Simplified dynamic analysis method and device for arc-shaped wheel rail of retractable roof based on finite mass point method

Abstract

The invention discloses a finite mass point method-based arc-shaped wheel rail simplified dynamic analysis method for a retractable roof, which comprises the following steps of: taking the rolling center of a roller as a mass point, replacing the opening and closing of the roof with the movement of the roller, assuming the shape of the roller as a beam unit, and regarding an arc-shaped rail as a multi-section straight beam unit; the contact effect of a roller and an arc-shaped track is regarded as an elastic-plastic wheel-rail contact unit, the arc-shaped track is considered, a motion equation is iteratively solved, an analysis object of the retractable roof is perfected, and the defect of an analysis method of the retractable roof based on the arc-shaped track is overcome; and improving the elastic-plastic analysis of the wheel-rail simplified model by using a method for establishing the wheel-rail elastic-plastic contact unit. The invention further provides a simplified dynamic analysis device for the arc-shaped wheel rail of the retractable roof. According to the method provided by the invention, the structural response of the whole moving process of the retractable roof is accurately obtained, and the defects in the field of power analysis of simplified modeling and unfolding processes of the retractable roof at present are overcome.

Description

Technical Field

[0001] The invention belongs to the technical field of building structures, and in particular relates to a simplified dynamic analysis method and device for an arc-shaped wheel-track of a retractable roof based on a finite mass method. Background Art

[0002] Application background of retractable roof An important structural type in modern sports buildings, it has been used in many important sports venues. The retractable roof can complete the opening and closing movement in a relatively short time, realize the multifunctional utilization requirements of the sports venues, and enhance the ability of the sports venues to cope with weather changes. The retractable roof system consists of a retractable roof and a supporting structure, which is a heavy-load low-speed motion system that mainly bears gravity loads. The roof track system is an important part of the track-type retractable roof system and plays a vital role in the entire structural system. In actual projects, the roof track includes linear tracks and curved tracks.

[0003] Patent document CN103866890A discloses a retractable roof track system and its design and installation method, including a track beam assembly, a track assembly, an upper and lower car block; the track beam assembly is connected to the fixed roof through a track beam support; the track assembly is fixed to the top surface of the track beam assembly through bolts and pressure blocks; the movable roof opening stop position is provided with an lower car block, and the movable roof closing stop position is provided with an upper car block, and the lower and upper car blocks are both connected to the top surface of the track beam assembly. The design method extracts the track beam load, selects the typical opening and closing state analysis according to the overall calculation model, extracts the forces under each state for comparison, and extracts the most unfavorable force as the design load of the later track beam and the track beam support.

[0004] Patent document CN117661771A discloses a curved opening and closing roof system, which includes a curved track travel system, a curved rack thrust system, a hydraulic damping reduction motor power system, a universal transmission system, and a frequency conversion control system; the curved track travel system is arranged above the main structure of the curved opening and closing roof building system, and is used to support the curved opening and closing roof frame. The curved track travel system includes a curved track, a travel wheel fixedly connected to the curved opening and closing roof frame that plays a walking role, a guide wheel that plays a guiding role, and an anti-lifting wheel that prevents the curved opening and closing roof frame from lifting, which cooperate with each other to embrace the curved track to ensure the load support of the opening and closing roof and safe and smooth walking along the curved track.

[0005] At present, the dynamic analysis methods for modeling and unfolding of retractable roofs often have the following defects:

[0006] 1) Existing research on wheel-rail structure modeling and dynamic analysis methods mostly focuses on the wheel-rail structure system of the railway system.

[0007] 2) The existing wheel-rail structure analysis methods of retractable roofs usually conduct static analysis of the specific opening and closing degree of the retractable roof to evaluate the overall structural response.

[0008] 3) The existing methods for modeling and dynamic analysis of the unfolding process of retractable roofs are mostly based on linear tracks, and rarely involve the dynamic analysis of curved tracks.

[0009] 4) The existing retractable roof modeling and deployment process dynamic analysis methods have certain defects in dealing with the dynamic problems of wheel-rail motion.

[0010] 5) Existing methods for modeling and dynamic analysis of the unfolding process of retractable roofs all use fine solid units to simulate rollers and tracks.

