Locomotive adhesion optimization utilization method based on axle load transfer dynamic compensation

Abstract

The present invention discloses a method for optimizing the utilization of locomotive adhesion based on dynamic compensation for axle load transfer, which relates to the field of rail transit technology, including: establishing a locomotive axle load transfer model that takes into account the rotation of a traction rod; and establishing a mapping relationship between traction force and the change in axle load of each axle; when a motor outputs a specified traction force, the adhesion coefficient required for each axle to fully exert the adhesion force is calculated in combination with the static axle load of the locomotive; the adhesion coefficient of each axle and the axle load transfer change are used as constraints, the maximum sum of the traction forces of each axle is used as the optimization target, and the traction force applied to each axle is optimized based on a sequential quadratic programming algorithm, so as to obtain a traction force electrical compensation coefficient that compensates for the axle load transfer; the object of the present invention is to reduce the probability of idling and slipping of unloaded wheelsets while ensuring the exertion of traction force.

Description

Technical Field

[0001] The invention relates to the technical field of rail transit, and in particular to a method for optimizing the utilization of locomotive adhesion based on dynamic compensation of axle load transfer. Background Art

[0002] In recent years, the length and carrying capacity of heavy-duty trains have continued to increase, driving the large-scale deployment of high-power electric locomotives capable of transporting tens of thousands of tons of cargo. Locomotives rely on the wheel-rail creep force transmitted between the wheels and the rails to overcome running and slope resistance. Typically, the contact patch area between the wheel and the rail is less than one square centimeter, and tens of thousands of Newtons of wheel-rail creep force need to be transmitted. On tracks with low adhesion coefficients, the wheels are prone to idling due to excessive traction applied to the wheels. Idling wheels can cause wheel abrasions, aggravate wheel-rail interaction, and reduce the service life of the wheels. In addition, the locomotive may have difficulty in fully utilizing its traction capacity, which may lead to starting difficulties. This situation may cause line delays and even lead to unexpected situations such as line rescue in railway operations. Therefore, optimizing traction to improve wheel-rail adhesion utilization is a specific and realistic task, requiring locomotives to exert maximum traction even under low adhesion conditions.

[0003] Locomotive wheel spin is usually due to insufficient adhesion on a single axle, and it is rare for all axle wheels to spin simultaneously. This phenomenon can be attributed to axle weight transfer, which causes the axle weight on some axles to increase and the axle weight on other axles to decrease when the locomotive applies traction. When traction is applied to the axles synchronously, the wheels of the axles with reduced axle weight are more likely to slip. The existing technologies for solving severe wheel spin mainly rely on sand spreading devices, anti-skid controllers and modifying the proportion of traction applied to each axle. The inventors found in actual use that these prior arts have at least the following technical problems:

[0004] 1. The locomotive's sand spreading device can increase the adhesion between the wheels and the rails, but it is only effective for some wheels at start-up.

[0005] 2. When the wheels are spinning, the anti-skid controller can only passively unload the motor torque or maintain it at the peak of adhesion, and cannot help the locomotive obtain maximum traction under low adhesion conditions.

[0006] 3. Effective strategies to improve traction include reducing the traction of the axle when the load is reduced and increasing the traction capacity of the axle when the load is increased. A significant problem with this approach is that the traction distribution on each axle is completely dependent on the technician's experience, which is obtained through repeated iterative fine-tuning. Summary of the invention

[0007] In order to solve the problems existing in the prior art, the purpose of the present invention is to provide a method for optimizing locomotive adhesion based on dynamic compensation of axle load transfer. The present invention introduces a calculation method based on sequential quadratic programming theory to determine the traction of the locomotive under low adhesion conditions under the influence of axle load transfer. The goal of this method is to reduce the probability of idling and slipping of the unloaded wheelset while ensuring the traction.

