Full analytical method and device for wheel-rail conformal contact geometry considering head-shaking angle

Abstract

The present application relates to a wheel-rail conformal contact geometry relationship full analytical method and device considering the head shaking angle, first, according to the wheelset side roll angle and the head shaking angle, the potential contact line of the wheelset is calculated from the wheelset local coordinates by the projection profile method. Then, it is assumed that the potential contact point of the wheelset and the rail has the same X coordinate, and on this basis, the outer normal vector of each point on the wheelset potential contact line is solved, and the adjacent discrete points on the rail are constructed as a rail element, the projection point coordinates of the wheelset potential contact point on the rail element are solved, and the gap value is calculated. The contact point gap value is screened, and the boundary points of the potential contact area are solved in turn, and the potential contact area in the X-Y plane projection is drawn. By the method, the wheel-rail conformal contact state under complex conditions such as head shaking angle and wheel concave grinding can be accurately identified, and a continuous and complete potential contact area is obtained, which provides an accurate geometric basis for wheel-rail wear prediction.

Description

Technical Field

[0001] The embodiments in this specification relate to the field of railway vehicle-track system dynamics simulation technology, and in particular to a fully analytical method and apparatus for wheel-rail conformal contact geometry considering the yaw angle. Background Technology

[0002] Wheel-rail contact geometry determination is fundamental to the dynamics simulation of multi-body systems in railway vehicles. Its core task is to accurately and efficiently locate the contact point or contact area between the wheel and rail. The accuracy of wheel-rail contact location determination directly determines the effectiveness of subsequent wheel-rail wear prediction. When a vehicle runs smoothly on a straight section, non-conformal contact occurs between the wheelset and the rail, and the potential contact area is generally a small, elliptical region. However, when the vehicle passes through a small-radius curve or when wheel wear defects occur, the contact type changes from non-conformal to conformal. Compared to non-conformal contact, conformal contact has a larger potential contact area distribution, a more irregular shape, and generates a larger maximum contact force, occurring more frequently on high-speed railways where wheel wear is prone to occur. Accurately and quickly determining wheel-rail conformal contact and identifying the contact area distribution is a fundamental requirement for realizing the dynamics simulation of multi-body systems in vehicles. Summary of the Invention

[0003] To address the problems existing in the prior art, this specification provides a fully analytical method and apparatus for wheel-rail conformal contact geometry considering the head-up angle.

[0004] The specific technical solutions of the embodiments in this specification are as follows: On the one hand, the embodiments of this specification provide a fully analytical method for the conformal contact geometry of wheel and rail considering the head-up angle, the method comprising: Based on the wheel roll angle and yaw angle, the potential contact line of the wheel is calculated from the local coordinates of the wheel set using the projection profile method. Adjacent discrete points on the track are constructed into track units. The projection points of points on the potential contact line on the track units are calculated, and the gap value between the points on the potential contact line and their corresponding projection points is calculated. Points and projection points that meet the requirements of the gap value are used to form potential contact point pairs. Based on the coordinates of the projection points in the potential contact point pair, the rolling circle radius corresponding to the point in the potential contact point pair, and the gap value corresponding to the potential contact point pair, the boundary points of the potential contact area of ​​the wheel and rail are determined. The region outline of the potential contact area is formed based on the boundary points of the potential contact area.

[0005] Furthermore, based on the wheelset roll angle and yaw angle, the potential contact line of the wheel is calculated from the local coordinates of the wheelset using the projection profile method, including: Based on the wheel-rail profile data, establish the local and global coordinate systems for the wheelset; Construct a transformation matrix from the local coordinates of the wheelset to the global coordinate system based on the wheelset roll angle and yaw angle. The potential contact line is obtained by transforming the contour line of the bottom of the wheel that satisfies the projection contour condition from the local coordinate system of the wheelset to the global coordinate system using the transformation matrix.