[0011] 6) The existing simplified modeling and dynamic analysis methods of retractable roofs and the deployment process mostly use the wheel-rail elastic contact model in the analysis of retractable roof systems.

[0012] In summary, the existing retractable roof modeling and deployment process dynamic analysis methods have problems such as lack of modeling and analysis methods for retractable roofs, lack of analysis methods for the entire process of retractable roofs, less involvement of curved track structures, defects in handling wheel-rail dynamic problems, high calculation costs, and failure to consider nonlinear contact between wheels and rails. Summary of the invention

[0013] The purpose of the present invention is to provide a simplified dynamic analysis method and device for a retractable roof curved wheel-rail based on a finite mass method. The method takes into account the modeling of the curved track and the elastoplastic contact between the wheel and the rail, accurately obtains the structural response of the entire movement process of the retractable roof, and supplements and improves the current deficiencies in the field of simplified modeling and dynamic analysis of the unfolding process of the retractable roof.

[0014] In order to achieve the first object of the present invention, the following scheme is provided: a simplified dynamic analysis method of an arc wheel-track of an opening and closing roof based on a finite mass method, wherein the roof comprises a fixed roof part connected to a building wall and a movable roof part for completing the opening and closing action of the roof, the fixed roof part is provided with an arc track, and the fixed roof part is provided with a roller that slides with the arc track, and the simplified dynamic analysis method of the arc wheel-track of the opening and closing roof comprises: constructing a simulation model based on the movement characteristics of the roller during the opening and closing process of the roof, the simulation model uses the rolling center of the roller as a mass point and replaces the opening and closing of the roof with the movement of the roller, virtualizes the roller shape as a beam unit, regards the arc track as a multi-segment straight beam unit, and regards the contact between the roller and the arc track as an elastic-plastic wheel-track contact unit;

[0015] The trajectory of the roller in the simulation model is calculated based on the finite mass method. The process is as follows:

[0016] The beam element is analyzed by using virtual reverse kinematics to calculate the internal force corresponding to the deformation of the beam element;

[0017] A wheel-rail contact point solving algorithm is used for the multi-segment straight beam unit to determine the relative position relationship between the mass point of the roller and the multi-segment straight beam unit, wherein the relative position relationship includes the mass point not entering the current straight beam unit, the mass point entering the current straight beam unit, and the mass point leaving the current straight beam unit;

[0018] According to the normal deviation of the roller when entering the current track, the contact state between the roller and the track surface is determined by the elastic-plastic strengthening model, and the corresponding wheel-rail normal contact force is calculated based on the contact state, wherein the contact state includes elastic contact and elastic-plastic contact;

[0019] For the lateral deviation of the roller when entering the current track, the corresponding wheel-rail lateral contact force is calculated by the penalty function method;

[0020] Set the particle motion speed of the active roller, and construct the particle motion equation based on the internal force corresponding to the active roller, the wheel-rail normal contact force, and the wheel-rail lateral contact force;

[0021] Based on the two sets of displacement information of the particle corresponding to the active roller at the previous moment and the current moment, the displacement information of the particle at the next moment is output by solving the particle motion equation;

[0022] The above trajectory calculation is repeated to obtain the motion trajectory of the mass point corresponding to the roller within a period of time, and the dynamic analysis of the opening and closing action of the roof is performed based on the motion trajectory.

[0023] The present invention proposes a simplified modeling method for an arc-shaped wheel-track of a retractable roof, in which rollers and arc-shaped tracks are discretized into mass points, the rollers are simulated by mass points at the center, the roller shape is simulated by a virtual beam unit, the arc-shaped track is simulated by a multi-segment straight beam unit, the wheel-track contact effect is simulated by an elastic-plastic wheel-track contact unit, and the retractable roof drive is simulated by an active wheel drive unit; and the rollers and tracks are discretized into mass points by a finite mass method dynamic analysis, and the internal force and displacement of the mass points are obtained by iteratively solving the mass point motion equations, thereby simulating the roller motion, and separating the rigid body displacement and pure deformation by virtual inverse motion, so that the deformation of components in the opening and closing process of the roof can be effectively considered, and the accurate analysis of the unfolding process of the retractable roof can be achieved.

