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216 Dănuț Zahariea and Mihaela Tudorache 1.5…3, the adopted value is 2.0944), the shafts diameter can be calculated using the relationship: (1) d 3 16M tc = , πτ at the value d ≅ 0.065m being thus obtained. The material used for all components is steel with yield strength σ = 2.5 N/m 2 8 ⋅10 . a b Fig. 1 – Constructive types: a – with pins in the same plane; b – with pins in two different planes at 90 °. The geometric characteristics of the sleeve rigid coupling with cylindrical pins can be determined with the relationship: the outside diameter of the sleeve coupling D = kDd = 0.11 m (the coefficient kD shall be adopted within 1.5…1.8, the adopted value is 1.6923); the length of the sleeve coupling L = kLd = 0.2 m (the coefficient kL shall be adopted within 2…4, the adopted value is 3.0769); the diameter of the pins ds = ksd = 0.028 m (the coefficient ks shall be adopted within 0.25…0.44, the adopted value is 0.4308) [1], [2]. The sleeve coupling will be checked at the torsional strain with: (2) t = 4 4 π ( D − d ) 02 16DM tc τ . The pins will be checked at the shearing strain with:
Bul. Inst. Polit. Iaşi, t. LVI (LX), f. 2, 2010 217 4M τ = . tc (3) f 2 πdds The obtained values are within the safety range of the torsional strength and the shearing strength of the material. Even if as a result of these calculations a good dimensioning of the coupling will be obtained, to answer a series of additional issues (the torque asymmetry on the coupling parts, the distribution of critical sections on each coupling part, etc.) should be further analyzed by advanced numerical methods. 2. The Structural Analysis of the Sleeve Coupling with Pins in the same Plane The main steps of the procedure for structural analysis of sleeve couplings with cylindrical pins in the same plane using CATIA/Generative Structural Analysis environment are: 1. Creating the 3D model. Shall be carried out separately the five elements of the coupling using the Part workbench. The appropriate materials are assigned to each element. The assembly of the five coupling elements is carried out using the Assembly workbench, Fig. 2a. 2. Configuring the mesh. Shall be carried out separately for each element, by changing the characteristic parameters “Size” and “Sag”, Fig. 2b. 3. Applying the restraints. On the free extremity of the driven shaft a clamp condition must be applied, Fig. 2c. 4. Applying the loads. On the free extremity of the driving shaft an 800 Nm torque around the shaft axis will be applied, Fig. 2d. 5. Applying the conditions for the interaction between the five elements of the sleeve coupling. First, the interaction condition of General Analysis Connection type will be applied between the driving shaft and the first pin, between the first pin and the sleeve coupling, between the sleeve coupling and the second pin and finally, between the second pin and the driven shaft. Second, for all the active areas in terms of the torque transmission the shearing strain condition must be specified by setting the just property of interaction between the active coupling elements (Bolt Tightening Connection Property), Fig. 2e. 6. Launching the solver, running the numerical analysis and results visualization. The von Misses stress will be presented for both the driving and the driven shafts in Fig. 2f (scale factor 500), for both the cylindrical pins in Fig. 2g (scale factor 700) and, finally for the sleeve coupling in Fig. 2h (scale factor 500).
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BULETINUL INSTITUTULUI POLITEHNIC D
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