Optimization design analysis of damper In order to achieve the best vibration damping effect of the transmission damping system, it is necessary to optimize the calculation and analysis of the damper arrangement and the inherent properties of the damper. The goal of the optimization is to prevent the excitation force of the gearbox from being transmitted to the vehicle body as much as possible while ensuring that the overall structure of the gearbox is stable. In this study, the ADPL parametric design language programming optimization program in ANSYS was used to optimize the dynamics of the transmission damping system. The gearbox damping system optimization model is as follows.
Find the design variable X=[K1, K2, K3, K4, D, C] where K1, K2, K3, K4 are the stiffness of the damper. In order to ensure the stability of the gearbox during operation, it is desirable that the spring stiffness is sufficiently large. Since the gearbox mass distribution is relatively uniform, K1=K2=K3=K4 is approximated here, four identical dampers are symmetrically distributed, and the two springs at the input and output shaft ends are simplified into one, and then optimized, ie K =K1+K2=2K1=2K3. D is the spacing of the damper springs, and C is the damping of the damper.
The objective function (transmission rate) Q1 and Q2 are: Q1=11-(Ï‰/p1)2, Q2=11-(Ï‰/p2)2, where Q1 and Q2 are the lateral vibration isolation coefficient and the torsional vibration. The vibration coefficient, Ï‰ is the frequency of the excitation force, p1 is the natural frequency of the system transverse direction, and p2 is the torsional natural frequency of the system. Equation of state: 1) Torsional deformation condition: KÎ´Î¸>T2) Deformation condition under self-weight: MgK<Î´3) Distance between two dampers: 0.6mâ‰¤Dâ‰¤1.2m4) Gearbox stiffness: 13000kN where K is the damper spring stiffness M is the gearbox's own weight, D is the damper spring spacing, f0 is the natural frequency of the support system; f is the disturbance power frequency; Î· is the vibration isolation efficiency; Î¶ is the damping ratio of the vibration isolator; Î´Î¸ is the rotation angle; Î´ is Maximum deformation in the vertical direction, Î´ = 1 mm; T is the sum of input and output torque, T = Tint + Tout.
Through the modal analysis, the natural frequency of the gearbox in the vertical and torsional directions can be obtained and substituted into the transfer rate formula to find the objective function. To achieve multi-objective optimization, the two objective functions Q1, Q2 are multiplied by a weight: Q = w1Q1 + w2Q2 takes w1 = w2 = 1, and increases the state equation: Q1 < Q1max where Q1max is the maximum allowed transfer rate. The first-order optimization method is used to optimize the objective function. The convergence criterion is that the difference between the objective function values â€‹â€‹obtained twice before and after is less than 0.01. After 20 iterations, the result converges, and the optimal iterations 2, 3, 4, and 5 are obtained.
Objective function (transmission rate of vertical vibration and torsional vibration) 3 design variable (stiffness of spring) 4 design variable (distance between springs) 5 design variable (damping) 2 is vertical vibration and torsional vibration transmission rate due to gearbox The system has a small moment of inertia and a relatively high natural frequency, which in turn leads to a high transfer rate. The stiffness of the spring is the main parameter affecting the vibration isolation effect. In this study, the traditional theoretical formula is used to calculate, and a reference stiffness of 17000kN/m is set as the initial value, which converges to 14000kN/m through 9 iterations. In 4, the spring spacing mainly affects the vibration isolation effect of the torsional vibration. When the spacing between the two springs is large, the torsional rigidity of the system is large. A large torsional stiffness will result in an increase in the transmission rate of the system, but the torsional stiffness is too small to meet the overall stiffness requirements, and it converges to 0.712 m after optimization.
The vibration damping optimization result test re-establishes the dynamic model of the gearbox based on the optimized result data, and introduces the dynamics simulation into Adams to obtain the optimized result, thereby verifying the optimization effect. Through the motion simulation under full load conditions, the reaction force of the foundation support and the damper deformation are obtained respectively. After the vibration reduction, the reaction force of the support is 23% of the reaction force of the support before the vibration reduction, and the vibration reduction effect is achieved. In addition, the maximum amplitude of the gearbox under the excitation force is 0.0072 mm, which is significantly reduced. The analysis proves that the damping effect is remarkable and can meet the engineering requirements.
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