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Thin-walled cylinder The disc-shaped flexible wheel integral flexible wheel and the flexible wheel structure with screws and shafts at the ends belong to this type of structure, and the flexible wheel structure in which the ends are connected by screws and shafts is the most common. The hysteresis caused by the elastic torsional deformation of the flexible wheel of this structure under load is equal to the sum of the hysteresis caused by the elastic deformation of the thin-walled cylinder and the elastic deformation of the thin-walled disc [1, 3].
For the elastic torsional deformation of the thin-walled cylindrical portion, the calculation can be directly calculated according to the formula (1), that is, U1=TlGJp(2) where U1 is the elastic torsion angle (rad) of the cylindrical portion of the flexible wheel. For the elastic deformation of thin-walled discs, the calculation can be based on the conclusion of the literature [4], that is, the ring is fixed on the inner boundary, and the shear force S0 is distributed on the outer boundary of the ring, as shown.
(1) Theoretical calculation The flexible wheel structure of this model belongs to the flexible wheel of the thin-walled cylindrical disc structure, which can be solved by directly applying the formula (5). According to the load that can be transmitted by the flexible wheel of this type [6], The torque T=800Nm, that is, the elastic deformation of the disc structure has a great influence on the elastic deformation of the entire flexible wheel structure, which cannot be ignored. (2) ANSYS software simulation and simulation The B3-160 type flexible wheel calculated by the above theory is taken as an example, and the corresponding size is modeled, and then the finite element mesh is divided. The finite element meshing result is as shown.
The meshing result shows that the external load torque T=800Nm applied according to the theoretical calculation is realized in the following equivalent way in ANSYS simulation, and the flexible wheel output end (ie, the inner diameter of the disc) is fixed on the left side. The equivalent uniform circumferential force is applied to the meshing teeth, and then the elastic deformation of the flexible wheel is calculated. The output of the simulated elastic deformation is as shown (the numerical result in the figure is the tangential displacement of the outer boundary of the flexible wheel). The elastic deformation amount of the end to the intersection of the disc and the cylinder (ie the disc structure) U disk = 211078@10-4rad, the total elastic deformation of the flexible wheel U round the total = 417304@10-4rad, thereby It is possible to calculate the amount of elastic deformation of the cylindrical portion of the flexible wheel U cylinder = 216225@10-4rad. Tangential deformation cloud map (3) Data comparison and error analysis The above theoretical calculations are compared with the data of ANSYS simulation, and the simulation values ​​of ANSYS simulation are used to verify the theoretical calculation values, and the corresponding errors are calculated. As shown.
From the above data comparison and error analysis, we can see that: (1) The theoretical calculation values ​​are larger than the ANSYS simulation simulation value. The reason is: the theoretical calculation does not consider the soft wheel bottom/rounding 0 effect, but considers the finite element modeling. The soft wheel bottom/rounding 0 effect increases the stiffness of the flexible wheel cylinder; that is, the theoretical calculation of the length l (the flexible wheel cylinder portion l = 0152 m) and the outer disk radius rco (flexible disk Partial rco=0108m) is larger than the effective length taken by ANSYS simulation (l valid=011395m, rco effective=010781m); and the error of the two is less than 10, therefore, the theoretical analysis derived in the paper is derived from the flexible wheel torsion The deformation calculation formula is basically accurate. (2) Converting the numerical unit to the angle unit, the theoretical calculation of the total elastic deformation of the flexible wheel is 11770c, and the elastic deformation of the disk is 01794c, which accounts for 44186 of the total elastic deformation of the flexible wheel, and the value is large. Therefore, when analyzing the harmonic gear transmission hysteresis, the impact is large and cannot be ignored.