A simulation and optimization design method and system for EMU snow plows based on multi-physics field coupling

Abstract

This application discloses a simulation and optimization design method for a snow plow for EMUs based on multi-physics field coupling. Efficient snow plow design is achieved through three stages: physical modeling, experimental verification, and parameter optimization. The method collects environmental parameters for line snowfall and snow density, establishes a soft-ball dynamics model for snow particles based on the Hertz-Mindlin with JK R Cohesion contact model, and simulates the wall-covering snow process using a discrete phase model. The simulation accuracy is verified through snow removal experiments. A parameterized snow plow model is constructed, and shape parameters are introduced to modify the driving resistance coefficient, evaluate snow removal performance, and select the optimal geometric parameter combination. The vehicle model is constructed by integrating the front end, modifying the snow removal resistance formula under multi-body coupling, and generating snow plow selection recommendations. Simulating different snow depth and speed conditions, a correlation model is established, and the maximum safe vehicle speed threshold that meets operational constraints is output. Through multi-physics field coupling simulation and parameter optimization, the limitations of traditional design relying on experience are overcome, achieving coordinated optimization of snow removal efficiency, driving safety, and structural strength.

Description

Technical Field

[0001] The present invention relates to the technical field of obstacle clearance for rail vehicles, and particularly to a simulation and optimization design method and system for a snow plow of a multiple unit train based on multi-physical field coupling. Background Art

[0002] Frequent snowfall has severely restricted the railway transportation capacity in alpine regions. The impact of snow accumulation on the rail surface on railway transportation is mainly divided into the impact of the resistance generated by snow removal on train operation and the impact of snow removal on the surrounding environment, such as causing deeper snow accumulation on adjacent railways. When a high-speed train travels on a snow-covered route, the snow layer accumulated along the running line collides with the train body, and the resulting snow removal resistance in the running direction will increase the burden on the train's power system; the snow removal process may also affect the wheel load of the train, reducing the running stability and comfort, and in severe cases, there is a risk of overturning.

[0003] Currently, for snow accumulation on the track, a snow plow device is mostly installed at the front end of the train to discharge the snow above the rail into the snow ditch to ensure the continuous running of the train. The snow plow is a plow-shaped snow removal device installed at the front end of the train, and this device is an important structure for preventing snow on the train. In recent years, the structural design of the plow-shaped snow removal device has become an important part of the structural design of railway locomotives and vehicles in some countries; in the initial stage of snowfall, when the depth of snow accumulation does not seriously affect train safety, the train with a plow-shaped snow removal device installed at the front can smoothly discharge the snow above the rail into the snow ditch, thus ensuring that the train can continue to run. Such an autonomous snow removal driving measure can effectively improve the transportation efficiency of the train under snowfall conditions, thereby greatly reducing the negative impacts caused by snowfall.

[0004] However, the existing design of snow plows mainly relies on experience and physical tests, lacking in-depth research on the snow removal mechanical mechanism under different snow depths, vehicle speeds, and snow plow geometries. This design method is not only costly and time-consuming during the test process, but also difficult to adjust and optimize the design scheme in a timely manner when dealing with rapidly changing actual working conditions. Especially in the case of deeper snow accumulation or high-speed train operation, the snow removal resistance may suddenly increase, resulting in the wheel load reduction rate exceeding the safety design standard, posing a serious threat to the running safety of the train.

[0005] Therefore, there is an urgent need for a multi-physical field coupling simulation and analysis method for the external shape design of snow plows and the determination of vehicle speed limits. Summary of the Invention

[0006] Object of the Invention: To overcome the above deficiencies, the object of the present invention is to provide a simulation and optimization design method and system for a snow plow of a multiple unit train based on multi-physical field coupling.

[0007] To solve the above technical problems, the present invention provides a simulation and optimization design method for a snow plow of a multiple unit train based on multi-physical field coupling, including:

[0008] Step S1: Collect the snow environment parameters of the target line, where the environment parameters at least include snowfall data and snow accumulation data; Step S2: Establish a soft sphere model of snow particles and adopt a contact model of Hertz-Mindlin with JKR Cohesion to calculate the contact force between snow particles; Step S3: Based on the wall snow covering criterion and adopt the discrete phase model to conduct snow covering simulation, and then verify the correctness of the snow removal resistance formula in the snow covering simulation by comparing with the preset snow removal experiment data; Step S4: Establish a snow plow model by using the parametric modeling method, and introduce shape parameters into the snow removal resistance formula according to the simulation results to simplify the driving resistance coefficient, and then evaluate the snow removal performance of the snow plow under the preset shape parameter combination to determine the snow removal resistance formula of the snow plow; Step S5: Add a locomotive head to the snow plow model to form a whole vehicle model and conduct simulation according to the whole vehicle model, and then correct the snow removal resistance formula and generate a snow plow selection recommendation; Step S6: Conduct simulation under the driving speed in the preset snow depth environment to obtain the forces on the train and the snow removal path under different snow depth and driving speed conditions, and then generate the maximum speed that can meet the actual operation requirements under different snow depth conditions according to the preset constraint conditions; Step S7: Output the optimal design parameters of the snow plow.

[0009] Among them, the target line is selected by the test personnel according to actual needs.

[0010] On the one hand, in Step S2, the method for establishing the soft sphere model of snow particles includes: the soft sphere model simplifies the contact process between particles into the damped vibration of a spring oscillator, and its motion equation is: where x is the displacement from the equilibrium position, m is the mass of the oscillator, and c and k are the spring damping coefficient and elastic coefficient respectively;

[0011] where the normal elastic coefficient k n is: where E and v are the elastic modulus and Poisson's ratio of the particle material respectively, R is the particle radius, and the subscripts i and j respectively represent the particles i and j in contact. When the particles i and j belong to the same homogeneous material and have the same particle size, then k n is where the tangential elastic coefficient k t is: where α is the normal overlap, G i and G j are the shear moduli of particles i and j respectively. When the particles i and j belong to the same homogeneous material and have the same particle size, then k t is

[0012] On the one hand, the method for determining the damping coefficient includes: for a spring oscillator with a mass of m, if it is in the critical damping state, the mechanical energy decays at the fastest speed, and at this time, the normal damping coefficient c n and the tangential damping coefficient c t are respectively:

[0013] Or, the damping coefficient is coupled with the restitution coefficient e:

[0014] wherein, e is determined by experiments.

[0015] On the one hand, in step S2, the method for defining the Hertz-Mindlin with JKR Cohesion contact model includes: the JKR normal force is based on the overlap δ, the interaction parameter, and the surface energy γ: wherein, E* is the equivalent Young's modulus, and R* is the equivalent radius; the damping force has the expression: wherein, is the equivalent mass, is the normal component of the relative velocity, and β and S n has the expression: The tangential force F t has the expression: wherein, S t is the tangential overlap, G* is the equivalent shear modulus, is the tangential component of the relative velocity; wherein, the tangential force is restricted by the Coulomb friction μ s F n where μ s is the static friction coefficient, and the rolling friction exerts a moment on the contact surface: τ i =-μ r F n R i ω i , wherein, μ r is the rolling friction coefficient, R i is the distance from the contact point to the centroid, and ω i is the unit angular velocity vector of the object at the contact point; the maximum gap with non-zero cohesion between particles is calculated by the following formula: where when δ < δ c , the model returns 0; when the particles are not in actual contact and the interval is less than δ c , the cohesion reaches the maximum value. Thus, the maximum cohesion is: The force required to separate two particles depends on the liquid surface tension γ sand the wetting angle.

[0016] On the one hand, in step S3, the discrete phase model includes: the discrete phase model continuity and momentum conservation equations are respectively: where ρ f , u and P are respectively the density, velocity and pressure of the fluid, t is the time, g is the acceleration due to gravity, and α f is the fluid volume fraction, calculated by V c , V p are respectively the total volume of the control volume unit and the particle volume; F f-p is the force between the air phase and the snow phase, mainly the particle drag force F drag ; τ is the fluid viscous stress tensor, calculated by , where I is the unit tensor and μ f is the fluid viscosity including the kinematic viscosity and the turbulent viscosity; for the snow phase, the snow particles are regarded as spheres, and its force balance equation is: where m p , u p and ρ p are respectively the mass, velocity and density of the snow particles, and F is the additional external field; where where d p is the snow particle diameter, C D is the particle drag coefficient, and according to the smooth sphere model, it is determined by a set of empirical constants a e,p -a 1 -a 3 determined by the range of the particle Reynolds number R Calculating the particle trajectory: Solving this differential equation along each coordinate direction to obtain the trajectory of the discrete phase; using the traditional SIMPLE method to solve the control equation of the fluid phase, and then cooperating with the explicit time integration method to realize the solution of the motion equation of the particles in the flow field.

[0017] On the one hand, in step S3, the wall snow covering criterion includes: when the incident angle α is less than the capture angle α t , the snow particles are captured by the wall; when the local friction velocity is less than the preset threshold friction velocity, the snow particles will not be carried away by the wind and accumulate; when the particle collision velocity u p is less than the critical capture velocity u trap , the viscous force of the wall on the particles is large and the particles will be captured; when the particles meet the above three wall snow covering criteria, the snow particles will be captured by the wall and stably accumulate on the wall to achieve snow covering of the wall.

[0018] On the one hand, in step S4, the method of establishing a snow plow model using parametric modeling includes: Step S41: Select a horizontal plane and determine the specific position and length of the line segment based on the opening angle and vehicle width; Step S42: Select the vertical symmetry plane of the snow plow and determine the leading edge line segment and the angle-of-attack constraint line of the snow plow based on the total height and lower half height of the snow plow; Step S43: Generate the lower half plane of the snow plow from the determined line segments; Step S44: Project the bottom line onto the upper edge plane of the snow plow through converting solid reference to determine the datum plane where the rear spline curve is located; Step S45: Determine the rear spline curve based on the suppression angle and vehicle width, with the boundary conditions being tangent to the plane determined by the angle of attack, suppression angle constraint, and suppression angle height constraint; Step S46: Determine the front spline curve, with the boundary conditions being the protruding distance at the very front of the snow plow and being tangent to the angle-of-attack plane and the line segment; Step S47: Generate a surface and a plane to complete the modeling of half of the snow plow, and then mirror the entity to complete the snow plow modeling.

