Snap-Fit Joints Design

Contents

A

Snap Joints /General  Common features • Types of snap joints • Comments on dimensioning

B

Cantilever Snap Joints Calculations • Hints for design Calculations • Permissible undercut • Deflection force, mating force • Calculation examples

C

Torsion Snap Joints • Deflection • Deflection force

D The illustration above above shows a photograph o f two snap-fit models taken in polarized

Annular Snap Joints • Permissible undercut

light; both have the same displacement (y) and deflective force (P).

• Mating force • Calculation example

Top: The cantilever arm of unsatisfactory

E

Both Mating Parts Elastic

F

Symbols

design has a constant cross section. The non-uniform distribution of lines (fringes) indicates a very uneven strain in the outer fibers. This design uses 17% more material and exhibits 46% higher strain than the optimal design.

Bottom: The thickness of the optimal snapfit arm decreases linearly to 30% of the original cross-sectional area. The strain in the outer fibers is uniform throughout the length of the cantilever.

Page 2 of 26

Snap-Fit Joints for Plastics - A Design Guide

Snap

Joi Joints Genera eral

A

Common Common featur features es Snap Snap join joints ts are are a very very simp simple le,, econ econom omic ical al and rapid way of join-ing two different component ents. All typ types of snap snap join oints have in comm common on the the prin princi cipl plee that that a prot protru rudi ding ng part part of one one comp compon onen ent, t, e.g. e.g.,, a hook hook,, stud stud or bead bead is defle deflecte cted d briefl briefly y durin during g the joinin joining g operaoperation tion and and catc catche hess in a depr depres es-s -sio ion n (und (under ercu cut) t) in the mating mating compon component ent.. After After the joinin joining g operat operation ion,, the snap-f snap-fit it feafeatures should return to a stress-free condition. The The join jointt may may be sepa separa rabl blee or inse insepa para rabl blee depe depend ndin ing g on the the shap shapee of the the unde underc rcut ut;; the the forc forcee requi required red to sepa separat ratee the the comp compoo-ne nent ntss vari varies es grea greatl tly y acco accord rdin ing g to the the desi design gn.. It is parti particul cularl arly y im-por im-portan tantt to bear bear the follow following ing factor factorss in mind mind when when design designing ing snap snap joints joints:: • Mecha Mechanic nical al load load durin during g the assemb assembly ly operation. • Force Force requir required ed for assemb assembly ly..

Page 3 of 26


A

Types of snap joints A wide range of of design possi-bilities possi-bilities exists for snap joints. In view of their high level of flexibility, plastics are usually very suitable materials for this joining technique. In the following, the many design possibilities have been reduced to a few basic shapes. Calculation principles have been derived for these basic designs.

The most important are: • Cantilever Cantilever snap joints joints The load here is mainly flexural.

• U-shaped snap joints A variation of the cantilever cantilever type. type.

• Torsion snap joints joints Shear stresses carry the load.

• Annu Annular lar snap snap join joints ts These are rotationally rotationally sym-metrical and involve multiaxial stresses.

Page 4 of 26


Snap Snap Joint Joints/G s/Gen ener eral al

A

Cantilever snap joints The four cantilevers on the control panel module shown in Fig. 1 hold the module firmly in place in the grid with their hooks, and yet it can still be removed when required. An economical and reliable snap joint can also be achieved by rigid lugs on one side in combination with snap-fitting hooks on the other (Fig. 2). This design is particularly effective for joining two similar halves of a housing which need to be easily separated. The positive snap joint illustrated in Fig. 3 can transmit considerable forces. The cover can still be removed easily from the chassis, however, since the snap-fitting arms can be re-leased by pressing on the two tongues in the direction of the arrow. The example shown in Fig. 4 has certain similarities with an annular snap joint. The presence of slits, however, means that the load is predominantly flexural; this type of joint is therefore classified as a "cantilever arm" for dimen-sioning purposes.

Fig 4: Discontinuous annular sna p joint

Page 5 of 26


A Torsi orsion on snap snap join joints ts The tor-sion snap joint of the design shown for an inst instru rume ment nt hous housin ing g in Fig. Fig. 5 is stil stilll unco uncommmonin thermop thermoplas lastic tics, s, despi despite te thefact that that it, too, too, amou amount ntss to a sophi sophist stic icat ated ed and and econ econom omic ical al join join-ing meth method od.. The The desi desig gn of a rocke ockerr arm arm whose ose defle deflect ctio ion n force force is give given n larg largel ely y by torsi torsion on of its its shaft shaft perm permit itss easy easy openi pening ng of the the cove coverr unde underr a forc forcee P; the the tors torsio ion n bar bar and and snap snap-f -fit itti ting ng rock rocker er arm arm are are int integra egrall lly y mold molded ed with with the the lowe lowerr part part of the housing housing in in a single single shot. shot.

Annu Annula larr snap snap join joints ts A typica typicall applic applicati ation on for annul annular ar snap snap joints joints is in lamp lamp hous housin ings gs (Fig (Fig.. 6). Here, ere, quit quitee smal smalll under undercu cuts ts give give joint jointss of consi conside derab rable le streng strength th..

