Compliance (material science)

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The compliance in the sense of engineering mechanics or the elasticity theory describes the property of a body as a result of the action of a force or a torque elastically deforming. It can generally be determined as the reciprocal of the stiffness .

definition

The definition of flexibility results - according to the type of load - as a quotient of the respective deformation measure (change in length, expansion , shear distortion , deflection , curvature , angle of rotation) and the respective load measure ( normal force , transverse force , bending moment , torsion moment ).

The resilience of an initially unstressed, vertically hanging helical tension spring is calculated over the length under the action of the weight of an attached weight

with … length under load and … change in length . The "elongation flexibility" of the spring has z. B. the physical unit ( millimeter per Newton ) and represents the reciprocal of the spring stiffness or the spring constant .

If the spring element has a uniform, orthogonally loaded cross-sectional area (e.g. designed as a hanging rubber band) and if its length is only slightly stretched, so that a change in cross-section due to transverse contraction can be neglected, then using Hook's law for the " Elongation flexibility "

with ... elongation , ... tension and ... modulus of elasticity .

The following applies to the "elasticity" of a body with a uniform cross-sectional area under uniaxial normal force loading :

.

Here, the “elasticity” is the reciprocal of the elasticity .

Resilience of a screw

The flexibility of screws is an important element in calculating the assembly preload . A high degree of flexibility is required when screws are dynamically loaded by operating forces. This will stretch these screws further (they give way) instead of breaking.

The screw compliance is made up of the compliance of the individual sub-elements:

With
... flexibility of the screw head
... flexibility of the screwed-in threaded part
... the indulgence of the mother

Resilience of the screw head δ K

With
... screw head length; for hexagon screws (e.g. M6 → d = 6) or for hexagon socket screws
... modulus of elasticity of the screw material
... nominal cross-section of the screw

Resilience of the screwed-in threaded part δ G

With
... core cross-section of the screw thread

Compliance of the nut δ M

with , for push-through connection (e.g. M6 → d = 6) or , for screw-in connection

Resilience of the cylindrical sub-elements δ i

This includes sections such as: Unscrewed thread, waist of different thicknesses, shaft of normal thickness.

Cross-sectional areas A

... nominal cross-section of the screw
... core cross-section of the screw
... cross-sectional area of ​​the cylindrical section i

Compliance of bolted plates

The difference between sections with different moduli of elasticity must also be taken into account when it comes to the flexibility of the screwed plates . These are calculated individually and then added up. In most cases, however, there is a single material. Then the formula applies:

with ... clamping length or thickness of the clamped parts

Replacement cross-section A replacement

  1. ,
    only applies to .
    ... outside diameter of the clamped sleeves / plates
    ... outside diameter of the flat screw head contact surface
    ... (inside) diameter of the through hole
  1. ,
    only applies to .
    With
    ,
    .
  1. ,
    only applies to .
    Where .

See also

Individual evidence

  1. Roloff Matek: machine elements. 17th edition, p. 212.