, 0.58; for 4 module, 0.50; for 3 module, 0.41; for 2.5 module, 0.36; for 2 mod-ule, 0.31; for 1.75 module, 0.28; for 1.5 module, 0.25; for 1.25 module, 0.22; for 1 module, 0.19; for0.75 module, 0.15; for 0.5 module, 0.11; and for 0.25 module, 0.06.d See Table 17 for values of es/tan α D.
Table 14. Tooth Thickness Modification, es, for Selected Spline Fit Classes External Splinesa External Splinesa Selected Fit Class Selected Fit Class Pitch Pitch d e f h d e f h Diameter in Diameter in Tooth Thickness Modification Tooth Thickness Modification mm, mm, (Reduction) Relative to Basic (Reduction) Relative to Basic D D Tooth Thickness at Pitch Tooth Thickness at Pitch ≤ 3 0.020 0.014 0.006 0 > 120 to 0.145 0.085 0.043 0 > 3 to 6 0.030 0.020 0.010 0 180 0.170 0.100 0.050 0 > 6 to 10 0.040 0.025 0.013 0 > 180 to 0.190 0.110 0.056 0 > 10 to 18 0.050 0.032 0.016 0 250 0.210 0.125 0.062 0 > 250 to > 18 to 30 0.065 0.040 0.020 0 0.230 0.135 0.068 0 > 30 to 50 0.080 0.050 0.025 0 315 0.260 0.145 0.076 0 > 315 to > 50 to 80 0.100 0.060 0.030 0 0.290 0.160 0.080 0 > 80 to 120 0.120 0.072 0.036 0 400 0.320 0.170 0.086 0 > 400 to a Internal splines are fit class H and have space width modification from basic space width equal to zero; thus, an H/h fit class has effective clearance cv = 0.
Note: The values listed in this table are taken from ISO R286 and have been computed on the basis of the geometrical mean of the size ranges shown. Values in boldface type do not comply with any documented rule for rounding but are those used by ISO R286; they are used in this table to comply with established international practice.
Basic Rack Profiles: The basic rack profile for the standard pressure angle splines are shown in Figs. 6a, 6b, 6c, and 6d. The dimensions shown are for maximum material condition and for fit class H/h.
Spline Machining Tolerances and Variations.— The total tolerance (T + λ), Table 15, is the sum of Effective Variation, λ, and a Machining Tolerance, T.
Table 15. Space Width and Tooth Thickness Total Tolerance, (T + λ), in Millimeters Spline Formula for Spline Tolerance Total Tolerance, Tolerance Class Class T + λ) Formula for Total Tolerance, (T + λ) In these formulas, i* and i** are tolerance units based upon pitch diameter and tooth thickness, respectively: (√ is radication) i?= 0.001 (0.45 *3√D+0.001D) for D≤500 mm i?= 0.001 (0.004D + 2.1 ) for D > 500 mm i??= 0.001 (0.45 *3 √(Sbsc) + 0.001 Sbsc ) 4 5 10i* + 40i** 16i* + 64i** 6 7 25i* + 100i** 40i* + 160i** Effective Variation: The effective variation, λ, is the combined effect that total index variation, positive profile variation, and tooth alignment variation has on the effective fit of mating involute splines. The effect of the individual variations is less than the sum of the allowable variations because areas of more than minimum clearance can have profile, tooth alignment, or index variations without changing the fit. It is also unlikely that these variations would occur in their maximum amounts simultaneously on the same spline. For this reason, total index variation, total profile variation, and tooth alignment variation are used to calculate the combined effect by the following formula:
millimeters
The above variation is based upon a length of engagement equal to one-half the pitch diameter of the spline; adjustment of λ may be required for a greater length of engagement. Formulas for values of Fp, ff, and Fβ used in the above formula are given in Table 16.