Fig Fig 5: Torsi orsion on snap snap join jointt on a hous housin ing g made made of Makr Makrol olon on poly polyca carb rbon onat atee

Fig 6: A cont contin inuo uous us annu annula larr snap snap join joint t offe offers rs a semi semi-h -her erme meti ticc seal seal and and is bett better er for single assembly applications applications

Page 6 of 26


Snap Joints/General Comb Combin inat atio ion n of diff diffeerent ent snap snap joint systems – The The traf traffic fic ligh lightt illu illuss-

• The The refl reflec ecto torr catc catche hess at thre threee poin points ts on the the

A Assumptions

peri periph pher ery y. Eith Either er a snap snap-f -fit itti tin n hook hook 3a or a

trate rated d in Fig. Fig. 7 is an exam exampl plee of an effe effect ctiv ivee

pressure pressure point point 3b may may be chos chosen en here here,, so

The The calc alculat ulatio ion n proc proced edur ures es appl applic icab able le to

desig esign n for for a func functi tion onal al unit unit.. All the the comp compoo-

that that ther theree is poly polygo gona nall defo deform rmat atio ion n of the the

vari variou ouss type typess of join joints ts are are brie briefl fly y desc descri ribe bed d

nent nentss of the the hous housin ing g are are join joined ed toge togeth ther er by

inne innerr ring ring of the the hous housin ing. g.

on the the foll follow owin ing g page pages, s, but but in such such a way way as

snap joint. joint.

to be as general ral as possi ssible. The user ser can • The lens ens in the the fro front door is eith ither pro

Details:

duce duced d in the the seco second nd of two two mold moldin ings gs 4a

• Hous Housin ing g and and fron frontt acce access ss door door enga engage ge at

or, or, if a glas glasss lens lens is desi desire red, d, this this can can be

the fulcru fulcrum m 1a. The The lugs lugs 1b (pressure

held held by severa severall cantil cantileve everr snaps snaps 4b .

poin point) t) hold hold the the door door open open,, whic which h is usef useful ul for changi changing ng bulbs. bulbs. • The The cant cantil ilev ever er hook hook 2 lock lockss the the door door.. The The door door can can be open opened ed agai again n by pres pressi sing ng the the

there therefo fore re appl apply y this this info informa rmati tion on to type typess of joints not dealt with directly. directly. In all all the the snap snap-f -fit it desi design gnss that that foll follow ow,, it is assumed initially that one of the mating parts

• The sun sun viso isor engage gagess at 5 like like a bayo bayone nett

remains rigid. This assumption represents an

catch. catch. Good service-a service-abili bility ty and low-cost low-cost

additi additiona onall precau precautio tion n agains againstt materia materiall failfail-

produc productio tion n can be achiev achieved ed with with carefu carefully lly

ure. ure. If the the two two comcom-po pone nent ntss are are of appr approx oxii-

thoug thoughtht-out out desig designs ns such such as this. this.

mate mately ly equa equall stif stiffn fnes ess, s, half half the the defl deflec ecti tion on

hook hook thro throug ugh h the the slit slit in the the hous housin ing g at 2.

can can be assi assign gned ed to each each part part.. If one one comp compoonent is more rigid than the other and the total stre stren ngth gth availa ailab ble is to be util utiliz ized ed to the the fulles t,

the

more

c om plex

pro ce du re

desc descri ribe bed d in Sect Sectio ion n E must must be adop adopte ted. d. Wha t is sai d in the rem a ind er o f th e broc brochu hure re take takess into into acco accoun untt the the fact fact that that the the plas plasti tics cs part partss conc concer erne ned d are, are, for for brie brieff peri peri-ods, su bj bjecte d to ver y high mechani ca cal load s. s. This mea ns ns that the stress -s -st ra rain beha behavi vior or of the the mate materi rial al is alre alread ady y outs outsid idee the linear range and the ordinary modulus of elas elasti tici city ty must must ther theref efor oree be repl replac aced ed by the the strain strain dependen dependentt secant secant modulus. modulus.

Fig. ig. 7: Cros Crosss-se sect ctio iona nall sket sketch ch (abov (above) e) and and phot photo o (bel (below ow)) of a traf traffi ficc ligh lightt made made of Makrolon®polycarb Makrolon®polycarbonate. onate. All the components components are held together together entirely entirely be means of snap joints joints

Page 7 of 26


Cantilever Snap Joints

B

Design Design Hints Hints A larg largee prop propor orti tion on of snap snap join joints ts are are basi basica call lly y simple cantilever snaps (Fig. 8), which may be of rect rectaangul ngulaar or of a geome eometr tric ical ally ly more more compl complex ex cross cross sectio section n (see (see Table able 1). It is suggested to design the f in inger so that either its thickness (h) or width (b) tapers from the root to the hook; in this way the load-bearing cro cross sect sectiion at any point bears a more more appro ppropr pria iate te rela relati tio on to the the loca locall loa load. The maxi maximu mum m stra strain in on the the mate materi rial al can can ther theref efor oree be redu reduce ced, d, and and less less mate materi rial al is need needed ed.. Fig. 8: Simple snap-fitting hook

Good Good resu result ltss have have been been obta obtain ined ed by redu reduci cing ng the the thic thickn knes esss (h) (h) of the the cant cantil ilev ever er line linear arly ly so that that its its valu valuee at the the end end of the the hook hook is equa equall to one-half the value at the root; alternatively, the fing finger er widt width h may may be redu reduce ced d to oneone-qu quar arte terr of the the base base valu valuee (see (see Table able 1, desi design gnss 2 and and 3). 3). With the designs illustrated in Table 1, the vulnera nerabl blee cros crosss sect sectio ion n is alwa always ys at the the root root (see (see also also Fig. Fig. 8, Deta Detail il A). A). Spec Specia iall atte attent ntio ion n must must ther theref efor oree be give given n to this this area area to avoi avoid d stre stress ss concentration. Fig. 9 graphically represents the effect the root radi radius us has has on stre stress ss conc concen entr trat atio ion. n. At firs firstt

Fig. 9: Effects of a fillet radius on stress concentration concentration

glan glance ce,, it seem seemss that that an opti optimu mum m redu reduct ctio ion n in stress stress conce concentr ntrati ation on is obtain obtained ed using using the the ratio ratio R/h as 0.6 sinc ince only a marg margin inaal redu reducctio tion occu occurs rs afte afterr this this poin point. t. Howe Howeve verr, usin using g R/h R/h of 0.6 0.6 woul would d resu result lt in a thic thick k area area at the the inte inters rsec ec-tion of the snap-fit arm and its base. Thick section tionss will will usua usuall lly y resu result lt in sink sinkss and/ and/or or void voidss which are signs of high residual stress. For this reas reason on,, the the desi design gner er shou should ld reac reach h a comp compro ro-mise mise betw betwee een n a larg largee radi radiu us to redu reduce ce stre stress ss conc concen entr trat atio ion n and and a smal smalll radi radius us to redu reduce ce the the pote potent ntia iall for for resi residu dual al stre stress sses es due due to the the crecreatio ation n of a thic thick k secsec-ti tion on adja adjace cent nt to a thin thin secsection tion.. Inte Intern rnal al test testin ing g show showss that that the the radi radius us should not be less than 0.015 in. in any instance.

