A vibration isolation design method for casting vibration conveying equipment

Abstract

The present invention discloses a vibration isolation design method for casting vibration conveying equipment. The invention includes: performing vibration analysis on the vibration conveying equipment according to the initial scheme to obtain the vibration response, and determining the final scheme according to the comparison result between the vibration response and the allowable vibration requirement, wherein the initial scheme includes non-vibration isolation design and vibration isolation design, the non-vibration isolation design includes the vibration conveying equipment and the non-vibration isolation calculation model, the non-vibration isolation calculation model includes two-degree-of-freedom equations and six-degree-of-freedom equations, the vibration isolation design includes the vibration conveying equipment, the vibration isolation unit and the vibration isolation calculation model, and the vibration isolation calculation model includes three-degree-of-freedom equations and nine-degree-of-freedom equations. Through the present invention, the problem of large workload and low efficiency of traditional vibration isolation scheme design and analysis in the related art is solved.

Description

Technical Field

[0001] The invention relates to the technical field of vibration control, and in particular to a vibration isolation design method for casting vibration conveying equipment. Background Art

[0002] The design of the power machine foundation is crucial for vibration control of the foundation itself and the surrounding environment. The role of the power machine foundation is to ensure that the equipment can operate normally and that the surrounding environment meets the requirements of the allowable vibration limit. Regarding the active vibration isolation design of the power machine foundation, there are mainly two types of solutions commonly used. One is to use a heavy block concrete structure, commonly known as the "rigid solution"; the other is to use a vibration isolation unit device for vibration isolation, commonly known as the "flexible solution."

[0003] Basic vibration control solutions have been widely used in industrial engineering, especially in the field of large power machine foundations and micro-vibration control, and are very mature vibration control solutions.

[0004] There are many methods for vibration calculation and analysis, including the vibration response method of solving dynamic equations (also known as dynamic numerical integration method) and finite element software simulation method. There are many numerical methods for solving the dynamic response of mechanical systems, such as the Newmark method, Runge-Kutta method, central difference method, etc. Their main idea is to convert the dynamic equations corresponding to the structure into a set of linear algebraic equations for solution. This method is relatively mature and will not be repeated here. The finite element simulation method usually uses large-scale finite element software, such as Sap2000, Abaqus, Ansys, etc., to model the mechanical system in the finite element software, and then solve the dynamic response of the structure. With the improvement of computer computing power and the development of large-scale finite element software, the finite element simulation method has been widely used.

[0005] In the prior art, the technical problems of large workload and low efficiency in the design and analysis of traditional vibration isolation schemes have not yet been effectively solved.

[0006] Currently, no effective solution has been proposed for the above-mentioned problems existing in the related technologies. Summary of the invention

[0007] The purpose of the present invention is to provide a vibration isolation design method for casting vibration conveying equipment to solve the problems of large workload and low efficiency in the design and analysis of traditional vibration isolation schemes in the related art.

[0008] In order to achieve the above object, the present invention adopts the following technical solutions:

[0009] A vibration isolation design method for casting vibration conveying equipment comprises: performing vibration analysis on the vibration conveying equipment according to an initial scheme to obtain a vibration response, and determining a final scheme according to a comparison result between the vibration response and an allowable vibration requirement, wherein the initial scheme comprises a non-vibration isolation design and a vibration isolation design, the non-vibration isolation design comprises a vibration conveying equipment and a non-vibration isolation calculation model, the non-vibration isolation calculation model comprises a two-degree-of-freedom equation and a six-degree-of-freedom equation, the vibration isolation design comprises a vibration conveying equipment, a vibration isolation unit and a vibration isolation calculation model, and the vibration isolation calculation model comprises a three-degree-of-freedom equation and a nine-degree-of-freedom equation; when the initial scheme is a non-vibration isolation design, if the comparison result meets the requirement, the initial scheme is determined to be the final scheme; when the initial scheme is a non-vibration isolation design, if the comparison result does not meet the requirement, the initial scheme is modified to a vibration isolation design; when the initial scheme is a vibration isolation design, if the comparison result meets the requirement, the initial scheme is determined to be the final scheme; when the initial scheme is a vibration isolation design, if the comparison result does not meet the requirement, the vibration isolation design is optimized until the comparison result of the vibration response meets the requirement, and then the final scheme is determined.

[0010] Furthermore, a non-vibration isolation calculation model is determined based on the structural characteristics of the vibrating conveying equipment and the exciting force; and a vibration isolation calculation model is determined based on the structural characteristics of the vibrating conveying equipment, the vibration isolation unit and the exciting force.

[0011] Furthermore, when the exciting force is in a vertical direction and the line of action passes through the center of gravity of the vibration conveying equipment, the stiffness center of the vibration isolator of the vibration conveying equipment, the center of gravity of the foundation and the stiffness center of the elastic effect of the soil on the foundation, the non-vibration isolation calculation model is determined to be a two-degree-of-freedom equation; when the exciting force is in a vertical direction and its line of action does not pass through the center of gravity of the vibration conveying equipment, the stiffness center of the vibration isolator of the vibration conveying equipment, the center of gravity of the foundation and the stiffness center of the elastic effect of the soil on the foundation, the non-vibration isolation calculation model is determined to be a six-degree-of-freedom equation; when the exciting force is not in a vertical direction, the non-vibration isolation calculation model is determined to be a six-degree-of-freedom equation.

[0012] Furthermore, the vibration response amplitude is calculated based on the two-degree-of-freedom equation; and the vibration response is calculated based on the six-degree-of-freedom equation.

[0013] Furthermore, a two-degree-of-freedom periodic function group is obtained based on the two-degree-of-freedom equation, and a two-degree-of-freedom vibration response amplitude is obtained, wherein the two-degree-of-freedom vibration response amplitude includes an equipment amplitude equation and a vibration amplitude equation; the first-order derivatives and second-order derivatives corresponding to the two-degree-of-freedom periodic function group are substituted into the two-degree-of-freedom equation to solve and obtain the undetermined coefficients; the undetermined coefficients are substituted into the two-degree-of-freedom vibration response amplitude to obtain the equipment amplitude and the vibration displacement amplitude.

[0014] Furthermore, a first motion equation is established for the mass of the moving part of the vibration conveying equipment; a second motion equation is established for the sum of the non-moving part of the vibration conveying equipment and the foundation mass; damping is added to the first motion equation and the second motion equation to obtain a final dynamic equation with six degrees of freedom, and the final dynamic equation with six degrees of freedom is calculated to obtain the vibration response.

[0015] Furthermore, when the exciting force is in a vertical direction and the line of action passes through the center of gravity of the vibration conveying equipment, the stiffness center of the vibration isolator of the vibration conveying equipment, the mass center of the vibration isolation unit, the stiffness center of the vibration isolation unit, the center of gravity of the foundation and the stiffness center of the elastic effect of the soil on the foundation, the vibration isolation calculation model is determined to be a three-degree-of-freedom equation; when the exciting force is in a vertical direction and the line of action does not pass through the center of gravity of the vibration conveying equipment, the stiffness center of the vibration isolator of the vibration conveying equipment, the mass center of the vibration isolation unit, the stiffness center of the vibration isolation unit, the center of gravity of the foundation and the stiffness center of the elastic effect of the soil on the foundation, the vibration isolation calculation model is determined to be a nine-degree-of-freedom equation; when the exciting force is not in a vertical direction, the vibration isolation calculation model is determined to be a nine-degree-of-freedom equation.

[0016] Furthermore, the vibration response amplitude is calculated based on the three-degree-of-freedom equation; and the vibration response is calculated based on the nine-degree-of-freedom equation.

[0017] Furthermore, a three-degree-of-freedom periodic function group is obtained based on the three-degree-of-freedom equation, and a three-degree-of-freedom amplitude equation group is obtained, wherein the three-degree-of-freedom amplitude equation group includes a device amplitude equation, a vibration isolation unit amplitude equation and a vibration amplitude equation; the first-order derivatives and second-order derivatives corresponding to the three-degree-of-freedom periodic function group are substituted into the three-degree-of-freedom equation to solve and obtain the undetermined coefficients; the undetermined coefficients are substituted into the three-degree-of-freedom amplitude equation group to obtain the device amplitude, the vibration isolation unit amplitude and the vibration amplitude.

[0018] Furthermore, a third motion equation is established for the mass of the moving part of the vibrating conveying equipment; a fourth motion equation is established for the sum of the mass of the non-moving part of the vibrating conveying equipment and the vibration isolation unit; a fifth motion equation is established for the foundation mass; the third motion equation, the fourth motion equation and the fifth motion equation are added with damping to obtain a final dynamic equation with nine degrees of freedom, and the final dynamic equation with nine degrees of freedom is calculated to obtain the vibration response.

