A nonlinear stiffness suspension and its design method

Abstract

The present invention discloses a nonlinear stiffness suspension, comprising a lower platform, a fixed seat, a push rod, a horizontal spring, a first roller, an X-shaped rod, an upper platform, a slot structure, a guide rail platform, a fixed support, a sliding plate support, a first pin, a second pin, a second roller, a third pin, a fourth pin, a threaded screw, a handle and a push block. The present invention also discloses a design method for a nonlinear stiffness suspension. The present invention has the following beneficial effects: compared with a cam structure, a slot structure is easier to realize a movement with a larger stroke, so that a nonlinear stiffness characteristic can be obtained within a larger displacement range; the slot structure has an adjustable inclination angle, and has more applicable occasions.

Description

Technical Field

[0001] The present invention relates to the field of vibration reduction technology, and in particular to a nonlinear stiffness suspension and a design method thereof, which can be applied to ship equipment vibration reduction, seat vibration reduction, etc., and realizes nonlinear stiffness characteristics through groove surfaces with different inclination angles or different groove surface curves. Background Art

[0002] Most of the current vibration reduction structures focus on controlling high-frequency, small-amplitude vibrations. However, in the field of low-frequency vibration reduction, such as vibration reduction of offshore ships, some current structures have many disadvantages. The cam roller structure that is used more often only has good nonlinear stiffness characteristics within a certain range, and the structure needs to be adjusted to a certain extent when the load changes. The realization of nonlinear stiffness for a large stroke requires a larger cam radius, so the structure cannot be effectively applied to vibration reduction scenarios for a large stroke. Summary of the invention

[0003] The purpose of the present invention is to provide a nonlinear stiffness suspension and a design method thereof, which has a relatively simple structure and can realize the characteristics of nonlinear stiffness in a larger range, and can be applied to low-frequency and large-stroke vibration reduction scenarios, thereby solving the technical problems designed in the background technology.

[0004] The technical solution of the present invention is:

[0005] A nonlinear stiffness suspension, comprising a lower platform, a fixed seat, a push rod, a horizontal spring, a first roller, an X-shaped rod, an upper platform, a groove structure, a guide rail platform, a fixed support, a sliding plate support, a first pin, a second pin, a second roller, a third pin, a fourth pin, a threaded screw, a handle and a push block, wherein the lower platform and the upper platform are spaced apart from each other, the number of the fixed seats is two and they are respectively installed on two surfaces of the lower platform and the upper platform that are opposite to each other and are arranged opposite to each other; the number of the X-shaped rods is two, one end of the X-shaped rod is hinged to the fixed seat on the lower platform, the other end is installed with the first roller and abuts against the upper platform through the first roller; one end of the other X-shaped rod is hinged to the fixed seat on the upper platform, the other end is installed with the first roller and abuts against the lower platform through the first roller; The intersection of the two X-shaped rods is hinged by the first pin; the groove structure is fixed on the X-shaped rod; the guide rail platform is installed on the lower platform, and a guide rail is provided on the top of the guide rail platform, the fixed support is fixed on the top of the guide rail platform, the threaded screw is installed on the fixed support and is threadedly connected with the fixed support, the sliding plate support is installed on the top of the guide rail platform and can move along the track, the handle and the push block are respectively installed on the two ends of the threaded screw and the push block abuts against the sliding plate support, the push rod is assembled on the sliding plate support and can move along the sliding plate support, the second roller is rotatably installed on one end of the push rod and abuts on the groove structure, the horizontal spring is sleeved on the push rod and one end is fixed on the other end of the push rod, and the other end is fixed on the sliding plate support.

[0006] As a preferred improvement of the present invention, the X-shaped rod is hinged to the fixing seats on the upper and lower platforms respectively through second pins.

[0007] As a preferred improvement of the present invention, the first roller is hinged to the two X-shaped rods respectively through a third pin.

[0008] As a preferred improvement of the present invention, the second roller is hinged to the push rod via a fourth pin.