Page 8 of 26



B

Calculations

Table 1: Equations Equations for dimensioning dimensioning cantilevers cantilevers

Symbols

Notes

y

1)

E at

The The sec section tion modu odulus lus shou should ld be determ determine ined d for the surfac surfacee subjec subjectt to

= (pe (perm rmis issi sibl ble) e) stra strain in in the the out outer er fibe fiberr

stre stress ss is in the the smal smalll surf surfac acee area area b. If it

tensil tensilee stress stress.. Sectio Section n moduli moduli for crosscross-

the roo root; in for formulae: E as absolute

occu occurs rs in the the larg larger er surf surfac acee area area a, howhow-

sect sectio ion n shap shapee type type C are are give given n in Fig. Fig. 11.

value = percentage/100 (see Table 2)

ever ever,, a and and b must must be inte interc rcha hang nged ed..

Sectio Section n moduli moduli for other other basic basic geome geometri trical cal

1

= length of arm

h

= thickness at root

b

= width at root

c

= dista stance nce betw betweeen outer ter fib fiber and

shap shapes es are are to be foun found d in mech mechan anic ical al 2)

If the the tens tensiile stre stress ss occurs curs in the the conv conveex surf surfac ace, e, use use K2, K2, in Fig. Fig. 10; 10; if it occu occurs rs

Permis Permissib sible le stres stresses ses are are usua usuall lly y more more affec affecte ted d

in the the conc concav avee surf surfac ace, e, use use K1, K1,

by tempe temperat rature uress than than the assoc associat iated ed strain strains. s. One One

accordingly.

neutral fiber (center of gravity) Z

4)

Thes Thesee form formu ulae lae app apply when the the tens tensiile

= (per (permi miss ssib ible le)) defl deflec ecti tion on (=un (=unde derc rcut ut))

= section modulus Z = I c, where I = axial moment of inertia

Es

= se secan cant mod modu ulus lus (se (seee Fig Fig.. 16 16)

P

= (pe (permis rmissi sib ble) defle flectio ction n forc forcee

K

= geomet ometri ricc fac factor tor (se (see Fig Fig. 10)

3)

c is the dista stance nce betw betweeen the outer ter fib fiber and and the the cent center er of grav gravit ity y (neu (neutr tral al axis axis)) in the surfac surfacee subjec subjectt to tensil tensilee stress stress..

pref-erably determines the strain associated with the the perm permis issi sibl blee stre stress ss at room room temp temper erat atur ure. e. As a firs firstt appr approx oxim imat atio ion, n, the the comp compuu-ta tati tion on may may be base based d on this this valu valuee rega regard rdle less ss of the the temp temper eraature ture.. Alth lthoug ough the equati uatio ons in Table ble 1 may may appe appear ar unfa unfami mili liar ar,, they they are are simp simple le mani manipu pula la-tions of the conventional engineering equa-tions to put put the the anal analys ysis is in term termss of perm permis issi sibl blee stra strain in levels.

Page 9 of 26


Geometric Geometric factors factors K and Z for ring segment segment

Fig 10: Diagrams for determining determining K1 and K2 for cross-sectional shape type C in Table Table 1. K1: Concave Concave side under under tensile tensile load, K2: Convex Convex side under under tensile tensile load

Fig 11: Graphs for determining the dimensionless dimensionless quantity (Z/r23) used to derive the section modulus (Z) for crosssectional shape C in Table 1. Z1: concave side under tensile stress, Z2: convex side under tensile tensile stress

Page 10 of 26



B

Fig 12: 12: Undercut for snap joints

Fig 13: Determination of the permissible permissible strain for the joining joining operation (left: (left: material with distinct distinct yield point; right: glass-fiber-reinfor glass-fiber-reinforced ced material without yield point)

Permissible undercut

In gene genera ral, l, duri during ng a singl single, e, brie brieff snap snap-fi -fitt ttin ing g operat operation ion,, partia partially lly crysta crystalli lline ne materi materials als may

The deflection y occurring during the joining

be stre stress ssed ed almo almost st to the the yiel yield d poin point, t, amor amor--

operation is equal to the undercut (Fig. 12).

phous ones up to about 70% of the yield strain.

Glass-fiber-reinforced molding compounds do not normally have a distinct yield point. The permis-sible strain for these materials in the case of snap joints is about half the elongation at break (see Fig. 13)

The permissible deflection y (permissible undercut) depends not only on the shape but also on the permissible strain E for the material used.