[0019] Compared with the prior art, the beneficial technical effects of the present invention are:

[0020] 1. The present invention assumes that the mechanical model of the casting vibration conveying equipment and its basic components is a two-degree-of-freedom model or a six-degree-of-freedom model according to its own characteristics and exciting force properties; the mechanical model of the casting vibration conveying equipment, the vibration isolation unit and the basic components is assumed to be a three-degree-of-freedom model or a nine-degree-of-freedom model according to its own characteristics and exciting force properties. Dynamic equations are established for the above four mechanical models respectively, and the solutions of the dynamic equations are converted into solutions of a multivariate linear equation group. By solving a multivariate linear equation group, the basic vibration response can be obtained, and then the vibration isolation efficiency of the vibration isolation system can be obtained. This method can not only meet the vibration isolation efficiency requirements analyzed by structural engineers, but also has good versatility, especially when considering a variety of vibration isolation design schemes, it has the advantages of simplicity and convenience.

[0021] 2. Analysis based on finite element software is also one of the commonly used methods for vibration calculation and analysis of equipment and its foundation mechanical model. Finite element-based vibration calculation and analysis is to divide the equipment and its foundation into multiple solid units, consider thousands or tens of thousands of degrees of freedom, and fully consider the elastic effects of the equipment itself, the vibration isolation unit (the counterweight mass block is usually a concrete structure) and the foundation. However, these contents are not the key factors to consider when performing vibration analysis on the system. On the contrary, considering the elastic effects of these objects makes it difficult for structural engineers to identify the key factors of vibration control.

[0022] 3. Without changing the process requirements of the vibration conveyor line and the process conditions of the casting vibration conveyor equipment itself, a vibration isolation design is adopted between the vibration conveyor equipment and the foundation. That is, by adding a set of vibration isolation units (concrete counterweight mass block + vibration isolator, the vibration isolation unit usually includes technical parameters of mass, stiffness and damping) between the equipment and its foundation, the transmission and impact of the large vibration of the vibration conveyor equipment to the surrounding environment can be reduced. This design method does not depend on the technical parameters of the vibration conveyor equipment, has strong versatility, and is not only suitable for initial design projects, but also more suitable for renovation design projects.

[0023] 4. By adopting a vibration isolation design scheme for the vibrating conveying equipment, the vibration response of the conveying equipment foundation will be significantly reduced, effectively reducing the vibration impact of the vibrating conveying equipment on the surrounding environment, buildings, adjacent machining equipment and human body during operation. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] In order to more clearly illustrate the specific implementation methods of the present invention or the technical solutions in the prior art, the drawings required for use in the specific implementation methods or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are some implementation methods of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0025] Figure 1 It is a flow chart of a vibration isolation design method for casting vibration conveying equipment;

[0026] Figure 2 Flow chart for basic vibration calculation and analysis of casting vibration conveying equipment;

[0027] Figure 3 It is a schematic diagram of a two-degree-of-freedom system;

[0028] Figure 4 It is a schematic diagram of a six-degree-of-freedom system;

[0029] Figure 5 This is a schematic diagram of the vibration isolation design scheme for vibrating conveying equipment;

[0030] Figure 6 It is a schematic diagram of a three-degree-of-freedom system;

[0031] Figure 7 Schematic diagram of the nine-degree-of-freedom system.

[0032] Figure numerals: 1. Vibrating conveying equipment; 2. Concrete counterweight mass block; 3. Foundation; 4. Vibration isolation device. DETAILED DESCRIPTION

[0033] The technical solution of the present invention will be described clearly and completely below in conjunction with the accompanying drawings. 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.

[0034] In the description of the present invention, it should be noted that the terms "center", "upper", "lower", "left", "right", "vertical", "horizontal", "inner", "outer", etc., indicating the orientation or positional relationship, are based on the orientation or positional relationship shown in the drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as limiting the present invention. In addition, the terms "first", "second", and "third" are used for descriptive purposes only, and cannot be understood as indicating or implying relative importance.

[0035] In the description of the present invention, it should be noted that, unless otherwise clearly specified and limited, the terms "installed", "connected", and "connected" should be understood in a broad sense, for example, it 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 it can be indirectly connected through an intermediate medium, or it can be the internal communication of two components. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0036] Example

[0037] Reference Figure 1 , which is a vibration isolation design method for casting vibration conveying equipment disclosed in the present invention, and the invention includes:

[0038] Step S101, according to the initial plan, vibration analysis is performed on the vibration conveying equipment 1 to obtain the vibration response, and the final plan is determined according to the comparison result between the vibration response and the allowable vibration requirement, wherein the initial plan includes non-vibration isolation design and vibration isolation design, the non-vibration isolation design includes the vibration conveying equipment 1 and the non-vibration isolation calculation model, the non-vibration isolation calculation model includes two-degree-of-freedom equations and six-degree-of-freedom equations, the vibration isolation design includes the vibration conveying equipment 1, the vibration isolation unit and the vibration isolation calculation model, the vibration isolation calculation model includes three-degree-of-freedom equations and nine-degree-of-freedom equations; the vibration isolation unit includes mass, stiffness and damping, that is, the concrete counterweight block and the vibration isolation device 4.

[0039] Step S102, when the initial solution is a non-vibration isolation design and the comparison result meets the requirements, the initial solution is determined as the final solution;

[0040] Step S103, when the initial solution is a non-vibration isolation design and the comparison result does not meet the requirements, the initial solution is modified to a vibration isolation design;

[0041] Step S104, when the initial solution is a vibration isolation design and the comparison result meets the requirements, the initial solution is determined as the final solution;

[0042] Step S105, when the initial solution is a vibration isolation design and the comparison result does not meet the requirements, the vibration isolation design is optimized until the vibration response meets the comparison result and the final solution is determined.

[0043] exist Figure 2 The basic vibration calculation and analysis process framework diagram of the casting vibration conveying equipment 1 shows the basic design process of the casting vibration conveying equipment 1, especially the calculation and analysis of the vibration response of the foundation 3 based on the exciting forces of different properties. Figure 2 The steps for the dashed box content shown in the figure are as follows:

[0044] Step (1) Determine the calculation model based on the basic preliminary design plan:

[0045] When designing the foundation of the vibrating conveying equipment 1, a non-vibration isolation design is usually adopted. Only when the non-vibration isolation design does not meet the vibration tolerance requirements, the vibration isolation design will be considered. Therefore, considering various factors such as economy and construction, the non-vibration isolation design is preferred. The calculation model of the vibrating conveying equipment 1 and its foundation 3 is determined according to the excitation force characteristics of the vibrating conveying equipment 1.

[0046] Step (2) Establish the kinetic equation of the calculation model:

[0047] According to the calculation model of the vibrating conveying device 1 and its foundation 3, the dynamic equation of the mechanical system is established, and the vibration response and vibration isolation efficiency of the foundation 3 are quickly solved based on the numerical method established in the present invention.

[0048] Step (3) determines whether the vibration response of foundation 3 meets the allowable vibration requirements:

[0049] The vibration response of the foundation 3 calculated in step (2) is compared with the allowable vibration requirement of the surrounding environment. If the comparison result meets the allowable vibration requirement of the environment, the casting vibration conveying device 1 can adopt the initial solution; if the comparison result does not meet the allowable vibration requirement of the environment, proceed to step (4). In addition, when judging whether the vibration response of the foundation 3 meets the allowable vibration requirement, if the comparison result does not meet the allowable vibration requirement of the environment, and the vibration value of the foundation 3 is not much different from the allowable value of the environment, the preliminary design of the foundation 3 can be readjusted and the vibration response of the foundation 3 can be solved again.

[0050] Step (4) Determine the vibration isolation design scheme and complete the preliminary design of the vibration isolation foundation:

[0051] When the conventional foundation design of the casting vibration conveying equipment 1 cannot meet the requirements of allowable vibration, vibration isolation design is required. There are many vibration isolation design schemes. The patent of the present invention mainly considers the "flexible scheme" in the active vibration isolation scheme, that is, adding a set of vibration isolation units between the casting vibration conveying equipment 1 and its foundation 3. Based on the vibration isolation design scheme, the preliminary design of the foundation 3 is completed.

[0052] Step (5) Determine the calculation model of the system based on the vibration isolation design scheme adopted:

[0053] According to the calculation model after adopting the vibration isolation design scheme, the calculation model of the casting vibration conveying equipment 1, the vibration isolation unit and the foundation 3 is determined according to the exciting force characteristics of the vibration conveying equipment 1 and the assumed conditions of the entire mechanical system.

[0054] Step (6) Establish the dynamic equation of the calculation model after adopting the vibration isolation design scheme:

[0055] According to the calculation model of the vibrating conveying equipment 1, the vibration isolation unit and the foundation 3, the dynamic equation of the mechanical system is established, and the vibration response of the foundation 3 is quickly solved based on the numerical method established in the patent of the present invention.