[0019] On the one hand, in step S4, the method further includes: The expression for calculating the snow removal resistance is: F p =ChwρV 2 , where h is the snow removal depth, w is the snow removal width, ρ is the snow density, V is the driving speed; C is the coefficient for calculating the driving resistance, C = C 0 +C 1 +C 2 , where C 0 is obtained by linear interpolation from a preset table, C 1 =0.028(δ + 2γ)×10 -4 , δ is the suppression angle, γ is the angle of attack; for C 2 : when θ < 45°, C 2 ={5.64 + 0.008×(45 - θ)}×10 -4 ; when 45° ≤ θ ≤ 90°, C 2 ={5.64 + 0.0025×(θ - 45)}×10 -4 , where θ is the inclination angle.

[0020] On the one hand, in step S6, the method includes: Taking the wheel load reduction rate not exceeding a preset value and combined with clear driver's line of sight as the constraint conditions, and through simulation under the driving speed in a preset snow depth environment, generating the highest speed that can meet the actual operation requirements under different snow depth conditions.

[0021] The present application also provides a simulation and optimization design method for a multiple - physical - field - coupled EMU snowplow using the above - mentioned method, including: a data acquisition module for collecting snow environment parameters of a target line, where the environment parameters at least include snowfall data and snow accumulation data; a model processing module for establishing a soft - sphere model of snow particles and using a contact model of Hertz - Mindlin with JKR Cohesion to calculate the contact force between snow particles; a simulation and simulation module for performing snow - covering simulation based on the wall - snow - covering criterion and using the discrete - phase model, and then verifying the correctness of the snow - removal resistance formula in the snow - covering simulation by comparing with preset snow - removal experiment data; a resistance determination module for establishing a snowplow model using the parametric modeling method, and introducing shape parameters into the snow - removal resistance formula according to the simulation results to simplify the running resistance coefficient, and then evaluating the snow - removal performance of the snowplow under a preset combination of shape parameters to determine the snow - removal resistance formula of the snowplow; a snowplow selection module for adding a locomotive head to the snowplow model to form a whole - vehicle model and performing simulation according to the whole - vehicle model, and then correcting the snow - removal resistance formula and generating snowplow selection suggestions; a design optimization module for performing simulation at a preset speed in a snow - depth environment to obtain the forces on the train and the snow - removal path under different snow - depth and driving - speed conditions, and then generating the maximum speed that can meet the actual operation requirements under different snow - depth conditions according to preset constraint conditions; a design output module for outputting the optimal design parameters of the snowplow.

[0022] The above - mentioned technical solution of the present application has the following advantages compared with the prior art:

[0023] 1. A wedge - shaped body snow - covering test was carried out using real snow and compared with the simulation, verifying the effectiveness of the wall - capturing criterion in simulating snow - covering, which can be used for vehicle snow - accumulation simulation in the later stage. The discrete - element method was used to simulate and restore the snow - removal test of the plow - type snowplow. The error between the simulated and experimental snow - removal resistances was about 3.5%. The variation trend of the snow - removal resistance with vehicle speed, snow depth, snow width, and snow density was consistent with the snow - removal resistance formula, proving the reliability of the Hertz - Mindlin with JKR Cohesion collision model.

[0024] 2. Snow - removal simulations were carried out on various snowplow shapes and locomotive heads, obtaining the influence law of shape parameters on the snow - removal resistance, determining the basis for the fixed value of the correction coefficient in the snow - removal resistance formula, and predicting the snow - removal resistance in advance, which can provide a reference for vehicle power configuration. Considering both the snow - removal resistance and the snow - removal path, optimal snowplow shape parameters were generated.

[0025] 3. Compared with traditional empirical design, it can more accurately predict the snow - removal resistance and its impact on vehicle safety; it can be quickly adjusted according to the snowfall amount, snow density, and vehicle type of different railway lines; using multiple - physical - field - coupled simulation, multiple schemes can be batch - tested on a computer, greatly shortening the design cycle. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are only the embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained according to the provided drawings without creative efforts.

[0027] Figure 1 It is a schematic diagram of the shape parameters of the snow removal plow provided by the embodiment of the present invention.

[0028] Figure 2 It is a schematic diagram of the soft sphere model in contact with each other provided by the embodiment of the present invention.

[0029] Figure 3 It is a schematic diagram of the simplified treatment of the contact force between particles by the soft sphere model provided by the embodiment of the present invention.

[0030] Figure 4 It is a schematic diagram of the low / normal temperature snowfall simulation wind tunnel provided by the embodiment of the present invention.

[0031] Figure 5 It is a schematic diagram of the test equipment provided by the embodiment of the present invention.

[0032] Figure 6 It is a schematic diagram of the wall snow covering criterion provided by the embodiment of the present invention.

[0033] Figure 7 It is a schematic diagram of the wedge-shaped body models of two shapes provided by the embodiment of the present invention.

[0034] Figure 8 It is a schematic diagram of the snow covering of the first wedge-shaped body provided by the embodiment of the present invention.

[0035] Figure 9 It is a schematic diagram of the snow covering of the second wedge-shaped body provided by the embodiment of the present invention.

[0036] Figure 10 It is a schematic diagram of the simulation calculation domain provided by the embodiment of the present invention.

[0037] Figure 11 It is a schematic diagram of the comparison of the snow covering results of the first wedge-shaped body provided by the embodiment of the present invention.

[0038] Figure 12 It is a schematic diagram of the cloud map of the particle capture criterion and the flow field of the first wedge-shaped body provided by the embodiment of the present invention.

[0039] Figure 13 It is a schematic diagram of the comparison of the snow covering results of the second wedge-shaped body provided by the embodiment of the present invention.

[0040] Figure 14 It is the contour map of the second wedge-shaped particle capture criterion and the schematic diagram of the flow field provided by the embodiment of the present invention.

[0041] Figure 15 It is the schematic diagram of the regression fitting of the DEM simulation data provided by the embodiment of the present invention.

[0042] Figure 16 It is the schematic diagram of snow density - snow removal resistance provided by the embodiment of the present invention.

[0043] Figure 17 It is the schematic diagram of model width - snow removal resistance provided by the embodiment of the present invention.

[0044] Figure 18 It is the schematic diagram of snow removal depth - snow removal resistance provided by the embodiment of the present invention.

[0045] Figure 19 It is the schematic diagram of the simulation results of the opening and closing type and closed type snow plows provided by the embodiment of the present invention.

[0046] Figure 20 It is the schematic diagram of the simulation results of the 60 - 45 - 0 - 55 vehicle model provided by the embodiment of the present invention.

[0047] Figure 21 It is the schematic diagram of the position of the pressure measurement point provided by the embodiment of the present invention.

[0048] Figure 22 It is the comparison schematic diagram of the snow removal width with different suppression angles provided by the embodiment of the present invention.

[0049] Figure 23 It is the comparison schematic diagram of the snow removal height with different suppression angles provided by the embodiment of the present invention.

[0050] Figure 24 It is the schematic diagram of the numerical simulation calculation domain provided by the embodiment of the present invention.

[0051] Figure 25 It is the schematic diagram of the height of the end of the downward pressing wing provided by the embodiment of the present invention. Detailed implementation manners

[0052] The embodiments of the present invention will be described in detail below. Examples of the embodiments are shown in the accompanying drawings, where the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are intended to explain the present invention and should not be construed as limiting the present invention.

[0053] Considering the snow accumulation on the track caused by snowfall, a snow plowing device is installed at the head of the train to help the train plow snow at high speed autonomously in the initial stage of snow accumulation. For the snow plow at the head of the multiple unit train, the snow plowing resistance generated during the snow plowing process is of particular concern in this application. This parameter is affected by many factors such as the running speed, the shape of the snow plow and the snow accumulation environment. In particular, referring to the parameters given by the Railway Technical Research Institute of Japan, the shape of the snow plow is mainly controlled by four parameters, namely the opening angle α, the inclination angle β, the attack angle γ, and the suppression angle δ. For specific reference, see Figure 1 as shown.

[0054] In this application, the discrete element numerical calculation method is used to evaluate different combinations of the above shape parameters of the snow plow, and to evaluate the snow plowing performance of the snow plow under different parameter combinations; to determine the prediction formula of the snow plowing resistance of the snow plow, so as to provide data support for traction checking. Numerical simulation calculations are not affected by the constraints of test conditions. Various phenomena or conditions can be considered separately, and the mechanism of the phenomena can be studied in depth to obtain quantitative results of nonlinear problems. During the engineering design process, the influence of different parameter changes on the optimization target can be obtained through calculation, which is convenient for multi-scheme comparison. It has the characteristics of short research cycle and low cost, and has its superiority compared with various model tests and real vehicle tests.

[0055] The discrete element method is a method for analyzing particulate discrete materials. The basic idea of the discrete element method is to separate the discontinuous body into a set of rigid elements, make each rigid element satisfy the motion equation, and use the time-step iteration method to solve the motion equations of each rigid element, and then obtain the overall motion form of the discontinuous body. Using the discrete element method for simulation analysis, a large amount of complex behavior information of discrete materials and particle-scale behavior information that is not easy to measure can be directly obtained, and an advanced solution approach can be provided for the motion, force, heat, and energy transfer of particle flows. In addition, the discrete element method can use simple equations to simulate the quasi-static and dynamic behaviors of highly complex systems, making the solution approach simple and feasible. For the mechanical behavior of materials that cannot be explained and analyzed by the continuous medium theory, the discrete element method can also make accurate predictions and analyses.

[0056] The discrete element method regards the discrete body as a set of discrete particle units with a certain shape and mass, and each particle is an unit. For the convenience of analysis, the following assumptions are made:

[0057] (1) The particles are rigid bodies, and the deformation of the particle system is the sum of the deformations at the contact points of these particles;

[0058] (2) The contact between particles occurs in a very small area, that is, point contact;

[0059] (3) The particle contact characteristic is soft contact, that is, the rigid particles allow a certain amount of overlap at the contact point. The amount of overlap between particles is very small compared to the particle size, and the deformation of the particles themselves is also much smaller than the translation and rotation of the particles.

