A semi-active control method for posture of articulated vehicle oil-gas interconnected ISD suspension vehicle body
By using the oil-gas interconnected ISD suspension system and semi-active control methods, the pitch and roll problems of articulated vehicles on unstructured roads have been solved, enabling adaptive adjustment to complex road conditions and improving vehicle ride comfort and safety.
Patent Information
- Application Number
- CN202410879285.4
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2024-07-02
- Publication Date
- 2025-11-07
- Estimated Expiration
- 2044-07-02
AI Technical Summary
Articulated vehicles have large pitch and roll angles on unstructured roads, which affects ride comfort and safety. Furthermore, existing suspension systems cannot effectively cope with complex road conditions, making the articulation points prone to damage.
The system employs an oil-gas interconnected ISD suspension system, which combines solenoid valves, electromagnetic proportional valves, flow sensors, PLC controllers, and vehicle posture monitoring devices. By monitoring the vehicle posture and switching the oil flow direction, it achieves semi-active control and adjusts the suspension output force to adapt to different operating conditions.
It effectively reduces pitch and roll angles, prevents damage to articulation points, improves ride comfort and handling stability, and enhances driving safety.
Smart Images

Figure CN119261468B_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The present application belongs to the field of large engineering vehicle chassis suspension, and is suitable for articulated vehicles facing unstructured roads, and relates to a vehicle body posture control system, and particularly relates to a semi-active control method for an oil-gas interconnected ISD suspension vehicle body posture. BACKGROUND
[0002] The research and application of vehicle posture adjustment has a long history, and vehicle posture adjustment is of great significance to improve its mobility. When driving in the jungle and mountainous area, the position of the vehicle body is raised to enable the vehicle to pass through various complex obstacle road surfaces; when the vehicle needs to be transferred and transported in batches, the position of the vehicle body is lowered to enable the vehicle to adapt to more transport carriers and reduce the center of gravity of the vehicle to stabilize the vehicle body; when driving on flat roads, the vehicle body is adjusted to be low to improve the stability of the vehicle driving; the driver adjusts the vehicle body posture through a display control terminal according to different road surfaces to enable the vehicle to maintain excellent driving performance on different roads. The vehicle body posture adjustment system can adjust the attitudes of the vehicle such as high, medium, low, roll, pitch, etc., and the core is an oil-gas spring assembly. By setting the connection mode and timely controlling the opening and closing of the oil circuit, the support size of the oil-gas spring can be adjusted to achieve the purpose of adjusting the vehicle body posture.
[0003] At present, the vehicle body posture of the oil-gas suspension vehicle is passively controlled, and cannot be adjusted according to the driving conditions of the vehicle, resulting in a large brake pitch angle of the vehicle and a large roll angle during steering, which affects the smoothness and safety of the vehicle driving. Compared with the traditional suspension system, the interconnected suspension can effectively improve the overall handling stability of the vehicle while ensuring the comfort of the vehicle, such as the front and rear interconnected suspension which can effectively improve the anti-pitch performance, and the left and right interconnected suspension which can optimize the anti-rollover performance of the vehicle.
[0004] The passive suspension cannot adjust the technical parameters such as stiffness and damping, and can only achieve the optimal performance for a certain road condition in the matching design and optimization design, and there is always a contradiction between the handling stability and the smoothness in the variable working condition, and the performance of the vehicle cannot be better on complex road surfaces. The active suspension generates and adjusts an additional output force by setting an external energy source to actively control the overall suspension output force, so that the vehicle is in the best damping state, but its structure is complex, the energy consumption is high, the production difficulty and production cost are high, and the working stability and reliability are poor, which greatly limits the research and application of the active suspension. Therefore, the semi-active suspension has a wide application prospect due to its simple structure, low cost, low energy consumption and excellent performance, and can be used not only in commercial vehicles but also in passenger cars and special vehicles.
[0005] At the same time, due to the non-structured road, the articulated vehicle is prone to jolt, and the inerter has low-frequency large-amplitude damping effect, which can inhibit low-frequency vibration, improve the smoothness and ride comfort of the vehicle, and has important significance for the suspension research of large engineering vehicles. SUMMARY
[0006] The purpose of the patent is to reduce the pitch angle and roll angle of the articulated vehicle on the non-structured road, to cope with complex working conditions such as muddy road, mine complex road and mountain road, and to avoid the damage of the hinge point due to the existence of limit, and to provide a vehicle body posture semi-active control method based on oil-gas interconnection ISD suspension.
[0007] To achieve the above-mentioned purpose of the application, the technical scheme adopted by the present application is an articulated vehicle oil-gas interconnection ISD suspension vehicle body posture semi-active control system, which comprises two-position two-way electromagnetic valve, two-position four-way electromagnetic valve, three-position four-way electromagnetic valve, spiral pipe, electromagnetic proportional valve, flow sensor, PLC controller, vehicle body posture monitoring device and six oil-gas hydraulic cylinders, and the functions of the whole method are realized through the following steps:
[0008] 1. First, design the oil-gas interconnection ISD suspension system, the oil-gas hydraulic cylinder A and the oil-gas hydraulic cylinder B are installed between the driver's cabin vehicle body and the wheels where the driver's cabin is located, the two oil-gas hydraulic cylinders are connected with two different oil paths in the rodless cavity, and one oil path in the rod cavity, one of the oil paths in the rodless cavity of the oil-gas hydraulic cylinder A and the oil path in the rod cavity are connected with two ports of the three-position four-way electromagnetic reversing valve respectively, after the electromagnetic valve, the other two ports of the electromagnetic valve are connected with two spiral pipes in the middle in series, the other end of the spiral pipe is communicated with one of the oil paths in the rodless cavity and the oil path in the rod cavity of the oil-gas hydraulic cylinder B, realizing the communication of the cavities of the corresponding hydraulic cylinders under different working conditions, and connecting both spiral pipes with an electromagnetic proportional valve and a flow sensor. The oil-gas hydraulic cylinder C, the oil-gas hydraulic cylinder D, the oil-gas hydraulic cylinder E and the oil-gas hydraulic cylinder F are installed between the cargo compartment and the wheels where the cargo compartment is located. The other oil path in the rodless cavity of the oil-gas hydraulic cylinder A is connected with the rodless cavity of the oil-gas hydraulic cylinder C through the two-position two-way electromagnetic valve D, and the other oil path in the rodless cavity of the oil-gas hydraulic cylinder B is connected with the rodless cavity of the oil-gas hydraulic cylinder D through the two-position two-way electromagnetic valve F; at the same time, the rodless cavities of the oil-gas hydraulic cylinder C and the oil-gas hydraulic cylinder D are connected through the two-position two-way electromagnetic valve E, and the rodless cavities of the oil-gas hydraulic cylinder E and the oil-gas hydraulic cylinder F are connected through the two-position two-way electromagnetic valve G. Then connect the rodless cavity and the rod cavity of the oil-gas hydraulic cylinder C and the oil-gas hydraulic cylinder D with two ends of the two-position four-way electromagnetic valve B and C respectively, and connect the other two ends of the electromagnetic valve B and C with the rodless cavity and the rod cavity of the oil-gas hydraulic cylinder F and the oil-gas hydraulic cylinder E respectively.