[0056] Step (7) determines whether the vibration response of foundation 3 meets the allowable vibration requirements:

[0057] The vibration response of the foundation 3 calculated in step (6) is compared with the allowable vibration requirements of the surrounding environment, and the comparison result can be fed back to the vibration isolation design scheme of the foundation, and the vibration isolation foundation 3 design scheme is optimized to be economical, reasonable and effective. If the vibration of the foundation 3 meets the allowable vibration requirements of the environment, the casting vibration conveying equipment 1 can adopt the vibration isolation design scheme; if the vibration of the foundation 3 does not meet the allowable vibration requirements of the environment, other vibration isolation design schemes are considered, or multiple vibration isolation design schemes are adopted at the same time.

[0058] Specifically, it is determined whether the vibration response of the foundation 3 meets the allowable vibration requirements: since there are many vibration equipment in the sand processing workshop, there are also many machining equipment that are susceptible to vibration. In addition to meeting the corresponding national standards and specifications, the vibration response of the foundation of the casting vibration conveying equipment 1 should also meet the allowable vibration requirements of the surrounding environment. When the vibration of the foundation of the casting vibration conveying equipment 1 cannot meet the allowable vibration requirements of the surrounding environment, corresponding vibration reduction and isolation measures need to be taken. There are many vibration reduction and isolation measures, including active vibration isolation technology for the casting vibration conveying equipment 1, passive vibration isolation technology for vibration-sensitive equipment, and corresponding barrier vibration isolation technology for the propagation path. The latter two vibration reduction and isolation technologies are not involved in the present invention, and the active vibration isolation technology for the casting vibration conveying equipment 1 is emphasized in the implementation steps below. In addition, when judging whether the vibration response of the foundation meets the allowable vibration requirements, if the vibration response does not meet the allowable vibration requirements of the environment, and the foundation vibration value is not much different from the allowable value of the environment, the preliminary design of the foundation 3 can be readjusted and the vibration response can be solved again.

[0059] In an optional embodiment, a non-vibration isolation calculation model is determined based on the structural characteristics of the vibrating conveying equipment 1 and the exciting force; and a vibration isolation calculation model is determined based on the structural characteristics of the vibrating conveying equipment 1, the vibration isolation unit and the exciting force.

[0060] Specifically, there are many casting vibration conveying equipment 1, such as vibration conveying troughs, vibration sand-falling conveyors, boiling cooling beds, and eccentric connecting rod conveyors. When designing the foundation 3 of these devices, they are usually set as independent foundations 3. By understanding the structural characteristics, exciting force properties, and preliminary design scheme of the foundation 3 of the casting vibration conveying equipment 1, the calculation model of the mechanical system composed of the equipment and the foundation 3 is determined. The casting vibration conveying equipment 1 usually has a vibration isolation device, which not only reduces the vibration impact on the foundation 3 when the equipment is running, but also enables the equipment to operate to meet the conditions required by its process.

[0061] When performing vibration calculations and analysis, the following two assumptions need to be considered:

[0062] 1) As mentioned above, the casting vibration conveying device 1 itself can be divided into a moving part and a non-moving part, which are connected by a spring unit (stiffness and damping). When performing vibration analysis, the upper and lower parts of the spring unit need to be considered separately;

[0063] 2) When calculating and analyzing the vibration response of the equipment foundation 3, the soil under the foundation 3 needs to be regarded as an elastic medium, which can be converted into a spring unit (stiffness and damping). When the foundation 3 adopts a pile foundation, it can also be converted into a spring unit (stiffness and damping) according to the "Design Standard for Power Machinery Foundation" GB50040.

[0064] In an optional embodiment, when the exciting force is in a vertical direction and the line of action passes through the center of gravity of the vibration conveying equipment 1, the stiffness center of the vibration isolator of the vibration conveying equipment 1, the center of gravity of the foundation 3 and the stiffness center of the elastic effect of the soil on the foundation 3, the non-vibration isolation calculation model is determined to be a two-degree-of-freedom equation; when the exciting force is in a vertical direction and its line of action does not pass through the center of gravity of the vibration conveying equipment 1, the stiffness center of the vibration isolator of the vibration conveying equipment 1, the center of gravity of the foundation 3 and the stiffness center of the elastic effect of the soil on the foundation 3, the non-vibration isolation calculation model is determined to be a six-degree-of-freedom equation; when the exciting force is not in a vertical direction, the non-vibration isolation calculation model is determined to be a six-degree-of-freedom equation.

[0065] Specifically, the dynamic system of two-degree-of-freedom equations is as follows Figure 3 As shown, the dynamic system of the six-degree-of-freedom equation is as follows Figure 4 shown.

[0066] In an optional embodiment, the vibration response amplitude is calculated based on the two-degree-of-freedom equation; a two-degree-of-freedom periodic function group is obtained based on the two-degree-of-freedom equation, and the two-degree-of-freedom vibration response amplitude is obtained, wherein the two-degree-of-freedom vibration response amplitude includes a device amplitude equation and a vibration amplitude equation; the first-order derivatives and second-order derivatives corresponding to the two-degree-of-freedom periodic function group are substituted into the two-degree-of-freedom equation to solve and obtain undetermined coefficients; the undetermined coefficients are substituted into the two-degree-of-freedom vibration response amplitude to obtain the device amplitude and the vibration displacement amplitude.

[0067] Specifically, under the action of vertical non-eccentric load, the casting conveying equipment and its foundation 3 system can be simplified as follows: Figure 3 The two-degree-of-freedom computational model shown.

[0068] In such Figure 3 The mechanical system composed of the device and foundation 3 shown in the figure, Represents the upper mass of the spring unit in the device (mass of the moving part); It represents the sum of the mass of the lower part of the spring unit (mass of non-moving parts), the mass of foundation 3 and the mass of the vibration soil in the equipment; and They represent the stiffness and damping of the spring unit in the device respectively; and represent the stiffness and damping of the foundation soil below foundation 3 respectively.

[0069] Under the load dominated by vertical exciting force, Figure 1 The mechanical system composed of the equipment and the foundation 3 can be simplified into a two-degree-of-freedom system, and the two-degree-of-freedom equation is shown in the following formula (1):

[0070] [ m 1 0 0 m 3 ] [ x ¨ 1 x ¨ 3 ] + [ c 1 − c 1 − c 1 c 1 + c 3 ] [ x ˙ 1 x ˙ 3 ] + [ k 1 − k 1 − k 1 k 1 + k 3 ] [ x 1 x 3 ] = [ F sin ( oh t ) 0 ] (1)

[0071] in and Represents the mass points The vibration acceleration and vibration velocity, and Respectively Vibration acceleration and vibration velocity.

[0072] There are many methods for solving the dynamic equations, such as the Newmark method, the Runge-Kutta method, and the central difference method. The main idea of ​​these methods is to convert the dynamic equations corresponding to the structure into a set of linear algebraic equations for solution, and then perform step-by-step integration to solve them. This method is relatively complex and requires programming or computer calculation to implement.

[0073] In actual engineering, structural engineers are often concerned about the vibration response amplitude of foundation 3. So a method for quickly solving the vibration response of foundation 3 is established below.

[0074] When the equipment is operating normally, the exciting force is a steady-state function, and the solution of the dynamic equation can be assumed to be in the form of the following formula (2):

[0075] (2)

[0076] in , , , , and are all unknown coefficients, and they have the following relationship:

[0077] (3)

[0078] In the formula and Represent the vibration displacement amplitude of the equipment and foundation respectively. Substituting formula (2) and its corresponding first-order derivative and second-order derivative into formula (1), the following formula (4) can be obtained:

[0079] [ ( k 1 − m 1 oh 2 ) C 1 − c 1 oh C 2 − k 1 D 1 + c 1 oh D 2 ] sin ( oh t ) + [ c 1 oh C 1 + ( k 1 − m 1 oh 2 ) C 2 − c 1 oh D 1 − k 1 D 2 ] cos ( oh t ) = F sin ( oh t ) [ − k 1 C 1 + c 1 oh C 2 + ( k 1 + k 3 − m 3 oh 2 ) D 1 − ( c 1 + c 3 ) oh D 2 ] sin ( oh t ) + [ − c 1 oh C 1 − k 1 C 2 + ( c 1 + c 3 ) oh D 1 + ( k 1 + k 3 − m 3 oh 2 ) D 2 ] cos ( oh t ) = 0 (4)

[0080] For any Established, we can get the following formula (5):

[0081] [ k 1 − m 1 oh 2 − c 1 oh − k 1 c 1 oh c 1 oh k 1 − m 1 oh 2 − c 1 oh − k 1 − k 1 c 1 oh ( k 1 + k 3 ) − m 3 oh 2 − ( c 1 + c 3 ) oh − c 1 oh − k 1 ( c 1 + c 3 ) oh ( k 1 + k 3 ) − m 3 oh 2 ] [ C 1 C 2 D 1 D 2 ] = [ F 0 0 0 ] (5)

[0082] In the quaternary linear equation formula (5), the coefficient matrix is ​​a known parameter, so by solving equation (5) we can get , , and , and then according to formula (3) we get and .