[0024] Specifically, the specific construction process of the simulation model is as follows:

[0025] The arc track is divided into multiple segments of sequentially connected straight tracks, and the straight tracks are discretized into mass points to construct corresponding multiple straight beam units;

[0026] The roller is discretized into a mass point at the center and a mass point at the projection on the arc track, and a virtual beam unit is set based on the composition of the mass point at the center and the mass point at the projection to characterize the roller radius;

[0027] The contact action between the roller and the curved track is divided into normal force and lateral force. The normal force is modeled based on the normal topological relationship between the wheel and rail and the nonlinear contact relationship between the wheel and rail. The lateral force is modeled based on the lateral curved topological relationship between the wheel and rail and the lateral contact relationship between the wheel and rail. The modeling of the normal force and the lateral force is combined to form an elastic-plastic wheel-rail contact unit.

[0028] Specifically, the analysis process of the virtual beam unit is as follows:

[0029] Establish a follow-up local coordinate system to separate beam element deformation and rigid body displacement;

[0030] The beam element is translated to the preset initial position through virtual reverse motion to calculate the translation displacement increment and rotation displacement increment of the beam element from the final state to the initial state, and the axial deformation and bending deformation are determined by comparing the beam element before and after the virtual reverse motion;

[0031] Calculate the internal force increment of the beam element based on the axial deformation and bending deformation of the beam element;

[0032] The internal force increment is converted into the global coordinate system through the transformation matrix between the global coordinate system and the follower local coordinate system, and applied to the beam unit mass point as an external force to obtain the internal force corresponding to the deformation of the beam unit.

[0033] Specifically, the relative position relationship is expressed as follows:

[0034]

[0035] Among them, m is the mass point corresponding to the previous straight beam unit, n is the mass point corresponding to the next straight beam unit, O is the center mass point of the arc track corresponding to the multi-segment straight beam unit, and i is the contact point between the roller and the arc track.

[0036] Specifically, the calculation process of the wheel-rail normal contact force is as follows:

[0037] In the elastic-plastic strengthening model, set the mass point corresponding to the first straight beam unit, the mass point corresponding to the second straight beam unit, the mass point at the center of the arc track corresponding to the multi-segment straight beam unit, and the contact point between the roller and the arc track;

[0038] Based on the mass point corresponding to the previous straight beam unit, the mass point corresponding to the next straight beam unit and the mass point at the center of the circle, the corresponding normal vector of the orbital surface is constructed;

[0039] Based on the center mass point and the contact point, the corresponding contact vector is constructed;

[0040] Based on the track surface normal vector and the contact vector, the normal displacement of the roller relative to the current track is calculated;

[0041] When the normal displacement is less than or equal to the preset elastic critical displacement, the contact between the roller and the track is elastic, otherwise it is elastoplastic contact;

[0042] When it is determined to be elastic contact, the corresponding elastic contact stress is calculated by the normal displacement, and the corresponding wheel-rail normal contact force is converted based on the elastic contact stress;

[0043] When it is determined to be an elastic-plastic contact, the distribution ratio of the elastic zone and the plastic zone is calculated by using the yield stress and the elastic contact stress, and an equation relationship is established based on the distribution ratio and the stress of the corresponding area;

[0044] Iteratively solving the equation relationship to obtain stress distribution in the contact area;

[0045] The stress distribution is integrated to obtain the wheel-rail plastic contact force, and the corresponding wheel-rail normal contact force is converted based on the wheel-rail plastic contact force.

[0046] Specifically, the calculation process of the wheel-rail lateral contact force is as follows:

[0047] F l =K l disp l

[0048] Among them, disp l represents the lateral displacement of the roller relative to the track, K l is the lateral stiffness of the track.

[0049] Specifically, the expression of the particle motion equation is as follows:

[0050]

[0051] Among them, m α is the mass of particle α, is the external force on the particle α, is the normal contact force of particle α, is the lateral contact force of particle α, is the internal force of particle α, Represents the α damping force of the particle.

[0052] In order to achieve the second object of the present invention, the following technical solution is provided: a simplified dynamic analysis device for a retractable roof curved wheel-track, used to execute the steps of the simplified dynamic analysis method for a retractable roof curved wheel-track based on the finite mass method.

