Tolerancing Guidelines

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Testing and Tolerancing

T - Tolerancing Guidelines

Tolerances

Determination of a specific tolerance is highly dependent on the specific spring design, material used, equipmentused to manufacture the spring, and heat treating methods used in spring processing. The tolerances presentedare "normally achievable." However, the spring manufacturer should be consulted before finalizing. In severalareas, different grade levels are available. One should be aware that selection of the highest grade (moststringent) could have significant cost implications.

Today, use of statistical controls allows both the spring manufacturer and the customer a high level of confidencethat the spring "properly toleranced" will meet or exceed the performance requirements. Once again it is importantto have both the designer and the manufacturer work closely together to establish the "process capability" whichwill determine the quality level obtainable.

WARNING

Actual quality levels (Cpk) on many toleranced dimensions can only be determined through process capabilitystudies.

Note:It is possible to obtain tighter tolerancing with the intervention of special equipment. These specialprocesses frequently add significant cost. Do not use standard block tolerances.

Note:All English units of measure are shown in bold face type.

Compression Spring Load Tolerances

Regression formulas derived from industry standards for helical round wire compression springs (based onsprings with parallel sides and constant pitch.)

There are two factors to calculate before computing the load tolerance. The first factor, (Af), is based on wire (d)and mean diameter (D). Since the specification was formulated to work with metric input, you must first convertEnglish data to metric.

Therefore, for conversion to inches:

d = d * 25.4

D = D * 25.4

Also, the math operators are written to accommodate programming. The following symbols are represented in theformula.

* = multiplication/ = division^ = exponentiation (raised to the power of the number to it's immediate right)

c (index) = D/d

Af = 65.92 * (d ^ 3.3 / D ^ 1.6) * (-0.84 * (c / 10) ^ 3 + 3.781 * (c / 10) ^ 2 - 4.244 (c /10) + 2.274) (T-1)

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The second factor (Kf) is based on active material (Na).

The tolerance formula is then calculated as shown below. (If English, convert the load in pounds, to Newtons withp = p * 4.44822)

To convert to English, divide the result by 4.44822 for pounds.

Example: (See Figure T-1 on page 3)

Design parameters:

Figure T-1. Compression Spring.

1. Convert English parameters to metric:

2. Calculate Af:

Af = 65.92 * (3.175^3.3 / 27.94^1.6) * (-.84 * (8.8/10)^3 + 3.781 * (8.8/10)^2 - 4.244 * (8.8/10) + 2.274

Af = 12.95864

3. Calculate Kf:

Kf = 1 / (3 * 5.274^2) + 8 / (5 * 5.274) + .803

Kf = 1.11836

Kf = 1 / (3 * Na ^ 2) + 8 / (5 * Na) + .803 (T-2)

Tol = Af * Kf + (1.5 * p) / 100 (T-3)

d = .125

D = 1.100

Na = 5.274

p = 50 lbs

R = 50 lbs/in

d =.125 * 25.4 = 3.175 mm

D = 1.100* 25.4 = 27.94 mm

p = 50* 4.44822 = 222.411 N

c = 27.94/ 3.175 = 8.8

R = 50/ 5.71 = 8.76 N/mm




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4. Calculate the load tolerance:

Tol = 12.958 * 1.11836 + (1.5 * 222.411) / 100

Tol = 17.828 N (pounds = 17.828 / 4.44822 = 4.008 lbs)

Quality grades for load tolerances

Load tolerances calculated from the previous formulas establish the base (precision tolerance). This precisiontolerance is considered to be optimum, which would result in Cpk of 1.2 or less. The precise tolerance can only bedetermined by a capability study. Commercial tolerance may also be calculated as indicated below. When usingcommercial tolerances, Cpk >1.2 can "normally" be expected.

Precision = 1.0

Commercial = 1.6

When using the Grade factor (Q), multiply the Grade factor by the calculated tolerance. From our example:

Tolerance = 4.008 lbs

Therefore:

Precision = 4.008* 1.0 = 4.008 lbs

Commercial = 4.008* 1.6 = 6.413 lbs

Compression Spring Free Length Tolerances

The following formula may be used to calculate the Free Length tolerance for an unloaded compression spring:

Using our example:

FL Tol = (12.95864 * 1.11836 * 1) / 8.76

FL Tol = 1.654 mm (1.654 / 25.4 = .065")

For unground springs, multiply FL Tol by 1.7.

Extension Spring Load Tolerances

Regression formulas derived from industry standard for helical round wire Extension springs.

The Af factor for calculating extension spring load tolerances is identical to that of the compression formula.

The second factor (Kf), however, is as shown below.

FL Tol = (Af * Kf * Q / R) (T-4)

Af = 65.92 * (d ^ 3.3 / D ^ 1.6)* (-0.84 * (c / 10) ^ 3 + 3.781 * (c / 10) ^ 2 - 4.244 (c /10) + 2.274) (T-5)

Kf = 5.61 / Na + .7 (T-6)




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The tolerance formula is also identical to the compression calculation.