[0083] When the equipment is operating normally, the two-freedom system is in forced vibration, and the vibration response of each particle is also in the form of a periodic function, so the vibration displacement response amplitude is and The vibration velocity and vibration acceleration response amplitude can be converted by the following formula (6):

[0084] (6)

[0085] In the above solution process, the solution of the dynamic differential equation (1) is converted into the solution of a set of four-variable linear equations (5). The vibration response can be quickly obtained through equations (3) and (5).

[0086] In an optional embodiment, the vibration response is obtained by calculating the six-degree-of-freedom equation. A first motion equation is established for the mass of the moving part of the vibration conveying device 1; a second motion equation is established for the sum of the mass of the non-moving part of the vibration conveying device 1 and the foundation 3; the first motion equation and the second motion equation are added with damping to obtain a six-degree-of-freedom final dynamic equation, and the six-degree-of-freedom final dynamic equation is calculated to obtain the vibration response.

[0087] Under the action of vertical eccentric load or horizontal load, the casting vibration conveying device 1 and its foundation 3 can be simplified as follows Figure 4 The six degrees of freedom coefficients shown. According to the characteristics of the casting vibration conveying device 1 and its foundation 3, for example Figure 4 In the mechanical model shown, the parameters are described as follows:

[0088] 1) Consider the in-plane motion of the mechanical system, which has a total of 6 degrees of freedom: , and , , and ;

[0089] 2) The geometric shape of the vibration conveying equipment 1 is a rectangular parallelepiped with uniform mass distribution; the geometric shape of the equipment foundation 3 is a rectangular parallelepiped with uniform mass distribution, and the center of gravity is the geometric center;

[0090] 3) The mass of the moving part of the vibration conveying equipment 1 is , the sum of the non-moving parts and the foundation mass of the vibration conveyor 1 equipment is (Usually in vibrating conveying equipment, the moving part has a larger mass and the non-moving part has a smaller mass);

[0091] 4) The moment of inertia about its center of gravity is ; The moment of inertia about its center of gravity is ;

[0092] 5) The vertical stiffness and vertical damping of the two sets of springs below are , , and ; The vertical stiffness and vertical damping of the two sets of springs below are , , and ; The horizontal stiffness of the vertical spring is calculated according to its vertical stiffness times considered, that is ,generally ;

[0093] 6) For , center of gravity and The distance of the line of action is ,and The distance under action is , Center of Gravity The distance from the top and bottom of the device is ;for , center of gravity and The distance of the line of action is ,and The distance of the line of action is , Center of Gravity The distances from the top and bottom of the foundation are ;

[0094] 7) The exciting force only acts on Regardless of the magnitude and direction of the exciting force, it can be converted into , and .

[0095] for Figure 4 Shown Establish the first equation of motion (7):

[0096] m 1 x ¨ 1 = F x − β k 11 [ ( x 1 + l 1 i 1 ) − ( x 3 − l 3 i 3 ) ] − β k 12 [ ( x 1 + l 1 i 1 ) − ( x 3 − l 3 i 3 ) ] m 1 y ¨ 1 = F y − k 11 [ ( y 1 − l 11 i 1 ) − ( y 3 − l 31 i 3 ) ] − k 12 [ ( y 1 + l 12 i 1 ) − ( y 3 + l 32 i 3 ) ] J 1 i ¨ 1 = M i − β k 11 [ ( x 1 + l 1 i 1 ) − ( x 3 − l 3 i 3 ) ] l 1 − β k 12 [ ( x 1 + l 1 i 1 ) − ( x 3 − l 3 i 3 ) ] l 1 + k 11 [ ( y 1 − l 11 i 1 ) − ( y 3 − l 31 i 3 ) ] l 11 − k 12 [ ( y 1 + l 12 i 1 ) − ( y 3 + l 32 i 3 ) ] l 12 (7)

[0097] for Figure 4 Shown The second motion equation (8) is established:

[0098] m 3 x ¨ 3 =− β k 31 ( x 3 + l 3 i 3 ) − β k 32 ( x 3 + l 3 i 3 ) + β k 11 [ ( x 1 + l 1 i 1 ) − ( x 3 − l 3 i 3 ) ] + β k 12 [ ( x 1 + l 1 i 1 ) − ( x 3 − l 3 i 3 ) ] m 3 y ¨ 3 =− k 31 ( y 3 − l 31 i 3 ) − k 32 ( y 3 + l 32 i 3 ) + k 11 [ ( y 1 − l 11 i 1 ) − ( y 3 − l 31 i 3 ) ] + k 12 [ ( y 1 + l 12 i 1 ) − ( y 3 + l 32 i 3 ) ] J 3 i ¨ 3 =− β k 31 x 3 l 3 − β k 32 x 3 l 3 − β k 11 [ ( x 1 + l 1 i 1 ) − ( x 3 − l 3 i 3 ) ] l 3 − β k 12 [ ( x 1 + l 1 i 1 ) − ( x 3 − l 3 i 3 ) ] l 3 + k 31 ( y 3 − l 31 i 3 ) l 31 − k 32 ( y 3 + l 32 i 3 ) l 32 − k 11 [ ( y 1 − l 11 i 1 ) − ( y 3 − l 31 i 3 ) ] l 31 + k 12 [ ( y 1 + l 12 i 1 ) − ( y 3 + l 32 i 3 ) ] l 32 (8)

[0099] The first motion equation (7) and the second motion equation (8) are simplified and sorted out to obtain the following dynamic equation (9). Based on equation (9), formula (10) and formula (11) are obtained:

[0100] M [ u ¨ ] + K [ u ] = [ F ] (9)

[0101] in, [ u ¨ ] = [ x ¨ 1 y ¨ 1 i ¨ 1 x ¨ 3 y ¨ 3 i ¨ 1 ] [ u ] = [ x 1 y 1 i 1 x 3 y 3 i 3 ] [ F ] = [ F x F y M i 0 0 0 ] (10) M = [ m 1 0 0 0 0 0 0 m 1 0 0 0 0 0 0 J 1 0 0 0 0 0 0 m 3 0 0 0 0 0 0 m 3 0 0 0 0 0 0 J 3 ] K = [ kk 11 0 kk 13 kk 14 0 kk 16 0 kk 22 kk 23 0 kk 25 kk 26 kk 31 kk 32 kk 33 kk 34 kk 35 kk 36 kk 41 0 kk 43 kk 44 0 kk 46 0 kk 52 kk 53 0 kk 55 kk 56 kk 61 kk 62 kk 63 kk 64 kk 65 kk 66 ] (11)

[0102] Among them, the stiffness matrix Each element can be calculated by the following formula:

[0103]

[0104]

[0105]

[0106]

[0107]

[0108]

[0109]

[0110]

[0111]

[0112]

[0113]

[0114]

[0115]

[0116]

[0117]

[0118]

[0119]

[0120] For Figure 4 The dynamic system shown in the figure also needs to consider the damping effect, which is expressed in the dynamic equation (9). Equation (9) is converted into the final dynamic equation of six degrees of freedom, as shown in formula (12):

[0121] M [ u ¨ ] + C [ u ˙ ] + K [ u ] = [ F ] (12)

[0122] Damping can be calculated using the Rayleigh form using the following formula (13):

[0123] (13)

[0124] Among them, the Rayleigh damping coefficient and It can be calculated by the following formula (14):

[0125] (14)

[0126] Indicates the circular frequency, Represents the damping ratio.

[0127] Through the above description, the vibration conveying device 1 and its foundation 3 are simplified as follows: Figure 4 The mechanical system shown in the figure was used to establish the dynamic equation.

[0128] Similarly, based on the solution method of equations (2) to (5), the final dynamic equation (12) of six degrees of freedom is transformed into a solution of a twelve-variable linear equation, where the twelve-variable linear equation is as follows:

[0129]

[0130]

[0131]

[0132]

[0133]

[0134]

[0135]

[0136]

[0137]

[0138]

[0139]

[0140]

[0141] The vibration response of the foundation 3 can be obtained through the above twelve-variable linear equation.

