DSM snapfit_design

2023年12月7日发(作者：a4l落地价)

DSM Engineering Plastics

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Technical Guide

Snap fit design

Cantilever beam snap-fits

Cantilever beam type snap-fits can be calculated using a simplification of the general beam theory. However

the calculations are a simplification. In general, the stiffness of the part to which the snap-fit connects, is

important. The formulae mentioned only roughly describe the behavior of both the part geometry and the

material. On the other hand, the approach can be used as a first indication if a snap-fit design and material

choice are feasible.

Cantilever beam with constant rectangular cross section

A simple type of snap-fit, the cantilever beam, is demonstrated in the figure below, which shows the major

geometrical parameters of this type of snap-fit. The cross section is rectangular and is constant over the

whole length L of the beam.

The maximum allowable deflection y and deflection force Fb can be calculated with the following formulas if

the maximum allowable strain level ε of the material is known.

2 L2

y = -- . -- . ε

3 t

w . t2 . Es

Fb = ------------ . ε

6 . L

Date:23 February, 2005

1

All information supplied by or on behalf of DSM in relation to its products, whether in the nature of data, recommendations or otherwise, is supported by research and, in good faith, believed reliable, but DSM assumes no

liability and makes no warranties of any kind, express or implied, including, but not limited to, those of title, merchantability, fitness for a particular purpose or non-infringement or any warranty arising from a course of

dealing, usage, or trade practice whatsoever in respect of application, processing or use made of the aforementioned information or product. The user assumes all responsibility for the use of all information provided and

shall verify quality and other properties or any consequence from the use of all such Engineering Plastics

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Technical Guide

where

Es = secant modulus

L = length of the beam

t = height of the beam

w = width of the beam

ε = maximum allowable strain level of the material

The four dimensions that can be changed by the designer are:

- h, the height of the snap-fit lip. Changing the height might reduce the ability of the snap-fit to ensure a proper

connection.

- t, the thickness of the beam. A more effective method is to use a tapered beam. The stresses are more

evenly spread over the length of the beam.

- increasing the beam length, L, is the best way to reduce strain as it is represented squared in the equation

for the allowable deflection.

- the deflection force is proportional to the width, w, of the snap-fit lip.

Beams with other cross sections

The following general formulae for the maximum allowable deflection y and deflection force Fb can be used for

cantilever beams with a constant asymmetric cross section.

L2

y = ------- . ε

3 . e

Es . I

Fb = ------- . ε

e . L

where

Es = secant modulus

I = moment of inertia of the cross section

L = length of the beam

e = distance from the centroid to the extremities

ε = maximum allowable strain level of the material

Normally tensile stresses are more critical than compressive stresses. Therefore the distance from the

centroid to the extremities, e, that belongs to the side under tension is used in the above-mentioned formulae.

The moment of inertia and the distance from the centroid to the extremities is given in table 1 for some cross

sections.

Date:23 February, 2005

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All information supplied by or on behalf of DSM in relation to its products, whether in the nature of data, recommendations or otherwise, is supported by research and, in good faith, believed reliable, but DSM assumes no

liability and makes no warranties of any kind, express or implied, including, but not limited to, those of title, merchantability, fitness for a particular purpose or non-infringement or any warranty arising from a course of

dealing, usage, or trade practice whatsoever in respect of application, processing or use made of the aforementioned information or product. The user assumes all responsibility for the use of all information provided and

shall verify quality and other properties or any consequence from the use of all such information.

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Technical Guide

Table 1. Moment of inertia and distances from centroid to extremities

DSM Engineering Plastics

Date:23 February, 2005

3

All information supplied by or on behalf of DSM in relation to its products, whether in the nature of data, recommendations or otherwise, is supported by research and, in good faith, believed reliable, but DSM assumes no

liability and makes no warranties of any kind, express or implied, including, but not limited to, those of title, merchantability, fitness for a particular purpose or non-infringement or any warranty arising from a course of

dealing, usage, or trade practice whatsoever in respect of application, processing or use made of the aforementioned information or product. The user assumes all responsibility for the use of all information provided and

shall verify quality and other properties or any consequence from the use of all such Engineering Plastics

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Technical Guide

Tapered beams with a variable height

The following formulae can be used to calculate the maximum allowable deflection y and the deflection force

Fb for a tapered cantilever beam with a rectangular cross section. The height of the cross section decreases

linearly from t1 to t2, see figure above.