[0009] 2. The kinematic model of the articulated vehicle is established, and the hinge point is located at the midpoint of the rear axle of the tractor. The kinematic model includes the tractor and the semitrailer. Through the midpoint Of , rear axle midpoint O g , trailer axle midpoint O g and hinge point A r The vehicle kinematic model is derived from the geometric relationship in the earth coordinate system, whose coordinates are O f (x f , y f ), O q (x r , y r ), O g (x g , y g ) and A r (x a , y a ).
[0010] Step 2-1: It is known from the analysis that the tractor-semitrailer is a nonholonomic system, i.e., the number of control variables is less than the number of state variables, and the lateral motion and longitudinal motion of the vehicle are always coupled.
[0011]
[0012] wherein is the longitudinal motion speed of the vehicle, is the lateral motion speed of the vehicle, and θ is the heading angle of the vehicle.
[0013] Step 2-2: Without considering the lateral slip, the axial speeds of all axle midpoints of the tractor-semitrailer are zero, and the following equation is satisfied:
[0014]
[0015] wherein θ0 is the heading angle of the tractor, θ1 is the heading angle of the trailer, and δ f is the equivalent front wheel steering angle of the tractor.
[0016] Step 2-3: Taking the rear axle midpoint O q of the tractor as the reference point, the relationship between the rear axle midpoint O q (x r , y r ) of the tractor and the hinge point A r (x a , y a ) is established according to the geometric position relationship, as shown in the following equation (3):
[0017] x a = x f
[0018] y a = y r (3)
[0019] Step 2-4: According to the geometric position relationship, the relationship between the midpoint O q (x r , y r ) of the rear axle of the tractor and the midpoint O f (x f , y f ) of the front axle of the tractor is shown in the following formula (4):
[0020] x f = x r + L cos θ0
[0021] y f = y r + L sin θ0 (4)
[0022] In the formula, L is the wheelbase of the tractor, and θ0 is the heading angle of the tractor.
[0023] Step 2-5: According to the geometric position relationship, the relationship between the midpoint O q (x r , y r ) of the rear axle of the tractor and the midpoint O g (x g , y g ) of the axle of the trailer is shown in the following formula (5):
[0024] x g = x r - LT cos θ1
[0025] y g = y r - LT sin θ1 (5)
[0026] In the formula, LT is the distance between the hinge point and the midpoint of the trailer axle, and θ1 is the heading angle of the trailer.
[0027] Assuming that the speed of the midpoint O q (x r , y r ) of the rear axle of the tractor is V0, and the front wheel angle of the vehicle is δ f , then the lateral and longitudinal speeds of the midpoint O q of the rear axle of the tractor in the geodetic coordinate system can be represented by the following formula (6):
[0028]
[0029] In the formula, V0 is the speed of the midpoint of the rear axle of the vehicle, and θ0 is the heading angle of the tractor.
[0030] Step 2-6: By taking the derivative of equation (4), the speed relationship of the midpoint Of of the front axle of the tractor can be obtained, as shown in the following formula (7):
[0031]
[0032] where L is the distance between the front wheels of the tractor, and θ0is the heading angle of the tractor.
[0033] Step 2-7: By taking the derivative of equation (5), the speed relationship of the midpoint O of the trailer axle can be obtained as shown in equation (8) below: g
[0034]
[0035] where LTis the distance between the hinged point and the midpoint of the trailer axle, and θ1is the heading angle of the trailer.
[0036] Step 2-8: By substituting equation (7) into equation (2), the expression (9) for the yaw rate of the tractor can be obtained:
[0037]
[0038] θ0is the heading angle of the tractor, and δ f is the steering angle of the front wheels of the tractor.
[0039] Step 2-9: By substituting equation (8) into equation (2), the expression (10) for the yaw rate of the trailer can be obtained:
[0040]
[0041] V0is the speed of the midpoint of the rear axle of the vehicle, θ0is the heading angle of the tractor, θ1is the heading angle of the trailer, L is the distance between the front wheels of the tractor, and LTis the distance between the hinged point and the midpoint of the trailer axle.
[0042] Step 2-10: According to the above derivation, by integrating the equations, the kinematic model of the hinged point located at the midpoint of the rear axle of the tractor is:
[0043]
[0044] In equation (11), V0is the speed of the midpoint of the rear axle of the vehicle, θ0is the heading angle of the tractor, θ1is the heading angle of the trailer, L is the distance between the front wheels of the tractor, LTis the distance between the hinged point and the midpoint of the trailer axle, and δ f is the steering angle of the front wheels of the tractor.
[0045] Then, a mathematical model of the electromagnetic proportional valve is established. In this suspension system, the electromagnetic proportional valve serves as an actuator in the semi-active control system. By being connected in parallel with a spiral pipe, the opening of the electromagnetic proportional valve can be adjusted to change the flow in the electromagnetic proportional valve itself and the spiral pipe, thereby changing the suspension output force through the shunt method. The electromagnetic proportional valve and its spool structure used in this paper are shown in the figure.