[0142] In an optional embodiment, when the exciting force is in a vertical direction and the line of action passes through the center of gravity of the vibration conveying equipment 1, the stiffness center of the vibration isolator of the vibration conveying equipment 1, the mass center of the vibration isolation unit, the stiffness center of the vibration isolation unit, the center of gravity of the foundation 3 and the stiffness center of the elastic effect of the soil on the foundation 3, the vibration isolation calculation model is determined to be a three-degree-of-freedom equation; when the exciting force is in a vertical direction and the line of action does not pass through the center of gravity of the vibration conveying equipment 1, the stiffness center of the vibration isolator of the vibration conveying equipment 1, the mass center of the vibration isolation unit, the stiffness center of the vibration isolation unit, the center of gravity of the foundation 3 and the stiffness center of the elastic effect of the soil on the foundation 3, the vibration isolation calculation model is determined to be a nine-degree-of-freedom equation; when the exciting force is not in a vertical direction, the vibration isolation calculation model is determined to be a nine-degree-of-freedom equation.

[0143] Specifically, determine the vibration isolation design scheme and complete the vibration isolation design: the vibration isolation design scheme adopted in the present invention patent is to add a set of vibration isolation units (including dynamic parameters such as stiffness, mass and damping) between the casting vibration conveying equipment 1 and the foundation 3. The vibration isolation design scheme is shown in the figure below: Figure 5 As shown: Figure 5 In the vibration isolation design scheme diagram of the vibration conveying equipment 1 shown, the upper part is the vibration conveying equipment 1, the lower part is the foundation 3, the middle "T" shape is the concrete counterweight mass block 2, and the device between the mass block and the foundation 3 (located below the two ends of the concrete counterweight mass block 2) is the vibration isolation device 4, which is usually a metal coil spring. Usually, when designing the vibration isolation unit and the foundation 3, the center of gravity of the equipment, the center of gravity of the vibration isolation unit, the center of gravity of the foundation 3, the stiffness center of the newly added vibration isolation unit spring, and the stiffness center of the elastic effect of the soil on the foundation 3 are placed on the same plumb line as much as possible.

[0144] The dynamic system of three-degree-of-freedom equations is as follows Figure 6 As shown, the dynamic system of the nine-degree-of-freedom equation is as follows Figure 7 shown.

[0145] In an optional embodiment, the vibration response amplitude is obtained by calculating based on the three-degree-of-freedom equation; a three-degree-of-freedom periodic function group is obtained based on the three-degree-of-freedom equation, and a three-degree-of-freedom amplitude equation group is obtained, wherein the three-degree-of-freedom amplitude equation group includes a device amplitude equation, a vibration isolation unit amplitude equation and a vibration amplitude equation; the first-order derivatives and second-order derivatives corresponding to the three-degree-of-freedom periodic function group are substituted into the three-degree-of-freedom equation to solve and obtain the undetermined coefficients; the undetermined coefficients are substituted into the three-degree-of-freedom amplitude equation group to obtain the device amplitude, the vibration isolation unit amplitude and the vibration amplitude.

[0146] Under the action of vertical non-eccentric load, the casting vibration conveying equipment 1, a new set of units and foundation 3 can be simplified into a three-degree-of-freedom mechanical system, such as Figure 6 As shown, in Figure 6 The mechanical system composed of the casting vibration conveying device 1, the newly added vibration isolation unit and the foundation 3 shown in the figure can be simplified into a three-degree-of-freedom system under the action of vertical load. Figure 6 In the three-degree-of-freedom mechanical system shown, Represents the upper mass of the spring unit in the device (mass of the moving part); It represents the sum of the mass of the lower part of the spring unit (mass of non-moving parts) and the mass of the newly added vibration isolation unit in the equipment; It represents the sum of the mass of foundation 3 and the mass of the reference soil; and They represent the stiffness and damping of the spring unit in the device respectively; and Respectively represent the stiffness and damping of the newly added vibration isolation unit; and represent the stiffness and damping of the foundation soil below foundation 3 respectively.

[0147] Under the load dominated by vertical exciting force, Figure 4 The mechanical system consisting of the equipment, the newly added vibration isolation unit and the foundation 3 can be simplified into a three-degree-of-freedom system, and its dynamic equation is shown in formula (15):

[0148] [ m 1 0 0 0 m 2 0 0 0 m 3 ] [ x ¨ 1 x ¨ 2 x ¨ 3 ] + [ c 1 − c 1 0 − c 1 c 1 + c 2 − c 2 0 − c 2 c 2 + c 3 ] [ x ˙ 1 x ˙ 2 x ˙ 3 ] + [ k 1 − k 1 0 − k 1 k 1 + k 2 − k 2 0 − k 2 k 2 + k 3 ] [ x 1 x 2 x 3 ] = [ f 0 sin ( oh t ) 0 0 ] (15)

[0149] in , and Represents the mass points Vibration acceleration, vibration velocity and vibration displacement; , and Represents the mass points Vibration acceleration, vibration velocity and vibration displacement; , and Represents the mass points The vibration acceleration, vibration velocity and vibration displacement of the equipment are considered. When the equipment is operating normally, the exciting force is a steady-state function, and the solution of the dynamic equation can be assumed to be in the form shown in formula (16):

[0150] (16)

[0151] in , , and , , , , , There is a relationship as shown in formula (17):

[0152] (17)

[0153] In formula (17) , and are the vibration displacement amplitudes of the equipment, vibration isolation unit and foundation respectively. Substituting formula (16) and its corresponding first-order derivative and second-order derivative into formula (15), the following equation can be obtained, as shown in formula (18):

[0154] [ ( k 1 − m 1 oh 2 ) A 1 − c 1 oh A 2 − k 1 B 1 + c 1 oh B 2 ] sin ( oh t ) + [ c 1 oh A 1 + ( k 1 − m 1 oh 2 ) A 2 − c 1 oh B 1 − k 1 B 2 ] cos ( oh t ) = f 0 sin ( oh t ) [ − k 1 A 1 + c 1 oh A 2 + [ k 1 + k 2 − m 2 oh 2 ] B 1 − [ c 1 oh + c 2 oh ] B 2 − k 2 C 1 + c 2 oh C 2 ] sin ( oh t ) + [ − c 1 oh A 1 − k 1 A 2 + [ c 1 oh + c 2 oh ] B 1 + [ k 1 + k 2 − m 2 oh 2 ] B 2 − c 2 oh C 1 − k 2 C 2 ] cos ( oh t ) = 0 [ − k 2 B 1 + c 2 oh B 2 + [ k 2 + k 3 − m 3 oh 2 ] C 1 − [ c 2 oh + c 3 oh ] C 2 ] sin ( oh t ) + [ − c 2 oh B 1 − k 2 B 2 + [ c 2 oh + c 3 oh ] C 1 + [ k 2 + k 3 − m 3 oh 2 ] C 2 ] cos ( oh t ) = 0 (18)

[0155] For any If it holds, we can get the following linear equation of six variables, as shown in formula (19):

[0156] [ k 1 − m 1 oh 2 − c 1 oh − k 1 c 1 oh 0 0 c 1 oh k 1 − m 1 oh 2 − c 1 oh − k 1 0 0 − k 1 c 1 oh k 1 + k 2 − m 2 oh 2 − c 1 oh − c 2 oh − k 2 c 2 oh − c 1 oh − k 1 c 1 oh + c 2 oh k 1 + k 2 − m 2 oh 2 − c 2 oh − k 2 0 0 − k 2 c 2 oh k 2 + k 3 − m 3 oh 2 − c 2 oh − c 3 oh 0 0 − c 2 oh − k 2 c 2 oh + c 3 oh k 2 + k 3 − m 3 oh 2 ] [ A 1 A 2 B 1 B 2 C 1 C 2 ] = [ f 0 0 0 0 0 0 ] (19)

[0157] In the six-variable linear equation (19), the coefficient matrix is ​​a known parameter. Then, by solving equation (19), we can get , , , , , , and then according to formula (17) we get , and .

[0158] When the equipment is operating normally, the three-degree-of-freedom system is in forced vibration, and the vibration response of each particle is also in the form of a periodic function, so the amplitude of its vibration displacement response is , and When the vibration velocity and vibration acceleration response amplitude are calculated,

[0159] In an optional embodiment, the vibration response is obtained by calculating the nine-degree-of-freedom equation. A third motion equation is established for the mass of the moving part of the vibration conveying device 1; a fourth motion equation is established for the sum of the mass of the non-moving part of the vibration conveying device 1 and the vibration isolation unit; a fifth motion equation is established for the mass of the foundation 3; the third motion equation, the fourth motion equation, and the fifth motion equation are added with damping to obtain the nine-degree-of-freedom final dynamic equation, and the nine-degree-of-freedom final dynamic equation is calculated to obtain the vibration response.

[0160] Under the action of vertical eccentric load or horizontal load, the casting vibration conveying equipment 1, the newly added vibration isolation unit and the foundation 3 can be simplified as follows: Figure 7 The nine-degree-of-freedom system shown.