[0053] Compared with the prior art, the present invention has the following beneficial effects:

[0054] The wheel-track modeling and dynamic analysis method for retractable roofs suitable for heavy-loaded and low-speed movement was established. By establishing a calculation model of the wheel-track structure of the retractable roof, the wheel-track structure of the retractable roof was established by beam units, and the shapes of the retractable track and roller were simulated respectively. The slow rotation of the roof was achieved by the active wheel drive unit. Through the contact model that can consider a larger range of plastic areas, the wheel-track structure modeling and dynamic analysis method suitable for heavy-loaded and low-speed retractable roof systems were established.

[0055] The roller and its shape are simulated by two mass points and a single beam unit, the curved track is simulated by multiple straight beams, and the contact point coordinates are quickly calculated by the wheel-rail contact point algorithm, which effectively reduces the number of units in the wheel-rail structure simulation, realizes the rapid modeling of the retractable roof wheel-rail structure, and reduces the calculation cost;

[0056] An elastic-plastic contact model of wheel-rail contact on a retractable roof is proposed. By introducing a bilinear strengthening model for solid contact, the elastic-plastic contact stress between the wheel and rail is directly obtained by calculating the wheel-rail displacement. The wheel-rail elastic and plastic contact area sizes are quickly obtained by the Newton-Raphson method, and the wheel-rail contact force is then calculated. This realizes the elastic-plastic contact analysis of the wheel-rail contact, which can consider a wide range of elastic-plastic behaviors. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 A schematic diagram of the retractable roof structure provided in this embodiment;

[0058] Figure 2 A schematic diagram of the arc-shaped wheel-rail structure provided in this embodiment;

[0059] Figure 3 A flowchart of a simplified dynamic analysis method for curved wheel-track of a retractable roof based on a finite mass method provided in this embodiment;

[0060] Figure 4 A schematic diagram of virtual inverse motion of a beam unit provided in this embodiment;

[0061] Figure 5 A schematic diagram of an elastic-plastic wheel-rail contact unit provided in this embodiment;

[0062] Figure 6 A schematic diagram of the wheel-rail contact area provided for this embodiment;

[0063] Figure 7 A schematic diagram of the change of the normal elastic-plastic contact force between the wheel and rail provided in this embodiment;

[0064] In the figure, 1, driving wheel; 2, driven wheel; 3, arc track; 4, rotating shaft; 5, central particle; 6, particle at the projection; 7, track particle; 8, virtual beam unit; 9, straight beam unit; 10, arc track center particle. DETAILED DESCRIPTION

[0065] In order to make the purpose, technical scheme and advantages of the embodiments of the present invention clearer, the technical scheme in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in 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. The components of the embodiments of the present invention generally described and shown in the drawings here can be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the drawings is not intended to limit the scope of the claimed invention, but merely represents selected embodiments of the present invention. Based on the embodiments in the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0066] like Figure 1 and Figure 2 As shown, it is a partial schematic diagram of the motion characteristics construction simulation model provided by this embodiment, wherein the roof includes a fixed roof part connected to the building wall and a movable roof part for completing the opening and closing action of the roof, the fixed roof part is provided with an arc track 3, and the fixed roof part is provided with rollers (including a driving wheel 1 and a driven wheel 2) that slide with the arc track 3, and the specific construction process of the simulation model is as follows:

[0067] The arc track 3 is divided into a plurality of sequentially connected straight track segments, and the straight track is discretized into track particles 7 to construct corresponding multi-segment straight beam units 9;

[0068] The rotating shaft center 4 of the roller is discretized into a mass point 5 at the center and a mass point 6 at the projection on the arc track, and a virtual beam unit 8 is set based on the composition of the mass point 5 at the center and the mass point 6 at the projection to characterize the roller radius;

[0069] The contact action between the roller and the arc track 3 is divided into normal force and lateral force, wherein the normal force is modeled based on the normal topological relationship between the wheel and rail and the nonlinear contact relationship between the wheel and rail, and the lateral force is modeled based on the lateral arc topological relationship between the wheel and rail and the lateral contact relationship between the wheel and rail. The modeling of the normal force and the lateral force constitutes an elastic-plastic wheel-rail contact unit.

