Experimental and Analytical Study of Secondary Path Transfer Function in Active Hydraulic Mount with Solenoid Actuator

Abstract

The active hydraulic mount with solenoid actuator (AHM-SNA) does not require permanent magnets, is of low cost, and has attracted wide attention. This paper focuses on each link of the secondary path in AHM-SNA, the transfer functions (TFs) were studied one by one, and a simple and efficient expression for the total secondary path is discussed. First, based on the mathematical model of the hydraulic mount with inertia track and decoupling membrane, the TF from actuator active force to output force at frame side was analyzed, the results show that the TF was constant in the mid-frequency band. Second, based on the geometric parameters and cone air gap of solenoid actuator, it was obtained that the TF from the square of current to actuator active force is also constant; based on the relationship that the active force frequency is twice of the harmonic current frequency, the full-wave-rectified current was introduced. Utilizing the fact that the second harmonic component of the current is the main component, it was concluded that the total TF of the secondary path from current to active force and then to output force at frame side was constant in the mid-frequency band. Finally, two sets of experiments with full-wave-rectified current as the excitation were carried out, and the analytical conclusion was verified that the TF of the secondary path was constant as a proportional link and was convenient for the active control algorithms.

Fixed Points on Active and Passive Dynamics of Active Hydraulic Mounts with Oscillating Coil Actuator

“…Thus, K2 is set to zero, and the pressure fluctuation in the lower fluid chamber is ignored and set p2 = 0 [5,7−9]. Denote the length of inertia track as l2, the cross-sectional area as A2, the wet perimeter of cross section as L2, and the hydraulic diameter as d2 = Referring to the hydraulic mount mechanical models [5][6][7][8][9], a unified lumped parameter mechanical model for AHM-IT-DM and PHM-IT-DM is built, as shown in Figure 2. The displacement of the engine side is y 1 and the corresponding reaction force, i.e., the force acting on the mount, is f 1 .…”

“…These are variables for the lumped parameter model. Referring to the hydraulic mount mechanical models [5][6][7][8][9], a unified lumped parameter mechanical model for AHM-IT-DM and PHM-IT-DM is built, as shown in Figure 2. The displacement of the engine side is y1 and the corresponding reaction force, i.e., the force acting on the mount, is f1.…”

“…Due to the wrinkled rubber bellow, K 2 is several orders of magnitude smaller than K 1 . Thus, K 2 is set to zero, and the pressure fluctuation in the lower fluid chamber is ignored and set p 2 = 0 [5,[7][8][9]. Denote the length of inertia track as l 2 , the cross-sectional area as A 2 , the wet perimeter of cross section as L 2 , and the hydraulic diameter as d 2 = 4A 2 /L 2 .…”

“…Based on the unified mechanical model as shown in Figure 2, set m 1 = 0, y 5 = 0, and f a = 0 to obtain the following nonlinear mathematical model for passive dynamics [8,9]:…”

“…The excitation force is mainly balanced by elastic restoring force. Under this condition, the inertia and damping forces of the decoupler [6][7][8]11] may be neglected. Simplification of Equation (3) leads to the following mathematical model:…”