4/18/2017
`
`Fundamentals of Annular Snap-Fit Joints
`
`Snap-fit joints are the most widely used way of joining and assembling plastics. They
`are classified according to their spring element and by separability of the joint: Will
`it be detachable, difficult to disassemble, or permanent? The most common snap fit
`is the cantilever. It is based on a flexural beam principle where the retaining force is
`a function of the material's bending stiffness. The second most widely used is the
`torsional snap joint. Deflection comes from torsional deformation of the joint's
`fulcrum and shear stresses carry the load after assembly.
`
`But perhaps the least understood type is the annular snap joint (ASJ). Classic
`examples of ASJs include ballpoint pens with snap-on caps, and the child-resistant
`cap on Tylenol bottles. This type of snap fit is best for assembling axis-symmetrical
`(cylindrical) profiles. But ASJs are often good choices for compact, stiff joints even if
`the part is not annular.
`
`ASJs are generally stronger, but need greater assembly force than their cantilevered
`counterparts.
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`Fundamentals of Annular Snap-Fit Joints
`ASJs are basically interference rings. The smaller-diame
`has a bump or ridge feature around its
`circumference. The ridge diameter is slightly larger
`than the inside diameter of the mating tube-shaped
`female hub. Key to ASJ operation is to make the plug
`from a more rigid material than its mating female
`hub. Then the ridge will deflect the hub outward.
`Deflection imposes a relatively high onceonly or
`repeated short-term load (hoop stress) distributed along the axis of the hub as the
`plug slides into it. The ridge feature engages into an undercut grove molded into the
`inside diameter of the hub, at which point the assembly returns to a stress-free
`condition.
`
`The maximum permissible deformation of the hub, P, is limited by the maximum
`permissible strain or proportional limit of the material. This limit is typically 50% of
`the strain at break for most reinforced plastics (safety factor of two). It can be
`upwards of 60 to 70% of strain at break for more elastic polymers assuming the
`appropriate safety factor.
`
`The geometry of the ridge determines the
`assembly force, F, needed to engage the snap
`joint and whether or not the annular snap joint
`will be detachable or permanent. The lead
`angle, , is generally < 30°. Its corresponding
`return angle,
`
`, determines assembly separability. A shallow return angle (30°) easily separates, a
`90° angle is permanent, and a 45° angle is typical of most applications that
`disassemble.
`
`Returning to the example of the Tylenol bottle, one can see that the ridge profile has
`a 90° return angle. This in principal should make the cap impossible to remove from
`the bottle. The packaging designer employed a clever trick, explains design engineer
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`Fundamentals of Annular Snap-Fit Joints
`Mark Wichmann of DuPont to transform a permanent snap joint into one that
`easily disengages. "The trick," he says, "is notches molded into the ridge on the
`bottle. This intentional breach in the snap fit, under the right orientation (arrows
`lined up), lets the cap pop easily off."
`
`Despite the prolific use of snap-fit joints in every conceivable configuration for
`plastic assemblies, says Wichmann, designers often shy away from annular snap fits
`for two reasons. The first is ASJs are generally harder to mold and require more
`complex tooling than cantilevered versions.
`
`The second is material. Stress
`
`is a material's response to distortion. For any given
`uniaxial distortion (strain,
`
`) the stress response is given by the appropriate stress-
`strain curve. Stiffer, reinforced plastics don't recover as
`easily from deformation and will need engagement
`features ( undercuts and ridges) that are quite small so the plastic doesn't stretch
`beyond its elongation limit in the hoop direction, says Wichmann.
`
`In an annular snap fit, the hoop-direction distortion (strain) required of a hub when
`inserting a press-fit plug is a matter of the geometric interference. This required
`strain may be compared to the allowable strain of a material. Or it may be converted
`to how the material responds to the strain, its hoop stress, and then compared to the
`material's allowable stress. Hoop stress is a tensile stress for the female hub and a
`compressive stress for the male plug. If the joint stresses the material beyond its
`proportional limit, the plastic may stress-craze or crack causing the joint to fail.