[0070] like Figure 3 As shown, a simplified dynamic analysis method for curved wheel-track of a retractable roof based on the finite mass method is provided in this embodiment. The trajectory of the roller in the simulation model is calculated based on the finite mass method, and the process is as follows:

[0071] The beam element is analyzed by using virtual reverse kinematics to calculate the internal force corresponding to the deformation of the beam element;

[0072] A wheel-rail contact point solving algorithm is used for the multi-segment straight beam unit to determine the relative position relationship between the mass point of the roller and the multi-segment straight beam unit, wherein the relative position relationship includes the mass point not entering the current straight beam unit, the mass point entering the current straight beam unit, and the mass point leaving the current straight beam unit;

[0073] According to the normal deviation of the roller when entering the current track, the contact state between the roller and the track surface is determined by the elastic-plastic strengthening model, and the corresponding wheel-rail normal contact force is calculated based on the contact state, wherein the contact state includes elastic contact and elastic-plastic contact;

[0074] For the lateral deviation of the roller when entering the current track, the corresponding wheel-rail lateral contact force is calculated by the penalty function method;

[0075] Set the particle motion speed of the active roller, and construct the particle motion equation based on the internal force corresponding to the active roller, the wheel-rail normal contact force, and the wheel-rail lateral contact force;

[0076] Based on the two sets of displacement information of the particle corresponding to the active roller at the previous moment and the current moment, the displacement information of the particle at the next moment is output by solving the particle motion equation;

[0077] The above trajectory calculation is repeated to obtain the motion trajectory of the mass point corresponding to the roller within a period of time, and the dynamic analysis of the opening and closing action of the roof is performed based on the motion trajectory.

[0078] More specifically, if Figure 4 As shown in the figure, the beam unit analysis method separates the beam unit deformation and the rigid body displacement by establishing a follower local coordinate system; the beam unit is translated to the initial position by virtual inverse motion, and the beam unit translation displacement increment -Δx from the final state time t1 (= t0 + Δt) to the initial time t0 is calculated. A and rotation displacement increment –γ; determine the axial deformation and bending deformation of the beam element by comparing the initial state beam element and the beam element obtained by virtual inverse motion; obtain the internal force increment of the beam element through the beam element deformation calculation The internal force increment is converted into the global coordinate system through the transformation matrix between the global coordinate system and the follower local coordinate system, and applied to the beam unit mass point as an external force to obtain the unit internal force.

[0079] The beam element analysis method is described by setting a local coordinate system (LCS) that moves with the beam element. The deformation and motion of the beam element are separated, and the initial axis of the LCS is

[0080]

[0081] Determine the time t a Translational coordinates and rotational coordinates With time tb (=t a +Δt translation coordinates and rotation coordinates The displacement increment within Δt is calculated:

[0082]

[0083] Determine the angle increment within Δt:

[0084]

[0085] By virtual reverse motion, determine the b (=t a +Δt)A′B′ to time t a A”B” displacement increment - Δx A , –γ, compare the difference between A”B” and AB to determine the deformation of the beam element, the axial deformation is t a and t b The difference in connecting rod length at the moment, that is, Δ e = l b -l a ; The bending angles of particles A and B are and Determination of Element Internal Forces from Beam Element Deformations

[0086]

[0087]

[0088]

[0089]

[0090] The internal force increment is converted into the global coordinate system using the transformation matrix Ω and applied to the mass points B and C connected to the beam element to obtain the mass point internal force.

[0091] like Figure 5 and Figure 6 As shown, this embodiment divides the force between the wheel and rail into elastic contact and plastic contact based on the traditional analysis method.

[0092] Among them, the wheel-rail normal elastic-plastic contact unit is based on the roller projection mass point i, the adjacent track mass points m, n, and the arc track center mass point 10 (in the subsequent formulas, the mass point O and the roller projection mass point i are used to distinguish), the mass point i represents the contact point between the roller and the wheel-rail, and the beam unit mn represents the corresponding track; the normal vector of the track surface Omn is calculated by the coordinates of the mass points O, m, n:

[0093] m==rOm × On

[0094] where r ij (=x j -x i ) represents the vector from particle i to particle j. By calculating the vector r Om 、r On 、r Oi The angle relationship between them can be specifically expressed as:

[0095]

[0096] Determine whether the roller moves to track mn.

