Based on the analysis of the working principle of the vibration exciter, a general mathematical model of the optimization design of the shaker is established. Through the optimization method, the main geometric size of the vibration exciter is determined. The optimization example shows that compared with the conventional design, the mass of the shaker is reduced by 19.4%, and other performance indexes are also improved significantly.
1 Introduction
Banana screen is widely used in drilling fluid solid control system because of its simple structure, small power consumption and large processing capacity. Banana screen is mainly composed of vibration mass, vibration damping spring and vibrator, in order to ensure the normal work of the Banana screen, the design requirements of the center of the vibration center and the center of the body coincide, that is, the vibration force through the center of the body, for the single axis inertia banana screen, if ignoring the influence of damping and horizontal stiffness of its amplitude can be expressed as follows:
In the formula (1), A is the amplitude of the banana screen (m); M is the mass of the Banana screen body (kg),m is the eccentric mass of the shaker (kg); r is the eccentricity radius (m) of the shaker. It can be seen from Equation (1) that the eccentric mass and radius of the shaker can be determined under the condition that the reference mass and the required amplitude are known, and the shape of the shaker is generally designed as eccentric wheel type, eccentric shaft type and eccentric block type. In order to adapt to the needs of different drilling fluid treatment, eccentric block type Banana screen is generally designed to have two eccentric blocks with fan-shaped main and pair, as shown in Figure 1. This can change the amplitude of the Banana screen by adjusting the Angle of the two eccentric blocks. In order to adapt to the needs of different drilling fluid treatment, the eccentric block of the Banana screen is generally designed to be fan-shaped main and auxiliary eccentric blocks, as shown in Figure 1. This can change the amplitude of the Banana screen by adjusting the Angle of the two eccentric blocks. Conventional design, is generally based on experience and actual situation to determine the eccentric mass m and eccentric radius r, when the shaker installation space is affected
Limit, it is necessary to appropriately reduce r, increase m, on the contrary, it is necessary to reduce r, increase m, but because the structure of the eccentric block is fan, and it is divided into the main eccentric block and the auxiliary eccentric block, the shape is more complex, the conventional design calculation, the need to repeatedly trial calculation, direct approximation of the required amplitude, using this method, the calculation efficiency is low, and the calculation results may not fully meet the design requirements. Therefore, we establish a general mathematical model for the optimal design of eccentric block, and use the optimization algorithm to determine the main geometric size of eccentric block, so that the calculation results are more reasonable.
2.Establishment of mathematical model of optimal design
2.1 Design variables can be seen from the structural diagram of eccentric block of banana screen (as shown in Figure 1). The structural geometric dimension radius R, R2,R and thickness B, B2 of the main eccentric block are selected as design variables. The thickness B of the secondary eccentric block and the included Angle a are selected as design variables. The X = [R and R2, R, B, B2, a, B3] = [X, X2, X3, X4, Xs, X6, X,]
(2)2.2 Objective function
Different amplitude values can be obtained when the relative positions of the main and secondary eccentric blocks are different. Adjusting the relative position of the main and auxiliary eccentric blocks can make the shaker work under different amplitudes, so as to meet the needs of different drilling fluid treatment. When the main and secondary eccentric blocks overlap, the Banana screen gets the maximum amplitude Am, and when the main and secondary eccentric blocks are in relative positions, the minimum amplitude Amin is obtained. Let the maximum amplitude required for the Banana screen is A, and the minimum amplitude required is A2. Therefore, we hope that the maximum amplitude of the Banana screen A should be as close as possible to the maximum amplitude required, and the minimum amplitude A should be as close as possible to the minimum amplitude A2. This gives us the objective function F,F2
It can be seen from the optimization results that the mass of the shaker is reduced by 19.4% compared with the conventional design, and the approximation degree between the maximum amplitude and minimum amplitude of the shaker and the required maximum amplitude and minimum amplitude is also greatly improved. In summary, using the optimization method to optimize the design of the main geometric structure parameters of the banana screen vibrator, can effectively reduce the labor intensity of the designer, while improving the performance of the Banana screen, especially suitable for the development and design of new products.