[0009] As a preferred improvement of the present invention, the fixing seat is a double-ear fixing seat.

[0010] As a preferred improvement of the present invention, the handle is a five-pointed star handle.

[0011] The present invention also provides a design method for the nonlinear stiffness suspension, which comprises the following steps:

[0012] Step 1: Assume that the inclination angle between the X-shaped bar with the slot structure and the horizontal plane is θ at a certain moment, and further assume that the slot structure is installed at point A, then establish a ts coordinate system with point A as the origin. The curve equation of the slot structure in the ts coordinate system is: but The contact point of the second roller on the groove structure corresponds to the inclination angle of the groove structure. The yx coordinate system is established at the center axis O of the fixed seat. The conversion relationship of the curve equation of the groove structure in the two coordinate systems can be expressed by the following equations (1) to (3):

[0013]

[0014] That is:

[0015]

[0016]

[0017] Among them, s is the horizontal coordinate in the ts coordinate system, l is the distance between the installation point and the lower end of the X-bar;

[0018] Step 2: Assume the coordinates of the contact point M in the ts coordinate system are The installation height of the horizontal spring is H, and the coordinates of the contact point M in the yx coordinate system are (x M , H); let y = H in formula (3), Substituting into s M The relationship with θ is:

[0019] s M =f1(θ) (4)

[0020] Among them, f1 is the function symbol used to represent s M Relationship with θ;

[0021] Substituting equation (4) into equation (2), we can get the horizontal coordinate x of the contact point M in the yx coordinate system: M It is expressed by θ, which is:

[0022] x M =f2(θ) (5)

[0023] Among them, f2 is the function symbol used to represent x M Relationship with θ;

[0024] Step 3: Assume that the initial inclination angle of the X-shaped rod is θ0, then the initial horizontal coordinate of point M in the yx system can be expressed as:

[0025]

[0026] Therefore, the change in the horizontal spring extension Δx can be expressed as:

[0027]

[0028] Among them, x M is the horizontal coordinate of point M at any time in the yx coordinate system, is the horizontal coordinate of the initial equilibrium state of point M in the yx coordinate system;

[0029] Step 4: Assume the pre-stretching amount of the horizontal spring is δ0 and the elastic coefficient is k h , then the spring force f h Given by:

[0030] f h =k h (δ0+Δx) (8)

[0031] From equations (5), (6), (7), (8) and the given initial tilt angle θ0, the spring force f can be obtained: h Relationship with the rod inclination angle θ:

[0032] f h =f3(θ) (9)

[0033] Among them, f3 is the function symbol used to represent f h Relationship with the rod inclination angle θ;

[0034] The vertical displacement h of the upper platform can be given by:

[0035] h=L(sinθ0-sinθ) (10)

[0036] Where L is the total length of the X-bar;

[0037] For the whole structure composed of X-shaped structure, groove structure and roller-push rod structure, the virtual work equation is as follows:

[0038] δW=0 (11)

[0039] Among them, δ represents a tiny amount, and W is the total virtual work produced by the virtual displacement;

[0040] Right now:

[0041] F·δy G +f h ·δx M =0 (12)

[0042] Write the coordinates yG of point G using θ as a parameter:

[0043] y G =Lsinθ (13)

[0044] Its variations are:

[0045] δy G =Lcosθδθ (14)

[0046] Coordinate x of point M M Given by formula (5), its variation is:

[0047] δx M =f2′(θ)δθ (15)

[0048] Among them, f2′ is the characterization of x M The function sign of the derivative with respect to θ;

[0049] Substituting equations (15) and (16) into equation (13) and combining them with equation (9), we can obtain the relationship between load F and rod inclination angle θ, namely:

[0050] F=f5(θ) (16)

[0051] Among them, f5 is the function symbol used to represent the relationship between F and the rod inclination angle θ;

[0052] From formula (10), we can get:

[0053]

[0054] Substituting equation (17) into equation (16), we can obtain the relationship between load force F and vertical displacement h:

[0055] F=f6(h) (18)

[0056] Among them, f6 is the function symbol used to represent the relationship between F and the vertical displacement h;

[0057] Therefore, the system stiffness can be obtained as follows:

[0058] K=f6′(h) (19)

[0059] Wherein, f6′ is the function symbol representing the derivative of F with respect to h.