Page 11 of 26


B Deflec Deflectio tion n force force Usin Using g the the equa equati tion onss give given n in Table able 1, the the perpermissib missible le deflec deflectio tion n y can be determ determine ined d easily easily even even for for cros crosss sect sectio ions ns of comp comple lex x shap shapes es.. The The proc proced edur uree is expl explai aine ned d with with the the aid aid of an example example which which follows. follows. A part partic icul ular arly ly favo favorab rable le form form of snap snap-fi -fitt ttin ing g arm arm is desi design gn 2 in Table able 1, with with the the thic thickn knes esss of the arm decreasing linearly to half its initial valu value. e. This This versi version on incr increa ease sess the the permi permiss ssib ible le defle eflect ctio ion n by more more than than 60% 60% comp compar ared ed to a

Fig. 14: Determination of the secant secant modulus

snap-fi -fitting arm of consta stant cros ross section ion (design (design 1). Complex designs such as that shown in Fig. 15 may may be used sed in appl applic icat atio ions ns to incr increa ease se the the

Permissible short term strain limits at 23˚C (73˚F)

effec effec-ti -tive ve lengt length. h. Poly Polymer merss Divis Divisio ion n Desi Design gn Engi Engine neer erin ing g Serv Servic ices es woul would d be plea please sed d to

Unreinforced

assist sist you in a curve rved beam ana analysis if you

Apec®

High High Heat Heat PC

4%

Baybl blend®

PC/ABS

2.5%

Makrobl blend®

Polycarbonate Blends

3.5%

Makrolon®

PC

4%

choo choose se this this type type of desi design gn.. The The defl deflec ecti tion on forc forcee P requ requir ired ed to ben bend the the fing finger er can can be calc calcu ulate lated d by use use of the the equa equa-tions in the bottom row row of Table 1 for for cross ross sectio sections ns of variou variouss shapes shapes..

Glass-Fiber-Reinforced rced (%G (%Glass lass))

Es is the the stra strain in depe depend nden entt modu modulu luss of elas elasti tici ci--

Makrolon®(10%) PC

2.2%

ty or "sec "secan antt modu modulu lus" s" (see (see Fig. Fig. 14). 14).

Makrolon®(20%) PC

2.0%

Valu alues for for the the sec secant ant mod modulu ulus for for vario arious us

Tabl Tablee 2: Gene Genera rall guid guidee data data for for the the allo allowa wabl ble e

Bayer Bayer engine engineeri ering ng plasti plastics cs can be determ determine ined d

shor shortt-te term rm stra strain in for for snap snap join joints ts (sing (single le join join -

fro from Fig Fig. 16. The The stra strain in value used sed sho should

ing ing oper operat atio ion) n);; for for freq freque uent nt sepa separa rati tion on and and

alwa always ys be the the one one on whic which h the the dime dimens nsio ioni ning ng

rejo rejoin inin ing, g, use use abou aboutt 60% 60% of thes thesee valu values es

of the the unde underc rcut ut was was base based. d.

Fig Fig. 15: 15: U-sh U-shap aped ed snap snap-f -fit itti ting ng arm arm for for a lid fastenin fastening g

Polyureth Polyurethane ane Snap-Fits Snap-Fits Snap-fits are possible using certain pol polyurethane sys systems. For more info inform rmat atio ion n call call Poly Polyme mers rs Desi Design gn Engineer Engineering ing at 412-777412-777-4952 4952..

Page 12 of 26



B

Fig. Fig. 16: Secant Modulus for Bayer engineering engineering plastics at 23°C (73°F)

Page 13 of 26


B

Fig. Fig. 17: Relationship between deflection force force and mating force

Mating Mating Force Force Duri During ng the the asse assemb mbly ly oper operat atio ion, n, the the defl deflec ecti tion on forc forcee P and and fric fricti tion on forc forcee F have have to be over overco come me (see (see Fig. Fig. 17). 17). The The mati mating ng forc forcee is give given n by: by: W = P • ta t an (  + p) = P

µ + tan  1 – µ tan 

µ + tan  The value for 1 — µ tan  can can be take taken n dire direct ctly ly from from Fig. Fig. 18. 18. Fric Fricti tion on coef coeffi fici cien ents ts for for vari variou ouss mate materi rial alss are are give given n in Table able 3.

separation force In case case of sepa separa rabl blee join joints ts,, the the separation can be determined in the same way as the mating forc forcee by usin using g the the abov abovee equa equati tion on.. The The angl anglee of incl inclin inat atio ion n to be used used here here is the the angl anglee  '

Page 14 of 26



The figures depend on the relative speed of the mating parts, the pressure applied and on the surface quality. Friction between two different plast plastic ic mater material ialss gives gives value valuess equal equal to to or slightly below those shown in Table 3. With two components of the same plastic material, the friction coefficient is generally higher. Where the factor is known, it has been indicated in parentheses.

B

PTFE PE rigid PP POM PA PBT PS SAN PC PMMA AB S PE flexible PVC

0.12-0.22 0.20-0.25 0.25-0.30 0.20-0.35 0.30-0.40 0.35-0.40 0.40-0.50 0.45-0.55 0.45-0.55 0.50-0.60 0.50-0.65 0.55 .55-0.60 .60 0.55-0.60

(x ( x 2.0) (x (x 1.5) (x (x 1.5) (x (x 1.5) (x (x 1.2) (x (x 1.2) (x ( x 1.2) (x ( x 1 .2 ) (x 1.2) .2) (x ( x 1 .0 )

Table 3: Friction coefficient, µ. (Guide data from literature for the coefficients of friction of plastics on steel.)

Page 15 of 26


B Calculation example I snap-fitting hook This calculation is for a snap-fitting hook of rectangular cross section with a constant decrease in thickness from h at the root to h/2 at the end of the hook (see Fig. 19). This is an example of de-sign type 2 in Table 1 and should be used whenever possible to per-mit greater deformation and to save material.