[0046] The relationship between the flow rate through the electromagnetic proportional valve, the opening of the electromagnetic proportional valve, and the pressure across the electromagnetic proportional valve is described by the following equation:
[0047]
[0048] h = x0+ x (14)
[0049]
[0050] where C d is the flow coefficient of the electromagnetic proportional valve; A d (h) is the flow area of the electromagnetic proportional valve; A i is the cross-sectional area of the solenoid tube; h is the opening of the electromagnetic proportional valve; P cr is the minimum turbulent pressure; Re cr is the initial Reynolds number; v is the kinematic viscosity of the fluid; D H is the instantaneous hydraulic diameter of the electromagnetic proportional valve; x o is the initial opening; x is the displacement of the valve ball relative to the initial position; A leak is the leakage area; A max is the maximum opening; r0, d0 are the orifice radius and diameter, respectively; r B , d B are the valve ball radius and diameter, respectively; q1 is the flow rate through the electromagnetic proportional valve; q2 is the flow rate through the solenoid tube; P1 is the pressure at the front of the electromagnetic proportional valve and solenoid tube; P2 is the pressure at the back of the electromagnetic proportional valve and solenoid tube; μ is the viscosity coefficient of the oil; r is the solenoid tube inner diameter; p is the oil density; D is the hydraulic diameter of the electromagnetic proportional valve; h max is the maximum opening of the electromagnetic proportional valve.
[0051] Since the turbulent pressure loss in the system is not considered in this document, the value of P cr is considered to be zero, which can be further expressed as:
[0052]
[0053] Therefore, the damping characteristics of the electromagnetic proportional valve are considered to be consistent with the damping valve. Therefore, the pressure drop ΔP e across the electromagnetic proportional valve can be expressed as:
[0054]
[0055] Since the electromagnetic proportional valve is connected in parallel with the solenoid tube, according to fluid mechanics, the pressure drop across the electromagnetic proportional valve is equal to the pressure drop across the solenoid tube, and therefore the relationship between the flow rates through the electromagnetic proportional valve and the solenoid tube is:
[0056]
[0057] Further, by solving equation (22), we have:
[0058]
[0059] where l is the length of the straightened spiral tube; A i is the cross-sectional area of the spiral tube; μ is the viscosity coefficient of the oil; A b is the flow area of the spiral tube.
[0060] 3. The vehicle body posture monitoring device is composed of a gyroscope sensor, an acceleration sensor, and a vehicle body height sensor. The vehicle body posture monitoring device is installed in the driver's cabin and the cargo compartment. The angular velocity of the roll or pitch of the driver's cabin and the cargo compartment is measured by two gyroscopes in a certain period of time, and the roll or pitch angle is obtained by integrating the angular velocity. However, the angle obtained by integration has an error, and the error will increase with time. At this time, the acceleration sensor is used to assist in calculating the posture angle of the driver's cabin and the cargo compartment. The calculated data is then sent to the controller for analysis to obtain the angle θ1 caused by the roll and the angle δ1 caused by the pitch, as well as the vehicle body vibration frequency f0. The angles θ1 and δ1 are compared with the pre-set roll angle θ0, pitch angle δ0, and vehicle body low-frequency vibration threshold f1 and high-frequency vibration threshold f2. If the threshold is exceeded, the electromagnetic valve position and electromagnetic proportional valve opening are changed according to the pre-set strategy to control the vehicle body posture, achieve the purpose of switching the working condition and suppressing vibration.
[0061] 4. A PLC controller is added. The PLC controller part includes a PLC controller 1, a lithium battery 2, and a power detection module 3. The power supply end of the PLC controller 1 and the power detection module 3 are electrically connected to the power supply end of the lithium battery 2. The PLC controller 1 and the power detection module 3 are electrically connected. The control ends of each electromagnetic valve, electromagnetic proportional valve, flow sensor, and vehicle body posture detection device are electrically connected to the I / O port of the PLC controller 1. The data measured by the flow sensors A and B and the vehicle body posture detection devices A and B are input to the input interface 13-16. The electromagnetic proportional valves A and B and the electromagnetic valves A-G are connected to the output interface.
[0062] 5. By collecting the vehicle body longitudinal, lateral acceleration and angular velocity signals by the vehicle body posture monitoring device, sending them to the PLC controller, the controller compares the current vehicle state parameters with the threshold set in the system, judges whether it is a muddy road condition, a mine complex road condition and a mountain road condition, adjusts the working position of the electromagnetic valve corresponding to the working position, realizes the different flow direction of the oil in the oil-gas circuit under different conditions, the oil-gas interconnection system of the application is divided into three conditions, including: muddy road condition, mine complex road condition and mountain road condition, in order to facilitate the description of the working principle of the interconnected oil-gas system, the rodless cavity and the rod cavity of the oil-gas hydraulic cylinder A, B, C, D, E, F are marked as a1, a2, b1, b2, c1, c2, d1, d2, e1, e2, f1, f2 respectively, and the corresponding spiral pipe of electromagnetic proportional valve A and B is l1, l2.
[0063] 5-1. Muddy road condition: when the vehicle drives on the muddy road, the hinged point between the driver's cabin and the cargo cabin is easy to be damaged due to the road settlement, at this time, the vehicle body posture monitoring device collects the vehicle body longitudinal, lateral acceleration, angular velocity and height signals, sends them to the PLC controller, obtains the height and pitch angle of the driver's cabin and the cargo cabin after calculation, further calculates the hinged point angle, if the hinged point angle exceeds the threshold set in advance, i.e. δ1> δ0, the muddy road condition starts to work, the electromagnetic valve A is adjusted to the lower T end by the instruction of the PLC controller. The hydraulic oil in the rodless cavity a1 of the oil-gas hydraulic cylinder A is communicated with the spiral pipe l1 through the three-position four-way electromagnetic valve A, and then connected with the rodless cavity b1 of the hydraulic cylinder B, forming the main oil circuit La, at this time, the rodless cavities a1 and b1 are interconnected, and the oil liquid is mutually communicated; the hydraulic oil in the rodless cavity a2 is communicated with the spiral pipe l2 through the electromagnetic valve A, and then connected with the rod cavity b2 of the hydraulic cylinder B, forming the main oil circuit Lb, at this time, the rod cavities a2 and b2 are interconnected. The electromagnetic valves D and F are switched to the T end, the electromagnetic valves are opened, the electromagnetic valves E and G are placed in the O end, the electromagnetic valves B and C are in the T end, the oil liquid in a1 and b1 is communicated to c1 and d1 through electromagnetic valves D and F, at this time, the hydraulic cylinders A and B are interconnected with the hydraulic cylinders C and D in front and back, effectively reducing the angle of the hinged point and preventing the damage of the hinged point.