[0008] To achieve the above object, the technical solution adopted by the present invention is: a method for optimizing the utilization of locomotive adhesion based on dynamic compensation of axle load transfer, comprising the following steps:

[0009] Step 1: Establish a locomotive axle weight transfer model that takes into account the rotation of the traction rod; and establish a mapping relationship from the traction force to the change in axle weight of each axle;

[0010] Step 2: When the motor outputs the specified traction force, the adhesion coefficient required for each axle to fully exert adhesion is calculated in combination with the static axle weight of the locomotive;

[0011] Step 3: Taking the adhesion coefficient and axle load transfer changes of each axle as constraints, and the maximum sum of the traction forces of each axle as the optimization target, the traction force applied to each axle is optimized based on the sequential quadratic programming algorithm, so as to obtain the traction force electrical compensation coefficient that compensates for the axle load transfer.

[0012] As a further improvement of the present invention, the step 1 is specifically as follows:

[0013] The axle load transfer model is a quasi-static equilibrium equation group of the forces on each component of the locomotive obtained by force analysis. The rotation of the locomotive traction rod needs to be considered in the axle load transfer model. Assuming that the longitudinal, pitch and vertical movements of the vehicle body and frame are considered, only the traction force is used as the external force input system in the axle load transfer model. The traction force vector in the axle load transfer model is as follows:

[0014] ;

[0015] Perform force analysis on the motor components and derive the force equation of the motor:

[0016] ;

[0017] in, α is the gear meshing angle; F m1 is the motor suspension force; F g1 is the gear meshing force; F gbv is the force exerted by the gearbox on the axle; R g and R p are the radii of the large and small gears respectively;

[0018] The motor boom force and the resulting axle load transfer are thus derived:

[0019] ;

[0020] The primary and secondary suspension forces are calculated by the displacement of the vehicle body and frame. The expression for calculating the suspension force is as follows:

[0021] ;

[0022] in k sz and k sx is the vertical stiffness and longitudinal stiffness of the secondary suspension; k pz is the vertical stiffness of the primary suspension; L c is half the bogie centerline spacing; L t Half the wheelbase of the bogie; L s It is half of the longitudinal spacing of the secondary suspension; H sc and H sb They are the heights of the secondary suspension to the center of mass of the vehicle body and frame;

[0023] For the drawbar, the node displacements at both ends are as follows:

[0024] ;

[0025] in x qbhi and z qbvi are the longitudinal and vertical node displacements connecting the drawbar to the frame, respectively; x qchi and z qcvi They are the displacements of the nodes connecting the drawbar to the vehicle body; L qyg and β qi0 are the length and initial angle of the drawbar, respectively;

[0026] From this, the forces and moments acting on the nodes at both ends of the traction rod are derived:

[0027] ;

[0028] in, k q and k qsare the radial stiffness and angular stiffness of the drawbar, respectively; L qyb and H qb are the longitudinal and vertical distances of the frame mass center from the drawbar frame node, respectively; L qc and H qc are the longitudinal and vertical distances of the center of mass of the vehicle body from the drawbar-body node, respectively;

[0029] The interaction between the coupler buffer and the car body is simplified as a linear spring force element; the coupler in the axle load transfer model is assumed to be fixed, so the coupler buffer force is calculated as follows:

[0030] ;

[0031] in k gh is the buffer stiffness, γ is the vertical swing angle of the coupler;

[0032] The forces and moments applied to the body and frame are as follows:

[0033] ;

[0034] in, F tj is the traction force acting on the wheelset; z bi0 is the initial vertical position of the centroid of the frame; z c0 is the initial vertical position of the vehicle’s center of mass; H cg is the height of the coupler from the ground;

[0035] The force balance equations of the vehicle components are finally derived into the following set of equations:

[0036] ;

[0037] The change of locomotive posture after axle load transfer is determined by solving a nonlinear system of 15 degrees of freedom equations with specific traction input;

[0038] The axle load transfer calculation solves the nonlinear response of a locomotive with a geometrically nonlinear structure under external loads, which is expressed in the following equation:

[0039] ;

[0040] in, x is a state vector composed of the displacements of the degrees of freedom of each component of the vehicle; K ( x )andF is the corresponding nonlinear stiffness matrix and the generalized external forces derived from Eq.