Given: a. Material = Makrolon® polycarbonate b. Length (1) = 19 mm (0.75 in) c. Width (b) = 9.5 mm (0.37 (0.37 in) d. Undercut (y) = 2.4 mm (0.094 in) e. Angle of inclination inclination (a) = 30°

Find: a. Thickness h at which full deflection y will cause a strain of one-half the permissible strain. b. Deflection force P c. Mating force W

Fig. Fig. 19: 19: Snap-fi Snap-fittin tting g hook, hook, design design type type 2, shape shape A

Solution: a. Determination Determination of wall thickness thickness h Permissible strain from Table 2: pm = 4% Strain required here  = 1/2 pm = 2% Deflection equation from Table 1, type 2, shape A: Transposing in terms of thickness

2 y = 1.09 1 h

h = 1.09  12 y = 1.09 x 0.02 x 19 2 2.4 = 3.28 .28 mm (0.1 (0.13 3 in) in)

b. Determination of deflection force P Deflection force equation equation from Table Table 1, cross section A A:: P = bh 2 6

•

Es  1

From Fig. 16 at  = 2.0% Es = 1,815 N/mm 2 (264,000 psi) P = 9.5 mm x (3.28 (3.28 mm)2 6 = 32.5 N (7.3 lb)

•

1,815 N/mm 2 x 0.02 19 mm

c. Determinatio Determination n of mating force force W W = P•

µ + tang tang  1 – µ tan 

Friction coefficient from Table 3 (PC against PC) µ = 0.50 x 1.2 = 0.6 From Fig. 18:

µ + tan  1—µ tan 

= 1.8 For µ = 0.6 and a = 30°

W = 32.5 N x 1.8 1.8 = 58.5 N (13.2 lb)

Page 16 of 26



B

Calculation example II snap-fitting hook This calculation example is for a snap-fitting hook with a segmented ring cross section decreasing in thickness thickness from h at the root to h/2 at the end of the hook (see Fig. 20). This is design type 2, shape C in Table 1. This taper ratio should be used when possible to evenly distribute stresses during arm deflection. It also reduces material usage.

Given: a. Material = Bayblend® PC/ABS b. Length (1) = 25.4 mm (1.0 in) c. Angle Angle of arc ( ) = 75° d. Outer radius (r 2) = 20 mm (0.787 in) e. Inner radius (r 1) = 17.5 mm (0.689 in) f. Thickness (h) = 2.5 mm (0.1 in) g.

 / = /2=37.5°

Find: a. The maximum allowable deflection for a snap-fit design which will be assembled and unassembled frequently.

Fig. Fig. 20: Snap-fi Snap-fittin tting g hook, design design type 2, shape C

Solution: The permissible strain for a one-time snap-fit assembly in Bayblend® resin is 2.5%. Since the design is for frequent separation and rejoining, 60% of this value should be used or  pm = (0.6) (2.5%) = 1.5%. Deflection equation from fro m Table Table 1, type 2, shape C: y = 1.64 K (2)  12

r2

The variable for K (2) can be obtained from the curves in Fig. 10. Note that if the member is deflected so that the tensile stress occurs in the convex surface, the curve for K 1 should be used; if it occurs in the concave surface, K 2 should be used. In this case, the tensile stress will occur in the convex surface, therefore the curve for K 2 should be used. r1 /r2 = 0.875 and 0 = 75° from Fig. 10, K (2) = K2 = 2.67 y – 1.64

(2.67) (0.015) (25.4 mm) 2 = 2.11 mm (0.083 in) 20 mm

Alternate Solution: This method may be used as a check or in place of using the curves in Fig. 10.

 12

Deflection equation from Table 1, type 2, shape D: y = 0.55

The value for c (3) which is the distance from the neutral axis to the outermost fiber, can be calculated from the equations shown below: c2 = r2[1– 2 sin  (1 – h/r2 + 3  c1 = r2[

2 sin  + (1 – —) h  ) r2 3 (2 _ h/r2

1 )] 2–h/r 2

2 sin  – 3 cos  ] 3

Use c2 for c(3), if the tensile stress occurs in the convex side of the beam. Use c 1 for c(3) if the tensile stress occurs in the concave side. For this particular problem, problem, it is i s necessary to calculate c 2. c(3) = c2 = 20 mm [1

2 sin 37.5

3 (0 (0.654) Solving for y using c 2 yields;

(1 –

2.5 mm 20 mm mm

+

1

] = 2.52 mm

2 – 2.5 mm mm/20mm

(0.015) 5) (25.4 (25.4 mm)2 = 2.11 mm (0.083 in) y = 0.55 (0.01 (2.5 (2.52 2 mm Both methods result in a similar value for allowable deflection.

Page 17 of 26


Torsion Snap Joints Deflection In the the case case of tors torsio ion n snap snap join joints ts,, the the defl deflec ec-tion tion is not not the the resu result lt of a flex flexur ural al load load as with with cant cantil ilev ever er snap snapss but but is due due to a tors torsio iona nall defo deform rmat atio ion n of the the fulc fulcru rum. m. The The tors torsio ion n bar bar (Fig (Fig.. 21) 21) is subj subjec ectt to shea shearr.

C

The following relationship exists between the total angle of twist --and the deflections y

1 or y2 (Fig.

21):

where sin  =

y1 = y2



= angl anglee of twis twistt

11 12

Y1 , Y2 11, 12

= deflecti deflections ons = leng length thss of leve leverr arm arm

The maximu maximum m permis permissib sible le angle angle  pm is limi limite ted d by the the pers persmi miss ssib ible le shea shearr stra strain in  pm: where 180 p m • 1  pm =

 •

pm

= permis permissib sible le total total angle angle of twis twistt in degr degree eess

pm 1 r

= permis permissib sible le shear shear strain strain = le l ength of of to t orsion ba b ar = ra radius of of to torsion ba bar

r

(valid fo for ci circular cr cross se section)

The maximu maximum m permis permissib sible le shear shear strain strain  pm for plasti plastics cs is approx approxima imatel tely y equal equal to: where pm

