Лако-красочные материалы — производство

The fundamental design parameter of press-fitted and adhesively bonded couplings is the axial release force Ftot. Based on the principle of the superposition of the effects, Ftot can be computed as in Eq. (1), by combining the effects of interference (Fint) and of adhesion (Fad). The first term, Fint [N], depends on the axial static friction coefficient pA, on the coupling pressure pC [MPa] and the contact surface A [mm2] as indicated in Eq. (2). The second term, Fad [N], is related to the shear strength of the adhesive zad [MPa] and, again, to the contact surface A [mm2] as indicated in Eq. (3). The term A is computed in Eq. (4), where DC [mm] is the coupling diameter, equal to the mean of the external shaft diameter Dext, S [mm] and the internal hub diameter Dint, H [mm], and LC [mm] is the coupling length.

It must be pointed out that the principle of superposition of effects (Eq. 1) holds true in the present case, because the adhesive used here belongs to the family of the so called “strong” anaerobics. In the case of “weak” anaerobics (such as LOCTITE243® and other similar ones), more general models must be more conveniently applied, like those put forward by Dragoni and Mauri [18] or by Dragoni and Castagnetti [19].

The axial static friction coefficient pA depends on the material characteristics and is strongly influenced by the surface conditions: as a consequence, pA may vary in a wide range, between 0.04 and 0.7 according to [20]. Thus, its accurate estimation is important in order to reduce the uncertainty affecting the calculation of Fint.

The first step for the determination of the friction coefficient consists in the estimation of the coupling pressure between the shaft and the hub. For this purpose, a strain gage must be applied to the external surface of the hub, along the tangential direction. The relationship between the pressure pC, the

tangential strain єв, and hub material and geometry can be easily retrieved (see Eq. (5)), based on the theory of thick walled cylinders (Lame’s Equation) and on the Hooke’s Law.

Where QH is the ratio between the internal and external diameters of the hub (QH=DintHIDextH). The practical procedure requires the careful measurement of strain variation, as the shaft is being press fitted into the hub, which is coupled with mere interference, without adhesive (in dry conditions). Upon the completion of the assembly procedure, the coupling pressure is computed by Eq. (5). One of the instrumented hubs is visible in Figure 2 (a), just before starting the pushing in of the shaft. The same hub is depicted after coupling and decoupling in Figures 2 (b) and 2 (c).

Once the pressure has been determined, the friction coefficient цл can be computed by inverting Eq. (2), as in Eq. (6):

The term Fint can be determined by running the release test after the shaft and the hub have been assembled under mere interference. The peak of the release force (Fint=Ftot, as Fad=0) can be accurately measured by the load cell of the standing press.

In the determination of Fint for each of the press-fitted and adhesively bonded specimens, the coupling pressure p(Z) is determined as a function of the actual interference Z [mm] between the shaft and the hub. The relationship reported in Eq. (7) is valid for shafts and hubs made of the same material.

p(Z)= 0.5• E-(1 — Є2) (7)

DC

DC [mm] is the coupling diameter, equal to the mean of the external shaft diameter Dext, S [mm] and the internal hub diameter DintH [mm], E [MPa] is the Young’s modulus. Moreover, the actual interference Z [mm] is lower than the nominal one U [mm], when the shaft is press-fitted into the hub, operating at room temperature. If the stiffness of the parts has a similar value (for example, when they are made of the same material), the difference between U and Z can be related to the surface roughness Ra [mm] of the mating components (hub: RaH; shaft: Ra, S), as proposed in [14] and reported in Eq. (8).

Z = (Dext, S — DintH )- 3 • (Ra, H + Ra, S ) = U — 3 — (Ra, H + Ra, S ) (g)

The reduction of interference in Eq. (8) is related to the crests of surface roughness being chopped during the pin insertion into the hub.

Eq. (1) is recast into Eq. (9), assuming that, in the presence of adhesive, the friction coefficient value jxA can be considered equal to that relevant to the dry joint. Such occurrence is due to the fact that metals remain in contact in the peaks of the roughness, while the liquid adhesive fills the voids of all depressions [1]. Therefore, Fad can be calculated as the difference between the measured overall strength of the joint (Ftot) and the assumed frictional
contribution (Fint). Finally, by dividing Fad by the mating area, it is possible to estimate the adhesive shear strength rad, as indicated in Eq. (10).

Ftot = Fnt + Fad = Pa ■ Pc ■ A + Fd ‘ A ^

^ Fad =?ad ■ A = Ftot — Fnt = Ftot — Pa ‘ Pc ‘ A

The term Ki, which was cited in the Introduction Section, can be easily estimated, as in Eq. (11), by monitoring both the coupling and the release force, measured by the loading cell of the standing press, and computing the ratio between the related peak values.

F F + F

Ftot Fint ‘ Fad

1 = F ~ F

coupl coupl

The determination of Tad and K1 makes it possible to discuss the response of the adhesive in the case of HJs.

When considering SFJs, the coupling procedure is manually performed (as exposed in detail below), so it is not possible to compute the coefficient K1. The response of the adhesive is represented by the shear stress that can be easily determined, observing that Fint=0. Therefore, the ratio between the measured release force Ftot and the coupling surface A directly yields zad.