??0.6(Fp)2?(ff)2?(F?)2Copyright 2008, Industrial Press Inc., New York, NY - www.industrialpress.com
Machinery's Handbook 28th Edition
INVOLUTE SPLINES Page 37 of 38
Table 16. Formulas for Fp, ff , and Fβ used to calculate λ
Spline Total Index Variation, in mm, Total Profile Variation, in mm, Total Lead Variation, in Tolerance ff mm,Fβ Fp Class 4 5 6 7 0.001(2.5*√(mZπ/2)+6.3) 0.001(3.55*√(mZπ/2)+9) 0.001(5*√(mZπ/2)+12.5) 0.001(7.1*√(mZπ/2)+18) 0.001[1.6m(1+0.0125Z)+10] 0.001[2.5m(1+0.0125Z)+16] 0.001[4m(1+0.0125Z)+25] 0.001[6.3m(1+0.0125Z)+40] 0.001(0.8*√g+4) 0.001(1.0*√g+5) 0.001(1.25*√g+6.3) 0.001(2*√g+10) g = length of spline in millimeters. Table 17. Reduction, es/tan αD, of External Spline Major and Minor Diameters
Required for Selected Fit Classes
Pitch Diameter D in mm ≤3 >3 to 6 > 6 to 10 > 10 to 18 > 18 to 30 > 30 to 50 > 50 to 80 > 80 to 120 > 120 to 180 > 180 to 250 > 250 to 315 > 315 to 400 > 400 to 500 > 500 to 630 > 630 to 800 > 800 to 1000 30 37.5 d 0.035 0.052 0.069 0.087 0.113 0.139 0.173 0.208 0.251 0.294 0.329 0.364 0.398 0.45 0.502 0.554 0.026 0.039 0.052 0.065 0.085 0.104 0.13 0.156 0.189 0.222 0.248 0.274 0.3 0.339 0.378 0.417 0.02 0.03 0.04 0.05 0.065 0.08 0.1 0.12 0.145 0.17 0.19 0.21 0.23 0.26 0.29 0.32 45 Standard Pressure Angle, in Degrees 30 37.5 45 30 Classes of Fit e es/tan αD in millimeters 0.024 0.018 0.014 0.01 0.035 0.026 0.02 0.017 0.043 0.033 0.025 0.023 0.055 0.042 0.032 0.028 0.069 0.052 0.04 0.035 0.087 0.065 0.05 0.043 0.104 0.078 0.06 0.052 0.125 0.094 0.072 0.062 0.147 0.111 0.085 0.074 0.173 0.13 0.1 0.087 0.191 0.143 0.11 0.097 0.217 0.163 0.125 0.107 0.234 0.176 0.135 0.118 0.251 0.189 0.145 0.132 0.277 0.209 0.16 0.139 0.294 0.222 0.17 0.149 37.5 f 0.008 0.013 0.017 0.021 0.026 0.033 0.039 0.047 0.056 0.065 0.073 0.081 0.089 0.099 0.104 0.112 0.006 0.01 0.013 0.016 0.02 0.025 0.03 0.036 0.043 0.05 0.056 0.062 0.068 0.076 0.08 0.086 45 All h 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 These values are used with the applicable formulas in Table 13.
Machining Tolerance: A value for machining tolerance may be obtained by subtracting the effective variation, λ, from the total tolerance (T + λ). Design requirements or specific processes used in spline manufacture may require a different amount of machining tolerance in relation to the total tolerance.
Fig. 6a. Profile of Basic Rack for 30° Flat Root Spline
Copyright 2008, Industrial Press Inc., New York, NY - www.industrialpress.com
Machinery's Handbook 28th Edition
INVOLUTE SPLINES Page 38 of 38
Fig. 6b. Profile of Basic Rack for 30° Fillet Root Spline
Fig. 6c. Profile of Basic Rack for 37.5° Fillet Root Spline
Fig. 6d. Profile of Basic Rack for 45° Fillet Root Spline
British Standard Straight Splines.— British Standard BS 2059:1953, ―Straight-sided Splines and Serrations‖, was introduced because of the widespread development and use of splines and because of the increasing use of involute splines it was necessary to provide a separate standard for straight-sided splines. BS 2059 was prepared on the hole basis, the hole being the constant member, and provide for different fits to be obtained by varying the size of the splined or serrated shaft. Part 1 of the standard deals with 6 splines only, irrespective of the shaft diameter, with two depths termed shallow and deep. The splines are bottom fitting with top clearance.
The standard contains three different grades of fit, based on the principle of variations in the diameter of the shaft at the root of the splines, in conjunction with variations in the widths of the splines themselves. Fit 1 represents the condition of closest fit and is designed for minimum backlash. Fit 2 has a positive allowance and is designed for ease of assembly, and Fit 3 has a larger positive allowance for applications that can accept such clearances.
Copyright 2008, Industrial Press Inc., New York, NY - www.industrialpress.com