[0097] Through the orbital surface normal vector m and vector r Oi Calculate the normal displacement disp of the roller relative to the track n :

[0098] disp n =dot(m,r Oi )

[0099] Through the elastic critical displacement δ y Determine the normal contact relationship between the wheel and rail. If disp n ≤δ y , then the wheel-rail is in elastic contact. If disp n >δ y , then the wheel-rail contact is plastic; when the wheel-rail contact is elastic, the normal displacement disp n The maximum elastic contact stress p0 is calculated, and then the wheel-rail normal contact force F is obtained n When the wheel-rail contact is elastoplastic, the wheel-rail contact parameter equations are established by the bilinear hardening model, and the wheel-rail contact force F is obtained by the Newton iteration method. n ; By converting the contact force F n Acting on the mass point, we get the force acting on the roller mass point i

[0100]

[0101] The forces acting on orbital particles m and n are calculated by linear interpolation.

[0102]

[0103] The wheel-rail lateral contact unit is modeled in the same way as the wheel-rail normal nonlinear contact unit to calculate the normal vector m (= r Om × On ); through the normal vectors m and r OiThe lateral displacement disp of the roller relative to the track is obtained by vector calculation l :

[0104] disp l =||r On ||-||r Oi -disp n m||

[0105] The lateral force of the track on the roller is then calculated using the penalty function:

[0106] F l =K l disp l

[0107] Where K l is the lateral stiffness of the track. l Acting on the mass point, we get the force acting on the roller mass point i

[0108]

[0109] The force of orbital particles m and n is calculated by linear interpolation:

[0110]

[0111] The driving wheel driving unit is configured to calculate the driving force of the driving wheel mass by setting the speed of the driving wheel mass moving around the axis; the driving force is applied to the driving wheel mass to drive the driven wheel to rotate, thereby realizing the specified speed rotation of the opening and closing roof.

[0112] The particle motion equation is assumed to be in dynamic equilibrium at each time step. m α is the mass of particle α, and They represent the particle's α external force, normal contact force, lateral contact force, internal force and damping force respectively; by iteratively solving the particle's motion equation through the central difference method, the displacement of the particle within the time step can be directly obtained, and the position and deformation of the unit at the next moment can be calculated.

[0113] like Figure 7 As shown in the figure, the wheel-rail normal elastic-plastic contact force calculation method is to use the wheel-rail contact elastic-plastic strengthening model, and the roller normal displacement disp n Directly obtain the maximum contact stress p0 in the wheel-rail contact area; through the roller normal displacement disp n Determine the wheel-rail contact type; if the wheel-rail contact is elastic, the maximum compressive stress in the contact area is:

[0114]

[0115] Among them, m, n, A, and B are the wheel-rail cross-sectional dimension parameters, which can be obtained by looking up the table. Then, by establishing the contact force F n , contact area parameters a, b equation group:

[0116]

[0117] Get the elastic contact force F n .

[0118] If the wheel-rail contact is elastoplastic, the maximum contact stress can be calculated by the contact bilinear elastoplastic model:

[0119]

[0120] Among them, p y , Represent the regional stress and the corresponding roller compression displacement, respectively, and k represents the strengthening coefficient of the bilinear elastic-plastic model in the plastic stage. By solving the maximum contact stress The corresponding maximum contact stress p0 in the elastic state is:

[0121]

[0122] Among them, E t represents the isopole hardening modulus in the plastic region. Further comparison with the yield stress p y and the maximum contact stress p0 in the elastic state, the elastic zone a, b and the plastic zone a are calculated p 、b p The distribution ratio of:

[0123]

[0124] Furthermore, the equation relationship between p0, contact domain size parameters and contact force is established through the wheel-rail cross-section size parameters:

[0125]

[0126] Among them, f(x,y) represents the distribution function of compressive stress in the contact area, S1 and S2 represent the elastic area and plastic area respectively. Then, the relevant equations are established for the contact area size parameters:

[0127]

[0128] in, is the imaginary wheel-rail contact force corresponding to p0. Combining the above equations, we can establish an equation group f(a, b, a p ,b p). Since it is difficult to find the analytical solution of the above equation, the Newton-Raphson method is used to iteratively solve the above equation. First, based on the equation group G(x) = G(a, b, a p ,b p ) to build its Jacobian matrix:

[0129]

[0130] Then, according to the current roller normal displacement disp n Solve the wheel-rail contact area parameters a and b corresponding to elastic contact as initial estimates, denoted as a0 and b0; and a p 、b p The initial estimate of

[0131] [a p ,b p ]=[0,0]

[0132] Set the initial value x0 = [a, b, a p ,b p ]=[a0,b0,0,0] and substitute it into the following equation:

[0133] J(x0)Δx 0 = -G(x0)

[0134] Update estimates:

[0135] x1=x0+Δx 0

[0136] Then, the above process is iterated continuously until G(x k+1 ) is close enough to the zero vector or Δx k If it is small enough, stop iterating. Output the final result x k , and obtain the parameters of the wheel-rail elastoplastic contact area. Substitute it into the above contact force calculation formula, integrate the distributed stress in the contact area, and calculate the plastic contact force F between the wheel and rail: n .