[0060] (4) Within each time step, the perturbation cannot be propagated from any particle to its adjacent particles simultaneously. At all times, the resultant force acting on any particle can be uniquely determined by the interaction between the particles in contact with it.

[0061] The most important point in the discrete element method is to use an efficient computational method to determine the contact between three-dimensional particles. The form of the expressed contact can be the contact between arbitrary-shaped blocks, and the geometric and physical characteristics of the contact can be expressed.

[0062] The soft-sphere model simplifies the normal force between particles into a spring and a damper, and the tangential force into a spring, a damper, and a slider. Parameters such as the elastic coefficient and the damping coefficient are introduced. Without considering the surface deformation of the particles, the contact force is calculated based on the normal overlap and the tangential displacement between particles, without considering the loading history of the contact force. The calculation intensity is relatively small and is suitable for the numerical calculation of engineering problems. The hard-sphere model completely ignores the magnitude of the particle contact force and the details of the particle surface deformation. The contact process is simplified to an instantaneous collision process, and the post-collision velocity is directly given, which is the result of the time integration of the force during the contact process. The dissipation of energy during the collision process is expressed using the coefficient of restitution. The hard-sphere model is mainly applied to the numerical simulation of fast-moving and low-concentration particle systems. Due to the relatively large concentration of snow particles during the train snow removal process and considering the errors caused by the deep simplification of the actual physical process by the hard-sphere particles, the soft-sphere model is used in this application for simulation calculations.

[0063] The soft-sphere model simplifies the particle contact process into the damped vibration of a spring oscillator, and its motion equation is: where x is the displacement from the equilibrium position, m is the mass of the oscillator, and c and k are the spring damping coefficient and the elastic coefficient respectively.

[0064] It can be seen from this motion equation that the restoring force acting on the particle is proportional to the magnitude of the displacement, and the viscous resistance is proportional to the magnitude of the velocity and in the opposite direction. Therefore, the energy of the spring oscillator gradually decays. As the damping increases, the spring oscillator exhibits underdamped vibration, critically damped vibration, and overdamped vibration respectively.

[0065] Reference Figure 2 As shown, particle i contacts particle j at point C under inertia or external force, and the dotted line represents the position of particle i at the beginning of contact; as the two particles move relative to each other, the particle surfaces gradually deform and generate a contact force. The soft-sphere model does not consider the details of this deformation and only calculates the normal overlap α and the tangential displacement δ, and then obtains the contact force.

[0066] The soft-sphere model sets springs, dampers, sliders, and couplers between particle i and particle j. The coupler is used to determine the paired relationship of the particles in contact without introducing any force. In the tangential direction, if the tangential force exceeds the yield value, the two particles slide under the action of the normal force and the frictional force, and this is achieved by the sliding damper. The soft-sphere model needs to introduce parameters such as the elastic coefficient k and the damping coefficient c to quantify the effects of the spring, damper, and slider. Refer to Figure 3 as shown.

[0067] The normal force is the resultant of the elastic force and the damping force acting on particle i by the spring and the normal damper. Refer to Figure 2 and Figure 3 as shown. For two-dimensional particles, the magnitude of the elastic force is proportional to the overlap, and the damping force is proportional to the relative velocity of the particles. Then F nij = (-k n α - c n v ij ·n)n, where α is the normal overlap; v ij is the velocity of particle i relative to particle j, v ij = v i - v j ; n is the unit vector from the center of particle i to the center of particle j, k n and c n are the normal elastic coefficient and the normal damping coefficient of particle i.

[0068] For three-dimensional spherical particles, according to Hertz contact theory, F nij is expressed as This tangential force F nij is expressed as F nij = -k t δ - c τ v ct , where k t and c τ are the tangential elastic coefficient and the tangential damping coefficient; v ct is the slip coefficient at the contact point, δ is the tangential displacement at the contact point, and in three-dimensional motion, it is not necessarily in the same direction as the sliding velocity vector v ct .

[0069] The sliding velocity vector v ct is: v ct = v ij - (v ij ·n)n + R i ω i ×n + R j ω j ×n, where R i and R j are the radii of particle i and particle j respectively; ω i and ωj They are the angular velocities of particle i and particle j respectively.

[0070] If |F tij | > μ s |F nij |, then particle i slides, and the tangential force is F tij = -μ s |F nij |n t , that is, Coulomb's friction law, where μ s is the static friction coefficient.

[0071] The tangential unit vector n t is determined by the following formula: The resultant force and resultant moment acting on particle i are F ij = F nij + F tij , T ij = r in × F tij , where r is the distance from the centroid of the particle to the contact point. When the particle concentration is high, particle i can be in contact with several particles simultaneously. Then the total force and total moment acting on particle i are:

[0072] F i = ∑ j (F nij + F tij ), T i = ∑ j (R i n × F tij ).

[0073] The damping coefficient of the elastic coefficient introduced by the soft - sphere model is related to parameters such as the elastic modulus and Poisson's ratio of the particle material, but it cannot be directly measured and needs to be calibrated. The normal elastic coefficient k n is determined by Hertz contact theory:

[0074] where E and v are the elastic modulus and Poisson's ratio of the particle material respectively, R is the particle radius, and the subscripts i, j represent particle i and particle j in contact respectively. When particle i and particle j are of the same homogeneous material and have the same particle size, then k n is

[0075] The tangential elastic coefficient k t is: where α is the normal overlap, G i and G j are the shear moduli of particle i and particle j respectively. When particle i and particle j are of the same homogeneous material and have the same particle size, then k t is

[0076] During the particle contact process, k n and k t are related to the normal overlap and need to be calculated in real time according to the contact process. However, the computational amount is very large. For the sake of computational convenience, the soft-sphere model usually assumes that the elastic coefficient, damping coefficient, etc. remain unchanged throughout the contact process, ignoring details such as the loading history and deformation.

[0077] If a spring oscillator with mass m is in the critical damping state, the mechanical energy decays at the fastest speed. At this time, the normal damping coefficient c n and the tangential damping coefficient c t are respectively:

[0078]

[0079] Or, the damping coefficient is coupled with the restitution coefficient e:

[0080] where e is determined by experiments.

[0081] Particles interact with each other and with the wall, and contacts are established through the forces between them. Physically contacting particles in relative motion generate forces accordingly, and they are said to be in the contact state. Each contact is divided into a contact stiffness model, a sliding model, and a bonding model according to different constitutive relations. In the contact stiffness model, the contact force and the relative displacement are linearly related. The sliding model allows the two contacting entities to slide relative to each other and separate. The bonding model provides normal tensile and tangential shear strengths for each contact point. In this project, the Hertz-Mindlin with JKR Cohesion model is selected to simulate snow particles.

[0082] Hertz-Mindlin with JKR (Johnson-Kendall-Roberts) Cohesion is a cohesive contact model that allows users to simulate strongly adhesive systems, such as dry powders or wet particles. In this model, the normal elastic contact force is implemented based on the Johnson-Kendall-Roberts theory.

[0083] The Hertz-Mindlin (no slip) model is the default model used in EDEM and is accurate and efficient in force calculation. In this model, the normal force component is based on Hertzian contact theory, and the tangential force model is based on the research work of Mindlin-Deresiewicz. Both the normal force and the tangential force have damping components. The tangential frictional force obeys Coulomb's friction law. The rolling frictional force is realized through a contact-independent oriented constant torque model.

[0084] Normal force Among them, the equivalent Young's modulus \(E^*\) and the equivalent radius \(R^*\) are defined as:

[0085] where \(E\) i , \(v\) i , \(R\) i and \(E\) j , \(v\) j , \(R\) j are the Young's modulus, Poisson's ratio, and the radius of the contact sphere, respectively.

[0086] In addition, the expression of the damping force \(F_d\) is: where is the equivalent mass, is the normal component of the relative velocity, and the expressions of \(\beta\) and \(S\) n are:

[0087] where \(e\) is the coefficient of restitution.

[0088] The tangential force \(F_t\) t depends on the tangential overlap \(\delta\) t and the tangential stiffness \(S\) t , that is: \(F_t\) t = -\(S\) t \(\delta\) t , where

[0089] \(G^*\) is the equivalent shear modulus; thus, the expression of the tangential force \(F_t\) t is:

[0090] where is the tangential component of the relative velocity; among them, the tangential force is limited by the Coulomb friction \(\mu\) s \(F_t\) n where \(\mu\) s is the coefficient of static friction, and the rolling friction exerts a moment on the contact surface:

[0091] \(\tau\) i = -\(\mu\) r \(F_t\) n \(R\) i \(\omega\) i , where \(\mu\) r is the coefficient of rolling friction, \(R\) i is the distance from the contact point to the centroid, and \(\omega\) i is the unit angular velocity vector of the object at the contact point.

[0092] Hertz-Mindlin with JKR Cohesion uses the same method as the Hertz-Mindlin (no slip) contact model to calculate forces in the following forms: tangential elastic force, normal dissipative force, and tangential dissipative force.

[0093] The JKR normal force is based on the overlap δ, the interaction parameter, and the surface energy γ:

[0094] where E* is the equivalent Young's modulus and R* is the equivalent radius;

[0095] This model provides attractive cohesion even when the particles are not in direct contact. The maximum gap with non-zero cohesion between particles is calculated by: where when δ < δ c , the model returns 0;

[0096] When the particles are not in actual contact and the separation is less than δ c , the cohesion reaches its maximum value. Thus, the maximum cohesion is called the pull-out force and is: The calculation of the frictional force is different from the Hertz-Mindlin (no slip) contact model in that it depends on the positive repulsive part of the JKR normal force. Therefore, the JRK friction model provides a greater frictional force when the cohesive component of the contact force is larger. This model is designed for fine, dry particles and can also be used to simulate wet particles. The force required to separate two particles depends on the liquid surface tension γ s and the wetting angle.