[0161] According to the casting vibration conveying equipment 1, the new vibration isolation unit and the foundation 3 characteristics, for example Figure 7 In the mechanical model shown, the parameters are described as follows:

[0162] 1) Considering the in-plane motion of the mechanical system, there are a total of 9 degrees of freedom: , and , , and , , and ;

[0163] 2) The geometric shape of the vibration conveying equipment 1 is a rectangular parallelepiped with uniform mass distribution; the vibration isolation unit (usually a concrete counterweight block + a metal spiral spring) is a rectangular parallelepiped with uniform mass distribution; the geometric shape of the equipment foundation 3 is a rectangular parallelepiped with uniform mass distribution; that is, the center of gravity of the above three units is the geometric center;

[0164] 3) The mass of the moving part of the vibration conveying equipment 1 is , the sum of the mass of the non-moving part of the vibration conveying equipment and the newly added vibration isolation unit is The basic quality is ;

[0165] 4) The moment of inertia about its center of gravity is , The moment of inertia about its center of gravity is , The moment of inertia about its center of gravity is ;

[0166] 5) The vertical stiffness and vertical damping of the two sets of springs below are , , and ; The vertical stiffness and vertical damping of the two sets of springs below are , , and ; The vertical stiffness and vertical damping of the two sets of springs below are , , and ; The horizontal stiffness of the vertical spring is calculated according to its vertical stiffness times considered, that is ,generally ;

[0167] 6) For , center of gravity and The distance of the line of action is ,and The distance under action is , Center of Gravity The distance from the top and bottom of the device is ;for , center of gravity and The distance of the line of action is ,and The distance under action is , Center of Gravity The distance from the top and bottom of the device is ;for , center of gravity and The distance of the line of action is ,and The distance of the line of action is , Center of Gravity The distances from the top and bottom of the foundation are ;

[0168] 7) The exciting force only acts on Regardless of the magnitude and direction of the exciting force, it can be converted into , and .

[0169] for Figure 7 Shown The third motion equation is established as shown in formula (20):

[0170] m 1 x ¨ 1 = F x − β k 11 [ ( x 1 + l 1 i 1 ) − ( x 2 − l 2 i 2 ) ] − β k 12 [ ( x 1 + l 1 i 1 ) − ( x 2 − l 2 i 2 ) ] m 1 y ¨ 1 = F y − k 11 [ ( y 1 − l 11 i 1 ) − ( y 2 − l 21 i 2 ) ] − k 12 [ ( y 1 + l 12 i 1 ) − ( y 2 + l 22 i 2 ) ] J 1 i ¨ 1 = M i − β k 11 [ ( x 1 + l 1 i 1 ) − ( x 2 − l 2 i 2 ) ] l 1 − β k 12 [ ( x 1 + l 1 i 1 ) − ( x 2 − l 2 i 2 ) ] l 1 + k 11 [ ( y 1 − l 11 i 1 ) − ( y 2 − l 21 i 2 ) ] l 11 − k 12 [ ( y 1 + l 12 i 1 ) − ( y 2 + l 22 i 2 ) ] l 12 (20)

[0171] for Figure 7 Shown The fourth motion equation is established as shown in formula (21):

[0172] m 2 x ¨ 2 =− β k 21 [ ( x 2 + l 2 i 2 ) − ( x 3 − l 3 i 3 ) ] − β k 22 [ ( x 2 + l 2 i 2 ) − ( x 3 − l 3 i 3 ) ] + β k 11 [ ( x 1 + l 1 i 1 ) − ( x 2 − l 2 i 2 ) ] + β k 12 [ ( x 1 + l 1 i 1 ) − ( x 2 − l 2 i 2 ) ] m 2 y ¨ 2 =− k 21 [ ( y 2 − l 21 i 2 ) − ( y 3 − l 31 i 3 ) ] − k 22 [ ( y 2 + l 22 i 2 ) − ( y 3 + l 32 i 3 ) ] + k 11 [ ( y 1 − l 11 i 1 ) − ( y 2 − l 21 i 2 ) ] + k 12 [ ( y 1 + l 12 i 1 ) − ( y 2 + l 22 i 2 ) ] J 2 i ¨ 2 =− β k 21 [ ( x 2 + l 2 i 2 ) − ( x 3 − l 3 i 3 ) ] l 2 − β k 22 [ ( x 2 + l 2 i 2 ) − ( x 3 − l 3 i 3 ) ] l 2 − β k 11 [ ( x 1 + l 1 i 1 ) − ( x 2 − l 2 i 2 ) ] l 2 − β k 12 [ ( x 1 + l 1 i 1 ) − ( x 2 − l 2 i 2 ) ] l 2 + k 21 [ ( y 2 − l 21 i 2 ) − ( y 3 − l 31 i 3 ) ] l 21 − k 22 [ ( y 2 + l 22 i 2 ) − ( y 3 + l 32 i 3 ) ] l 22 − k 11 [ ( y 1 − l 11 i 1 ) − ( y 2 − l 21 i 2 ) ] l 21 + k 12 [ ( y 1 + l 12 i 1 ) − ( y 2 + l 22 i 2 ) ] l 22 (twenty one)

[0173] for Figure 7 Shown The equation of motion is established as shown in formula (22):

[0174] m 3 x ¨ 3 =− β k 31 ( x 3 + l 3 i 3 ) − β k 32 ( x 3 + l 3 i 3 ) + β k 21 [ ( x 2 + l 2 i 2 ) − ( x 3 − l 3 i 3 ) ] + β k 22 [ ( x 2 + l 2 i 2 ) − ( x 3 − l 3 i 3 ) ] m 3 y ¨ 3 =− k 31 ( y 3 − l 31 i 3 ) − k 32 ( y 3 + l 32 i 3 ) + k 21 [ ( y 2 − l 21 i 2 ) − ( y 3 − l 31 i 3 ) ] + k 22 [ ( y 2 + l 22 i 2 ) − ( y 3 + l 32 i 3 ) ] J 3 i ¨ 3 =− β k 31 x 3 l 3 − β k 32 x 3 l 3 − β k 21 [ ( x 2 + l 2 i 2 ) − ( x 3 − l 3 i 3 ) ] l 3 − β k 22 [ ( x 2 + l 2 i 2 ) − ( x 3 − l 3 i 3 ) ] l 3 + k 31 ( y 3 − l 31 i 3 ) l 31 − k 32 ( y 3 + l 32 i 3 ) l 32 − k 21 [ ( y 2 − l 21 i 2 ) − ( y 3 − l 31 i 3 ) ] l 31 + k 22 [ ( y 2 + l 22 i 2 ) − ( y 3 + l 32 i 3 ) ] l 32 (twenty two)

[0175] After simplifying and arranging formula (20), formula (21) and formula (22), the following dynamic equation (23) can be obtained. Based on equation (23), formula (24), formula (25) and formula (26) can be obtained:

[0176] M [ u ¨ ] + K [ u ] = [ F ] (twenty three)

[0177] in,

[0178] [ u ¨ ] = [ x ¨ 1 y ¨ 1 i ¨ 1 x ¨ 2 y ¨ 2 i ¨ 2 x ¨ 3 y ¨ 3 i ¨ 3 ] [ u ] = [ x 1 y 1 i 1 x 2 y 2 i 2 x 3 y 3 i 3 ] [ F ] = [ F x F y M i 0 0 0 0 0 0 ] (twenty four)

[0179] M = [ m 1 m 1 J 1 m 2 m 2 J 2 m 3 m 3 J 3 ] (25)

[0180] K = [ kk 11 0 kk 13 kk 14 0 kk 16 0 0 0 0 kk 22 kk 23 0 kk 25 kk 26 0 0 0 kk 31 kk 32 kk 33 kk 34 kk 35 kk 36 0 0 0 kk 41 0 kk 43 kk 44 0 kk 46 kk 47 0 kk 49 0 kk 52 kk 53 0 kk 55 kk 56 0 kk 58 kk 59 kk 61 kk 62 kk 63 kk 64 kk 65 kk 66 kk 67 kk 68 kk 69 0 0 0 kk 74 0 kk 76 kk 77 0 kk 79 0 0 0 0 kk 85 kk 86 0 kk 88 kk 89 0 0 0 kk 94 kk 95 kk 96 kk 97 kk 98 kk 99 ] (26)

[0181] The stiffness matrix Each element can be calculated by the following formula:

[0182]

[0183]

[0184]

[0185]

[0186]

[0187]

[0188]

[0189]

[0190]

[0191]

[0192]

[0193]

[0194]

[0195]

[0196]

[0197]

[0198]

[0199]

[0200]

[0201]

[0202]

[0203]

[0204]

[0205]

[0206]

[0207]

[0208]

[0209]

[0210]

[0211] For Figure 7 The dynamic system shown in the figure also needs to consider the damping effect, which is expressed in the dynamic equation (23). Equation (23) is converted into the final dynamic equation of nine degrees of freedom, as shown in formula (27):

[0212] M [ u ¨ ] + C [ u ˙ ] + K [ u ] = [ F ] (27)

[0213] Damping can be Rayleigh damping, which is calculated in the same way as equations (13) and (14).