[0041] Solve the force balance equations of the vehicle components to obtain the nonlinear system of equations in the final derived system, and obtain the nonlinear response of the locomotive under external loads x , thus deriving the axle load transfer of each axis:

[0042] ;

[0043] Thus, a mapping relationship from traction force to axle load transfer of each axle of the locomotive is established.

[0044] As a further improvement of the present invention, in step 2, the adhesion coefficient calculation method is specifically as follows:

[0045] ;

[0046] in, u is the vector of adhesion coefficients; P 0 is the vector of static shaft load; F 0 is the intended applied traction force.

[0047] As a further improvement of the present invention, the step 3 is specifically as follows:

[0048] The goal of traction optimization is to maximize the sum of traction on all wheelsets under the constraint of wheel adhesion. The nonlinear optimization form of traction is expressed as follows:

[0049] ;

[0050] By solving the nonlinear programming problem, the optimal traction force of each axle under the action of axle load transfer is obtained, and the traction force electrical compensation coefficient is calculated as shown in the following formula:

[0051] ;

[0052] in, ξ is the electrical compensation coefficient for traction, F opt It is the optimized traction.

[0053] In the present invention, the locomotive is a certain type of high-power electric locomotive, and its traction rod is a single-rod low-position central traction; the adhesion coefficient of each axle as a constraint condition is determined by the given traction force and the axle weight after the axle weight of each axle is transferred; the vertical swing angle of the locomotive can be given according to actual conditions.

[0054] The beneficial effects of the present invention are:

[0055] The present invention solves the problem that the locomotive axle weight transfer under the action of traction causes the wheelset with reduced axle weight to be more prone to idling based on sequential quadratic programming, and reduces the probability of idling and slipping of the unloaded wheelset while ensuring the traction. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Figure 1 A schematic diagram of a flow chart of an embodiment of the present invention;

[0057] Figure 2 It is a schematic diagram of a locomotive axle load transfer model considering the rotation of the traction rod in an embodiment of the present invention;

[0058] Figure 3 is a force diagram of a traction rod in an embodiment of the present invention;

[0059] Figure 4 is a force diagram of the gear box in an embodiment of the present invention;

[0060] Figure 5 The force diagram of the large gear in the embodiment of the present invention;

[0061] Figure 6 is a force diagram of a pinion in an embodiment of the present invention;

[0062] Figure 7 is a force diagram of a wheel in an embodiment of the present invention;

[0063] Figure 8 It is a schematic diagram of the calculation results of axle load transfer of the proposed model and the traditional model without considering the rotation of the traction rod tested under a traction force of 244.4 kN in an embodiment of the present invention;

[0064] Fig. 9 It is a schematic diagram of the optimized traction force and axle load transfer of a locomotive when the adhesion condition is 0.2 in an embodiment of the present invention;

[0065] Fig.10 It is a schematic diagram of the traction force of each axle when the locomotive is running on a low-adhesion road section before the traction force is optimized in an embodiment of the present invention;

[0066] Fig.11 It is a schematic diagram of the traction force of each axle when the locomotive is running on a low-adhesion section after the traction force is optimized in an embodiment of the present invention. DETAILED DESCRIPTION

[0067] The embodiments of the present invention are described in detail below with reference to the accompanying drawings.

[0068] Example

[0069] like Figure 1 As shown, a method for optimizing the utilization of locomotive adhesion based on dynamic compensation of axle load transfer includes the following steps:

[0070] S1. First, establish a locomotive axle weight transfer model that takes into account the rotation of the traction rod; and establish a mapping relationship from the traction force to the change in axle weight of each axle;

[0071] S2. When the motor outputs the specified traction force, the adhesion coefficient required for each axle to fully exert its adhesion can be calculated in combination with the static axle weight of the locomotive;

[0072] S3. Taking the adhesion coefficient and axle load transfer changes of each axle as constraints, and the maximum sum of the traction forces of each axle as the optimization goal, the traction force applied to each axle is optimized based on the sequential quadratic programming algorithm, so as to obtain the traction force electrical compensation coefficient that compensates for the axle load transfer.

[0073] The locomotive axle load transfer model is a quasi-static equilibrium equation set of forces on each component of the locomotive obtained through force analysis. The rotation of the locomotive traction rod needs to be considered in the model.