[0097] Simulation study of the wind-snow coupling effect. For the simulation of the snow phase, the treatment methods can be divided into the Euler method and the Lagrangian method. For the former, the snow phase is treated as a continuous medium that interpenetrates with the fluid (air) phase. By introducing the phase volume fraction, the gas-solid phases in the control volume are distinguished and used to guide the solution of the conservation equations of each phase. For the latter, the fluid (air) phase is the continuous phase, while the snow phase is treated as a discrete particle system. The gas-solid phase coupling is achieved through parameters such as the particle drag force, and then the exchange of phase quantity and momentum is calculated. Among them, the Lagrangian method represented by the discrete phase model is widely used in the simulation study of snow-covered walls.

[0098] Its continuity and momentum conservation equations are respectively:

[0099] where ρ f , u, and P are the density, velocity, and pressure of the fluid respectively, t is the time, g is the acceleration due to gravity, α f is the fluid volume fraction, and

[0100] α f = 1 - V p / V c Calculation, V c 、V p are the total volume of the control volume element and the particle volume respectively; F f-p is the force between the air phase and the snow phase, mainly the particle drag force F drag ; τ is the fluid viscous stress tensor, calculated by

[0101] where I is the unit tensor, and μ f is the fluid viscosity including the kinematic viscosity and the turbulent viscosity, which can be applied in the selected turbulent models, such as the RANS Reynolds-averaged model, the LES large eddy model, and the DNS direct simulation model, etc.

[0102] For the snow phase, the snow particles are regarded as spheres, and its force balance equation is: where m p 、u p and ρ p are the mass, velocity, and density of the snow particle respectively, and F is the additional external force field; where,

[0103] where d p is the snow particle diameter, C D is the particle drag coefficient, which is determined according to the smooth sphere model by a set of empirical constants a e,p determined by the range of the particle Reynolds number R 1 -a 3 ;

[0104]

[0105] Calculating the particle trajectory: Solve this differential equation along each coordinate direction to obtain the trajectory of the discrete phase.

[0106] Based on this, by using the traditional SIMPLE method to solve the control equation of the fluid (air) phase and cooperating with the explicit time integration method, the solution of the motion equation of the particles in the flow field can be realized.

[0107] When snow particles impact the wall surface, whether they can adhere to the wall surface and accumulate stably requires a suitable wall surface snow - covering criterion for judgment. The motion behavior of snow particles after colliding with the wall surface is the key to determining whether snow - covering occurs. The motion behavior after collision mainly depends on the collision characteristics between the particles and the wall surface and the flow - field action on the wall surface. From the perspective of energy, the collision between snow particles and the wall surface is an inelastic collision. The degree of kinetic - energy loss after collision determines the adhesion or rebound behavior. However, the loss of kinetic energy of snow particles (consumed or converted into bonding internal energy) is related to many complex factors such as the snow's own crystal type, moisture - containing characteristics, and inter - crystal viscosity. Therefore, it cannot be described solely by the traditional coefficient of restitution or splash function. In addition, whether snow particles can stably or continuously adhere to the wall surface under the action of the flow field is also related to the wall - shear stress (friction velocity). When the wall - friction velocity u * is greater than a certain threshold friction velocity u *t , the snow particles on the wall surface will be eroded and thus cannot stably adhere to the wall surface. Therefore, as shown in Figure 6 , the wall - surface snow - covering criterion includes the following three items:

[0108] When the incident angle α is less than the capture angle α t , the snow particles are captured by the wall surface;

[0109] When the local friction velocity is less than the preset threshold friction velocity, the snow particles will not be carried away by the wind and will accumulate;

[0110] When the particle - collision velocity u p is less than the critical capture velocity u trap , the viscous force of the wall on the particles is large and the particles will be captured;

[0111] When the particles meet the above three wall - surface snow - covering criteria, the snow particles will be captured by the wall surface and stably accumulate on the wall surface to achieve snow - covering of the wall surface.

[0112] Exemplarily, the present application conducts surface snow - covering experiments using different wedge - shaped bodies to explore the snow - distribution forms on the surfaces of different wedge - shaped bodies. At the same time, a numerical - simulation method is used to conduct numerical - simulation research on the experiments.

[0113] Specifically, the experiments are carried out in the low - temperature / normal - temperature snow - falling simulation wind tunnel shown in Figure 4 and Figure 5 . This wind tunnel is located in a closed environment, is of the direct - flow type, with a total length of 14 m, a test section length of 6 m, and a cross - section side length of 1.2. The maximum experimental wind speed of the wind tunnel is 10 m / s. Utilizing the low - temperature (below - 20 °C) and snowy conditions in winter in Harbin, experiments are carried out using real snow. The experimental equipment mainly includes four parts:

[0114] Wind - tunnel equipment system: It includes components such as a fan and a wind - tunnel chamber, providing a stable and uniform wind - field environment for the snow - covering experiment.

[0115] Snowfall system: It includes a vibrating screen for spreading particles and a water mist gun, providing a snow source with uniform, stable and snow particles with a certain water content for the snow covering experiment.

[0116] Model system: It includes an experimental model and a rigid support. The support has considerable weight and stiffness, so that the model will not be blown down under the condition of a strong wind field, nor will it deform and affect the original wind field.

[0117] Data acquisition system: It includes an anemometer (UNIT UT363 series) and a scanner to obtain the experimental wind speed and the snow covering result on the model surface; the snow sensor adopts the FlowCapt snow sensor series.

[0118] The overall idea of the snow covering experiment is to use a uniform and stable wind field inflow to simulate the stable static flow field of natural wind speed, transport the snow particles falling from the vibrating screen to the model surface. During this process, the high-pressure water mist gun emits delicate and uniform water mist. This water mist gun can generate a water pressure of 3.5 MPa and can shoot out high-pressure fine water mist. This high-pressure fine water mist is a highly atomized water mist with a diameter of 10 - 100 μm. It combines with the snow particles (with a diameter of about 700 - 900 μm) in the wind field, forms a thin water film on the surface of the snow particles, simulates the non-negligible adhesion force caused by the water content of the snow particles under actual conditions, combines with the snow particles during the snow blowing process, makes the snow particles have a certain water content, and finally adheres to the model surface.

[0119] The wedge-shaped model is divided into the following two shapes. One is a right-angled wedge-shaped body, including two sizes, and the other is a general wedge-shaped body; refer to Figure 7 as shown.

[0120] During the experiment, the snow particles are the newly collected local natural snowfall, with a snow density of 320 kg / m³ and an average particle size of 0.8 mm. The test temperature is below -25 °C, the snow transport flux is 3.5 kg / m²·h, all four models are vertically facing the wind at 0°, the wind speed is 5 m / s, and the snow blowing time is 10 minutes.

[0121] Snow covering result of the first wedge-shaped body: The mass before snow covering is 1850 g, the mass after snow covering is 1970 g, and the snow accumulation mass is 120 g.

[0122] After the snow covering is completed, use a Leica MS-60 total station scanner for scanning and measurement. After scanning, the distorted points that appear during the measurement process should be corrected or deleted first, and then the preliminary processed point cloud data is interpolated. After interpolation, the shape cloud maps of the original model and the model surface after snow covering can be obtained. Finally, the two groups of data before and after snow covering need to be subtracted to obtain the snow depth of the snow covering on the model surface and draw the snow depth cloud map of the snow accumulation. Refer to Figure 8As shown in the figure, the snow accumulation on the top surface and the inclined surface is concentrated in the upper-middle area. The peak snow depth at the top is 1.07 times that of the extreme snow depth on the inclined surface. However, the snow accumulation on the top surface first increases and then decreases as the distance from the top increases, while the snow accumulation on the inclined surface shows a decreasing trend as the distance from the top increases, and the snow accumulation has a tendency to extend towards the lower right corner.

[0123] Snow accumulation result of the second wedge: The mass before snow accumulation is 3040 g, the mass after snow accumulation is 3195 g, and the snow accumulation mass is 155 g.

[0124] After snow accumulation, use the Leica MS-60 total station scanner for measurement to obtain the final snow-covered point cloud data. For the distorted points that appear during the measurement process, they need to be corrected or deleted. After that, the initially processed point cloud data is interpolated. Finally, the difference between the two groups of data before and after snow accumulation is processed to obtain the snow depth of the snow accumulation on the model surface and draw the snow depth cloud map of the snow accumulation. From the overall snow accumulation map, it can be seen that only sporadic snow particles adhere to the inclined surface with an inclination angle of 72°, so it can be ignored. After that, only the snow accumulation distribution on the top surface and the 45° inclined surface is discussed. Reference Figure 9 As shown in the figure, the snow accumulation on the top surface and the inclined surface is concentrated in the upper-middle area. The peak snow depth at the top is 1.05 times that of the extreme snow depth on the inclined surface and appears in the area slightly to the left of the middle. However, the snow accumulation on the top surface first increases and then decreases as the distance from the top increases, while the snow accumulation on the inclined surface shows a decreasing trend as the distance from the top increases. There is a symmetrically distributed snow accumulation peak area in the upper-middle area, and the snow accumulation has a tendency to extend towards the lower right corner.

[0125] The numerical simulation model uses the discrete phase model. Based on the test conditions, during the numerical simulation process, a numerical simulation model with the same size and the same boundary as the test conditions is established. Finite element model reference Figure 10 As shown in the figure, the size of the computational domain is 3.9 m × 1.65 m × 1.65 m. The position where the particles are introduced is the same as the position of the vibrating screen in the test, and the size of the plane where the particles are introduced is 0.74 m × 0.74 m.