= permis permissib sible le shear shear strain strain

pm  (1 + ) pm

pm

= permis permissib sible le strain strain

pm  1.35 pm



= Poisso Poisson's n's ratio( ratio(for for plastics plastics approx. approx. 0.35) 0.35)

Fig. ig. 21: 21: Snap-f Snap-fitt itting ing arm with with torsi torsion on bar

Page 18 of 26


Torsion Snap Joints

C

Deflec Deflectio tion n force force A forc forcee P is requ requir ired ed to defl deflec ectt the the leve leverr arm arm by the the amou amount nt y (1,2). The The defl deflec ecti tion on forc forcee can can act at points ints 1 or 2. For For examp ample see see Fig Fig. 21. In this this case case,,  P1l1 = P212 = GIp (x2)* r

where G = shea sheari ring ng modu modulu luss of elas elasti tici city ty  = shea shearr stra strain in IP = pola polarr mome moment nt of iner inerti tiaa 4  r = ; for for a soli solid d circ circul ular ar cros crosss sect sectio ion n 2

*Not *Note: e: The The fact factor or 2 only only appl applie iess wher wheree ther theree are are two two tors torsio ion n bars bars,, as in Fig. Fig. 21. 21. The The shea shearr modu modulu luss G can can be dete determ rmin ined ed fairly fairly accura accuratel tely y from from the secant secant modulu moduluss as follows: follows: G=

Example of snap-fitting snap-fitting rocker rocker arm (flexure and torsion about the Y axis)

Es 2(1+ )

where ES = secant secant modulu moduluss  = Poisso Poisson's n's ratio ratio

Page 19 of 26


Annular Snap Joints

D

Permissibl Permissiblee undercu undercutt The The annu annula larr snap snap join jointt is a concon-ve veni nien entt form form of joint joint betwee between n two two rotati rotationa onally lly symmet symmetric ric parts parts.. Here, Here, too, too, a large largely ly stress stress-fre -free, e, positi positive ve joint is normally ob-tained. The joint can be either either detac detachab hable le (Figs. (Figs. 22a, 22a, 23), 23), diffi difficul cultt to disas disassem sembl blee or insepa inseparab rable le (Fig. (Fig. 22b) 22b) depe depend ndin ing g on the the di-m di-men ensi sion on of the the bead bead and and the the re-tur re-turn n angle angle.. Insepa Inseparab rable le desig designs ns should should be avoi avoide ded d in view view of the the comp comple lex x tool toolin ing g requir required ed (split (split cavity cavity mold). mold). The The allow allowabl ablee deform deformati ation on should should not not be excee exceeded ded either either durin during g the ejecti ejection on of the part part from from the the mold mold or duri during ng the the join joinin ing g operation.

Fig. Fig. 23: Annular snap joint on a lamp housing housing

The The perm permis issi sibl blee unde underc rcut ut as show shown n in Fig. Fig. 24 is limite limited d by the the maxi-m maxi-mum um permi permissi ssible ble strain Ypm = pm .d Note: pm is absolu absolute te value. value. This This is base based d on the the assu assump mpti tion on that that one one of the the mati mating ng part partss re-m re-mai ains ns rigi rigid. d. If this this is not not the the case case,, then then the the actu actual al load load on the the mate materi rial al is correspon corresponding dingly ly smaller. smaller. (With (With compocomponents nents of equal equal flexib flexibili ility ty,, the strain strain is halved halved,, i.e. i.e.,, the the unde underc rcut ut can can be twic twicee as larg large. e.)) W = mati mating ng forc forcee y = unde underc rcut ut  = lead lead angl anglee

Fig. Fig. 24: 24: Annula Annularr snap snap joint— joint—sym symbol bolss used used

' = retu return rn angl anglee t = wall wall thic thickn knes esss d = diam diamet eter er at the the join jointt

Fig. Fig. 22: 22: Annul Annular ar snap snap joint joint

Page 20 of 26


Annular Snap Sna p Joints

D

Defl Deflect ectio ion n forc force, e, mati mating ng force force The The dete determ rmin inat atio ion n of the the mati mating ng forc forcee W is somewhat more com-plicated for annular snap joints. This is because because the snap-fitting snap-fitting bead on the the shaf shaftt expa expand ndss a rela relati tive vely ly larg largee port portio ion n of the the tube tube (Fig (Fig.. 25). 25). Acco Accord rdin ingl gly y, the the stre stress ss is also distributed o ver a large ar ea of the materi material al surrou surround nding ing the bead. bead. Exp er imenta lly p rove n an swer s to th is prob roblem lem are based on the "th "theory of a beam of in fin ite le ngth res ting on a res ilie nt foun founda dati tion on." ." Two extre extreme me case casess are are depi depict cted ed in Fig. Fig. 26. 26.

Fig. 25: Stress distribution distribution during joining operation operation

Fig. 26: Beam resting on a resilient resilient foundation 1

The The forc forcee P is appl applie ied d at the the end end of the the beam beam.. (Thi (Thiss corr corres espo pond ndss to a snap snap join jointt with with the the groo groove ve at the the end end of the the tube tube.) .)

A some somewh what at simp simpli lifi fied ed vers versio ion n of the the theo theory ry may may be expr expres esse sed d as foll follow owss for for join joints ts near near the the end end of the tube: tube: P = y • d • Es • X where P = tran transv sver erse se forc forcee y = unde underc rcut ut d = diam diamet eter er at the the join jointt ES = seca secant nt modu modulu luss Es = secant secant modulu moduluss X = geom geomet etri ricc fact factor or

W=P

As far far as the the mati mating ng forc forcee is conc concer erne ned d, fric fricti tion on cond condit itio ions ns and and join jointt angl angles es must must also also be take taken n into into consideration.