[0060] As a preferred improvement of the present invention, the X-shaped structure consists of an upper platform, a lower platform and two X-shaped rods.

[0061] The beneficial effects of the present invention are as follows:

[0062] 1. Compared with the traditional roller-cam structure, the roller-groove structure in the present invention is easier to achieve movement with a larger stroke and has good nonlinear stiffness characteristics, thereby being able to achieve nonlinear stiffness within a larger displacement range;

[0063] 2. The inclination angle of the groove structure is adjustable, which has more applicable occasions. In addition, the contact surface of the groove can be any curved shape to meet the needs of different tasks;

[0064] 3. The groove installed in the present invention can be adjusted, including the adjustment of the installation angle and the adjustment of the groove shape curve, so as to obtain various stiffness characteristics to meet various vibration reduction scenarios and solve various practical needs. For example, it can be adjusted according to actual conditions for motorized equipment such as ships to effectively reduce the risk of equipment damage, and it can be used for seat vibration reduction to adapt to different road excitations to increase seat comfort.

[0065] 4. The idea provided by the present invention is not limited to realizing nonlinear stiffness. A damper can be placed at the structure where the horizontal spring is installed to generate nonlinear damping to achieve different characteristics. Therefore, the idea provided by the present invention can realize both nonlinear stiffness and nonlinear damping. BRIEF DESCRIPTION OF THE DRAWINGS

[0066] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for describing the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative work, among which:

[0067] Figure 1 It is a schematic diagram of the three-dimensional structure of the nonlinear stiffness suspension of the present invention;

[0068] Figure 2 It is a schematic diagram of the main structure of the nonlinear stiffness suspension of the present invention;

[0069] Figure 3 It is a schematic diagram of the structure of the nonlinear stiffness suspension of the present invention. DETAILED DESCRIPTION

[0070] The technical solutions in the embodiments of the present invention will be described clearly and completely below in combination with the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0071] It should be noted that all directional indications in the embodiments of the present invention (such as up, down, left, right, front, back, etc.) are only used to explain the relative position relationship, movement status, etc. between the components under a certain specific posture (as shown in the accompanying drawings). If the specific posture changes, the directional indication will also change accordingly.

[0072] In addition, in the present invention, descriptions such as "first", "second", etc. are only used for descriptive purposes and cannot be understood as indicating or implying their relative importance or implicitly indicating the number of the indicated technical features. Therefore, the features defined as "first" or "second" may explicitly or implicitly include at least one of the features. In the description of the present invention, the meaning of "plurality" is at least two, such as two, three, etc., unless otherwise clearly and specifically defined.

[0073] In the present invention, unless otherwise clearly specified and limited, the terms "connection", "fixation", etc. should be understood in a broad sense. For example, "fixation" can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection or an indirect connection through an intermediate medium, it can be the internal connection of two elements or the interaction relationship between two elements, unless otherwise clearly defined. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0074] In addition, the technical solutions between the various embodiments of the present invention can be combined with each other, but it must be based on the fact that ordinary technicians in the field can implement it. When the combination of technical solutions is contradictory or cannot be implemented, it should be deemed that such combination of technical solutions does not exist and is not within the scope of protection required by the present invention.

[0075] See also Figure 1 and 2 As shown, the present invention provides a nonlinear stiffness suspension, including a lower platform 1, a fixed seat 2, a push rod 3, a horizontal spring 4, a first roller 5, an X-shaped rod 6, an upper platform 7, a groove structure 8, a guide rail platform 9, a fixed support 10, a sliding plate support 11, a first pin 16, a second pin 12, a second roller 14, a third pin 13, a fourth pin 15, a threaded screw 17, a handle 18 and a push block 19.