[0126] The structured grid is used for this simulation model. The minimum grid size is 0.005 m, the number of grids is 4 million. The inflow boundary of the computational domain is a velocity inlet, and the inflow velocity is taken as 5 m / s. The outlet is a stable outflow. The surface of the model is a no-slip boundary, and the side boundaries and the bottom surface of the computational domain are symmetric boundaries. The specific settings of the flow field boundary conditions are shown in the following table:

[0127]

[0128] In the simulation, the fluid is regarded as a continuous phase. The Realizable k-ε turbulence model is selected for the flow field simulation. According to the snow-covered test of the wedge model, a uniform steady flow field is adopted, and the inlet wind speed is 5 m / s. The air density parameter is taken as 1.255 kg / m3, and the viscosity is 1.78×10-5. The SIMPLE (Semi-Implicit Method for Pressure Linked Equations) algorithm is used for the steady-state solution until the calculation converges. Among them, the second-order upwind scheme is selected for both the pressure term and the momentum term, the implicit first-order scheme is selected for the time term, and the first-order upwind scheme is selected for the turbulent kinetic energy and the turbulent diffusion rate.

[0129] The snow particles are set as a discrete phase in the simulation. The physical properties of the snow particles are based on the measured values of snowfall in Harbin. The skeleton density is taken as 320 kg / m3. In this paper, the Rosin-Rammler distribution is considered. The maximum particle size and the minimum particle size are set as 0.9 mm and 0.7 mm respectively, and the average particle size is 0.8 mm. The setting of the discrete phase boundary conditions: the fluid inlet and the fluid outlet are set as escape conditions, the sides, the top surface and the bottom surface of the computational domain are all set as bounce conditions, and the wedge model is set as a custom wall with a snow-covered criterion embedded in the wall, which can judge the adhesion situation after the particles collide with the wall. In the custom capture, the rebound motion of the particles when they do not meet the discrimination conditions is considered. The tangential velocity recovery coefficient (the ratio of the tangential velocity after rebound to the tangential velocity before rebound) is 0.7, and the normal velocity recovery coefficient is 0.1. The random walk model is turned on in the simulation.

[0130] Comparison of the snow-covered results of the first wedge:

[0131] Reference Figure 11 As shown, from the comparison of the snow-covered contour maps, it can be seen that compared with the experimental results, the overall distribution of the contour maps is similar, showing a trend of more snow cover in the upper part and less snow cover in the lower part. The peak snow accumulation on the top surface is in the upper-middle area, while for the inclined plane experiment, the peak snow accumulation is in the middle area. In the simulation results, the peak snow accumulation on the inclined surface is in the upper-right area, and the snow accumulation shows a decreasing trend from the upper-right to the lower-left, with certain errors, but it is generally in agreement with the experiment.

[0132] Result analysis:

[0133] Reference Figure 12 As shown, the incident angle of the particles on the inclined plane and the friction velocity increase diagonally towards the lower left corner. The incident angle of the particles on the top surface is smaller and shows an increasing trend from top to bottom. There is a region with a lower friction velocity in the upper part of the top surface, mainly because blunt body flow occurs there, resulting in a decrease in the wind speed and the appearance of a particle accumulation area. The particle collision velocity in the middle area of the top surface and the middle area of the inclined plane is lower, and the particles are prone to accumulate, which is in agreement with the experimental results.

[0134] Comparison of the snow-covered results of the second wedge:

[0135] Reference Figure 13 As shown, from the comparison of the snow-covered cloud images, it can be seen that compared with the experimental results, the overall distribution of the cloud images is similar. There is a trend of more snow cover in the upper part and less snow cover in the lower part. However, the snow accumulation amount is slightly less than that in the experiment. In the experiment, the peak snow accumulation on the top surface is in the upper-middle left area, while in the simulation result, the peak on the top surface is in the upper area. In the experiment, the peak snow accumulation on the inclined surface is in the upper-middle area, while in the simulation result, the peak snow accumulation on the inclined surface is in the upper-right area, and the snow accumulation shows a decreasing trend from the upper-right to the lower-left.

[0136] Result analysis:

[0137] Reference Figure 14 As shown, the incident angle of the particles on the inclined surface and the friction velocity increase along the diagonal towards the lower left corner. And the incident angle of the particles on the inclined surface is significantly larger compared with that of a 36° right-angled wedge. This is mainly due to the change in the inclined surface angle, which causes a large change in the flow-around characteristics of the wind field at this place. The incident angle of the particles on the top surface is smaller and shows an increasing trend from top to bottom, making it easier for particles to accumulate in the upper area. There is a region with a lower friction velocity in the upper part of the top surface, mainly because bluff-body flow occurs at this place, resulting in a decrease in the wind speed and the appearance of a particle accumulation area. There is a concentrated area with a lower particle collision velocity in the upper-middle part of the top surface, and particles are prone to accumulate in this area, which is consistent with the snow accumulation area appearing at this place in the experiment.

[0138] Through the comparison of the above snow depth cloud image results, it can be seen that the snow cover distributions of wedges with different angles and sizes are basically consistent with the simulation results. Since more attention is paid to the areas with more snow cover on the wall surface in practical engineering applications, at the same time, to further quantitatively analyze the snow depth scale of the test and simulation results, in this paper, the local profile snow depth data in the snow accumulation areas of the test and simulation results are selected for analysis; the specific data are shown in the following table:

[0139]

[0140] From the experimental data of the snow depth on the top surface of the model in the above table, it can be seen that the snow depth in the snow accumulation area on the top surface of the model shows a trend of first increasing and then decreasing as the distance from the top of the model decreases. This is relatively consistent with the simulation results. At the same time, the difference between the experimental results and the simulation results at the position of the snow depth extreme value is very small, basically below 4%, and the peak snow depth at the local position reaches consistency, with a good fit.

[0141]

[0142] From the experimental data of the snow depth on the inclined surface of the model in the above table, it can be seen that the snow depth in the snow accumulation area on the inclined surface of the model shows a trend of first increasing as the distance from the top of the model decreases, and the snow depth is smaller at the boundary position. This is relatively consistent with the simulation results. At the same time, the difference between the experimental results and the simulation results at the position of the snow depth extreme value is very small, basically below 4%, with a good fit.

[0143] To verify the feasibility of using the discrete element method to simulate the snow plowing of the target snow plow, this study further carried out numerical simulation analysis based on the snow plowing (real snow / artificial snow) test of the scaled snow plow model carried out by the Railway Technical Research Institute of Japan. Numerical simulation studies under the same boundary conditions were carried out using the 200-type and B60-type snow plow models mentioned in Japanese literature.

[0144] Based on this, a quantitative analysis and comparison of the snow plowing resistance was carried out. Considering that the bulk density of the test snow recorded in the literature is 200 kg / m3, according to the porous medium powder particle packing theory, the density conversion formula is given for reference: where ρ s is the particle density, ρ s，0 is the apparent density, β p is the particle volume fraction, ρ a is the air density, taking 1.225 kg / m 3 .

[0145] Assuming that the natural snow accumulation method is random accumulation, then β p ≈60% is used to determine the absolute density of a single snow particle to be 333 kg / m 3 , specifically, the snow particles used in the DEM simulation are 333 kg / m 3 . On the other hand, the selection of parameters such as the friction coefficient in the collision parameters (such as elastic modulus, Poisson's ratio, restitution coefficient) refers to the following material parameter table and collision parameter table:

[0146] Material Parameter Table

[0147]

[0148] Collision Parameters

[0149]

[0150] The calculation expression for the snow plowing resistance is: F p =ChwρV 2 , where h is the snow removal depth, w is the snow removal width, ρ is the snow density, V is the driving speed; C is the calculated driving resistance coefficient.

[0151] Through the DEM numerical simulation calculation, it can be obtained that the simulation results are in good agreement with the test results, and the corresponding data are compared as shown in the following table.

[0152]

[0153] Specifically, compared with the test prototype, the average error of the snow plowing resistance obtained in this simulation study is about 3.5%. Through the regression fitting analysis of the snow plowing force of the snow plow under different operating speed conditions of the snow plow, it can be obtained that the snow plowing resistance of the snow plow and the speed can be approximately in a quadratic relationship. Refer toFigure 15 as shown

[0154] The influence of snow density change on the snow plow's snow removal resistance was studied, and the following table shows the results obtained through numerical simulation calculations.

[0155]

[0156] By analyzing the simulation results, it can be found that the existence of differences in the physical properties of snow particles also has a certain impact on the simulation results. There is an approximate linear relationship between snow density and snow removal resistance. Refer to Figure 16 as shown

[0157] To explore the influence of the snow plow width on the snow removal resistance, a snow plow with the "90 - 45 - 55 - 44" shape parameters was used for modeling. The total width of the snow plow was adjusted based on a 2m width to establish snow plows with different widths. The specific model

[0158] parameters are as follows:

[0159]

[0160] Since the snow removal width and height of the snow plow mainly affect the snow removal area, regarding the influence of width and height changes on the snow removal resistance, it is considered as the influence of the change in snow removal area caused by width or height changes on the snow removal resistance. According to the above working conditions, simulations were carried out at a vehicle speed of 30m / s, and the results are as follows:

[0161]

[0162] By analyzing the simulation results, it can be found that there is an approximate linear relationship between the snow removal area and the snow removal resistance, and since the change in snow removal area is similar to the change in snow plow width, it can be simplified to an approximate linear relationship between the snow removal width and the snow removal resistance. Specifically refer to Figure 17 as shown

[0163] To explore the change in snow removal resistance with snow removal depth, the method of changing the snow laying depth was used. The snow plow model used was a snow plow with the "90 - 45 - 55 - 44" shape parameters. Similar to the snow removal width, the influence of snow removal depth was considered by changing the snow removal area. According to the above five working conditions, simulations were carried out at a vehicle speed of 30m / s, and the results are as follows:

[0164] Snow removal depth working condition

[0165]

[0166] Snow removal depth - Snow removal resistance

[0167]

[0168] By analyzing the simulation results, it can be found that when the snow removal depth exceeds the height of the snow plow's downforce wing, that is, the snow removal depth is normal, it can be considered that the snow removal depth and the snow removal resistance have a linear relationship. However, in extreme cases, that is, when the snow depth is large, the result will not satisfy the linear relationship due to the influence of the snow plow's shape. For details, refer to Figure 18 shown.

[0169] In summary, the numerical simulation results are in good agreement with the experimental results. According to the simulation results of the influence of snow density and vehicle speed on snow removal resistance, the snow removal resistance of the snow plow satisfies the formula: F p =ChwρV 2 .