Page 21 of 26

The The forc forcee P is appl applie ied d a long long dist distan ance ce (co) (co) from from the the end end of the the beam beam.. (Thi (Thiss is equi equiva vale lent nt to an annu annula larr snap snap join jointt with with the the groo groove ve remo remote te from from the the end end of the the tube tube))

µ + tan  1 — µ t a n 

where µ = fricti friction on coeffi coefficie cient nt  = lead lead angl anglee

The The geom geomet etri ricc fact factor or,, assu assumi ming ng that that the the shaf shaftt is rigid and the outer tube (hub) is elastic, is as follows: XN = 0.62 0.62

The The geome eomettric ric fac factor tor X tak takes into nto acc accoun ount the the geometric rigidity. rigidity.

2

 (d0 /d — 1) / (d0 /d + 1)

[( d0 /d)2 + 1]/[ 1]/[(d (d0 /d)2 – 1 ] +

where d0 = exte extern rnal al diam diamet eter er of the the tube tube d = diam diamet eter er at the the join jointt  = Poisso Poisson's n's ratio ratio


D If the tube is rigid and the hollow shaft elastic, then Xw = 0.62

 (d/di – 1)/(d/di + 1)

[(d/di)2 + 1]/[(d/di)2 – 1] – 

where d = diameter at the joint di = internal diameter of the hollow shaft The geometric factors X N and Xw can be found in Fig. 27. The snap joint is considered "remote" if the distance from the end of the tube is at least   1.8  d • t

where d = joint diameter t = wall thickness In this case, the transverse transverse force P and mating force W are theoretic theoretically ally four four times as great as when the joint is near the end of the tube. However, tests have shown that the actual mating forces rarely exceed the factor 3 Premote  3Pnear Wremote  3Wnear This means that if the joint lies be-tween O and  minimum, then the factor is between 1 and 3. The secant modulus E s must be determined as a function of the strain e from Fig. 16. For the sake of simplicity, it may be assumed here that the strain

Fig. 27: Diagrams Diagrams for determining the geometric factor X for annular snap joints

y  = d . 100% where y = undercut d = diameter, over the entire wall thickness. (In fact, it varies at different points and in different directions on the wall cross section).

Page 22 of 26


Annular Snap Joints

D

Solution Seca Secant nt modu modulu luss ES from from Fig. Fig. 16

Strain: y = d

1 mm*  = 200 mm • 100%

 = 0.5% 0.5%

Fig. ig. 28: 28: Lamp Lamp hous housin ing g with with cove cover r

Calcula Calculatio tion n exampl examplee annular annular snap snap join jointt

*Since *Since both both mating mating parts parts have have approx approxima imatel tely y equal equal stiffn stiffness ess,, the deflec deflectio tion n for each each part part is approx approxima imatel tely y half half the the underc undercut. ut. This This strain strain is permis permissib sible le for polyc polycarb arbona onate te accord accordin ing g to Table able 2.

Ex = 2,20 2,200 0 MPa MPa (320 (320,0 ,000 00 psi) psi) P = 1 mm x 200 mm x 2,200 MPa x 1.7 x 10 -3 = 748 N P = 748 N (168 lb)

Mating Mating force force, µ = 0.6 from Table 3: W=P

µ + tang 

= 748 N x 1.8 =

1 — µ t a n 

= 1,34 1,346 6N

Transve ransverse rse force force P:

Value alue 1.8 1.8 (from (from Fig. Fig. 18) 18)

P = y • d Es • X

W = 1,34 ,346 N (302 (302.5 .5 lb)

As the mating par ts ts are of approximately eq ua l sti ffn es s, s, the ca lc lcu lat io ion may be perfo performe rmed d for for eith either er comp compon onen ent. t. In this this case case the the lamp lamp cove coverr (hub (hub)) has has been been chos chosen en..

The The mati mating ng and and open openin ing g forc forcee W in this this case case is a cons consid ider erab able le forc force. e. It shou should ld be reme rememmbere bered, d, howe howeve ver, r, that that such such a forc forcee woul would d only only occu occurr if mati mating ng part partss in true true axia axiall alig alignn-me ment nt were were join joined ed by mach machin ine. e. In manu manual al asse assemb mbly ly,, the the grea greate terr part part of the the bead bead is firs firstt intr introd oduc uced ed into the gr oove at an angle and only the rema remain inin ing g port portio ion n is pres presse sed d or knoc knocke ked d into into posi positi tion on.. The The mati mating ng force forcess occu occurri rring ng unde underr these these circu circumst mstanc ances es are much much smalle smaller, r, as only only part part of the the bead bead is defo deform rmed ed..

Given: Lamp Lamp cove coverr and and hous housin ing g made made of Makr Makrol olon on® polycarbonate. Snap-f Snap-fitt itting ing groov groovee near near the end. end. Dimensions: d = 200 mm (7.87 in) t = 2.5 2.5 mm (0.0 (0.098 98 in) in) for for both both mati mating ng part partss y = 2 x 1 mm (0.039 in)  = 45° 45°

XN from from Fig. Fig. 27 with with d0 = 200 + 2 x 2.5 = 1.025 d 200 XN = 0.0017 = 1.7 x 10 -3

The The lead lead and and retu return rn angl anglee is 45°. 45°. The The edge edge is rounde rounded, d, howev however er,, and and the effect effectiv ivee angle angle may may be assu assume med d to be  = 30°. 30°.

Required: Occurring Occurring strain strain  Defle Deflecti ction on force force P Mati Mating ng forc forcee W

Page 23 of 26


Both Mating Parts Elastic With all the the exam exampl ples es of sna snap join jointts menmentioned so far, the stiffer of the two mating parts was as sum e d to be ab sol ute ly rigid. Conseq sequent ently, ly, the the more more flex flexib ible le of the the two two com-p com-pon onen ents ts was was theo theoret retic icall ally y defor deformed med by the the full full amou amount nt of the the unde underc rcut ut.. Wher Wheree both both part partss are are defo deform rmab able le,, howe howeve verr, the the sum sum of thes thesee defo deform rmat atio ions ns is equa equall to the the under undercut cut,, i.e., i.e., each each deform deformati ation on is smalle smaller. r.