[0064] 5-2. Mine complex road conditions: when the vehicle is driving in the mine, due to the complex road conditions, the road subsidence and the road protrusion are more, at the same time, it is easy to produce pitch and roll, at this time, the vehicle body posture monitoring device collects the vehicle body longitudinal, lateral acceleration, angular velocity and height signal, and sends it to the PLC controller, after calculation, the driving cabin and the cargo cabin roll or pitch angle is obtained, if the roll and pitch angle exceeds the threshold set in advance, that is, δ1> δ0 and θ1> θ0, electromagnetic valve A, B, C is adjusted to the upper P end, electromagnetic valve D, E, F, G is placed in O end. The hydraulic oil in the rodless cavity a1 of the oil hydraulic cylinder A flows into the spiral pipe l2 through the reversing valve A, and then flows to the rod cavity of the hydraulic cylinder B, forming the main oil circuit Lc, at this time, the rodless cavity a1 and the rod cavity b2 are interconnected, and the oil liquid flows to each other; while the oil liquid in the rod cavity a2 flows into the rodless cavity of the hydraulic cylinder B through the reversing valve A, forming the main oil circuit Ld, at this time, the rod cavity a2 and the rodless cavity b1 are interconnected, and the oil hydraulic cylinder A and B are interconnected in reverse. The oil liquid in the rodless cavity c1 of the oil hydraulic cylinder C flows to the rod cavity f2 of the hydraulic cylinder F through the electromagnetic valve B, and the oil liquid in c2 flows into f1 through the electromagnetic valve B; the oil liquid in the rodless cavity d1 of the oil hydraulic cylinder D flows into the rod cavity e2 of the hydraulic cylinder E through the electromagnetic valve C, and the oil liquid in d2 flows into e1 through the electromagnetic valve C, at this time, the four hydraulic cylinders of the four corners X type of the cargo cabin are interconnected, and the anti-roll and anti-pitch performance is improved.
[0065] 5-3: mountain road conditions: when the vehicle is driving on the mountain road, the vehicle body longitudinal, lateral acceleration and angular velocity signals collected by the vehicle body posture monitoring device are calculated and analyzed by the PLC controller, if the vehicle is in a roll state for a long time, that is, θ1> θ0, switch to mountain road conditions, at this time, the PLC controller switches the electromagnetic valve A to the working end P, the electromagnetic valve B and C to the T end, the electromagnetic valve D and F to the O end, and the electromagnetic valve E and G to the T end. The main oil circuit Lc, Ld of the driving cabin is connected, and the hydraulic cylinder A and B are interconnected in reverse. The oil liquid in the rodless cavity c1 of the hydraulic cylinder C flows into the rodless cavity d1 of the hydraulic cylinder D through the electromagnetic valve E, and the oil liquid in the rodless cavity e1 flows into the rodless cavity f1 of the hydraulic cylinder F through the electromagnetic valve G, at this time, the hydraulic cylinder C and D are interconnected on the left and right, the hydraulic cylinder E and F are interconnected on the left and right, and the anti-roll performance is improved.
[0066] 6. Add spiral pipe type inertial container to the interconnected oil circuit, the oil liquid in the spiral pipe flows spirally at a large speed, thereby amplifying the moment of inertia of the oil liquid in the spiral pipe; the oil gas spring integrates the damping valve, which can be matched with the accumulator, the nitrogen gas in the accumulator is used as the elastic medium to store or release the elastic potential energy through gas compression and expansion, and the combination of the two can simultaneously play the roles of buffering and damping. Based on the new electromechanical similarity theory, through the medium of oil liquid, the organic combination of the three can effectively attenuate low-frequency vibration, and improve the riding comfort and road friendliness of the vehicle.
[0067] 7. In the oil-gas mutual loop, a solenoid proportional valve and a flow sensor are connected in parallel with the solenoid proportional valve, the flow sensor detects the oil flow in the parallel oil circuit, and the controller can control the opening of the solenoid proportional valve according to the pre-set control strategy, so as to change the oil flow through the solenoid proportional valve, comprehensively adjust the damping force and inertial force of the suspension system, realize the adjustable suspension output force, and adapt to different working conditions. When the vehicle is in low-frequency vibration, i.e. f0 < f1, the opening h of the solenoid proportional valve can be appropriately reduced, so as to increase the flow through the solenoid proportional valve. This adjustment fully utilizes the attenuation advantage of the inertial damper in low-frequency vibration, and effectively suppresses the influence of low-frequency vibration on the stability of the vehicle; when the vehicle is in high-frequency vibration, i.e. f0 > f2, the opening h of the solenoid proportional valve can be increased, so as to reduce or block the flow through the solenoid proportional valve, thereby avoiding the negative effect of the inertial damper in high-frequency vibration.
[0068] 8. Compared with the prior art, the beneficial effects of the present application are:
[0069] (1). Compared with the passive suspension, the present application can better cope with muddy roads, complex mine roads and mountain roads and other working conditions, reduce the pitch and roll angle, and prevent rollover;
[0070] (2). At the same time, the electromagnetic proportional valve can be used to realize the semi-active control of the suspension to cope with complex working conditions and improve the ride comfort and handling stability of the vehicle;
[0071] (3). According to the vehicle body posture monitoring system, the damage to the hinge point caused by excessive roll or pitch angle is avoided, and the driving safety of the vehicle is improved. BRIEF DESCRIPTION OF DRAWINGS
[0072] Figure 1 It is the control logic diagram of the whole system
[0073] Figure 2 It is the oil circuit diagram of the whole system
[0074] Figure 3 It is the spool structure of the electromagnetic proportional valve
[0075] Figure 4 a) is the internal oil passage diagram of the three-position four-way electromagnetic valve P end; b) is the internal oil passage diagram of the three-position four-way electromagnetic valve T end
[0076] Figure 5 It is the oil circuit connection diagram under muddy road conditions
[0077] Figure 6 It is the oil circuit connection diagram under complex mine road conditions
[0078] Figure 7 It is the oil circuit connection diagram under mountain road conditions
[0079] Figure 8 Circuit connection diagram for PLC controller
[0080] Figure 9 Internal structure diagram for PLC controller DETAILED DESCRIPTION
[0081] The present application is further described below in conjunction with the accompanying drawings and examples. The function of the articulated vehicle oil-gas interconnected ISD suspension body posture semi-active control system of the present application is shown in the drawings. The muddy road condition, the mine complex road condition, and the mountain road condition are mainly aimed at the working state of each electromagnetic valve. The muddy road condition mainly reduces the articulation point angle. The mine complex road condition mainly effectively improves the roll stiffness and pitch stiffness at the same time. The mountain road condition mainly responds to long-term roll to prevent rollover and improve handling stability.
