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Dynamical Formulation and Analysis of double crank ring-plate-type pin-cycloidal gear planetary drive Keywords: Mechanical Transmission; pin-cycloid drive; double crank ring-plate-type pin-cycloidal gear planetary drive; dynamical analysis; lumped-parameter method 52567
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Abstract. On the assumption that the ring-plate and gear case as rigid body, taken into account the influence of arm bearing and support bearing’s stiffness, and the distortion of gear at meshing, paper built a dynamical model for double crank ring-plate-type pin-cycloidal gear planetary drive, calculated the meshing stiffness for the involute gear and the pin-cycloid gear by program, based on Newton second law, a 33-DOF dynamical model include input and output shaft, ring-plate, involute gear and gear box was formulated by lumped-parameter method， obtained the natural frequency and vibration character for the system with bending and torsion coupling working condition, calculate results show that between 600-800Hz and some other frequency bands the system my easily cause resonance when input shaft turning at 1500r/min, which was approximately match with the prototype vibration test. For the problem that the first prototype has obvious oscillation and noise, improvement method about reinforce the gear case stiffness, increase the first transmission ratio and enlarge the output shaft stiffness was applied, theory analysis show that this measures may better decrease the vibration and noise for this kind of new drive. The double crank ring-plate-type pin-cycloid gear planetary drive is a new type of transmission, which innovation and development based on traditional pin-cycloid gear planetary drive [1, 2], the working principle see figure 1, the inner structure see figure 2. It not only has many advantages possessed by pin-cycloid gear planetary drive, such as smaller volume, wider range of transmission ratio, the usage of hardened gear tooth, the multi-tooth engagement, the larger load-carrying capacity, the higher transmission efficiency and the smoother operating, but also has many other advantages, such as the arm bearing is placed outside of cycloid gear, the radial size of the bearing is no longer restricted any more and to obtain high load-carrying capacity.Because of a short history, special structure and working principle, there are few detailed dynamical research on this new kind of transmission, reference [3,-7] expounded the dynamical formulation theory on RV reducer, which also a king of pin-cycloid planetary reducer, reference 8 detail introduced the dynamical formulation and analysis of RV reducer. Being page limits, taken into account the mesh stiffness change of the cycloid-needle pair, paper focus on the formulation and analysis of this new reducer with lumped-parameter method, the calculation of bearing stiffness can see reference 9, the calculation of meshing stiffness can see reference [8 ,10]. Dynamical Model and Equation For it is difficult to establish and analyze elasticity kinetics, there must be simplified and assumption. The hypothesis is as follows. (1) Assume the stiffness of the revolution bearing as a constant; (2) Ignore the integrate stiffness change of the involutes pair; (3) 源'自^优尔;文,论`文'网]www.youerw.com
The input shaft turning speed as invariable; (4) Ignore the damp, import the normal model damp at the final equation. In the double crank ring-plate-type pin-cycloidal gear planetary drive, being connected by key, taken the input shaft and the middle involute gear, the two driven gear and the crankshaft, the output shaft and the cycloid gear all as single part.For the crankshaft and input shaft, taken into account the torsion stiffness . Being the arm bearing endured high force from ring-plate, taken into account the bending stiffness of the two crankshafts. For the four ring-plates, being it has complex structure and has large stiffness, so equivalent it as rigid body. For the meshing between three involute gear and the pin-cycloid gear, the support bearing and arm bearing regard them as spring. The final dynamical Fig. 3 Dynamic model of double crank ring-plate-type pin- cycloidal gear planetary drive model has 33-DOF, in it, 3-DOF with input shaft, each one the two crankshafts has 10-DOF, every of the four ring-plates has 2-DOF, and the output shaft has 2-DOF.The dynamical model see figure 3. Dynamical Model of Input Shaft and Three Involute Gears. Assume the mss of input shaft is m1, moment of inertia is J1, vibrate torsion angle is θ11. Each of the mass and moment of inertia of driving and driven gear is m12, J12, m21, J21, m31, J31.