[0006] Furthermore, the formula for constructing the transformation matrix from the local coordinate system of the wheelset to the global coordinate system based on the wheelset roll angle and yaw angle is as follows:

[0007] in, For the transformation matrix, The rotation matrix is ​​determined by the roll angle. The rotation matrix is ​​determined by the wheel yaw angle. For wheelset roll angle, The wheel's head-shaking angle.

[0008] Further, the contour line of the wheel bottom satisfying the projection contour condition is transformed from the local coordinate system of the wheelset to the global coordinate system using the transformation matrix to obtain the potential contact line, including: In the local coordinate system of the wheelset, the points on the contour line of the bottom of the wheel that satisfy the projection contour condition are... The expression is shown as:

[0009] In the formula For the local coordinate system of the wheelset, the point is... The Y-coordinate of the intersection point of the rolling circle and the generatrix. Let Z be the Z coordinate of the intersection point. For point The deflection angle relative to the intersection point; Using the transformation matrix to transform the points The points on the potential contact line are obtained by transforming the local coordinate system of the wheelset to the global coordinate system. The expression is:

[0010] Deflection angle The solution formula is:

[0011] In the formula , These represent the translations of the local coordinate system of the wheelset along the Y-axis and Z-axis, respectively. Point in the global coordinate system Coordinates on the X, Y, and Z axes.

[0012] Further, calculating the projection points of the points on the potential contact line onto the track unit includes: Calculate the outward normal vector of the point on the potential contact line; Two adjacent points on the track and Comprising orbital units, in which, Let j be the j-th point on the track. Let j be the (j+1)th point on the track; Calculate the intersection point between the external normal vector and the track unit, and use it as the projection point of that point on the potential contact line onto the track unit.

[0013] Furthermore, the coordinates of the i-th point on the potential contact line are: , Let be the coordinates of the i-th point on the potential contact line in the global coordinate system on the X-axis. Let be the Y-coordinate of the i-th point on the potential contact line in the global coordinate system. Let be the coordinates of the i-th point on the potential contact line in the global coordinate system on the Z-axis; The formula for calculating the outward normal vector of a point on the potential contact line is:

[0014] In the formula Let be the external normal vector of the i-th point on the potential contact line. Let be the coordinates of the (i+1)th point on the potential contact line in the global coordinate system on the Z-axis. Let be the coordinates of the (i-1)th point on the potential contact line in the global coordinate system along the Z-axis. Let be the coordinates of the (i+1)th point on the potential contact line in the global coordinate system on the Y-axis. Let be the coordinates of the (i-1)th point on the potential contact line in the global coordinate system on the Y-axis.

[0015] Further, calculating the intersection point between the external normal vector and the track unit, as the projection point of that point on the potential contact line onto the track unit, includes: calculate ,like This indicates that there is an intersection point between the outer normal vector and the orbital unit. , The intersection That is, the projection point of the i-th point on the potential contact line onto the track unit, where, Let be the tangent vector at the i-th point on the potential contact line. .

[0016] Further, the gap value between a point on the potential contact line and its corresponding projection point is calculated. The formula is:

[0017] in, , The projection point in the global coordinate system In the X-axis coordinate, The projection point in the global coordinate system In the Y-axis coordinate, The projection point in the global coordinate system The coordinates on the Z-axis.

[0018] Furthermore, the points corresponding to the required gap values ​​and the projected points are used to form potential contact point pairs, including: Determine the minimum clearance value from all clearance values ​​for this wheel; The following conditions will be met: The point corresponding to the gap value and projection point Forming a potential contact point pair, To predetermine the tolerance value, , where n represents the number of points on the potential contact line of the wheel. This represents the clearance value corresponding to the i-th point on the potential contact line of the wheel. This represents the minimum gap value.