[0082] The working principle of the two-position four-way electromagnetic valve is as follows: when the valve core is in the upper P position, the A port communicates with the P port, and the B end communicates with the O end through the lower oil return port; when the valve core is in the lower T position, the four oil ports are blocked by the valve core, independent of each other, and the oil does not communicate with each other.
[0083] The working principle of the three-position four-way electromagnetic valve is as follows: when the valve core is in the lower T position, the electromagnetic valve A port communicates with the O port, and the B port communicates with the P port; when the valve core is in the upper P position, the A port communicates with the P port, and the B end communicates with the O end through the lower oil return port; when the valve core is in the middle position, the four oil ports are blocked by the valve core, independent of each other, and the oil does not communicate with each other.
[0084] The specific steps are as follows:
[0085] 1. Muddy road working condition: when the vehicle is running on the muddy road, the hinge point between the driver's cabin and the cargo compartment is easy to be damaged due to the road subsidence, at this time the vehicle body posture monitoring device collects the vehicle body longitudinal, lateral acceleration, angular velocity and vehicle body height signals, and sends them to the PLC controller, after calculation, the pitch angle and the height of the driver's cabin and the cargo compartment are obtained, and the hinge point angle is further calculated, if the hinge point angle exceeds the threshold value set in advance, i.e. δ1>δ0, the pitch angle of the driver's cabin and the cargo compartment will be too large to make the hinge point angle exceed the limiting angle, the vehicle handling stability, ride comfort and driving safety will be reduced, at this time the current vehicle posture needs to be corrected, the controller issues an instruction to control the electromagnetic valve A to the lower position, and the valve core is fixed at the T end. At this time, the electromagnetic valve core outside O port is connected with the rodless cavity a1 of the oil-gas hydraulic cylinder A, the P port is connected with the rod cavity a2, the A port is connected with one end of the spiral pipe oil line l1, and the B port is connected with one end of the spiral pipe oil line l2. The rodless cavity a1 passes through the O port and the A port of the reversing valve to the spiral pipe l1, and then to the rodless cavity b1 to form a main oil line La; the rod cavity a2 passes through the P port and the B port of the reversing valve to the spiral pipe l2, and then to the rod cavity b2 to form another main oil line Lb. The electromagnetic valves D and F are switched to the T end, the electromagnetic valves are opened, the electromagnetic valves E and G are placed at the O end, the electromagnetic valves B and C are all at the T end, the oil in a1 and b1 flows through the electromagnetic valves D, F to c1, d1, at this time the hydraulic cylinders A, B are respectively connected with the hydraulic cylinders C, D in front and back, like Figure 5The hinge point angle will be larger and the vehicle body will change its posture when the vehicle pitches due to road subsidence. Assuming that the vehicle cabin passes through road subsidence and the vehicle body tilts forward, the hydraulic cylinders A and B in the cabin move downward, and the hydraulic cylinders C and D move upward. At this time, the oil pressure in the rodless chambers a1 and b1 decreases, so that the oil in the hydraulic cylinder chambers c1 and d1 flows to the hydraulic cylinder chambers a1 and b1 through the electromagnetic valves and hydraulic pipelines, causing the hydraulic cylinders C and D to move downward and inhibit the upward movement of the cargo compartment. Conversely, the oil in the rodless chambers a1 and b1 flows to the hydraulic cylinder chambers c1 and d1 through the electromagnetic valves and hydraulic pipelines, causing the hydraulic cylinders C and D to move upward and inhibit the downward movement of the cargo compartment. At this time, the oil in the rodless chambers a1 and b1 of the cabin hydraulic cylinders flows through the spiral pipes and electromagnetic proportional valves and is interconnected, and the oil in the rod chambers a2 and b2 of the cabin hydraulic cylinders flows through the spiral pipes and electromagnetic proportional valves and is interconnected. The high-speed moving oil generates an inerter, greatly improving the tire dynamic load and its high-frequency peak value. The control of the opening size of the electromagnetic proportional valve can adopt a PID control strategy. When the vehicle body posture monitoring device sends the detected longitudinal and lateral acceleration and angular velocity signals of the vehicle body to the PLC controller, if it is analyzed that the vehicle is in low-frequency vibration, i.e. f0 < f1, the PLC controller sends a command to the electromagnetic proportional valve to control the electromagnetic proportional valve to reduce its opening f according to the control strategy, so as to increase the flow rate through the spiral pipe accordingly, so as to fully utilize the attenuation advantage of the inerter in low-frequency vibration. In this process, the flow sensor is responsible for detecting the oil amount in the parallel oil circuit, and the vehicle body posture monitoring device collects the vehicle body state information again and feeds it back to the PLC controller for analysis of the working condition and vibration frequency. The directional valve changes the working position again according to the analysis result, and the electromagnetic proportional valve adjusts the opening size again according to the set control strategy according to the size of the vehicle body vibration frequency, so as to make the suspension output appropriate inertial force and damping force again. Thus, the suspension bounce and vehicle body pitch are inhibited, the road friendliness is enhanced, and the driving safety is improved.