[0076] The lower platform 1 and the upper platform 7 are spaced apart from each other, specifically, spaced apart and parallel to each other.

[0077] There are two fixing seats 2, which are respectively installed on two surfaces of the lower platform 1 and the upper platform 7 facing each other and are arranged opposite to each other. Specifically, the fixing seat 2 is a double-ear fixing seat.

[0078] There are two X-shaped rods 6, one end of which is hinged to the fixing seat 2 on the lower platform 1, and the other end is equipped with the first roller 5 and abuts against the upper platform 7 through the first roller 5; one end of another X-shaped rod 6 is hinged to the fixing seat 2 on the upper platform 7, and the other end is equipped with the first roller 5 and abuts against the lower platform 1 through the first roller 5. It should be noted that the X-shaped rod is hinged to the fixing seats on the upper and lower platforms respectively through the second pin, and the first roller 5 is hinged to the two X-shaped rods 6 respectively through the third pin 13.

[0079] The intersection of the two X-shaped rods 6 is hinged by the first pin 16 to form an X-shaped rod structure, so that the two X-shaped rods 6 can rotate relative to each other. In addition, since one end of the two X-shaped rods 6 is in contact with the lower platform 1 and the upper platform 7 respectively through the first roller 5, the X-shaped rod 6 can be moved left and right relative to the upper and lower platforms.

[0080] The groove structure 8 is fixed on the X-shaped rod 6. Specifically, the length direction of the groove structure 8 is arranged at a certain angle with the X-shaped rod 6. Of course, the angle can be adjusted as needed.

[0081] The guide rail platform 9 is installed on the lower platform 1 , and a guide rail (not numbered) is provided on the top of the guide rail platform 9 .

[0082] The fixed support 10 is fixedly mounted on the top of the guide rail platform 9 .

[0083] The threaded screw 17 is mounted on the fixed support 10 and is threadedly connected to the fixed support 10 , so that the threaded screw 17 can be moved relative to the fixed support 10 by rotating the threaded screw 17 .

[0084] The sliding plate support 11 is mounted on the top of the guide rail platform 9 and can move along the track.

[0085] The handle 18 and the push block 19 are respectively mounted on both ends of the threaded screw 17 and the push block 19 abuts against the sliding plate support 11. Specifically, the handle 18 is a five-pointed star handle for easy gripping.

[0086] The push rod 3 is mounted on the sliding plate support 11 and can move along the sliding plate support 11, and the second roller 14 is rotatably mounted on one end of the push rod 3 and abuts against the groove structure 8. Specifically, the second roller 14 is hinged to the push rod 3 through a fourth pin 15. The groove structure 8 is provided with a groove that matches the second roller 14, and the cross-section of the groove can be designed into a variety of different curved shapes. The present invention takes a straight line shape as an example.

[0087] The horizontal spring 4 is sleeved on the push rod 3 and one end is fixed to the other end of the push rod 3, and the other end is fixed to the sliding plate support 11. In this way, the sliding plate support 11 can be controlled to move along the slide rail by the threaded screw 17 to adjust the pre-tensioning amount of the horizontal spring 4. It should be further explained that a damper can be added to the position of the horizontal spring 4, so that nonlinear damping can also be generated.

[0088] In order to prevent the sliding plate support 11 from being subjected to excessive bending moment, the slide rail is installed at a certain height and an additional push block 19 with a larger contact area than the threaded screw 17 is added to the sliding plate support 11. The threaded screw 17 contacts the push block 19 to push the sliding plate support 11 along the guide rail to control the preload force of the horizontal spring 4.