The matin mating g force force and the the deform deformati ation onss occur occur-ring ring in two two flex flexib ible le mati mating ng part partss can can be dete deterrmine mined d most most simp simply ly by usin using g a grap graph. h. For For this this purp purpos ose, e, the the tran transv sver erse se forc forcee for for each each comp compo onent nent is dete etermi rmined ned as a fun functi ction of defl deflec ecti tion on on the the assu assump mpti tion on that that the the othe otherr compo componen nentt is abso absolu lutel tely y rigid rigid;; a "defl "deflec ecti tive ve curv curve" e" is then then plot plotte ted d for for each each mati mating ng part part as show shown n in Fig. Fig. 29a 29a and and b.

E Thes Thesee "defle "deflect ctio ion n curve curves" s" are then then supe superim rim-pose posed d (Fig. (Fig. 29c) 29c).. The The poin pointt of inte interse rsect ctio ion n of the the two two curv curves es give ives the the actu actual al defle eflecctio tion forc forcee P and and the the defl deflec ecti tion onss y 1 and y2. With ith the the aid aid of thes thesee quan quanti titi ties es P, y 1 and y2, the individual strains and the mating force can then then be dete determ rmin ined ed with withou outt dif diff ic ulty, as described earlier. earlier.

Fig. 29: Determination of deformation and transverse transverse force when both mating parts are are flexible

Page 24 of 26


Symbols

F

a

dimensions



angle angle of inclin inclinati ation on

b

dimensions

'

return an angle

c

distance between outer fibre and and neut neutra rall fibr fibree



d

diameter at a t th t he jo j oint

distan distance ce of snap-f snap-fitt itting ing groove groove from from the the end end

di

internal internal diameter diameter



strain

do

external external diameter diameter

Pm

maximu maximum m allowa allowable ble strain strain

Eo

modulu moduluss of elasti elasticit city y (intri (intrinsi nsicc tangential tangential modulus) modulus)

ult

stra strain in at brea break k

y

yield yield strain strain

ES

secant secant modulus modulus



angl anglee of twis twistt

F

friction fo force



shear shear strain strain

G

shear mo modulus

µ

friction coefficient

H

height thickness at the root



Poisson's Poisson's ratio ratio

IP

pola polarr mome moment nt of iner inerti tiaa

P

angle of of re repose

K

geometric factor for ring segments



stress

1

length, length of lever arm



arc arc angl anglee of segm segmen entt

N

normal force due to insertion

P

deflection fo f orce

R

resultant insertion force

r

radius

t

wall th thickness

W

mating fo force

X

geometric factor for annular snap snap joint joint index W=shaft W=shaft index index N=hub N=hub

y

undercut, deflection

Z

axial section modulus

Heal Health th and and Safe Safety ty Info Informa rmati tion on Appr Approp opria riate te liter literat atur ure e has been been asse assemb mbled led which which prov provide ides s inform informat atio ion n perta pertain ining ing to the heal health th and and saf safety ety conc concer erns ns that hat must ust be obse observ rved ed when hen hand handli ling ng Bay Bayer prod prod-ucts ucts,, app appro ropr priat iate e indus industr trial ial hygie hygiene ne and othe otherr saf safety ety preca precaut ution ions s recom recomme mend nded ed by their manufacturer manufacturer should be followed. Before working with any product mentioned in this this publ public icat atio ion, n, you mu must st read read and and beco become me fam amil ilia iarr with with avail vailab able le inf informa ormati tion on conconcernin rning g its its haza hazard rds, s, prop proper er use use and and hand handli ling ng.. This This cann cannot ot be ove overemphasized. Inf Informa ormati tion on is avai availa labl ble e in sev several eral forms orms,, such such as Ma Mate teri rial al Saf Safety ety Data Data Shee Sheets ts and and Prod Produc uctt Labe Labels ls.. Cons Consul ultt your your Baye Bayerr Repr Repres esen enta tati tiv ve or cont contac actt the the Prod Produc uctt Saf Safety ety Manag Ma nager er for the the Baye Bayerr Ma Mate teria rialSc lScien ience ce with within in Baye Bayer’ r’s s Corpo Corpora rate te Occu Occupat patio ional nal and and Prod Produc uctt Safet afety y Depa Depart rtm ment ent, Bay Bayer Ma Matteri erialScience L L C, 100 100 Bay Bayer Road Road,, Pitt Pittsb sbur urgh gh,, PA 1520 15205 5 -974 -9741, 1, (412 (412)) 777 777-2 -200 000. 0.

Page 25 of 26


The manner in which you use and the purpose to which you put and utilize our products, technical assistance and information (whether verbal, written or by way of production evaluations), including any suggested formulations and recommendations are beyond our control. Therefore, it is imperative that you test our products, technical assistance and information to determine to your own satisfaction whether they are suitable for your your intended uses and applications. This application-specific analysis must at least include testing to determine suitability from a technical as well as health, safety, safety, and environmental standpoint. Such testing has not necessarily been done by us. Unless we otherwise agree in writing, all products are sold stri ctly pursuant to the terms of our standard conditions of sale. All information and technical assistance is given without warranty or guarantee guarantee and is subject to change without notice. It is expressly understood and agreed that you assume and hereby expressly release us from all liability, in tort, contract or otherwise, incurred in connection with the use of our products, technical assistance, and information. information. Any statement or recommendation not contained herein is unauthorized and shall shall not bind us. Nothing herein shall be construed as a recommendation to use any product in conflict with patents covering any material or its use. No license is implied or in fact granted under the claims of any patent.

Snap-Fit Joints Design

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