In essence, the bearing is a multi-degree-of-freedom transmission path of dissipative energy. When establishing the stiffness matrix, the coupling between the degrees of freedom must be considered. Generally, when calculating the stiffness matrix of the bearing, it should be considered comprehensively. Line displacement and angular displacement.
Therefore, the stiffness matrix of the bearing is 6@6 elements, the diagonal element is the main stiffness of the bearing in 6 degrees of freedom, and the non-diagonal element is the coupling stiffness between the degrees of freedom. The specific calculation of the matrix elements is available in the literature. [4]. Obviously, due to the symmetry of the bearing structure, Kb is also symmetrical. Regardless of the quality of the bearing, if the bearing stiffness matrix considers the influence of the bearing damping Cb, the composite stiffness can be obtained as Kb=Kb iXCb.
The above Zc is the displacement impedance matrix of the rigid box [5, 6]; Rbbj, Rtil respectively represent the coordinate transformation matrix of the joint between the two bearings and the box and the connection between the upper end of the isolator and the box to the centroid of the box in the local coordinate system. [5,6]; Dc represents the centroid displacement response of the box; Qtil represents the force of the Lth isolator to the box. Iij represents the moment of inertia, mc represents the mass of the box, and the vibration isolators are used to achieve the purpose of vibration isolation and noise reduction. The displacement of the L-th vibration isolator and the joint point of the box is DTil, which can be expressed as: Dtil=[util, vtil, wtil, Htilx, Htily, Htilz]T.
Qil=-KilDtil(l=1,2,,,4) is obtained by Hooke's law. Among them, Kil=(l jGil)KxlKylKzlGxlGylGzl where Gij, Kjl, Gjl(j=x, y, z) are vibration isolators respectively Damping loss factor, shaft (diameter) stiffness, torsional stiffness.
The coupled system is solved by the law of rigid body motion Dbbj=RbbjTDc(j=1,2)Dtil=RtilTDc(l=1,2,,,4) from the equation Dc=E-1(L SM-1N)Fs , wherein QbHbj, Dbbj can be obtained by the formula).
Example analysis Gear shaft length 600mm, diameter 36mm, Qs=7850kgPm3, E=1.21@1011Pa, G=4.43@1010Pa, gear left end shaft length l1=350mm, gear right end shaft length l2=250mm, box body 600mm@400mm@300mm Cube box, box wall thickness 20mm, Q=7000kgPm3, bearing 1 model see literature [1], under the action of unit excitation force and moment. Calculation results.
It is known that the formant of the flexible model contains the formants of the Kraus and Lim models, while the power transfer curve of the flexible model is higher than the power transfer curves of the Kraus and Lim models of the two models, and can reflect more Modal, this is mainly because the axis and bearing stiffness matrix of the flexible model are multidimensional. It can reflect the influence of force and moment on the input box power flow, but Kraus and Lim can't. Therefore, the flexible model can better reflect and meet the actual working conditions.
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