[0089] The present invention also provides a design method for the nonlinear stiffness suspension, which comprises the following steps:

[0090] Step 1: Recombination Figure 3 As shown, assuming that the inclination angle between the X-shaped rod 6 with the groove structure 8 and the horizontal plane is θ at a certain moment, and further assuming that the groove structure 8 is installed at point A, a ts coordinate system is established with point A as the origin, and the curve equation of the groove structure 8 in the ts coordinate system is but The contact point of the second roller 14 on the groove structure 8 corresponds to the inclination angle of the groove structure 8 at point M. Then, a yx coordinate system is established at the center axis O of the fixed seat 2. The conversion relationship between the curve equation of the groove structure 8 in the two coordinate systems can be expressed by the following equations (1) to (3):

[0091]

[0092] That is:

[0093]

[0094]

[0095] Among them, s is the horizontal coordinate in the ts coordinate system, l is the distance between the installation point and the lower end of the X-bar;

[0096] Step 2: Assume the coordinates of the contact point M in the ts coordinate system are The installation height of the horizontal spring is H, and the coordinates of the contact point M in the yx coordinate system are (x M , H); let y = H in formula (3), Substituting in s M The relationship with θ is:

[0097] s M =f1(θ) (4)

[0098] Among them, f1 is the function symbol used to represent s M Relationship with θ;

[0099] Substituting equation (4) into equation (2), we can get the horizontal coordinate x of the contact point M in the yx coordinate system: M It is expressed by θ, which is:

[0100] x M =f2(θ) (5)

[0101] Among them, f2 is the function symbol used to represent x M Relationship with θ;

[0102] Step 3: Assume that the initial inclination angle of the X-shaped rod is θ0, then the initial horizontal coordinate of point M in the yx system can be expressed as:

[0103]

[0104] Therefore, the change in the horizontal spring extension Δx can be expressed as:

[0105]

[0106] Among them, x M is the horizontal coordinate of point M at any time in the yx coordinate system, is the horizontal coordinate of the initial equilibrium state of point M in the yx coordinate system;

[0107] Step 4: Assume the pre-stretching amount of the horizontal spring is δ0 and the elastic coefficient is k h , then the spring force f h Given by:

[0108] f h =k h (δ0+Δx) (8)

[0109] From equations (5), (6), (7), (8) and the given initial tilt angle θ0, the spring force f can be obtained: h Relationship with the rod inclination angle θ:

[0110] f h =f3(θ) (9)

[0111] Among them, f3 is the function symbol used to represent f h Relationship with the rod inclination angle θ;

[0112] The vertical displacement h of the upper platform can be given by:

[0113] h=L(sinθ0-sinθ) (10)

[0114] Where L is the total length of the X-bar;

[0115] For the whole structure composed of X-shaped structure, groove structure and roller-push rod structure, the virtual work equation is as follows:

[0116] δW=0 (11)

[0117] Among them, δ represents a tiny amount, and w is the total virtual work produced by the virtual displacement;

[0118] Right now:

[0119] F·δy G +f h ·δx M =0 (12)

[0120] Write the coordinate y of point G using θ as the parameter G :

[0121] y G =Lsinθ (13)

[0122] Its variations are:

[0123] δy G =Lcosθδθ (14)

[0124] Coordinate x of point M M Given by formula (5), its variation is:

[0125] δx M =f2′(θ)δθ (15)

[0126] Among them, f2′ is the characterization of x M The function sign of the derivative with respect to θ;

[0127] Substituting equations (15) and (16) into equation (13) and combining them with equation (9), we can obtain the relationship between load F and rod inclination angle θ, namely:

[0128] F=f5(θ) (16)

[0129] Among them, f5 is the function symbol used to represent the relationship between F and the rod inclination angle θ;

[0130] From formula (10), we get:

[0131]

[0132] Substituting equation (17) into equation (16), we can obtain the relationship between load force F and vertical displacement h:

[0133] F=f6(h) (18)

[0134] Among them, f6 is the function symbol used to represent the relationship between F and the vertical displacement h;

[0135] Therefore, the system stiffness can be obtained as follows:

[0136] K=f6′(h) (19)

[0137] Wherein, f6′ is the function symbol representing the derivative of F with respect to h.