[0019] Furthermore, based on the coordinates of the projected points in the potential contact point pair, the rolling circle radius corresponding to the points in the potential contact point pair, and the gap value corresponding to the potential contact point pair, the formula for determining the boundary points of the potential contact area between the wheel and rail is as follows:

[0020] in, Let j be the gap value corresponding to the j-th potential contact point pair. Represents the projection point in the j-th potential contact point pair Coordinates on the X-axis This represents the point in the j-th potential contact point pair. The corresponding rolling circle radius, Let be the coordinates of the boundary point corresponding to the j-th potential contact point pair on the X-axis.

[0021] On the other hand, embodiments of this specification also provide a fully analytical device for wheel-rail conformal contact geometry considering the head-up angle, the device comprising: The potential contact line projection unit is used to calculate the potential contact line of the wheel from the local coordinates of the wheelset using the projection profile method based on the wheelset roll angle and yaw angle. The potential contact point pair screening unit is used to construct adjacent discrete points on the track into track units, calculate the projection points of points on the potential contact line onto the track units, and calculate the gap value between the points on the potential contact line and their corresponding projection points, and form potential contact point pairs with the gap values ​​that meet the requirements and the projection points. The boundary point determination unit determines the boundary points of the potential contact area between the wheel and rail based on the coordinates of the projection points in the potential contact point pair, the rolling circle radius corresponding to the points in the potential contact point pair, and the gap value corresponding to the potential contact point pair. A potential contact area forming unit is used to form the region outline of the potential contact area based on the boundary points of the potential contact area.

[0022] On the other hand, embodiments of this specification also provide a computer device, including a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the above-described method.

[0023] On the other hand, embodiments of this specification also provide a computer-readable storage medium storing a computer program that, when executed by a processor, implements the above-described method.

[0024] On the other hand, embodiments of this specification also provide a computer program product, which includes a computer program that, when executed by a processor, implements the above-described method.

[0025] The methods described in this specification have at least the following technical effects: The method described in this specification extracts the potential contact line of the wheelset using the projection profile method. The entire process employs analytical formulas to complete contact point pair matching, gap calculation, and region boundary solving, eliminating the need for large-scale mesh node traversal and iterative calculations. This reduces computational load while maintaining accuracy, making it suitable for the high-efficiency computational requirements of large-scale vehicle-track system dynamic simulations. Furthermore, it incorporates the influence of wheelset roll angle and yaw angle, allowing the entire calculation process to be completed based on discrete data of the wheel-rail profile, without relying on analytical expressions for the wheel-rail surface, thus meeting diverse railway dynamics simulation needs. Employing a fully analytical contact point pair determination method based on external normal vector projection, and combining the projection correspondence between the potential contact line of the wheelset and the rail profile elements to solve for the contact gap, it can accurately identify the conformal contact state of the wheel and rail under complex conditions such as yaw angle and wheel wear, obtaining a continuous and complete potential contact area, providing accurate geometric basis for wheel-rail wear prediction. Attached Figure Description

[0026] To more clearly illustrate the technical solutions in the embodiments of this specification or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the embodiments of this specification. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0027] Figure 1 The diagram shown is a flowchart illustrating a fully analytical method for wheel-rail conformal contact geometry considering head-up angle in an embodiment of this specification. Figure 2 The diagram shown is a schematic diagram of the potential contact line of the wheel when the wheelset has a certain yaw angle and roll angle in an embodiment of this specification. Figure 3 The diagram shown is a flowchart illustrating the process of calculating the potential contact line of a wheel from local coordinates of the wheelset using the projection profile method based on the wheelset roll angle and yaw angle in an embodiment of this specification. Figure 4 The diagram shown is a schematic diagram of wheel-rail contact determination in an embodiment of this specification; Figure 5 The diagram shown is a schematic diagram of the selection of contact point gap values ​​in the embodiments of this specification; Figure 6 and Figure 7 The diagram shown is a schematic of the potential contact area of ​​the revolver calculated using the existing 2D simplification method, node search method, and the full analysis method of the embodiments of this specification. Figure 8 The diagram shown is a structural schematic of a fully analytical device for wheel-rail conformal contact geometry considering head-up angle in an embodiment of this specification. Figure 9The diagram shown is a structural schematic of the computer device according to an embodiment of this specification.