`
`WHEN ANNULAR SNAP FITS MAKE SENSE
`It doesn't take an FEA Pro or an engineering Ph.D. to find out whether or not
`annular snap fits can handle a particular application, says Wichmann. Instead, he
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`Fundamentals of Annular Snap-Fit Joints
`suggests making a first order approximation using tried and true handbook
`calculations and a few basic assumptions.
`
`"Although it's a powerful design tool, a thorough, nonlinear FEA simulation (with
`contact elements) is time consuming and certainly not trivial for snap fits," says
`Wichmann. "Using simple handbook equations, it's possible, however, to calculate
`reasonably close approximations, often within 90 to 95% of an FEA analysis. The
`resulting ballpark, first-order approximation, is often enough for a working
`prototype. The prototype in turn gives feedback on fit, function, and resulting
`assembly/disassembly forces needed.
`
`For example, designers of a recent motor application wanted to employ an annular
`snap-fit connection between the encapsulated stator and motor housing. The first
`order of business, says Wichmann, was getting the motor designers to not worry
`about every conceivable material property that may affect assembly forces and other
`loads. Often, it's best to first make a few critical assumptions to see if the part
`geometry and material will handle an annular snap fit before going through lengthy
`FEA calculations.
`
`The first step was determining the necessary safety factor for the assembly. The
`engineers determined a safety factor of two was reasonable for the motor. Their
`thinking was the components would be assembled in a carefully controlled and
`fixtured assembly process. There would be no repeated disassembly, and no one's
`life would be at stake if the snap fit failed.
`
`Next, came an evaluation of material and geometry compatibility. Two approaches
`are possible, says Wichmann. "One is to first establish a particular geometry and
`then find a material which survives the deflection force (i.e., strain of assembly, P).
`In this case, the encapsulated stator slipped inside the motor mount, deflecting the
`annular snap joint in the process." The permissible deflection depends on the
`permissible strain for the material. Amorphous materials such as polycarbonate,
`polystyrene, PC/ABS, and ABS can be strained up to 70% of the yield strain during a
`single brief snap fit, he says. "Reinforced materials such as those the motor
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`Fundamentals of Annular Snap-Fit Joints
`designers were evaluating are less forgiving. So you would use the rule of thumb —
`50% strain at break (safety factor 2) — to make a reasonable material evaluation."
`
`The second approach starts with a material rather than a geometry. "This will give a
`known permissible strain (i.e., 50% strain at break). The geometry can then be
`tweaked to meet the permissible strain constraints," explains Wichmann. In the case
`of the motor, the geometry was the inside diameter of the female hub and the
`outside diameter of the male (stator) part plus ridge height.
`
`For the motor, the designers opted for the first method and initially defined the
`annular snap geometry. Next they assumed that all the deflection would come
`entirely from the motor mount housing. Then the deflection force or strain of
`assembly of the annular snap fit can be estimated from the geometry of each
`component. Minimum inside diameter of motor mount housing was 64.5 mm.
`Maximum outside diameter of stator was 66 mm with a 3-mm ridge or hook.
`
`The percent strain the motor-mount housing will see can be estimated by taking the
`ratio:
`
`where DS = the outside diameter of the stator (66 mm) and DH = the inside
`diameter of the motor mount housing (64.5 mm). The result, 2.3% strain, is a first-
`order approximation that is best for membrane stresses when the wall thickness is <
`0.1 the nominal diameter. For the motor, wall thickness was 2.5 mm, which is less
`than 0.1 66 = 6.6 mm so the approximation is reasonable.
`
`The next step in the approximation is to see whether the candidate polymer for the
`motormount housing, DuPont's Hytrel 8238 ( generalpurpose thermoplastic
`polyester), can survive the expected deflection stress at the predicted 2.3% strain.