[0138] It should be further explained that the X-shaped structure is composed of an upper platform 7 , a lower platform 1 and two X-shaped rods 6 .

[0139] The beneficial effects of the present invention are as follows:

[0140] 1. Compared with the traditional roller-cam structure, the roller-groove structure in the present invention is easier to achieve movement with a larger stroke and has good nonlinear stiffness characteristics, thereby being able to achieve nonlinear stiffness within a larger displacement range;

[0141] 2. The inclination angle of the groove structure is adjustable, which has more applicable occasions. In addition, the contact surface of the groove can be any curved shape to meet the needs of different tasks;

[0142] 3. The groove installed in the present invention can be adjusted, including the adjustment of the installation angle and the adjustment of the groove shape curve, so as to obtain various stiffness characteristics to meet various vibration reduction scenarios and solve various practical needs. For example, it can be adjusted according to actual conditions for motorized equipment such as ships to effectively reduce the risk of equipment damage, and it can be used for seat vibration reduction to adapt to different road excitations to increase seat comfort.

[0143] 4. The idea provided by the present invention is not limited to realizing nonlinear stiffness. A damper can be placed at the structure where the horizontal spring is installed to generate nonlinear damping to achieve different characteristics. Therefore, the idea provided by the present invention can realize both nonlinear stiffness and nonlinear damping.

[0144] Although the embodiments of the present invention have been disclosed as above, they are not limited to the applications listed in the specification and the embodiments. They can be fully applied to various fields suitable for the present invention. For those familiar with the art, additional modifications can be easily implemented. Therefore, without departing from the general concept defined by the claims and the scope of equivalents, the present invention is not limited to the specific details and the illustrations shown and described herein.

Claims

1. A nonlinear stiffness suspension, characterized in that: The invention comprises a lower platform, a fixed seat, a push rod, a horizontal spring, a first roller, an X-shaped rod, an upper platform, a groove structure, a guide rail platform, a fixed support, a sliding plate support, a first pin, a second pin, a second roller, a third pin, a fourth pin, a threaded screw, a handle and a push block. The lower platform and the upper platform are arranged at an interval up and down. There are two fixed seats, which are respectively installed on two surfaces of the lower platform and the upper platform facing each other and are arranged facing each other. There are two X-shaped rods, one end of which is hinged to the fixed seat on the lower platform, and the other end is equipped with the first roller and abuts against the upper platform through the first roller. One end of the other X-shaped rod is hinged to the fixed seat on the upper platform, and the other end is equipped with the first roller and abuts against the lower platform through the first roller. The two X-shaped rods are arranged at an interval up and down. The intersection of the X-shaped rod is hinged by the first pin; the groove structure is fixed on the X-shaped rod; the guide rail platform is installed on the lower platform, and a guide rail is provided on the top of the guide rail platform, the fixed support is fixed on the top of the guide rail platform, the threaded screw is installed on the fixed support and is threadedly connected with the fixed support, the sliding plate support is installed on the top of the guide rail platform and can move along the track, the handle and the push block are respectively installed on the two ends of the threaded screw and the push block abuts against the sliding plate support, the push rod is assembled on the sliding plate support and can move along the sliding plate support, the second roller is rotatably installed on one end of the push rod and abuts on the groove structure, the horizontal spring is sleeved on the push rod and one end is fixed on the other end of the push rod, and the other end is fixed on the sliding plate support.

2. A nonlinear stiffness suspension according to claim 1, characterized in that: The X-shaped rod is hinged to the fixing seats on the upper and lower platforms respectively through the second pin.

3. The nonlinear stiffness suspension according to claim 1, characterized in that: The first roller is hinged to the two X-shaped rods respectively through a third pin.

4. The nonlinear stiffness suspension according to claim 1, characterized in that: The second roller is hinged to the push rod through a fourth pin.