Example: (See Figure T-2 on page 6)

Design parameters:

d = .125"D = 1.300"Na = 22.792p = 20 lbsR = 7.009 Ibs/in


d = .125* 25.4 = 3.175 mmD = 1.300* 25.4 = 33.02 mmp = 20* 4.44822 = 88.96 Nc = 33.02/ 3.175 = 10.4

R = 7.009/ 5.71 = 1.227 N/mm

2. Calculate Af:

Af = 65.92 * (3.175^3.3 / 33.02^1.6) * (-.84 * (10.4/10)^3 + 3.781 * (10.4/10)^2 - 4.244 * (10.4/10) + 2.274

Af = 11.13894

3. Calculate Kf:

Kf = 5.61 / 22.792 + .7

Kf = .94614

4. Calculate the load tolerance:

Tol = 11.13894 * .94614 + (1.5 * 88.96) / 100

Tol = 11.873 N (pounds = 11.873 / 4.44822 = 2.669 lbs)

Quality Grades for Extension Spring Load Tolerances

The Quality Grades are the same for both compression and extension springs.

When using the Grade factor (Q), multiply the Grade factor by the calculated tolerance. From our example:

Tolerance = 2.669 lbs

Therefore:

Precision = 2.669* 1.0 = 2.669 lbs

Commercial = 2.669* 1.6 = 4.270 lbs

Tol = Af * Kf + (1.5 * p) / 100 (T-7)




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Table T-2. Free Length Tolerance (with lnitial Tension) English.

Table T-3. End Position Tolerance.

Torsion Spring Load Tolerances (Torque)

Regression formulas derived from Industry Standard for helical round wire Torsion springs. The factor (Kf) = 54

The tolerance formula is then as shown below.

Figure T-3. Torsion Spring.

Example: (See Figure T-3 above)

Design parameters:

d = .087"Na= 6.62


d = -.087* 25.4 = 2.21 mm

2. Calculate index:

Total Number of CoilsAngle Between

Loop Planes

3 67 9

10 12

13 16over 16

25 35 45

60Random

Tol = ( (1.3 * Kf * d ^ 3) / (Na ^ .24 * c ^ .5) ) * Q (T-9)




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Table T-9. Permissible Squareness Deviation, Springs With Unground Ends.

Tolerances for Retaining Rings

Ring diameters from .500 into 24.00 in(12.7 mm to 610 mm) can be produced on standard ring coilingmachines.

Diameter Tolerances

A good rule of thumb is .010 in(0.25 mm) per each 1.000 in(25.4 mm) of diameter. The exception is ringsunder 1.500 in(3.81 mm) which should remain at .015 in(0.38 mm).

Table T-10. Retaining Ring Free Dimension Tolerances.

Figure T-4. Internal Retaining Rings.

Figure T-5. External Retaining Rings.

Over 8to 10(203 to 254), incl 2 1/4

Over 10to 12(254 to 305), incl 2 1/4

Over 12to 14(305 to 356), incl 2 1/4

Over 14to 16(356 to 406), incl 2 1/4

@ Dia. 1.500 in

(> 38.1 mm)

Gap

Diameter (D)Tolerance

0.15 in(0.38 mm)

0.10 in(0.25 mm)per each

1.000 in (25.4 mm) ofDia.

Gap tolerance X 3Dia. tolerance




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Tolerances for Belleville Washers

Table T-11. Belleville Washer Diameter Tolerances.

Figure T-6. Belleville Washer.

Tolerances for Special Spring Washers

Table T-12. Load Tolerances for Special Spring Washers. (Apply to deflection ranges of 20% - 80% of

Diameter, in (mm)O.D. in (mm) I.D. in (mm)

+0.00 -0.00

Up to 0.197(5)0.197- 0.394(5 10)0.394- 0.984(10 25)

0.984- 1.969(25 50)1.969- 3.937(50 100)

- 0.008(- 0.20)- 0.010(- 0.25)- 0.012(- 0.30)

- 0.016(- 0.40)- 0.020(- 0.50)

+ 0.008(+ 0.20)+ 0.010(+ 0.25)+ 0.012(+ 0.30)

+ 0.016(+ 0.40)+ 0.020(+ 0.50)

Based on R* = 2. increased tolerances are required for lower Rratios.* (R = OD / ID)

Washer Stock Thicknessin mm Percent Load

Curved 0.004- 0.039 0.1 - 1.0 15

Wave 0.004- 0.0100.010- 0.0120.012- 0.0200.020- 0.0390.039- 0.079

0.1 - 0.250.25 - 0.30.3 - 0.50.5 - 1.01.0 - 2.0

3325201512




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available deflection.)

Figure T-7. Special Spring Washers.

Tolerances for Flat Springs

Table T-13. Flat Springs: Strip Thickness Tolerances, Tempered and Untempered.

Thickness Range in (mm)

Tolerance, in (mm)

0.125- 0.063(3.18) - (1.60)

0.00200(0.51)

0.062- 0.040(1.59) - (1.02)

0.00150(0.038)

0.039- 0.029(1.01) - (0.74)

0.00100(0.025)

0.028- 0.020(0.73) - (0.51)

0.00075(0.019)

0.019- 0.007(0.50) - (0.18)

0.00050(0.013)

Under 0.007(0.18) 0.00030(0.008)




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Figure T-8. Flat Springs.

Related Topics:

Tolerancing Guidelines

Guidelines for Spring Testing

Reference - Symbols for Spring Terms


Tolerancing Guidelines

Documents

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