[0086] 2. Mine complex road conditions: when the vehicle is running in the mine, due to the complex road conditions, the road subsidence and the road protrusion are more, and the pitch and roll are also easy to produce, that is, δ1> δ0 and θ1> θ0, the vehicle body posture monitoring device collects the longitudinal and lateral acceleration and angular velocity signals of the vehicle body, and sends them to the PLC controller, and after calculation, the roll or pitch angle and the height of the driver's cabin and the cargo cabin are obtained, if the roll or pitch angle is compared and exceeds the threshold value set in advance, it will lead to the roll or pitch angle of the driver's cabin and the cargo cabin being too large, and the hinge point angle exceeds the limit angle, the vehicle handling stability, ride comfort and driving safety are reduced, at this time, the current vehicle posture needs to be corrected, the controller issues instructions to control the electromagnetic valves A, B, C to the upper position, and the valve core is fixed at P; the electromagnetic valves D, E, F and G are all set to the lower position O. At this time, the outer O port of the valve core of electromagnetic valve A is connected with the rodless cavity a1 of the oil-gas hydraulic cylinder A, the P port is connected with the rod cavity a2, the A port is connected with the left end of the spiral pipe oil circuit l1, and the B port is connected with the left end of the spiral pipe oil circuit l2. The rodless cavity a1 is connected with the B port of the electromagnetic valve A through the O port of the electromagnetic valve A, and then connected with the spiral pipe l2, and then connected with the rod cavity b2 to form a main oil circuit Lc; the rod cavity a2 is connected with the A port of the reversing valve A through the P port of the reversing valve A, and then connected with the spiral pipe l1, and then connected with the rodless cavity b1 to form another main oil circuit Ld. The oil in the rodless cavity c1 of the oil-gas hydraulic cylinder C flows to the rod cavity f2 of the hydraulic cylinder F through the electromagnetic valve B, and the oil in c2 flows into f1 through the electromagnetic valve B; the oil in the rodless cavity d1 of the oil-gas hydraulic cylinder D flows into the rod cavity e2 of the hydraulic cylinder E through the electromagnetic valve C, and the oil in d2 flows into e1 through the electromagnetic valve C, at this time, the four hydraulic cylinders of the X type interconnection of the four corners of the cargo cabin are as follows Figure 6The vehicle encounters road subsidence or protrusion or makes a steering motion on the complex road surface of the mining area, the vehicle body will change in roll or pitch posture, at this time the pitch and roll stiffness need to be considered. Assuming that the vehicle makes a pitch motion, the vehicle body tilts forward, the driver's cabin hydraulic cylinders A and B make downward motion, the cargo cabin oil-gas hydraulic cylinders C and D make downward motion, and the oil-gas hydraulic cylinders E and F make upward motion. The oil pressure in the rodless cavities c1 and d1 of the oil-gas hydraulic cylinders C and D rises, pushing the oil to flow to f2 and e2 through electromagnetic valves B and C, respectively, the oil pressure in f2 and e2 rises, giving the oil-gas hydraulic cylinders E and F a downward force, causing the oil-gas hydraulic cylinders E and F to move downward, and inhibiting the upward motion of the oil-gas hydraulic cylinders E and F. At this time, the oil in the rodless cavity a1 and the rod cavity b2 of the driver's cabin hydraulic cylinder interconnects after flowing through the spiral tube and the electromagnetic proportional valve, the oil in the rod cavity a2 and the rodless cavity b1 of the driver's cabin hydraulic cylinder interconnects after flowing through the spiral tube and the electromagnetic proportional valve, and the oil-gas hydraulic cylinders E and F are inhibited. The inertance is generated by the high-speed moving oil, and the control of the opening size of the electromagnetic proportional valve can adopt the PID control strategy. When the vehicle body posture monitoring device sends the detected vehicle body longitudinal, lateral acceleration and angular velocity signals to the PLC controller, if it is analyzed that the vehicle is in high-frequency vibration, i.e. f0>f2, the PLC controller sends a command to the electromagnetic proportional valve, and the electromagnetic proportional valve increases its opening h according to the control strategy, prompting the flow through the spiral tube to be reduced accordingly, thereby avoiding the negative effect of the inertance device in high-frequency vibration. In this process, the flow sensor is responsible for detecting the oil amount in the parallel oil line, the vehicle body posture monitoring device collects the vehicle body state information again and feeds back to the PLC controller for analysis of the working condition and vibration frequency, the directional valve changes the working position again according to the analysis result, and the electromagnetic proportional valve adjusts the opening size again according to the set control strategy according to the size of the vehicle body vibration frequency, so as to make the suspension output appropriate inertial force and damping force. Thus, the suspension bounce and vehicle body roll are inhibited, the steering stability and smoothness are coordinated, and the driving safety is improved.
[0087] 3. Mountain road working condition: when the vehicle is driving on the mountain road, the vehicle is prone to long-term roll due to frequent steering. The vehicle body posture monitoring device collects the vehicle body longitudinal, lateral acceleration and angular velocity signals, and sends them to the PLC controller. After calculation, the roll angle and height of the driver's cabin and the cargo compartment are obtained. If the roll angle and roll time exceed the preset threshold value, that is, θ1> θ0, the vehicle has the risk of rollover, and the vehicle handling stability and driving safety are reduced. At this time, the current vehicle posture needs to be corrected, and the controller valve issues an instruction to control the electromagnetic valve A to switch to the working end P, the electromagnetic valves B and C to switch to the T end, the electromagnetic valves D and F to be placed in the O end, and the electromagnetic valves E and G to be placed in the T end. The main oil circuit Lc and Ld of the driver's cabin are connected, and the hydraulic cylinders A and B are left-right reversely interconnected. The oil in the rodless chamber c1 of the hydraulic cylinder C flows into the rodless chamber d1 of the hydraulic cylinder D through the electromagnetic valve E, and the oil in the rodless chamber e1 flows into the rodless chamber f1 of the hydraulic cylinder F through the electromagnetic valve G. At this time, the hydraulic cylinders C and D are left-right interconnected, and the hydraulic cylinders E and F are left-right interconnected. Due to the continuous steering of the vehicle on the mountain road, the vehicle body will roll for a long time, and due to the large steering angle of some sections, the risk of rollover will occur. At this time, the roll stiffness needs to be improved. Assuming that the vehicle is driving uphill along the mountain road, the vehicle body is inclined to the right, and the left hydraulic cylinders A, C and E of the whole vehicle run upward at the same time, and the right hydraulic cylinders B, D and F run downward at the same time. The oil pressure in the rodless chamber a1 of the driver's cabin oil and gas hydraulic cylinder A rises, pushing the oil in a1 to flow to b2 through the oil circuit Lc, giving the oil and gas hydraulic cylinder B an upward force, causing the oil and gas hydraulic cylinder B to run upward, and inhibiting the downward movement of the oil and gas hydraulic cylinder B. The oil pressure in the hydraulic cylinder chambers d1 and f1 of the cargo compartment is reduced, so that the oil in the hydraulic cylinder chambers c1 and e1 is pumped out through the electromagnetic valve and the hydraulic pipeline to the hydraulic cylinder chambers d1 and f1, causing the hydraulic cylinders D and F to run upward, and inhibiting the downward movement of the hydraulic cylinders D and F. Conversely, the oil in the rodless chamber a1 and the rod chamber b2 of the driver's cabin hydraulic cylinder is interconnected after flowing through the spiral pipe and the electromagnetic proportional valve, and the oil in the rod chamber a2 and the rodless chamber b1 of the driver's cabin hydraulic cylinder is interconnected after flowing through the spiral pipe and the electromagnetic proportional valve. The inertance is generated by the high-speed moving oil, and the control of the opening size of the electromagnetic proportional valve can adopt the PID control strategy.When the vehicle body attitude monitoring device sends the detected longitudinal and lateral acceleration and angular velocity signals of the vehicle body into the PLC controller, if it is analyzed that the vehicle is vibrating at a low frequency, that is, f0 < f1, the PLC controller sends a command to the electromagnetic proportional valve, making the electromagnetic proportional valve reduce its opening degree according to the control strategy, so as to promote the corresponding increase in the flow rate through the solenoid tube, thus making full use of the attenuation advantage of the inertance container in low-frequency vibration. During this process, the flow sensor is responsible for detecting the oil volume in the parallel oil circuit. The vehicle body attitude monitoring device collects the vehicle body state information again and feeds it back to the PLC controller for analyzing its working condition and vibration frequency. The reversing valve changes its working position again according to the analysis result, and the electromagnetic proportional valve adjusts the opening degree again according to the set control strategy according to the size of the vehicle body vibration frequency, so as to make the suspension output appropriate inertial force and damping force. In this way, it circulates repeatedly to suppress the suspension bounce and vehicle body roll, coordinate the handling stability and ride comfort, and improve the driving safety.