[0137] This embodiment also provides a simplified dynamic analysis device for a retractable roof curved wheel-track, which is used to execute the steps of the simplified dynamic analysis method for a retractable roof curved wheel-track provided in the above embodiment.

[0138] In summary, the technical solution provided by this embodiment realizes a method for establishing a curved wheel-rail structure of a retractable roof with a simplified model in the simplified modeling and dynamic analysis of the unfolding process of a curved wheel-rail retractable roof, realizing rapid modeling and effectively reducing the calculation cost of the retractable roof movement process; a method for considering the curved track and iteratively solving the motion equation improves the analysis object of the retractable roof, supplements the lack of the analysis method of the retractable roof based on the curved track, and realizes the full process analysis method of the retractable roof; a method for establishing a wheel-rail elastic-plastic contact unit improves the wheel-rail simplified model elastic-plastic analysis, and realizes a more accurate dynamic response analysis method for the retractable roof movement process. The model and analysis results established by this method can be directly applied to the application of curved wheel-rail retractable roof in international engineering, can truly simulate the actual situation, supplement the gap in the current engineering application field, and thus provide important basic conditions for promoting the use of retractable roofs and ensuring their design safety.

Claims

1. A simplified dynamic analysis method of an arc-shaped wheel-track of an opening and closing roof based on a finite mass method, wherein the roof comprises a fixed roof part connected to a building wall and a movable roof part for completing the opening and closing action of the roof, wherein the fixed roof part is provided with an arc-shaped track, and the fixed roof part is provided with a roller that slides with the arc-shaped track, wherein: The simplified dynamic analysis method of the retractable roof curved wheel-rail includes: A simulation model is constructed based on the movement characteristics of the roller during the opening and closing of the roof. The simulation model uses the rolling center of the roller as a mass point and replaces the opening and closing of the roof with the movement of the roller. The shape of the roller is virtually set as a beam unit, the curved track is regarded as a multi-segment straight beam unit, and the contact between the roller and the curved track is regarded as an elastic-plastic wheel-rail contact unit. The trajectory of the roller in the simulation model is calculated based on the finite mass method. The process is as follows: The beam element is analyzed by using virtual reverse kinematics to calculate the internal force corresponding to the deformation of the beam element; A wheel-rail contact point solving algorithm is used for the multi-segment straight beam unit to determine the relative position relationship between the mass point of the roller and the multi-segment straight beam unit, wherein the relative position relationship includes the mass point not entering the current straight beam unit, the mass point entering the current straight beam unit, and the mass point leaving the current straight beam unit; According to the normal deviation of the roller when entering the current track, the contact state between the roller and the track surface is determined by the elastic-plastic strengthening model, and the corresponding wheel-rail normal contact force is calculated based on the contact state, wherein the contact state includes elastic contact and elastic-plastic contact; For the lateral deviation of the roller when entering the current track, the corresponding wheel-rail lateral contact force is calculated by the penalty function method; Set the particle motion speed of the active roller, and construct the particle motion equation based on the internal force corresponding to the active roller, the wheel-rail normal contact force, and the wheel-rail lateral contact force; Based on the two sets of displacement information of the particle corresponding to the active roller at the previous moment and the current moment, the displacement information of the particle at the next moment is output by solving the particle motion equation; The above trajectory calculation is repeated to obtain the motion trajectory of the mass point corresponding to the roller within a period of time, and the dynamic analysis of the opening and closing action of the roof is performed based on the motion trajectory.