2 . L2

y = c .-------- . ε

3 . t1

2 w . t1 . Es

Fb = -------------- . ε

6 . L

where

Es = secant modulus

L = length of the beam

c = multiplier

w = width of the beam

t1 = height of the cross section at the fixed end of the beam

ε = maximum allowable strain level of the material

The formula for the deflection y contains a multiplier c that depends on the ratio t2 / t1, see table 2, where t1 is

the height of the beam at the fixed end and t2 is the height of the beam at the free end.

Date:23 February, 2005

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All information supplied by or on behalf of DSM in relation to its products, whether in the nature of data, recommendations or otherwise, is supported by research and, in good faith, believed reliable, but DSM assumes no

liability and makes no warranties of any kind, express or implied, including, but not limited to, those of title, merchantability, fitness for a particular purpose or non-infringement or any warranty arising from a course of

dealing, usage, or trade practice whatsoever in respect of application, processing or use made of the aforementioned information or product. The user assumes all responsibility for the use of all information provided and

shall verify quality and other properties or any consequence from the use of all such Engineering Plastics

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Technical Guide

Table 2. Multiplier c as a function of the height

t2 / t1 0.40 0.50 0.60 0.70 0.80 0.90 1.00

c 1.893 1.636 1.445 1.2971.1791.0821.000

Tapered beams with a variable width

The following formulae can be used to calculate the maximum allowable deflection y and deflection force Fb

for a tapered cantilever beam with a rectangular cross section. The width of the cross section decreases

linearly from w1 to w2, see figure above.

2 . L2

y = c .-------- . ε

3 . t

2 w1 . t . Es

Fb = -------------- . ε

6 . L

where

Es = secant modulus

L = length of the beam

c = multiplier

w1 = width of the beam at the fixed end of the beam

t = height of the cross section

ε = maximum allowable strain level of the material

Date:23 February, 2005

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All information supplied by or on behalf of DSM in relation to its products, whether in the nature of data, recommendations or otherwise, is supported by research and, in good faith, believed reliable, but DSM assumes no

liability and makes no warranties of any kind, express or implied, including, but not limited to, those of title, merchantability, fitness for a particular purpose or non-infringement or any warranty arising from a course of

dealing, usage, or trade practice whatsoever in respect of application, processing or use made of the aforementioned information or product. The user assumes all responsibility for the use of all information provided and

shall verify quality and other properties or any consequence from the use of all such Engineering Plastics

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Technical Guide

The multiplier c depends on the ratio w2 / w1, see table 3, where w1 is the width of the beam at the fixed end

and w2 is the width of the beam at the free end.

Table 3. Multiplier c as a function of the width

w2 / w1 0.125 0.25 0.50 1.00

c 1.368 1.284 1.158 1.000

Cylindrical snap-fits

One must distinguish between a cylindrical snap-fit close to the end of the pipe or remote from the end

Date:23 February, 2005

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All information supplied by or on behalf of DSM in relation to its products, whether in the nature of data, recommendations or otherwise, is supported by research and, in good faith, believed reliable, but DSM assumes no

liability and makes no warranties of any kind, express or implied, including, but not limited to, those of title, merchantability, fitness for a particular purpose or non-infringement or any warranty arising from a course of

dealing, usage, or trade practice whatsoever in respect of application, processing or use made of the aforementioned information or product. The user assumes all responsibility for the use of all information provided and

shall verify quality and other properties or any consequence from the use of all such Engineering Plastics

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Technical Guide

More material must be deformed if the snap fit is remote from the end, and the deflection force Fb and mating

force Fa will be a factor 3.4 higher. The snap-fit is regarded as being remote if

l > 1.8 . √ ( D . t )

where l = distance to the end of the pipe.

The following symbols are further used:

D = average diameter of the pipe = (Do + do) / 2

Do = outside diameter of the pipe

do = outside diameter of the shaft

di = inside diameter of the shaft

Δd / 2 = height of the bulge on the shaft = depth of the groove in the pipe

Es = shear modulus of the plastic

t = wall thickness of the pipe = (Do – do) / 2

μ = coefficient of friction

ν = Poisson’s ratio of the plastic

The formula for the deflection force Fb is given in table 4 for both a rigid (metal) shaft with a flexible pipe, and

a flexible shaft with a rigid (metal) pipe. Four cases can be distinguished.