[0088] In summary, the present invention can switch among three working conditions of the suspension to cope with different driving and road conditions; at the same time, it can achieve semi-active control of the suspension through the electromagnetic proportional valve to cope with complex working conditions, improve the ride comfort and handling stability of the vehicle; and according to the vehicle body attitude monitoring system, it can avoid damaging the hinge point due to excessive roll or pitch angle, and improve the driving safety of the vehicle.
Claims
1. A method for semi-active control of articulated vehicle ISD suspension vehicle body posture, characterized in that, The method comprises the following steps: Step 1, design the oil-gas interconnected ISD suspension system, arrange the oil circuit, and establish a hinged vehicle kinematics model with the hinge point located at the midpoint of the rear axle of the tractor and a mathematical model of the electromagnetic proportional valve as a reference model, the kinematics model comprising the tractor and the semitrailer; Step 2, use the gyroscope sensor, the acceleration sensor and the vehicle body height sensor to build a vehicle body posture monitoring device, and obtain the road information and the vehicle body posture information in real time; Step 3, add a PLC controller, adopt a corresponding control strategy according to the different vehicle body posture information obtained in step 2, control the electromagnetic reversing valve in the system through the PLC controller, change the different flow directions of the oil in the oil-gas circuit, realize the change of the oil-gas ISD suspension interconnection mode, and achieve the purpose of coping with three working conditions of muddy land, mine area and mountainous road, and avoiding damage of the driver's cabin and the cargo cabin of the hinged vehicle due to jolting on the unstructured road and exceeding the limiting angle of the hinge point; Step 4, embed a spiral tube type inertial container in the oil-gas interconnection circuit, store the kinetic energy of the oil, and improve the low-frequency vibration isolation performance of the vehicle; Step 5, connect an electromagnetic proportional valve in parallel with the spiral tube, adjust the opening of the electromagnetic proportional valve through the PLC controller to change the oil flow through the spiral tube, comprehensively adjust the damping force and the inertial force of the suspension system, realize the adjustable output force of the suspension, and thus realize the semi-active control of the vehicle body posture; Step 6, the vehicle body posture monitoring device collects the vehicle body state information again and feeds back to the PLC controller to analyze the working condition and the vibration frequency, the reversing valve changes the working position again according to the analysis result, and the electromagnetic proportional valve adjusts the opening size again according to the vehicle body vibration frequency according to the set control strategy; The design of the oil-gas interconnected ISD suspension system is realized through the following steps, and the system comprises two-position two-way electromagnetic valves, two-position four-way electromagnetic valves, three-position four-way electromagnetic valves, spiral tubes, electromagnetic proportional valves, flow sensors, a PLC controller, a vehicle body posture monitoring device and six oil-gas hydraulic cylinders; The six oil-gas hydraulic cylinders are respectively installed at the suspension positions corresponding to the six wheels, wherein the oil-gas hydraulic cylinder A and the oil-gas hydraulic cylinder B are installed between the driver's cabin body and the wheels of the driver's cabin, the rodless cavity of the two oil-gas hydraulic cylinders is connected with two different oil circuits, the rod cavity is connected with one oil circuit, one of the oil circuits of the rodless cavity of the oil-gas hydraulic cylinder A and the oil circuit of the rod cavity are connected with two ports of a three-position four-way electromagnetic reversing valve, after the electromagnetic valve, the other two ports of the electromagnetic valve are connected in series with two spiral tubes in the middle, the other end of the spiral tube is connected with one of the oil circuits of the rodless cavity of the oil-gas hydraulic cylinder B and the oil circuit of the rod cavity, the connection of the chambers of the corresponding hydraulic cylinders in different working modes is realized, and the two spiral tubes are connected in parallel with an electromagnetic proportional valve, a flow sensor is connected in series with the electromagnetic proportional valve in the branch to detect the flow of the related oil circuit. The oil-gas hydraulic cylinder C, the oil-gas hydraulic cylinder D, the oil-gas hydraulic cylinder E and the oil-gas hydraulic cylinder F are installed between the cargo compartment and the wheel on which the cargo compartment is located; the other oil passage of the rodless cavity of the oil-gas hydraulic cylinder A is connected with the rodless cavity of the oil-gas hydraulic cylinder C through the two-position two-way electromagnetic valve D, and the other oil passage of the rodless cavity of the oil-gas hydraulic cylinder B is connected with the rodless cavity of the oil-gas hydraulic cylinder D through the two-position two-way electromagnetic valve F; meanwhile, the rodless cavities of the oil-gas hydraulic cylinder C and the oil-gas hydraulic cylinder D are connected through the two-position two-way electromagnetic valve E, and the rodless cavities of the oil-gas hydraulic cylinder E and the oil-gas hydraulic cylinder F are connected through the two-position two-way electromagnetic valve G; the rodless cavities and the rod cavities of the oil-gas hydraulic cylinder C and the oil-gas hydraulic cylinder D are connected with two ends of the two-position four-way electromagnetic valve B and C respectively, and the other two ends of the electromagnetic valve B and C are connected with the rodless cavities and the rod cavities of the oil-gas hydraulic cylinder F and the oil-gas hydraulic cylinder E respectively; The electromagnetic valve A, the electromagnetic valve B, the electromagnetic valve C, the electromagnetic valve D, the electromagnetic valve E, the electromagnetic valve F, the electromagnetic valve G, the electromagnetic proportional valve A and the electromagnetic proportional valve B are connected with the PLC controller, and are controlled by the controller to realize the change of the working position of the electromagnetic reversing valve and the adjustment of the opening size of the electromagnetic proportional valve.