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`Fundamentals of Annular Snap-Fit Joints
`From the stress-strain curve for Hytrel 8238, the expected deflection stress at the
`predicted 2.3% strain is about 22.8 MPa (3,300 psi). Comparing this value to Hytrel
`8283 material property data shows it is less than the strain at break of 48.3 MPa
`(7,000 psi) and appears to be below the onset of significant plastic yield, the knee of
`the S/S curve. The SS curve reveals that the 2.3% strain value is below the significant
`transition (yield) at 32.4 MPa (4,700 psi). It is important that the force of assembly
`not exceed this value.
`
`This quick first-order approximation showed the designers that the annular snap
`geometry and the material were compatible. Thus the annular snap fit would have a
`good probability of not failing when it engaged.
`
`ASSEMBLY FORCE
`ESTIMATES
`With geometry and material
`defined, the next step is to
`estimate the assembly force to
`engage the snap fit. This employs a
`few basic handbook calculations
`similar to those for analyzing
`cantilever snap fit assembly forces.
`
`The force needed to assemble an annular snap fit is a function of two elements: the
`force to expand or deflect the hub outward, and the frictional force between the plug
`and the hub during assembly.
`
`An annular snap groove close to the end of the hub will have a different deflection
`force (P) than one remote from the end. As a rule, designers typically choose to place
`the groove in the hub close to the end, as was the case with the motor design. A
`groove is considered remote from the end of the hub when:
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`where
`
`Fundamentals of Annular Snap-Fit Joints
`
`= distance of the groove from the end of the hub, d = inside diameter of the hub, and
`t = hub wall thickness that will deflect under load. This relationship constitutes a
`simplification, assuming a constant strain through the wall thickness (which is not
`actually the case). Due to this dissimilar tangential hoop stressing, P for a snap-
`groove remote from the end is three times that of one close to the end.
`
`The following equation calculates P close
`to the end:
`
`where f = deflection distance, in this case
`1.5 mm, X = a geometry factor, and Es =
`Hytrel 8283 secant modulus in MPa.
`Using the calculation for the Hytrel's
`permissible deflection stress (22.8 MPa)
`at 2.3% strain, Es is approximately (22.8 MPa/0.023) or 991 MPa.
`
`The geometry factor, X, must be divided into two equations based on the flexibility
`or rigidity of the mating parts. When the outer mating female hub is flexible and the
`inner (male) plug is rigid X = XN. If the hub is rigid and the plug flexible then X
`=XW. The values for XN and XW are calculated from:
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`Fundamentals of Annular Snap-Fit Joints
`where da = outside diameter of the flexible hub, mm; d = outside diameter of the
`rigid plug, mm; di = inside diameter of the plug when the plug is flexible and the
`female hub is rigid, mm; and = Poisson's ratio for the Hytrel 8283 and is equal to
`0.45.
`
`For the motor design, the hub (Hytrel motor
`housing) was flexible and the plug or stator was
`rigid. The stator was from a 15% glass-reinforced
`polyethylene terephthalate, Rynite 415HP, also
`from DuPont. Additionally, the hub deflects a
`distance f equal the height of the ridge and is
`equal to 1.5 mm.
`
`When d = 66 mm and da = 71 mm, the value of X = XN and P are
`
`and
`
`Motor designers wanted to use an assembly
`fixture and about 300 lbf of force to
`assemble the motor. The geometry and
`selected materials led to calculating the force
`of assembly F as follows:
`
`= coefficient of friction and = lead angle. For the motor design, the lead angle on the
`stator was 35° and the coefficient of friction between the Hytrel and Rynite is about
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`0.45.
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`Fundamentals of Annular Snap-Fit Joints
`
`From the Diagram of coefficient of friction and lead-angle interaction, the value of
`
`is about 1.68 and the resulting force of assembly is 1,384 N or 311 lbf.
`
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