[0074] Taking a certain type of high-power AC locomotive with a single-pole low-positioned center traction rod as an example, the model only considers the longitudinal, pitching and vertical movements of the vehicle body and frame. In the model, only traction is used as the external force input system.

[0075] The traction force vector in the model is as follows.

[0076] ;

[0077] The degrees of freedom of each component of the model are shown in Table 1.

[0078] Table 1 Model degrees of freedom

[0079] Vertical Vertical nod Body <![CDATA[ x c ]]> <![CDATA[ z c ]]> <![CDATA[ β c ]]> Framework (=1-2) <![CDATA[ x ti ]]> <![CDATA[ z ti ]]> <![CDATA[ β ti ]]> Traction bar (=1-2) <![CDATA[ x qi ]]> <![CDATA[ z qi ]]> <![CDATA[ β qi ]]>

[0080] By analyzing the force on the motor components, the force equation of the motor can be derived. The equation is as follows:

[0081] ;

[0082] in, α is the gear meshing angle; F m1 is the motor suspension force; F g1 is the gear meshing force; F gbv is the force exerted by the gearbox on the axle; R g and R p are the radii of the large and small gears respectively.

[0083] Therefore, the motor boom force and the resulting axle load transfer can be derived.

[0084] ;

[0085] The primary and secondary suspension forces can be calculated from the displacement of the vehicle body and frame. The equations for calculating the primary and secondary suspension forces are as follows:

[0086] ;

[0087] in k sz and k sx is the vertical stiffness and longitudinal stiffness of the secondary suspension; k pz is the vertical stiffness of the primary suspension; L c is half the bogie centerline spacing; L t Half the wheelbase of the bogie; L s It is half of the longitudinal spacing of the secondary suspension; H sc and H sb They are the heights from the secondary suspension to the center of mass of the vehicle body and frame respectively.

[0088] For the drawbar, the node displacements at both ends are shown below.

[0089] ;

[0090] in x qbhi and z qbvi are the longitudinal and vertical node displacements connecting the drawbar to the frame, respectively; x qchi and z qcvi They are the displacements of the nodes connecting the drawbar to the vehicle body; L qyg and β qi0 are the length and initial angle of the traction bar respectively.

[0091] From this, the forces and moments acting on the nodes at both ends of the traction rod can be derived.

[0092] ;

[0093] in, k q and k qs are the radial stiffness and angular stiffness of the drawbar, respectively; L qyb and H qbare the longitudinal and vertical distances of the frame mass center from the drawbar frame node, respectively; L qc and H qc are the longitudinal and vertical distances from the vehicle body center of mass to the drawbar-body node, respectively.

[0094] The interaction between the coupler buffer and the car body is simplified as a linear spring force element. The coupler in the model is assumed to be fixed, so the coupler buffer force can be calculated as follows.

[0095] ;

[0096] in k gh is the buffer stiffness, γ is the vertical swing angle of the coupler.

[0097] In addition, the moments these forces exert on the body and frame are shown below.

[0098] ;

[0099] in F tj is the traction force acting on the wheelset; z bi0 is the initial vertical position of the centroid of the frame; z c0 is the initial vertical position of the vehicle’s center of mass; H cg It is the height of the coupler from the ground.

[0100] The force balance equations of the vehicle components can finally be derived as the equation group (9). By solving the 15-degree-of-freedom nonlinear equation group with a specific traction input, the change in the locomotive posture after the axle load transfer can be determined.

[0101] ;

[0102] Axle load transfer requires solving the structural response of the locomotive under the action of traction and coupler force. Under different traction forces, the structural stiffness matrix of the locomotive will also change accordingly due to the large angle deviation of the traction rod. Therefore, the calculation of axle load transfer is to solve the nonlinear response of the locomotive with geometric nonlinear structure under external loads, and its general form is shown in the following equation.

[0103] ;

[0104] in x is a state vector composed of the displacements of the degrees of freedom of each component of the vehicle; K ( x )and Fis the corresponding nonlinear stiffness matrix and the generalized external forces derived from Eq.