2. The simplified dynamic analysis method of curved wheel-rail of retractable roof based on finite mass method according to claim 1 is characterized in that: The specific construction process of the simulation model is as follows: The arc track is divided into multiple segments of sequentially connected straight tracks, and the straight tracks are discretized into mass points to construct corresponding multiple straight beam units; The roller is discretized into a mass point at the center and a mass point at the projection on the arc track, and a virtual beam unit is set based on the composition of the mass point at the center and the mass point at the projection to characterize the roller radius; The contact action between the roller and the curved track is divided into normal force and lateral force. The normal force is modeled based on the normal topological relationship between the wheel and rail and the nonlinear contact relationship between the wheel and rail. The lateral force is modeled based on the lateral curved topological relationship between the wheel and rail and the lateral contact relationship between the wheel and rail. The modeling of the normal force and the lateral force is combined to form an elastic-plastic wheel-rail contact unit.

3. The simplified dynamic analysis method of curved wheel-rail of retractable roof based on finite mass method according to claim 1 is characterized in that: The analysis process of the virtual beam unit is as follows: Establish a follow-up local coordinate system to separate the beam element deformation and rigid body displacement; The beam element is translated to the preset initial position through virtual reverse motion to calculate the translation displacement increment and rotation displacement increment of the beam element from the final state to the initial state, and the axial deformation and bending deformation are determined by comparing the beam element before and after the virtual reverse motion; Calculate the internal force increment of the beam element based on the axial deformation and bending deformation of the beam element; The internal force increment is converted into the global coordinate system through the transformation matrix between the global coordinate system and the follower local coordinate system, and applied to the beam unit mass point as an external force to obtain the internal force corresponding to the deformation of the beam unit.

4. The simplified dynamic analysis method of curved wheel-rail of retractable roof based on finite mass method according to claim 1 is characterized in that: The relative position relationship is expressed as follows: Among them, m is the mass point corresponding to the previous straight beam unit, n is the mass point corresponding to the next straight beam unit, O is the center mass point of the arc track corresponding to the multi-segment straight beam unit, and i is the contact point between the roller and the arc track.

5. The simplified dynamic analysis method of curved wheel-rail of retractable roof based on finite mass method according to claim 1 is characterized in that: The calculation process of the wheel-rail normal contact force is as follows: In the elastic-plastic strengthening model, set the mass point corresponding to the first straight beam unit, the mass point corresponding to the second straight beam unit, the mass point at the center of the arc track corresponding to the multi-segment straight beam unit, and the contact point between the roller and the arc track; Based on the mass point corresponding to the previous straight beam unit, the mass point corresponding to the next straight beam unit and the mass point at the center of the circle, the corresponding normal vector of the orbital surface is constructed; Based on the center mass point and the contact point, the corresponding contact vector is constructed; Based on the track surface normal vector and the contact vector, the normal displacement of the roller relative to the current track is calculated; When the normal displacement is less than or equal to the preset elastic critical displacement, the contact between the roller and the track is elastic, otherwise it is elastoplastic contact; When it is determined to be elastic contact, the corresponding elastic contact stress is calculated by the normal displacement, and the corresponding wheel-rail normal contact force is converted based on the elastic contact stress; When it is determined to be an elastic-plastic contact, the distribution ratio of the elastic zone and the plastic zone is calculated by using the yield stress and the elastic contact stress, and an equation relationship is established based on the distribution ratio and the stress of the corresponding area; Iteratively solving the equation relationship to obtain stress distribution in the contact area; The stress distribution is integrated to obtain the wheel-rail plastic contact force, and the corresponding wheel-rail normal contact force is converted based on the wheel-rail plastic contact force.

6. The simplified dynamic analysis method of curved wheel-rail of retractable roof based on finite mass method according to claim 1 is characterized in that: The calculation process of the wheel-rail lateral contact force is as follows: F l =K l disp l Among them, disp l represents the lateral displacement of the roller relative to the track, K l is the lateral stiffness of the track.

7. The simplified dynamic analysis method for curved wheel-rail of retractable roof based on finite mass method according to claim 1 is characterized in that: The particle motion equation is expressed as follows: Among them, m α is the mass of particle α, is the external force on the particle α, is the normal contact force of particle α, is the lateral contact force of particle α, is the internal force of particle α, Represents the α damping force of the particle.

8. A simplified dynamic analysis device for curved wheel-track of retractable roof, characterized in that: The method is used to execute the simplified dynamic analysis method of curved wheel-rail of retractable roof based on finite mass method as described in any one of claims 1 to 7.

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