[0214] Through the above description, the vibration conveying device 1, the newly added vibration isolation unit and the foundation 3 are simplified as follows: Figure 7 The mechanical system shown in the figure was used to establish the dynamic equation.

[0215] Similarly, based on the solution equations of equations (16) to (19), the final dynamic equation (27) of nine degrees of freedom is transformed into the solution of an 18-variable linear equation, where the 18-variable linear equation is as follows:

[0216]

[0217]

[0218]

[0219]

[0220]

[0221]

[0222]

[0223]

[0224]

[0225]

[0226]

[0227] The vibration response of the foundation 3 can be obtained through the above 18-variable linear equation.

[0228] A vibration isolation design scheme is adopted for the casting vibration conveying equipment 1, which can effectively reduce the vibration response of the foundation 3 of the casting vibration conveying equipment 1, and thereby reduce the vibration impact on surrounding equipment or people, so that the surrounding equipment can operate normally, while also meeting the comfort requirements.

[0229] The working principle and beneficial effects of the present invention are:

[0230] (1) For the vibration conveying equipment 1 and foundation 3 models, the calculation model and its corresponding dynamic equation were established according to the characteristics of the equipment, foundation 3 and the properties of the exciting force. According to the characteristics of the solution of the dynamic equation, the dynamic equation was converted into a multivariate linear equation system (four-variable linear equation system or twelve-variable linear equation system) for solution, which is efficient and accurate, greatly saving the workload of structural engineers in vibration analysis.

[0231] (2) For the vibration conveying equipment 1, the vibration isolation unit, the foundation 3 characteristics and the exciting force properties that adopt the vibration isolation design scheme, a calculation model and its corresponding dynamic equation are established. According to the characteristics of the solution of the dynamic equation, the dynamic equation is converted into a multivariate linear equation group (a six-variable linear equation group or an eighteen-variable linear equation group) for solution, which is efficient and accurate, greatly saving the workload of structural engineers in vibration analysis;

[0232] (3) A workflow for vibration calculation and analysis of the casting vibration conveying equipment 1 foundation 3 was established, which includes a vibration isolation design method for concrete counterweight blocks used in the casting vibration conveying equipment 1. The method is economical and applicable, and has excellent vibration isolation efficiency.