[0028] [Explanation of Figure Markers]: 1001, Potential contact line projection unit; 1002, Potential contact point pair screening unit; 1003. Boundary point determination unit; 1004. Potential contact area forming unit; 1102. Computer equipment; 1104. Processing equipment; 1106. Storage resources; 1108. Drive mechanism; 1110. Input / output module; 1112. Input devices; 1114. Output devices; 1116. Presentation device; 1118. Graphical User Interface; 1120. Network interface; 1122. Communication link; 1124. Communication bus. Detailed Implementation

[0029] The technical solutions in the embodiments of this specification will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the embodiments of this specification, and not all embodiments. Based on the embodiments of this specification, all other embodiments obtained by those skilled in the art without creative effort are within the protection scope of the embodiments of this specification.

[0030] It should be noted that the terms "first," "second," etc., in the description, claims, and accompanying drawings of the embodiments in this specification are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that the data can be used interchangeably where appropriate so that the embodiments described herein can be implemented in an order different from that illustrated or described in the specification. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover non-exclusive inclusion. For example, a process, method, apparatus, product, or device that includes a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to these processes, methods, products, or devices.

[0031] It should be noted that the acquisition, storage, use, and processing of data in the technical solutions of the embodiments of this specification all comply with the relevant provisions of national laws and regulations.

[0032] It should be noted that in the embodiments of this specification, certain software, components, models, and other existing solutions in the industry may be mentioned. These should be considered as exemplary, and their purpose is only to illustrate the feasibility of implementing the technical solution of this application, but does not mean that the applicant has already used or necessarily used such a solution. Similarly, the descriptions of prediction algorithms, table organization forms, and hardware structures are also exemplary.

[0033] The inventors discovered in their research that early vehicle multibody system dynamics simulations often employed 2D simplification methods. These methods simplified the wheel and rail from three-dimensional entities into two curves along the plane containing the wheel's generatrix. The difference in the ordinates between these two curves was used as the gap value, and the contact area was solved based on the Hertzian contact assumption. Although these methods are computationally efficient due to their simplicity, their overly simplified model design makes them unsuitable for increasingly complex dynamics simulation requirements.

[0034] Node search methods parameterize the wheel and rail surfaces, dividing them into numerous meshes and nodes, and searching for the corresponding contact relationships between these nodes. For example, a method that searches node by node specifically addresses the difficulty of finding contact points on non-convex rail surfaces and in conformal contact conditions using the minimum gap value method. A three-dimensional wheel-rail contact numerical algorithm based on the trace method is proposed, considering the asymmetric distribution of gap values ​​under the influence of the yaw angle. A method combining node search and table lookup methods is proposed to predict the jump position of wheel-rail contact points in turnout sections. A three-dimensional contact algorithm suitable for turnout sections that simultaneously considers the effects of switch rail cross-section and yaw angle changes is also proposed. After obtaining the initial wheel-rail contact area using the node search method, a curved reference surface is introduced, utilizing the curve coordinate correspondence between wheel and rail nodes to reduce the judgment error of planar algorithms in curved surface areas such as wheel flanges. Similar to node search methods, the finite element method can also accurately obtain the contact area by precisely simulating the geometric three-dimensional contact of wheel-rail contact; however, both are unsuitable for large-scale dynamic simulations due to their low computational efficiency, and are more often used as reference benchmarks for contact judgment accuracy.

