中国
马来西亚 
韩国 
美国 
加拿大 
英国 
德国 
墨西哥 
巴西 
捷克共和国 
法国 
西班牙 销
作者
下载白皮书An attempt is made to analyze strain and stress of different types of pins in more detail than the conventional consideration of the shear strength offers. The analysis reveals that there are cases in which the shear strength is not the criterion for the proper selection of size and type of pin. It depends upon the mutual interaction of the pin and the parts to be joined due to the fit as well as due to the lateral load which can be purely statical of dynamical. The theoretical analysis – even if it consisted sometimes of rough approximations – of the effects of fit and of lateral load and the trend of experimental results show very clearly that a spirally coiled pin can be selected instead of any other type of pin of the same size. It offers advantages when static loads as well as when fluctuating loads are involved.
Stress And Strain Due To Interference Fit
A pin is a machine element that secures the position of two or more parts of a machine relative to each other. A large variety of types has been known for a long time; the most commonly used are solid cylindrical pins, solid tapered pins, groove pins, tubular slotted pins and spirally coiled pins.1 The choice of size and type of a pin for a given application must be based on a sound balance of stress and strain of the pin and of stress and strain of the parts to be joined. Stress and strain of both depend upon the magnitude of the interference fit between pin and hole and upon the forces to be transmitted from one part through the pin to the other part. These forces can be constant, intermittent of fluctuating.
The diameter D1 of the pin must be larger than the diameter D0 of the hole in order to obtain a press fit. When the pin is pressed into the hole by an axial force F, Fig. 1, the pin as well as the parts to be connected experience deformations which depend upon the difference D1-D0, upon the moduli of elasticity of the materials of the pin and of the parts to be joined and upon the shape of the pin and the parts.
Figure 1
Solid Pin
Solid Cylindrical Pin
In the case of a solid cylindrical pin joining two parts of fairly large size compared with the diameter of the pin hole, strain and stress can be easily calculated, at least so long as they are within the elastic range. The bearing pressure p at the surface of the pin hole follows from
where
E0 = Modulus of elasticity of material of joined parts
E1 = Modulus of elasticity of material pin
v = Poisson’s ratio
and the difference in Poisson’s ratios for different materials (0.3 for steel, 0.34 for aluminum) has been neglected. In the special case where E0 equals E1 , the bearing pressure is simply
Figure 2
Slotted tubular pin
Figure 3
Deformation of slotted tubular pin
A= Elastic Line by Load p0
B= Circle
The Spirally Coiled Pin
Fig. 4 shows a cross section of a spirally coiled pin. The shape of the cross section is close to the shape of the spiral of Archimedes. The departure from this shape is made (a) to minimize the area of surface along which there is no contact between hole and pin, and (b) to prevent the end -j0 of the outer coil of the pin from slipping in the peripheral direction over the adjacent coil.
An analysis of the bearing pressure between pin and hole and of the stresses in the pin and in the parts to be joined by virtue of the press fit again can be based on the theory of the initially bent beam. As the radius b of the neutral fiber is no longer constant, it is necessary to subdivide the pin into several portions of suitable width in the peripheral direction – say seven or more – and to assume that the radius b is constant within each portion, but changes abruptly at the transition from one portion to the adjacent one. As Fig. 4 shows, the change in curvature of the second coil is quite considerable in the vicinity of the end -j0 of the outer coil; thus, the portions must here be shorter than along the remainder of the coil.
The deformation of a spirally coiled pin due to the bearing pressure can generally be a displacement in the radial as well as peripheral direction. The displacement could be quite large in the peripheral direction if the cross section would be an exact Archimedean spiral; by the peculiar bulging out of the second coil, however, a peripheral displacement is almost completely prevented. Thus, the pin is much stiffer than without the bulge.
The calculation of stress and strain is quite lengthy since displacement and slope of the elastic line must be matched at each transition from one portion to the next one and since a statically indeterminate load in the tangential direction must be applied at the outer edge in order to account for the effect of the bulge.
The material of the pin experiences a plastic deformation during the manufacturing process. When the pin leaves the forming tool, the stresses due to this deformation are released instantly and the coils which have been pressed against the tool and each other during the forming operation open up so that a small gap appears between the coils; thus, the diameter of the unstrained pin is larger than the diameter during the manufacturing process. By proper selection of the size of the tool compared with the size of the hole, it is possible to keep the bearing pressure and the stresses in the coils within the elastic limit when the pin is put into the hole.
If a spirally coiled pin and a slotted tubular pin of equal nominal diameter are subjected to the same press fit ratio (D1-D0 )/D0 , the coiled pin is less stressed than the slotted pin provided that the cross sections of both pins have the same area normal to the axis of the pin. This can be demonstrated by a rigorous analysis; it also follows from the following comparison.
A laminated cantilever beam consisting of n layers of height h1 is deflected by the same amount (proportional to D1-D0 ) as a solid cantilever beam of the same overall height h2 = nh1 . Presume that length of the beam and width of the cross sections are the same, the ratio of the maximum bending stress s1 in each layer to the maximum bending stress s2 of the solid beam equals 1/n. This comparison is qualitatively admissible, but quantitatively, it is merely a first-order approximation since the radius of the neutral f iber of the curved beam is not precisely equal to (D1 – h1 )/2, but smaller by the factor [1 – h1 2/3(D1 – h1 )2] and since the inner coil has a still smaller radius than the outer coil.
From this comparison, it also can be concluded that the power required for forming a pin decreases with decreasing thickness of the strip. This offers the possibility of manufacturing spirally coiled pins with diameters beyond the conventional range; i.e., larger than 1/2 inch provided that there is a demand for them.
Figure 4
Coiled rolled or SPIROL wrapped pin
Stress and Strain Due to External Load
The Solid Pin
Fig. 5 shows two slabs A and B of thickness hA and hB, respectively, being joined by a pin. A force P is applied at each slab; for establishing equilibrium of the whole system, moments M must also be applied of magnitude (hA + hB )P/2.
The slabs are assumed for a moment to be infinitely large in any direction perpendicular to the axis of the pin. It is quite obvious that any load applied at the cylindrical surface of the hole has little effect at any point far distant M hB P Fig. 5 External load of a pin. from the axis. Thus, it is justified to consider the remote portions of the slab as being absolutely rigid and only the portions within a cylinder of radius, re as elastically f lexible. If the elastic portion is replaced by a system of radial springs, a model is obtained which can be used for studying the interaction of pin and slabs and which can be made equivalent to the actual system by a suitable choice of the radius re and the stiffness of the springs.
The pair of action and reaction forces P creates a displacement y of slab A relative to slab B by virtue of the elasticity of the springs. If the pin is assumed to be absolutely rigid, it turns into a position as shown in Fig. 6. If the pin is elastically flexible, it does not only turn, but it is also bent as shown in Fig. 7. Obviously, the deformation is more concentrated at the immediate vicinity of the surface of contact between slabs A and B the weaker the pin is compared with the springs.
Figure 5
External load of a pin
Figure 6
Stiff pin
Figure 7
Flexible pin