2. The method of claim 1, wherein, A kinematic model of the articulated vehicle is established, in which the hinge point is located at the middle point of the rear axle of the tractor, and the kinematic model includes the tractor and the semitrailer; the middle point of the front axle of the tractor O f , the middle point of the rear axle of the tractor O g , the middle point of the trailer axle O g , and the hinge point A r The kinematic model of the vehicle is derived from the geometric relationship in the geodetic coordinate system; then, a mathematical model of the electromagnetic proportional valve is established, and the relationship between the flow through the electromagnetic proportional valve and the spiral pipe is derived; in the suspension system, the electromagnetic proportional valve plays the role of the actuator in the semi-active control system, and by being connected in parallel with the spiral pipe, the opening of the electromagnetic proportional valve can be adjusted to change the flow in the electromagnetic proportional valve itself and the spiral pipe, so as to change the suspension output force through the flow splitting method.
3. The method of claim 1, wherein, The vehicle body posture monitoring device is composed of a gyro sensor, an acceleration sensor and a vehicle body height sensor. Two gyro sensors measure the angular velocity of the cabin and the cargo compartment in a certain period of time, and the angular velocity is integrated to obtain the roll or pitch angle. The acceleration sensor is used to assist the calculation of the attitude angle of the cabin and the cargo compartment. The calculated data is sent to the controller for analysis to obtain the angle generated by the roll of the vehicle body θ 1 and the angle generated by the pitch δ 1 and the vehicle body vibration frequency f 0.
4. The method of claim 1, wherein, The controller is composed of the PLC controller, the lithium battery and the electric quantity detection module, the power supply end of the PLC controller and the electric quantity detection module are electrically connected with the power supply end of the lithium battery, the PLC controller is electrically connected with the electric quantity detection module, the control end of each electromagnetic valve, electromagnetic proportional valve, flow sensor and vehicle body posture detection device is electrically connected with the I / O port of the PLC controller.
5. The method of claim 1, wherein, In step 3, the switching of the interconnection mode generated by the three working conditions is realized by collecting the vehicle body longitudinal, transverse acceleration and angular velocity signals by the vehicle body posture monitoring device, sending them to the PLC controller, comparing the current vehicle state parameters with the threshold value set in the system by the controller, judging whether it is the muddy road working condition, the mine complex road working condition and the mountain road working condition, and then controlling the electromagnetic valve according to the working condition.
6. The method of claim 5, wherein, In step 3, the control of each electromagnetic reversing valve in the system is realized by the PLC controller to change the different flow directions of the oil in the oil and gas circuit, realize the change of the oil and gas ISD suspension interconnection mode, and achieve the purpose of coping with muddy, mining, and mountainous road conditions: 1) Muddy road conditions: when the vehicle is driving on the muddy road, the articulated vehicle is easy to cause damage to the articulation point due to road subsidence, the PLC controller switches electromagnetic valve A to the working end T, the oil and gas hydraulic cylinders A and B are interconnected in the forward direction, electromagnetic valves D and F are placed in the upper end, electromagnetic valves E and G are placed in the lower end, electromagnetic valves B and C are both in the T end, and the oil and gas hydraulic cylinders A and B are interconnected with the oil and gas hydraulic cylinders C and D in front and back, at this time, the oil channels corresponding to the positions are connected, effectively controlling the articulation point not to exceed the limit angle; 2) Mining complex road conditions: when the vehicle is driving on the mining road, due to the complexity of the mining road, there are more road subsidence or protrusions, at this time, the PLC controller switches electromagnetic valve A to the working end P, the oil and gas hydraulic cylinders A and B at the position of the driver's cabin are interconnected in the reverse direction through the intermediate oil circuit, electromagnetic valves D, E, F, and G are all placed in the lower end, electromagnetic valves B and C are placed in the P end, and the four oil and gas hydraulic cylinders C, D, E, and F at the position of the cargo cabin are interconnected in the X shape, at this time, the oil channels corresponding to the positions are connected, effectively improving the lateral and pitching stiffness; 3) Mountain road conditions: when the vehicle is driving on the mountain road, the vehicle is easy to tilt for a long time due to frequent turning, the PLC controller switches electromagnetic valve A to the working end P, electromagnetic valves B and C are switched to the T end, electromagnetic valves D and F are placed in the lower position, and electromagnetic valves E and G are placed in the upper position, at this time, the oil and gas hydraulic cylinders A and B at the position of the driver's cabin are interconnected in the reverse direction through the intermediate oil circuit, the oil and gas hydraulic cylinders C and E at the position of the cargo cabin are interconnected with D and F in the left and right directions, the oil channels corresponding to the positions are connected, and the lateral stiffness is effectively improved; the relevant oil channels in the three working conditions do not interfere with each other.
7. The method of claim 1, wherein, In step 4, a spiral tube is embedded in the interconnection circuit, the slender spiral tube serves as an inerter element to provide inertial force and parasitic damping force; the damping valve and the electromagnetic proportional valve serve as damping elements to provide damping force for damping, which is equivalent to the shock absorber in the mechanical suspension; two accumulators filled with a certain amount of high-pressure inert gas provide suspension elastic force, which is equivalent to the spring in the mechanical suspension, and plays a supporting and buffering role for the vehicle body.
8. The method of claim 1, wherein, In step 5, an electromagnetic proportional valve and a flow sensor are connected in parallel with the spiral tube, which can detect the flow in the oil circuit and adjust the oil flow through the spiral tube by controlling the opening of the electromagnetic proportional valve, thereby comprehensively adjusting the damping force and inertial force of the suspension system; when the vehicle is in low-frequency vibration, the attenuation advantage of the inerter in low-frequency vibration can be fully utilized to effectively suppress the influence of low-frequency vibration on the stability of the vehicle; when the vehicle is in high-frequency vibration, the opening is adjusted to avoid the negative effects of the inerter in high-frequency vibration.
Citation Information
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