[0233] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein by equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A vibration isolation design method for casting vibration conveying equipment, characterized in that: include: According to the initial scheme, a vibration analysis is performed on the vibration conveying device (1) to obtain a vibration response, and a final scheme is determined according to a comparison result between the vibration response and the allowable vibration requirement, wherein the initial scheme includes a non-vibration isolation design and a vibration isolation design, the non-vibration isolation design includes the vibration conveying device (1) and a non-vibration isolation calculation model, the non-vibration isolation calculation model includes a two-degree-of-freedom equation and a six-degree-of-freedom equation, the vibration isolation design includes the vibration conveying device (1), a vibration isolation unit and a vibration isolation calculation model, and the vibration isolation calculation model includes a three-degree-of-freedom equation and a nine-degree-of-freedom equation; According to the initial scheme, a vibration analysis is performed on the vibrating conveying device (1) to obtain a vibration response, and a final scheme is determined according to a comparison result between the vibration response and the allowable vibration requirement, including: determining a non-vibration isolation calculation model according to the structural characteristics of the vibrating conveying device (1) and the exciting force; determining a vibration isolation calculation model according to the structural characteristics of the vibrating conveying device (1), the vibration isolation unit and the exciting force; The non-vibration isolation calculation model is determined according to the structural characteristics of the vibration conveying equipment (1) and the exciting force, including: when the exciting force is in a vertical direction and the action line passes through the center of gravity of the vibration conveying equipment (1), the center of stiffness of the vibration isolator of the vibration conveying equipment (1), the center of gravity of the foundation (3) and the center of stiffness of the elastic effect of the soil on the foundation (3), the non-vibration isolation calculation model is determined to be the two-degree-of-freedom equation; when the exciting force is in a vertical direction and its action line does not pass through the center of gravity of the vibration conveying equipment (1), the center of stiffness of the vibration isolator of the vibration conveying equipment (1), the center of gravity of the foundation (3) and the center of stiffness of the elastic effect of the soil on the foundation (3), the non-vibration isolation calculation model is determined to be the six-degree-of-freedom equation; when the exciting force is not in a vertical direction, the non-vibration isolation calculation model is determined to be the six-degree-of-freedom equation; Determining a non-vibration isolation calculation model based on the structural characteristics of the vibrating conveying equipment (1) and the exciting force includes: calculating and obtaining the vibration response amplitude based on a two-degree-of-freedom equation, wherein the two-degree-of-freedom equation is: m1 is the upper mass of the spring unit in the equipment, m3 is the sum of the lower mass of the spring unit in the equipment (mass of non-moving parts), the mass of the foundation (3) and the mass of the vibration soil. and They represent the vibration acceleration and vibration velocity of mass point m1 respectively, and Respectively represent the vibration acceleration and vibration velocity of m3, k1 is the stiffness of the spring unit in the equipment, c1 is the damping of the spring unit in the equipment, k3 is the stiffness of the foundation soil below the foundation (3), c3 is the damping of the foundation soil below the foundation (3), and Fsin (ωt) is the equipment disturbance force of the non-vibration isolation calculation model; the vibration response is obtained by calculating according to the six-degree-of-freedom equation; The vibration response is obtained by calculating according to the six-degree-of-freedom equation, including: establishing a first motion equation for the mass of the moving part of the vibration conveying device (1), wherein the first motion equation is: Wherein, m1 is the upper mass of the spring unit in the device, x1 represents the vibration displacement in the x direction at the mass center of m1, x3 represents the vibration displacement in the x direction at the mass center of m3, y1 represents the vibration displacement in the y direction at the mass center of m1, θ1 represents the vibration angular displacement of the device rotating around the mass center of m1 in the XOY plane, θ3 represents the vibration angular displacement of the device rotating around the mass center of m3 in the XOY plane, is the vibration acceleration of m1 in the x direction, is the vibration acceleration of m1 in the y direction, is the angular acceleration of the base rotating around the center of mass of m1 in the XOY plane, F x represents the disturbance force in the x direction acting on the center of mass of m1; F y represents the disturbance force in the y direction acting on the center of mass of m1; M θ represents the disturbance moment around the center of mass of the device in the XOY plane, J1 is the moment of inertia around the center of mass of m1, and the vertical stiffness of the two sets of springs below m1 are k 11 , k 12 , for m1, the center of gravity and k 11 The distance of the line of action is l 11 , and k 12 The distance of the line of action is l 12 The distance between the center of gravity and the top and bottom of the equipment is l1, the distance between the center of gravity of m3 and the top and bottom of the foundation is l3, and the distance between the center of gravity of m3 and k 31 The distance of the line of action is l 31 , and k 32 The distance of the line of action is l 32 , the vertical stiffness of the two groups of springs below m3 are k 31 , k 32 , the horizontal stiffness of the vertical spring is obtained according to β times its vertical stiffness; a second motion equation is established for the sum of the mass of the non-moving part of the vibration conveying equipment (1) and the foundation (3), and the second motion equation is: Wherein, m3 is the sum of the mass of the lower part of the spring unit in the equipment (mass of non-moving parts), the mass of the foundation (3) and the mass of the vibration soil, x1 represents the vibration displacement in the x direction at the mass center of m1, x3 represents the vibration displacement in the x direction at the mass center of m3, y1 represents the vibration displacement in the y direction at the mass center of m1, y3 represents the vibration displacement in the y direction at the mass center of m3, θ1 represents the vibration angular displacement of the equipment rotating around the mass center of m1 in the XOY plane, θ3 represents the vibration angular displacement of the equipment rotating around the mass center of m3 in the XOY plane, is the vibration acceleration of m3 in the x direction, is the vibration acceleration of m3 in the y direction, is the vibration angular acceleration of the foundation rotating around the center of mass of m3 in the XOY plane, J3 is the moment of inertia around the center of mass of m3, and the vertical stiffness of the two sets of springs below m1 are k 11 , k 12 , for m1, the center of gravity and k 11 The distance of the line of action is l 11 , and k 12 The distance of the line of action is l 12 The distance between the center of gravity and the top and bottom of the equipment is l1, the distance between the center of gravity of m3 and the top and bottom of the foundation is l3, and the distance between the center of gravity of m3 and k 31 The distance of the line of action is l 31 , the center of gravity of m3 and k 32 The distance of the line of action is l 32 , the vertical stiffness of the two groups of springs below m3 are k 31 , k 32 , the horizontal stiffness of the vertical spring is obtained according to β times its vertical stiffness; the first motion equation and the second motion equation are added with damping to obtain a six-degree-of-freedom final dynamic equation, and the six-degree-of-freedom final dynamic equation is calculated to obtain the vibration response; The vibration isolation calculation model is determined according to the structural characteristics of the vibration conveying equipment (1), the vibration isolation unit and the exciting force, including: when the exciting force is in a vertical direction and the line of action passes through the center of gravity of the vibration conveying equipment (1), the center of stiffness of the vibration isolator of the vibration conveying equipment (1), the center of mass of the vibration isolation unit, the center of stiffness of the vibration isolation unit, the center of gravity of the foundation (3) and the center of stiffness of the elastic effect of the soil on the foundation (3), the vibration isolation calculation model is determined to be the three-degree-of-freedom equation; when the exciting force is in a vertical direction and the line of action does not pass through the center of gravity of the vibration conveying equipment (1), the center of stiffness of the vibration isolator of the vibration conveying equipment (1), the center of mass of the vibration isolation unit, the center of stiffness of the vibration isolation unit, the center of gravity of the foundation (3) and the center of stiffness of the elastic effect of the soil on the foundation (3), the vibration isolation calculation model is determined to be the nine-degree-of-freedom equation; when the exciting force is not in a vertical direction, the vibration isolation calculation model is determined to be the nine-degree-of-freedom equation; The vibration isolation calculation model is determined according to the structural characteristics of the vibration conveying equipment (1), the vibration isolation unit and the exciting force, including: obtaining the vibration response amplitude by calculation according to the three-degree-of-freedom equation, wherein the three-degree-of-freedom equation is: m1 is the upper mass of the spring unit in the equipment, m2 is the sum of the lower mass of the spring unit (mass of non-moving parts) and the mass of the newly added vibration isolation unit, and m3 is the sum of the mass of the foundation (3) and the mass of the reference soil. and x1 represent the vibration acceleration, vibration velocity and vibration displacement of mass point m1 respectively; and x2 represent the vibration acceleration, vibration velocity and vibration displacement of mass point m2 respectively; and x3 represent the vibration acceleration, vibration velocity and vibration displacement of mass point m2 respectively, k1 is the stiffness of the spring unit in the equipment, c1 is the damping of the spring unit in the equipment, k2 is the stiffness of the newly added vibration isolation unit, c2 is the damping of the newly added vibration isolation unit, k3 is the stiffness of the foundation soil under the foundation (3), and c3 is the damping of the foundation soil under the foundation (3); the vibration response is obtained by calculating according to the nine-degree-of-freedom equation; The vibration response is obtained by calculating according to the nine-degree-of-freedom equation, including: establishing a third motion equation for the mass of the moving part of the vibration conveying device (1), wherein the third motion equation is: Wherein, m1 is the upper mass of the spring unit in the device, x1 represents the vibration displacement in the x direction at the center of mass of the device, y1 represents the vibration displacement in the y direction at the center of mass of the device, and θ1 represents the vibration angular displacement of m1 rotating around the center of mass of m1 in the XOY plane. is the vibration acceleration of m1 in the x direction, is the vibration acceleration of m1 in the y direction, is the angular acceleration of the base rotating around the center of mass of m1 in the XOY plane, F x represents the disturbance force in the x direction acting on the center of mass of m1; F y represents the disturbance force in the y direction acting on the center of mass of m1; M θ represents the disturbance moment around the center of mass of the device in the XOY plane, J1 is the moment of inertia around the center of mass of m1, and the vertical stiffness of the two sets of springs below m1 are k 11 , k 12 , the center of gravity of m1 and k 11 The distance of the line of action is l 11 , and k 12 The distance of the line of action is l 12 , m1 The distance between the center of gravity and the top and bottom surfaces of the equipment is l1, and the horizontal stiffness of the vertical spring is obtained according to β times its vertical stiffness; A fourth motion equation is established for the sum of the mass of the non-moving part of the vibration conveying device (1) and the vibration isolation unit. The fourth motion equation is: Among them, m2 is the sum of the mass of the lower part of the spring unit (mass of non-moving parts) and the mass of the newly added vibration isolation unit, x1 represents the vibration displacement in the x direction at the center of mass of m1, y1 represents the vibration displacement in the y direction at the center of mass of m1, x2 represents the vibration displacement in the x direction at the center of mass of m2, y2 represents the vibration displacement in the y direction at the center of mass of m2, x3 represents the vibration displacement in the x direction at the center of mass of m3, y3 represents the vibration displacement in the y direction at the center of mass of m3, is the vibration acceleration of m2 in the x direction, is the vibration acceleration of m2 in the y direction, θ1 represents the vibration angular displacement of the device rotating around the mass center of m1 in the XOY plane, θ2 represents the vibration angular displacement of the device rotating around the mass center of m2 in the XOY plane, θ3 represents the vibration angular displacement of the device rotating around the mass center of m3 in the XOY plane, is the vibration angular acceleration of the foundation rotating around the center of mass of m2 in the XOY plane, the moment of inertia of J2 around the center of mass of m2, and the vertical stiffness of the two sets of springs below m2 are k 21 , k 22 , the center of gravity of m2 and k 21 The distance of the line of action is l 21 , and k 22 The distance under action is l 22 , the distance between the center of gravity of m2 and the top and bottom surfaces of the equipment is l2, the distance between the center of gravity and the top and bottom surfaces of the equipment is l1, and the horizontal stiffness of the vertical spring is obtained according to β times its vertical stiffness; the fifth motion equation is established for the mass of foundation (3), and the fifth motion equation is: in, is the vibration acceleration of m3 in the x direction, is the vibration acceleration of m3 in the y direction, is the vibration angular acceleration of the foundation rotating around the center of mass of m3 in the XOY plane. The vertical stiffnesses of the two sets of springs below m1 are k 11 , k 12 , the vertical stiffness of the two groups of springs below m2 are k 21 , k 22 , the vertical stiffness of the two groups of springs below m3 are k 31 , k 32 , the center of gravity of m1 and k 11 The distance of the line of action is l 11 , and k 12 The distance of the line of action is l 12 The distance between the center of gravity of m1 and the top and bottom surfaces of the equipment is l1, and the distance between the center of gravity of m2 and k 21 The distance of the line of action is l 21 , and k 22 The distance under action is l 22 The distance between the center of gravity of m2 and the top and bottom of the equipment is l2, and the distance between the center of gravity of m3 and k 31 The distance of the line of action is l 31 , the center of gravity of m3 and k 32 The distance of the line of action is l 32 , the horizontal stiffness of the vertical spring is obtained according to β times its vertical stiffness; the third motion equation, the fourth motion equation and the fifth motion equation are added with damping to obtain the final dynamic equation of nine degrees of freedom, and the final dynamic equation of nine degrees of freedom is calculated to obtain the vibration response: When the initial solution is the non-vibration isolation design and the comparison result meets the requirements, determining the initial solution as the final solution; When the initial solution is the non-vibration isolation design and the comparison result does not meet the requirement, modifying the initial solution to the vibration isolation design; When the initial solution is the vibration isolation design and the comparison result meets the requirements, determining the initial solution as the final solution; When the initial solution is the vibration isolation design and the comparison result does not meet the requirements, the vibration isolation design is optimized until the vibration response satisfies the comparison result that meets the requirements, and then the final solution is determined.

2. The method according to claim 1, characterized in that The vibration response amplitude is calculated based on the two-degree-of-freedom equation, including: Obtaining a two-degree-of-freedom periodic function group according to the two-degree-of-freedom equation, and obtaining a two-degree-of-freedom vibration response amplitude, wherein the two-degree-of-freedom vibration response amplitude includes a device amplitude equation and a vibration amplitude equation; Substituting the first-order derivative and the second-order derivative corresponding to the two-degree-of-freedom periodic function group into the two-degree-of-freedom equation to solve and obtain the undetermined coefficients; Substitute the undetermined coefficients into the two-degree-of-freedom vibration response amplitudes to obtain the equipment amplitude and the vibration displacement amplitude.

3. The method according to claim 1, characterized in that The vibration response amplitude is calculated based on the three-degree-of-freedom equation, including: Obtaining a three-degree-of-freedom periodic function group according to the three-degree-of-freedom equation, and obtaining a three-degree-of-freedom amplitude equation group, wherein the three-degree-of-freedom amplitude equation group includes a device amplitude equation, a vibration isolation unit amplitude equation, and a vibration amplitude equation; Substituting the first-order derivative and the second-order derivative corresponding to the three-degree-of-freedom periodic function group into the three-degree-of-freedom equation to solve and obtain the undetermined coefficients; Substituting the undetermined coefficients into the three-degree-of-freedom amplitude equation group, the equipment amplitude, the vibration isolation unit amplitude and the vibration amplitude are obtained.

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