[0105] The Levenberg-Marquardt algorithm is used to solve the nonlinear equations in equation (9) to obtain the nonlinear response of the locomotive under external loads: x , the change of the locomotive axle load transfer is related to the nodding and vertical displacement of the frame and the suspension force of the motor. Therefore, the axle load transfer of each axle can be derived:

[0106] ;

[0107] Thus, a mapping relationship from traction force to axle load transfer of each axle of the locomotive is established.

[0108] When the motor outputs a specified traction force, the adhesion coefficient calculation method required for each axis to fully exert adhesion is as follows:

[0109] ;

[0110] in, u is the vector of adhesion coefficients; P 0 is the vector of static shaft load; F 0 is the intended applied traction force.

[0111] This embodiment converts the optimal traction under axle load transfer into a nonlinear programming problem for solution. The goal of traction optimization is to maximize the sum of traction on all wheel pairs under the wheel adhesion constraint. The general form of nonlinear optimization of traction can be expressed as follows:

[0112] ;

[0113] By solving this nonlinear programming problem, the optimal traction force of each axle under the action of axle load transfer can be obtained, and the traction force electrical compensation coefficient is calculated as shown in the following formula;

[0114] ;

[0115] in, ξ is the electrical compensation coefficient for traction, F opt It is the optimized traction.

[0116] In this embodiment, the locomotive frame type includes but is not limited to the B0-B0 form or the C0-C0 form. At the same time, the locomotive does not only refer to a freight locomotive, but generally refers to all vehicles with power units including rail vehicles; the mapping relationship from traction to the change in axle weight of each axle is determined according to the given adhesion conditions and locomotive structural parameters and suspension parameters, and the parameters include but are not limited to the primary and secondary stiffness of the locomotive, the height of the traction point, the wheel radius, the vertical swing angle of the hook, etc. The traction rod form includes but is not limited to push-pull single-pole low-position traction and double-pole low-position traction. The solution method of the nonlinear equation group can adopt the Levenberg-Marquardt algorithm, and nonlinear iterative algorithms such as incremental iterative algorithms are also feasible alternatives.

[0117] Figure 2 A schematic diagram of the locomotive axle load transfer model considering the rotation of the traction rod in this embodiment is given. Figure 3-Figure 7 These are the force analysis diagrams of the traction rod, gearbox, large gear, small gear and wheel in the model. Figure 8 A comparison between the proposed model and the test results and the calculation results of the traditional model that does not consider the rotation of the traction rod is given. It can be seen that the proposed model that considers the rotation of the traction rod is closer to the test results, which proves the effectiveness of the model. Fig. 9 The optimized traction force and axle load transfer of the locomotive when the adhesion condition is 0.2 are given. In this case, the traction force that the locomotive can exert is increased by 6.68% compared with that before optimization. Fig.10 The traction force of each axle of the locomotive running on the low-adhesion road section before optimization is given, and it can be seen that one wheelset has idling. Fig.11 The traction force of each axle of the optimized locomotive running on the low-adhesion road section is given. It can be seen that there is a compensation amount for the traction force applied to each axle, and no idling occurs in each wheel pair.

[0118] The above-mentioned embodiments only express the specific implementation of the present invention, and the description thereof is relatively specific and detailed, but it cannot be understood as limiting the scope of the present invention. It should be pointed out that, for ordinary technicians in this field, several variations and improvements can be made without departing from the concept of the present invention, which all belong to the protection scope of the present invention.