[0170] Therefore, by conducting DEM discrete element simulation and experimental comparative analysis on snow removal of scaled snow plow model, the feasibility of the research method proposed in this study was verified from quantitative and qualitative perspectives. The specific conclusions are as follows:

[0171] (1) The different physical parameters of snow particles have a certain impact on the simulation results. The density and snow removal resistance are linearly related.

[0172] (2) Consistent with the test prototype results, the snow removal resistance of the snow plow and the speed are roughly quadratic and satisfy the snow removal resistance calculation formula;

[0173] (3) The snow plow snow removal simulation has a high consistency with the test in the starting mode, disengagement mode and snow removal path during the process;

[0174] (4) The simulated snow removal resistance is in good agreement with the experimental snow removal resistance, with an average error of about 3.5%. The feasibility of using numerical simulation for research is relatively high.

[0175] From this, the model of the snow plow is established:

[0176] In addition to the four angle parameters mentioned above, the snow plow shape should also be selected from the overall form before building the model. Currently, there are two main types of snow plows: open and closed snow plows.

[0177] The above-mentioned numerical simulation method is used to simulate two different types of snow plows to evaluate the snow plow shape from a qualitative perspective; the simulation results are referenced Figure 19 shown.

[0178] By comparing the simulation results, it can be found that the opening and closing snow plow will produce front-end overflow snow during the snow removal process. Further research on this phenomenon was conducted, and the snow removal process at different speeds was calculated when the snow depth was 0.25m. The speeds were 72km / h, 108km / h, 140km / h, and 180km / h.

[0179] As the driving speed increases, the phenomenon of snow overflow at the front end becomes more and more obvious. This phenomenon is not only more unfavorable to train travel from the perspective of force, but also more unfavorable to the control of the snow removal path because the flying snow is not removed along the regular path. The irregular snow removal path will even affect the line of sight in the cab, so a closed snow plow is selected to optimize the appearance parameters.

[0180] The parametric modeling method is used to construct the three-dimensional shape of the snow plow. The specific steps are as follows:

[0181] Select the horizontal plane, and determine the specific position and length of the line segment based on the opening angle and vehicle width;

[0182] Select the vertical symmetry plane of the snow plow, and determine the snow plow leading edge line segment and the angle of attack constraint line based on the total height and lower half height of the snow plow;

[0183] Generate the snow plow lower half plane from the determined line segments;

[0184] The bottom line is projected onto the snow plow upper edge plane by converting the entity reference to determine the reference plane where the rear spline curve is located;

[0185] The rear spline curve is determined by the restraint angle and the vehicle width, and the boundary conditions are tangent to the plane determined by the angle of attack, restraint angle constraint, and restraint angle height constraint;

[0186] Determine the front spline curve, the boundary conditions are the front end protrusion distance of the snow plow and the tangency to the angle of attack plane and line segment;

[0187] Generate surfaces and planes to complete the modeling of half of the snowplow, and then mirror the solid to complete the snowplow modeling.

[0188] The snow plow model is established in SolidWorks. The snow plow model is mainly controlled by the opening angle, inclination angle, angle of attack, and suppression angle. After the parameters are determined, the overall shape of the snow plow is determined by geometric relationships. The upper part of the snow plow is considered to be a surface for snow discharge, and the boundary is constrained by spline curves. The surface function is used to generate a snow plow model composed of four surfaces. Since the snow plow modeling process is cumbersome and a large amount of snow plow modeling is required during the optimization process, VBA is used to simplify the double spline curve snow plow modeling process in SolidWorks into a command flow.

[0189] For the shape parameters of the snowplow: opening angle α, inclination angle β, angle of attack γ, suppression angle δ, height, the snow removal resistance of the snowplow under different combinations is studied using numerical simulation method.

[0190] Through DEM numerical simulation calculation, it can be seen that the change of the opening angle has a significant impact on the snow removal resistance. As the opening angle increases, the snow removal resistance of the snow plow increases. The snow removal resistance at 60°~120° increases by 2%. For details, refer to the table below:

[0191]

[0192] For the data of the remaining tilt angle, suppression angle, and angle of attack, refer to the following table:

[0193] Tilt Angle - Snow Removal Resistance Table

[0194]

[0195] As the tilt angle increases, the change in snow removal resistance is about 2%, and it can be found that when the tilt angle is about 45°, the snow removal resistance is relatively small.

[0196] Suppression Angle - Snow Removal Resistance Table

[0197]

[0198] As the suppression angle increases, the change in snow removal resistance is about 4.7%, and the overall trend is still upward.

[0199] Angle of Attack - Snow Removal Resistance Table

[0200]

[0201] As the angle of attack increases, the change in snow removal resistance is about 7.2%, and the overall trend is still upward.

[0202] Furthermore, for the data of the snow removal plow height, refer to the following table:

[0203]

[0204] However, as the height of the snow removal device increases, the snow removal resistance increases. Since the height of the snow removal device directly affects the snow removal area, from the results, it can be seen that the change in the height of the snow removal device has a greater impact on the snow removal resistance. But according to different snow removal depths, it will affect the snow removal area of the snow plow with different heights of the snow removal device, so the height of the snow removal device should be determined according to the actual snow removal depth.

[0205] Therefore, based on the above snow removal resistance formula, according to the simulation results, a shape parameter is introduced into the formula to simplify the calculation method of the driving resistance coefficient, which is convenient for estimating the driving resistance coefficient values of snow plows with different external shape parameters based on the existing driving resistance coefficient.

[0206] The driving resistance coefficient C can be estimated according to the following formula: C = C 0 + C 1 + C 2 where C 0 is obtained by linear interpolation from the following table:

[0207]

[0208] C 1= 0.028(δ + 2γ)×10 -4 , where δ is the suppression angle and γ is the angle of attack;

[0209] C 2 Among them: when θ < 45°, C 2 = {5.64 + 0.008×(45 - θ)}×10 -4 ;

[0210] When 45° ≤ θ ≤ 90°, C 2 = {5.64 + 0.0025×(θ - 45)}×10 -4 , where θ is the inclination angle.

[0211] In order to consider the influence of the vehicle head on snow plowing in actual engineering, a simulation is carried out on the whole vehicle model with the vehicle head added, the influence of shape parameters on factors such as snow plowing resistance is analyzed, and the lateral and vertical forces received during the driving of the whole vehicle are obtained.

[0212] Taking the snow plow in the form of 60 - 45 - 0 - 55 (flare angle - inclination angle - angle of attack - suppression angle) as an example, the force on the whole vehicle is analyzed. The snow depth is 400 mm and the driving speed is 40 m / s. The simulation results are shown in Figure 20 as follows.

[0213] Summarize the snow plowing force of the simulation results:

[0214] (1) In the X direction, the overall snow plowing resistance of the whole vehicle model increases by 26% compared with the single snow plow;

[0215] (2) In the Y direction, the maximum lateral force during snow plowing is below 5 KN;

[0216] (3) In the Z direction, the force is 269.8 KN and the direction is upward (it should be further judged whether it meets the requirement that the wheel load reduction is not greater than 7%);

[0217] (4) The snow plowing resistance of the snow plow part in the whole vehicle model is reduced compared with the single snow plow.

[0218] For the force in the Z direction, further evaluation should be carried out with reference to the requirements given in the European standard. The standard gives corresponding requirements for the wheel load reduction specification, that is, the wheel load reduction should not exceed 7%. At the same time, it can be found that due to the vehicle head sharing the snow plowing resistance, the overall snow plowing resistance of the whole vehicle is reduced compared with the single snow plow simulation. The specific simulation results are as follows:

[0219]

[0220] According to the requirements of the task book, extract the wall pressure values at the corresponding pressure measurement points. The specific pressure values and the positions of the pressure measurement points are shown in Figure 21 and the following table:

[0221]

[0222] Analysis of the simulation results shows that the 1st measuring point did not participate in the snow removal process in this working condition, so there is no pressure value, while for other measuring point areas, the pressure in the middle part is relatively large. In addition, the overall pressure value is less than 1MPa. Compared with the experimental result of 1.18Mpa (snow bed apparent density 200kg / m3, driving speed 40m / s, snow depth 40mm, model scale ratio 1:5), it can be seen that the two are of the same order of magnitude and are credible; at the same time, the performance of this shape snow plow in this aspect is better than that of the experimental snow plow.

[0223] Due to the mutual influence between the front part of the vehicle and the snowplow model, the influence of the snowplow appearance parameters of the whole vehicle model on the snow removal process is different from that in the case of a single snowplow. Therefore, numerical simulation studies are carried out on the opening angle with a more obvious influence and the angle of attack that has a greater impact on the snow-facing area, and the snow removal resistance formula for a single snowplow is adjusted.

[0224] In order to consider the influence of the opening angle, the numerical simulation of the opening angle condition of a single snow plow including the front model is carried out:

[0225]

[0226] The simulation results show that the front model has a great influence on the movement of snow particles during snow removal. When the opening angle is 60° and 90°, the front is not conducive to reducing the snow removal resistance, while when the opening angle is 120°, the presence of the front model plays a favorable role in reducing the snow removal resistance. At the same time, the presence of the front further restricts the movement of snow particles. It can be found that the change of the opening angle in the whole vehicle model has a smaller impact on the snow removal resistance than that in the case of a single snow plow, but there is still a significant impact.

[0227] According to the above simulation results, the parameter C that takes into account the influence of the opening angle in the driving resistance coefficient given above is 0 The value of is adjusted. In the case of the whole vehicle model, as the opening angle changes, the resistance of the front part other than the snow plow changes little, so this part and the snow plow resistance are simplified into one item, that is, the snow removal resistance of the whole vehicle during driving. At the same time, since the snow depth is the same as the snow plow height, the front part of the vehicle model has little effect on the snow removal area when the opening angle changes. In order to simplify the calculation model, the influence of the rest of the front part on the snow removal area is ignored. In summary, for the whole vehicle model C 0 Adjustment should be made based on the vehicle's snow removal resistance, and the values ​​should be taken as follows:

[0228]

[0229] Since the change of angle of attack will have a certain impact on the snow-facing area, the change of snow removal resistance of the vehicle model with the change of angle of attack is also verified; the specific simulation results are shown in the table below:

[0230]

[0231] It can be seen from the simulation results that the change of the angle of attack has less influence on the snow removal resistance of the whole vehicle than that of a single snow plow. This phenomenon is because the train head model makes up for the change of the snow removal area caused by the change of the angle of attack in the case of a single snow plow. However, for the snow removal path, it can be seen that the change of the angle of attack has a certain influence on the distribution of the snow removal path during driving.