Date:23 February, 2005

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All information supplied by or on behalf of DSM in relation to its products, whether in the nature of data, recommendations or otherwise, is supported by research and, in good faith, believed reliable, but DSM assumes no

liability and makes no warranties of any kind, express or implied, including, but not limited to, those of title, merchantability, fitness for a particular purpose or non-infringement or any warranty arising from a course of

dealing, usage, or trade practice whatsoever in respect of application, processing or use made of the aforementioned information or product. The user assumes all responsibility for the use of all information provided and

shall verify quality and other properties or any consequence from the use of all such Engineering Plastics

–

Technical Guide

Table 4. Deflection force Fb

Rigid shaft,

flexible

pipe

Snap-fit

close

to the end

Flexible

shaft,

rigid pipe

Snap-fit

remote from

the end

Rigid shaft,

flexible

pipe

Flexible

shaft,

rigid pipe

√ [(Do / do - 1) / (Do / do + 1)]

0.62 . Δd . do . --------------------------------------------- . Es

[(Do / do)2 + 1] / [(Do / do)2 – 1] + ν

√ [(do / di - 1) / (do / di + 1)]

0.62 . Δd . do . --------------------------------------------- . Es

[(do / di)2 + 1] / [(do / di)2 – 1] – ν

√ [(Do / do - 1) / (Do / do + 1)]

2.1 . Δd . do . --------------------------------------------- . Es

[(Do / do)2 + 1] / [(Do / do)2 – 1] + ν

√ [(do / di - 1) / (do / di + 1)]

2.1 . Δd . do . -------------------------------------------- . Es

[(do / di)2 + 1] / [(do / di)2 – 1] – ν

If the deflection force Fb according table 4 has been calculated, the mating force Fa is found using the

expression

μ + tan α1

Fa = Fb . -----------------

1 – μ . tan α1

The highest tangential strain εφ in the plastic is approximately:

- Rigid shaft, flexible pipe: εφ = Δd / do (tension in the pipe)

- Flexible shaft, rigid pipe: εφ = - Δd / do (compression in the shaft)

The highest axial bending strain εa in the plastic is about a factor 1.59 higher :

εa = 1.59 . εφ (tension at one side and compression at the other side)

The calculation procedure when both parts are flexible and both are deformed is explained in the theory of

snap fits. As a first approach, for flexible materials with a comparable stiffness, one can assume that the total

deformation Δd is equally divided between the two parts.

Spherical snap-fits

The spherical snap-fit can be regarded as a special case of the cylindrical snap-fit. The formulas for a

cylindrical snap-fit close to the end of the pipe can be used.

Date:23 February, 2005

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All information supplied by or on behalf of DSM in relation to its products, whether in the nature of data, recommendations or otherwise, is supported by research and, in good faith, believed reliable, but DSM assumes no

liability and makes no warranties of any kind, express or implied, including, but not limited to, those of title, merchantability, fitness for a particular purpose or non-infringement or any warranty arising from a course of

dealing, usage, or trade practice whatsoever in respect of application, processing or use made of the aforementioned information or product. The user assumes all responsibility for the use of all information provided and

shall verify quality and other properties or any consequence from the use of all such Engineering Plastics

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Technical Guide

Mold construction

Mold construction costs are highly affected by the design of the snap fit.

Alternative B results in mold construction cost savings versus Alternative A

For design A, an expensive slide in the mold is required and the flat surfaces require expensive milling. No

slide is required for alternative B and the cylindrical outside surface can simply be drilled.

Date:23 February, 2005

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All information supplied by or on behalf of DSM in relation to its products, whether in the nature of data, recommendations or otherwise, is supported by research and, in good faith, believed reliable, but DSM assumes no

liability and makes no warranties of any kind, express or implied, including, but not limited to, those of title, merchantability, fitness for a particular purpose or non-infringement or any warranty arising from a course of

dealing, usage, or trade practice whatsoever in respect of application, processing or use made of the aforementioned information or product. The user assumes all responsibility for the use of all information provided and

shall verify quality and other properties or any consequence from the use of all such information.