Claims

1. A method for optimizing the utilization of locomotive adhesion based on dynamic compensation of axle load transfer, characterized in that: The following steps are involved: Step 1: Establish a locomotive axle weight transfer model that takes into account the rotation of the traction rod; and establish a mapping relationship from the traction force to the change in axle weight of each axle; Step 2: When the motor outputs the specified traction force, the adhesion coefficient required for each axle to fully exert adhesion is calculated in combination with the static axle weight of the locomotive; Step 3: Taking the adhesion coefficient and axle load transfer change of each axle as constraint conditions and the maximum sum of the traction forces of each axle as the optimization target, the traction force applied to each axle is optimized based on the sequential quadratic programming algorithm, so as to obtain the traction force electrical compensation coefficient that compensates for the axle load transfer; The step 1 is specifically as follows: The axle load transfer model is a quasi-static equilibrium equation group of the forces on each component of the locomotive obtained by force analysis. The rotation of the locomotive traction rod needs to be considered in the axle load transfer model. Assuming that the longitudinal, pitch and vertical movements of the vehicle body and frame are considered, only the traction force is used as the external force input system in the axle load transfer model. The traction force vector in the axle load transfer model is as follows: F t =[F t1 F t2 F t3 F t4 ] T Perform force analysis on the motor components and derive the force equation of the motor: Where α is the gear meshing angle; F m1 is the motor suspension force; F g1 is the gear meshing force; F gbv is the force exerted by the gearbox on the axle; R g and R p are the radii of the large and small gears respectively; The motor boom force and the resulting axle load transfer are thus derived: The primary and secondary suspension forces are calculated by the displacement of the vehicle body and frame. The expression for calculating the suspension force is as follows: where k sz and k sx is the vertical stiffness and longitudinal stiffness of the secondary suspension; k pz is the vertical stiffness of the primary suspension; L c It is half of the bogie centerline spacing; L t Half of the bogie wheelbase; L s It is half of the longitudinal spacing of the secondary suspension; H sc and H sb They are the heights of the secondary suspension to the center of mass of the vehicle body and frame; For the drawbar, the node displacements at both ends are as follows: where x qbhi and z qbvi are the longitudinal and vertical node displacements connecting the drawbar to the frame, respectively; x qchi and z qcvi are the displacements of the nodes connecting the traction rod to the vehicle body; L qyg and β qi0 are the length and initial angle of the drawbar, respectively; From this, the forces and moments acting on the nodes at both ends of the traction rod are derived: Among them, k q and k qs are the radial stiffness and angular stiffness of the drawbar respectively; L qyb and H qb are the longitudinal and vertical distances from the center of mass of the frame to the drawbar frame node; L qc and H qc are the longitudinal and vertical distances of the center of mass of the vehicle body from the drawbar-body node, respectively; The interaction between the coupler buffer and the car body is simplified as a linear spring force element; the coupler in the axle load transfer model is assumed to be fixed, so the coupler buffer force is calculated as follows: where k gh is the buffer stiffness, γ is the vertical swing angle of the coupler; The forces and moments applied to the body and frame are as follows: Among them, F tj is the traction force acting on the wheelset; bi0 is the initial vertical position of the centroid of the frame; z c0 is the initial vertical position of the vehicle's center of mass; H cg is the height of the coupler from the ground; The force balance equations of the vehicle components are finally derived into the following set of equations: The change of locomotive posture after axle load transfer is determined by solving a nonlinear equation system with 15 degrees of freedom and traction force input; The axle load transfer calculation solves the nonlinear response of a locomotive with a geometrically nonlinear structure under external loads, which is expressed in the following equation: K(x)·x=F Where x is the state vector consisting of the displacements of the degrees of freedom of each component of the vehicle; K(x) and F are the corresponding nonlinear stiffness matrices and the generalized external forces derived from the equations; Solving the force balance equations of the vehicle components finally leads to the nonlinear system of equations, and the nonlinear response x of the locomotive under the external load is obtained, so as to derive the axle load transfer of each axle: Thus, a mapping relationship between traction force and axle load transfer of each axle of the locomotive is established; The step 3 is as follows: The goal of traction optimization is to maximize the sum of traction on all wheelsets under the constraint of wheel adhesion. The nonlinear optimization form of traction is expressed as follows: By solving the nonlinear programming problem, the optimal traction force of each axle under the action of axle load transfer is obtained, and the traction force electrical compensation coefficient is calculated as shown in the following formula: Where ξ is the electrical compensation coefficient of traction force, F opt It is the optimized traction.

2. The method for optimizing locomotive adhesion based on dynamic compensation of axle load transfer according to claim 1, characterized in that: In step 2, the adhesion coefficient calculation method is as follows: Where u is the vector of adhesion coefficients; P0 is the vector of static axle loads; and F0 is the predetermined applied traction force.

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