[0232] Therefore, the selection suggestion of this application mainly considers the snow removal resistance, supplemented by the snow removal path and model factors. However, since the influence of the suppression angle on the snow removal resistance is not obvious, and the snow depth considered above is the snow in a relatively extreme case, the role of the suppression angle cannot be normally exerted and its influence on the snow removal path under this working condition is not clear. Considering the use of the snow plow under normal snow depth, the influence of the suppression angle on the snow removal resistance and path is further considered in the case of a smaller snow depth here.

[0233] In the case of a snow depth of 400 mm, due to the large snow removal volume and high speed, the influence of the suppression angle on the snow removal path is not obvious. Here, the influence of the suppression angle on the snow removal resistance and path is considered in the case of a smaller snow depth. The simulation is carried out under the working conditions of a snow depth of 150 mm and a driving speed of 30 m / s, and the other parameters remain unchanged. The results are as follows in the table:

[0234]

[0235] Reference Figure 22 and Figure 23 As shown, the snow removal width increases with the increase of the suppression angle, and at the same time, the movement speed of snow particles is greater during the snow removal process; by comparing the snow removal heights of different suppression angles, it can be found that for the snow removal path at the rear, when the suppression angle is smaller, the snow particles tend to be distributed in the lower part and the distributed snow particles are more concentrated and orderly. Obviously, a smaller suppression angle is more beneficial to controlling the movement path of the snow particles discharged during snow removal by the vehicle.

[0236] Therefore, the following snow plow selection suggestions are given: (1) The flare angle has the most obvious influence on the snow removal resistance. Considering the snow removal resistance, it is recommended to take the flare angle as 60°; (2) When the tilt angle is about 45°, the snow removal resistance in the X direction is the smallest. It is recommended to take the tilt angle as 45°; (3) For the attack angle, comprehensively consider the snow removal path: From the above results, it can be seen that the change of the attack angle has little influence on the snow removal force in the Z direction and the snow removal width, but it has a certain influence on the snow removal height, which is reflected in the decrease of snow particles at high places when the attack angle increases. At the same time, considering that the increase of the attack angle will lead to an increase in the snow removal resistance, it is recommended to take the attack angle as 5°; (4) In the case of a snow depth of 400 mm, the inhibition angle has little influence on the snow removal path, but in the case of a smaller snow depth condition, when the inhibition angle is 29°, the snow removal height can be better controlled and the snow removal resistance is smaller. It is recommended to take the inhibition angle as 29°; In summary, it is recommended to select a snow plow with the following external shape parameters: 60 (flare angle) - 45 (tilt angle) - 5 (attack angle) - 29 (inhibition angle).

[0237] The environmental snow depth has a very obvious influence on the force state of the vehicle body during driving. Considering that in actual engineering, vehicles not only need to run normally in the case of shallow snow depth, but may also run at a speed limit in the case of higher snow depth. Therefore, this application studies the driving speed in different snow depth environments, obtains the force and snow removal path of the train under different snow depth and driving speed conditions through numerical simulation methods, and gives the maximum speed that can meet the actual operation requirements under different snow depth conditions through constraint conditions, providing a reference for the train operation in the snow-covered environment.

[0238] Refer to the first item of the snow plow qualification / disqualification standard in Section 5.2.4 of the European standard "DSF / prEN 16251-2011", that is, "the reduction of wheel load should not exceed 7%", and conduct a quantitative evaluation on whether the snow plow meets the driving requirements; at the same time, take the second requirement, that is, "during the experiment, the driver's line of sight should be ensured to be clear" as an auxiliary condition for qualitative evaluation. The reduction of wheel load refers to the increase or decrease of the load acting on the wheels caused by the jacking force generated during the snow removal process when the vehicle is running. The reduction of wheel load has a great impact on driving safety. Since the snow plow is installed at the front end of the leading car, its influence on the reduction of wheel load only exists in the leading car. Here, only the reduction of wheel load of the leading car is considered. Specifically, it should meet the following formula:

[0239] Among them, Δp is the reduction of wheel load caused by snow removal, and p is the average net wheel load.

[0240] According to the design conditions, it is known that the weight of the leading car is 64 t, that is, p = 640 kN. It can be calculated from the formula that the reduction of wheel load caused by snow removal should meet Δp ≤ 44.8 kN.

[0241] Therefore, in this application, numerical simulations are carried out for snow depths of 150 mm, 300 mm, 600 mm, and 800 mm. The snow removal depth is obtained by setting the lower edge of the snow plow 150 mm above the rail surface as shown in Figure 24 Considering the influence of the snow laid from the rail surface to the lower edge of the snow plow on snow removal, the pre-laid snow depth is taken as the snow depth in the simulation, and the snow removal height is ensured by adjusting the model height, as shown in reference Figure 24 shown.

[0242] According to the above research, it can be seen that as the snow depth increases, the change in the reduction of wheel load caused by snow removal is obvious, which will lead to a large change in speed limit. In order to improve the calculation efficiency, the starting value of the driving speed under the condition of deeper snow depth is selected with reference to the simulation results of shallower snow depth conditions, and then it is decreased at a gradient of 20 km / h until the constraint conditions are met. The specific working conditions are summarized in the following table:

[0243]

[0244] The reduction of wheel load caused by snow removal under each working condition is obtained through numerical simulation. Combining with the snow removal path, the maximum operating speed that meets the requirements under different snow depths is obtained. According to the requirements of the task book, the pressure values at each pressure measurement point under the maximum driving speed are given, and the snow removal resistance in the traveling direction under the corresponding conditions is given for reference.

[0245] It can be seen from the simulation results that under the condition of a snow depth of 300 mm, that is, a snow removal depth of 150 mm, the train can run at a speed of 170 km / h while ensuring that the reduction of wheel load and the snow removal path meet the requirements. The specific results are as follows:

[0246]

[0247] The pressures at each measurement point on the train head when traveling at the limit speed under this snow depth condition are as follows:

[0248]

[0249] To sum up, under the condition of a snow depth of 300 mm, the driving limit speed between 170 km / h and 190 km / h can meet the above requirements for the reduction of wheel load and driving vision. According to the results of the vertical snow removal force, under this condition, the vertical snow removal force only exceeds the limit value by 23.9 kN when driving at full speed, which is 1.53 times the limit value, showing an obvious difference from the vertical snow removal force, indicating that the snow removal state is still relatively reasonable at this time.

[0250] It can be seen from the simulation results that under the condition of a snow depth of 600 mm, that is, a snow removal depth of 450 mm, the train can run at a speed of 50 km / h while ensuring that the reduction of wheel load and the snow removal path meet the requirements. The specific results are as follows:

[0251]

[0252] The pressures at each measuring point on the front of the vehicle when driving at the limit speed under the snow depth condition are as follows:

[0253]

[0254] Under this condition, the snow removal depth has exceeded the maximum height of the snow plow, and other parts of the vehicle body gradually start to directly participate in the snow removal process. It can also be seen from the pressure results that the vehicle body starts to participate in the snow removal process at measuring points 5 and 6 under this condition.

[0255] It can be known from the simulation results that under the condition of a snow depth of 800 mm, that is, a snow removal depth of 650 mm, the train can run at a speed of 30 km / h while ensuring that the reduction in wheel load and the snow removal path meet the requirements. The specific results are as follows:

[0256]

[0257] The pressures at each measuring point on the front of the vehicle when driving at the limit speed under the snow depth condition are as follows:

[0258]

[0259] This condition is the maximum snow depth in this report. Under this condition, it can be known from the pressure results that the structures at all measuring points participate in the snow removal process, and the speed limit value further decreases.

[0260] By observing the pressure distribution on the front of the vehicle and the surface of the snow plow during the snow removal process, it can be found that a relatively large pressure will be generated on the lower surface of the protruding part of the front of the vehicle when the snow depth is higher than the normal snow removal height of the snow plow. When the snow accumulation environment is relatively extreme, it can be considered to reduce the protruding part of the front of the vehicle. At the same time, after observing the snow removal paths of the single snow plow and the whole vehicle model, it can be found that this protruding part has a beneficial effect on controlling the height of the overflow snow at the front end during driving. Therefore, when shortening the protruding length of this structure in order to reduce the reduction in wheel load, attention should be paid to ensuring the line of sight requirements of the cab during driving, that is, the height of the flying snow at the front end.

[0261] According to the speed limit and the change results of resistance and lift given above, it can be found that when the snow depth increases from 150 mm to 250 mm, the snow depth reaches the normal snow removal height of the snow plow. During the snow removal process, due to particle extrusion, it enters a relatively unreasonable snow removal form (the surfaces of structures other than the snow plow on the front of the vehicle participate in the snow removal process). At the same time, the speed limit changes most significantly at this stage. The speed limit decreases from 170 km / h - 190 km / h at 150 mm of snow depth to 70 m / h - 90 km / h. Therefore, when it is necessary for the vehicle to operate in an environment with a greater snow depth, the normal use height of the snow plow, that is, the height of the end of the downward pressure wing, should be increased during design. Refer to Figure 25 as shown.

[0262] Therefore, this application takes two aspects, i.e., the wheel load reduction less than 7% and the snow flying path that ensures the cab line of sight, as the evaluation criteria, and explores the maximum train running speed in environments with different snow depths through numerical simulation methods. The results are summarized in the following table:

[0263]

[0264] The following conclusions can be drawn from the above results: (1) To reduce the wheel load reduction during snow removal, the distance from the snow plow to the front end of the vehicle head can be shortened while ensuring the cab line of sight; (2) In the case of a large snow depth in the operating environment, the height of the snow plow should be appropriately increased to ensure the rationality of the snow removal process.