5. The nonlinear stiffness suspension according to claim 1, characterized in that: The fixing seat is a double-ear fixing seat.

6. The nonlinear stiffness suspension according to claim 1, characterized in that: The handle is a five-pointed star handle.

7. A method for designing a nonlinear stiffness suspension according to any one of claims 1 to 6, characterized in that: The design method includes the following steps: Step 1: Assume that the inclination angle between the X-shaped bar with the slot structure and the horizontal plane is θ at a certain moment, and further assume that the slot structure is installed at point A, then establish a ts coordinate system with point A as the origin. The curve equation of the slot structure in the ts coordinate system is: but The contact point of the second roller on the groove structure is point M, corresponding to the inclination angle of the groove structure. Then, a yx coordinate system is established at the center axis O of the fixed seat. The conversion relationship between the curve equation of the slot structure in the two coordinate systems can be expressed by the following equations (1) to (3): That is: Among them, s is the horizontal coordinate in the ts coordinate system, l is the distance between the installation point and the lower end of the X-bar; Step 2: Assume the coordinates of the contact point M in the ts coordinate system are The installation height of the horizontal spring is H, and the coordinates of the contact point M in the yx coordinate system are (x M , H); let y = H in formula (3), Substituting in s M The relationship with θ is: s M =f1(θ) (4) Among them, f1 is the function symbol used to represent s M Relationship with θ; Substituting equation (4) into equation (2), we can get the horizontal coordinate x of the contact point M in the yx coordinate system: M It is expressed by θ, which is: x M =f2(θ) (5) Among them, f2 is the function symbol used to represent x M Relationship with θ; Step 3: Assume that the initial inclination angle of the X-shaped rod is θ0, then the initial horizontal coordinate of point M in the yx system can be expressed as: Therefore, the change in the horizontal spring extension Δx can be expressed as: Among them, x M is the horizontal coordinate of point M at any time in the yx coordinate system, is the horizontal coordinate of the initial equilibrium state of point M in the yx coordinate system; Step 4: Assume the pre-stretching amount of the horizontal spring is δ0 and the elastic coefficient is k h , then the spring force f h Given by: f h =k h (δ0+Δx) (8) From equations (5), (6), (7), (8) and the given initial tilt angle θ0, we can get the spring force f h Relationship with the rod inclination angle θ: f h =f3(θ) (9) Among them, f3 is the function symbol used to represent f h Relationship with the rod inclination angle θ; The vertical displacement h of the upper platform can be given by: h=L(sinθ0-sinθ) (10) Where L is the total length of the X-bar; For the whole structure composed of X-shaped structure, groove structure and roller-push rod structure, the virtual work equation is as follows: δW=0 (11) Among them, δ represents a tiny amount, and W is the total virtual work produced by the virtual displacement; Right now: F·δy G +f h ·δx M =0 (12) Write the coordinate y of point G using θ as the parameter G : y G =Lsinθ (13) Its variations are: δy G =Lcosθδθ (14) Coordinate x of point M M Given by formula (5), its variation is: δx M =f2′(θ)δθ (15) Among them, f2′ is the characterization of x M The function sign of the derivative with respect to θ; Substituting equations (15) and (16) into equation (13) and combining them with equation (9), we can obtain the relationship between load F and rod inclination angle θ, namely: F=f5(θ) (16) Among them, f5 is the function symbol used to represent the relationship between F and the rod inclination angle θ; From formula (10), we can get: Substituting equation (17) into equation (16), we can obtain the relationship between load force F and vertical displacement h: F=f6(h) (18) Among them, f6 is the function symbol used to represent the relationship between F and the vertical displacement h; Therefore, the system stiffness can be obtained as follows: K=f6′(h) (19) Wherein, f6′ is the function symbol representing the derivative of F with respect to h.

8. The design method of a nonlinear stiffness suspension according to claim 7, characterized in that: The X-shaped structure consists of an upper platform, a lower platform and two X-shaped rods.

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