[0265] Although the embodiments of the present invention have been shown and described above, it can be understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those of ordinary skill in the art can make changes, modifications, substitutions, and variations to the above embodiments within the scope of the present invention.

Claims

1. A simulation and optimization design method for EMU snow plow based on multi-physics field coupling, characterized in that: The following steps are involved: Step S1: collecting snow environment parameters of the target route, wherein the environment parameters at least include snowfall data and snow accumulation data; Step S2: Establish a soft ball model of snow particles and use the Hertz-MindlinwithJKRCohesion contact model to calculate the contact force between snow particles; Step S3: Based on the wall snow cover criterion and using the discrete phase model, a snow cover simulation is performed, and then the correctness of the snow removal resistance formula in the snow cover simulation is verified by comparing with the preset snow removal experimental data; Step S4: A parametric modeling method is used to establish a snowplow model, and shape parameters are introduced into the snow removal resistance formula to simplify the driving resistance coefficient according to the simulation results, so as to evaluate the snow removal performance of the snowplow under the preset shape parameter combination and determine the snow removal resistance formula of the snowplow; Step S5: adding a vehicle head to the snow plow model to form a whole vehicle model and performing simulation according to the whole vehicle model, thereby correcting the snow removal resistance formula and generating a snow plow selection recommendation; Step S6: Simulate the driving speed in a preset snow depth environment to obtain the driving force and snow removal path under different snow depth and driving speed conditions, and then generate the maximum speed that can meet the actual operation requirements under different snow depth conditions according to the preset constraints; Step S7: Output the optimal design parameters of the snow plow.

2. The method for simulating and optimizing the design of a snow plow for clearing obstacles on a train based on multi-physics field coupling according to claim 1 is characterized in that: In step S2, the method for establishing the snow particle soft ball model includes: The soft ball model simplifies the inter-particle contact process into the damped vibration of a spring oscillator, and its motion equation is: Where x is the displacement from the equilibrium position, m is the mass of the oscillator, c and k are the spring damping coefficient and elastic coefficient respectively; Among them, the normal elastic coefficient k n for: Where E and v are the elastic modulus and Poisson's ratio of the particle material, respectively, R is the particle radius, and the subscripts i and j represent the particles i and j that are in contact, respectively. When particles i and j are of homogeneous material and have equal particle sizes, then k n for Among them, the tangential elastic coefficient k t for: Among them, α is the normal overlap, G i and G j are the shear moduli of particles i and j, respectively. When particles i and j are homogeneous materials with equal particle sizes, k t for 3. The method for simulating and optimizing the design of a snow plow for clearing obstacles on a train based on multi-physics field coupling according to claim 2 is characterized in that: The damping coefficient can be determined by: If a spring oscillator with a mass of m is in a critical damping state, the mechanical energy decays at the fastest speed. At this time, the normal damping coefficient c is n and the tangential damping coefficient c t They are: Or, the damping coefficient is coupled with the restitution coefficient e: Here, e is determined by experiment.

4. The method for simulating and optimizing the design of a snow plow for clearing obstacles on a train based on multi-physics field coupling according to claim 1 is characterized in that: In step S2, the method of defining the Hertz-MindlinwithJKRCohesion contact model includes: The JKR normal force is based on the overlap δ and the interaction parameter, surface energy γ: Where, E* is the equivalent Young's modulus, R* is the equivalent radius; Damping force The expression is: in, is the equivalent mass, is the normal component of the relative velocity, β and S n The expression is: Tangential force F t The expression is: Among them, S t is the tangential overlap, G* is the equivalent shear modulus, is the tangential component of the relative velocity; where the tangential force is affected by the Coulomb friction μ s F n Limit, where μ s is the coefficient of static friction, and rolling friction exerts a torque on the contact surface: τ i =-μ r F n R i ω i , where μ r is the rolling friction coefficient, R i is the distance from the contact point to the center of mass, ω i is the unit angular velocity vector of the object at the contact point; The maximum gap between particles with non-zero cohesion is calculated by: When δ<δ c , the model returns 0; When the particles are not actually touching and the separation is less than δ c When , the cohesion reaches its maximum value, so the maximum cohesion is: The force required to separate the two particles depends on the surface tension of the liquid γ s and wetting angle.

5. The method for simulating and optimizing the design of a snow plow for clearing obstacles on a train based on multi-physics field coupling according to claim 1 is characterized in that: In step S3, the discrete phase model includes: The continuity and momentum conservation equations of the discrete phase model are: Among them, ρ f , u and P are density, velocity and pressure of the fluid respectively, t is time, g is gravitational acceleration, α f is the fluid volume fraction, α f =1-V p / V c Calculate, V c 、V p are the total volume of the control unit and the volume of the particle respectively; F f-p is the force between the air phase and the snow phase, mainly the particle drag force F drag ; τ is the fluid viscous stress tensor, Calculate, where I is the unit tensor, μ f is the fluid viscosity including kinematic viscosity and turbulent viscosity; For the snow phase, the snow particles are regarded as spheres, and the force balance equation is: Among them, m p 、u p and ρ p are the mass, velocity and density of snow particles respectively, and F is the additional external field; Among them, d p is the snow particle size, C D is the particle drag coefficient, according to the smooth ball model, by the particle Reynolds number R e,p It is determined by a set of empirical constants a1-a3 determined by the range; Compute particle trajectories: The differential equation is solved along each coordinate direction to obtain the trajectory of the discrete phase; The traditional SIMPLE method is used to solve the control equations of the fluid phase, and then the explicit time integration method is used to solve the motion equations of particles in the flow field.

6. The method for simulating and optimizing the design of a snow plow for clearing obstacles on a train based on multi-physics field coupling according to claim 5 is characterized in that: In step S3, the wall snow-covering criteria include: The incident angle α is smaller than the capture angle α t When the snow particles are captured by the wall; When the local friction velocity is less than the preset threshold friction velocity, the snow particles will not be carried away by the wind and will not accumulate; Particle collision velocity u p Less than the critical capture velocity u trap When the wall has a greater viscous force on the particles, the particles will be captured; When the particles meet the above three wall-covering snow criteria, the snow particles will be captured by the wall and stably accumulated on the wall to achieve snow-covering of the wall.

7. The method for simulating and optimizing the design of a snow plow for clearing obstacles on a train based on multi-physics field coupling according to claim 1 is characterized in that: In step S4, the method of establishing the snow plow model using the parameterized modeling method includes: Step S41: Select a horizontal plane, and determine the specific position and length of the line segment based on the opening angle and the vehicle width; Step S42: Select the vertical symmetry plane of the snow plow, and determine the snow plow leading edge line segment and the attack angle constraint line based on the total height and the lower half height of the snow plow; Step S43: generating a snow plow lower half plane from the determined line segments; Step S44: projecting the bottom surface line onto the snow plow upper edge plane by converting the entity reference to determine the reference plane where the rear spline curve is located; Step S45: determining the rear spline curve by the suppression angle and the vehicle width, with the boundary conditions being tangent to the plane determined by the angle of attack, suppression angle constraint, and suppression angle height constraint; Step S46: determining the front spline curve, the boundary conditions of which are the protruding distance of the front end of the snow plow and the tangency with the angle of attack plane and the line segment; Step S47: Generate curved surfaces and planes to complete the modeling of half of the snow plow, and then mirror the entity to complete the snow plow modeling.

8. The method for simulating and optimizing the design of a snow plow for clearing obstacles on a train based on multi-physics field coupling according to claim 1 or 7, characterized in that: In step S4, the method further includes: The calculation expression of snow removal resistance is: F p =ChwρV 2 , where h is the snow removal depth, w is the snow removal width, ρ is the snow density, and V is the driving speed; C is the calculated driving resistance coefficient, C = C0 + C1 + C2, where C0 is linearly interpolated by looking up the preset table, and C1 = 0.028 (δ + 2γ) × 10 -4 , δ is the suppression angle, γ is the angle of attack; in C2: when θ<45°, C2={5.64+0.008×(45-θ)}×10 -4 ; When 45°≤θ≤90°, C2={5.64+0.0025×(θ-45)}×10 -4 , where θ is the inclination angle.

9. The method for simulating and optimizing the design of a snow plow for clearing obstacles on a train based on multi-physics field coupling according to claim 1 is characterized in that: In step S6, the method comprises: With the wheel weight reduction rate not exceeding the preset value and the driver's clear line of sight as constraints, simulation is carried out at a preset snow depth environment driving speed to generate the maximum speed that can meet the actual operating requirements under different snow depth conditions.

10. A method for simulating and optimizing the design of a snow plow for clearing obstacles on a train based on multi-physics field coupling, using the method according to any one of claims 1 to 9, characterized in that: include: A data collection module, used to collect snow environment parameters of the target route, wherein the environment parameters include at least snowfall data and snow accumulation data; Model processing module, used to establish a soft ball model of snow particles and use the Hertz-MindlinwithJKRCohesion contact model to calculate the contact force between snow particles; The simulation module is used to simulate snow cover based on the wall snow cover criterion and adopt a discrete phase model, and then verify the correctness of the snow removal resistance formula in the snow cover simulation by comparing the preset snow removal experimental data; The resistance determination module is used to establish a snow plow model using a parametric modeling method, and introduce shape parameters into the snow removal resistance formula to simplify the driving resistance coefficient according to the simulation results, so as to evaluate the snow removal performance of the snow plow under the preset shape parameter combination and determine the snow removal resistance formula of the snow plow; The obstacle clearing model selection module is used to add a vehicle head to the obstacle clearing snow plow model to form a whole vehicle model and perform simulation according to the whole vehicle model, thereby correcting the snow clearing resistance formula and generating an obstacle clearing snow plow model selection recommendation; Design an optimization module to simulate the speed of the preset snow depth environment, obtain the train force and snow removal path under different snow depth and driving speed conditions, and then generate the maximum speed that can meet the actual operation requirements under different snow depth conditions according to the preset constraints; Design an output module to output the optimal design parameters of the snow plow.

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