[0035] The semi-analytical method combines the analytical expression of the wheel-rail surface of the node search method with the dimensionality reduction of the contact determination calculation to improve computational efficiency. For example, given the analytical expression of the wheel-rail surface, two methods are used to reduce the dimensionality of wheel-rail contact determination calculation: calculating the maximum of the strict spatial distance between the wheel and rail surfaces using the simplex method and finding the minimum of the vertical projection difference between the wheel and rail surfaces. An interpolation method is used to construct the turnout surface expression, and a semi-analytical method is used to determine two-point contact in the turnout section. The trace method treats the wheel tread as a series of rolling circles distributed along the wheelset centerline, obtaining the wheel-rail contact point traces on the wheel tread under the influence of the yaw angle, transforming the search for contact points on a two-dimensional surface into a one-dimensional spatial curve. The trace method and contour partitioning method are used to achieve wheel-rail contact determination considering the effects of wheel-rail lateral movement, yaw, and roll. The three-dimensional wheel-rail contact problem is reduced to a wheel-rail projection contour contact problem, and detailed calculation formulas for the wheel-rail projection contour under the influence of yaw angle and roll angle are given. Based on the projection contour method, the potential contact line of the wheel tread in three-dimensional space is constructed to simulate the contact area for solving the wheel-rail contact relationship in the turnout section. A semi-analytical algorithm based on curve coordinate correspondence is proposed based on Edwin's surface algorithm and the INFCON model. Although the semi-analytical method effectively improves the computational efficiency in wheel-rail contact, it still faces difficulties in determining conformal contact under the influence of head-up angle.

[0036] To address the problems existing in the prior art, this specification provides a fully analytical method for the conformal contact geometry of wheel and rail, considering the head-up angle. Figure 1 The diagram shown is a flowchart illustrating a fully analytical method for wheel-rail conformal contact geometry considering head-up angle, according to an embodiment of this specification. The order of steps listed in the embodiment is merely one possible execution order among many and does not represent the only possible order. In actual system or device products, the method can be executed sequentially or in parallel, as shown in the embodiment or accompanying drawings. Specifically, as... Figure 1 As shown, the method may include: Step 101: Based on the wheelset roll angle and yaw angle, calculate the potential contact line of the wheel from the local coordinates of the wheelset using the projection profile method; Step 102: Construct adjacent discrete points on the track into track units, calculate the projection points of points on the potential contact line onto the track units, and calculate the gap value between the points on the potential contact line and their corresponding projection points. Construct potential contact point pairs by matching the gap values ​​that meet the requirements with the projection points. Step 103: Determine the boundary points of the potential contact area of ​​the wheel and rail based on the coordinates of the projection points in the potential contact point pair, the rolling circle radius corresponding to the points in the potential contact point pair, and the gap value corresponding to the potential contact point pair. Step 104: Form the region outline of the potential contact region based on the boundary points of the potential contact region.

[0037] In the embodiments of this specification, the potential contact line of the wheel tread is the set of the lowest points of the cross-section of the wheel tread by various cross-sections along the Y-axis of the global coordinate system. For example... Figure 2 The diagram shown illustrates the potential contact line of the wheelset when it has a certain yaw angle and roll angle, as described in an embodiment of this specification. Using the potential contact line for contact determination reduces the wheel-rail contact determination process from searching on a two-dimensional surface to performing it on a one-dimensional curve.

[0038] Specifically, such as Figure 3 The diagram shown is a schematic representation of the process in this specification for calculating the potential contact line of the wheel from the local coordinates of the wheelset using the projection profile method based on the wheelset roll angle and yaw angle. The process includes: Step 301: Based on the wheel-rail profile data, establish the local coordinate system and the global coordinate system for the wheelset; Step 302: Construct a transformation matrix from the local coordinates of the wheelset to the global coordinate system based on the wheelset roll angle and yaw angle; Step 303: Using the transformation matrix, transform the contour line of the bottom of the wheel that satisfies the projection contour condition from the local coordinate system of the wheelset to the global coordinate system to obtain the potential contact line.

[0039] In this embodiment, wheel-rail profile data is input, and a local coordinate system and a global coordinate system for the wheelset are established. In the local coordinate system, the origin is located at the wheelset's centroid. The axle is located on a horizontal plane along the direction of travel of the wheelset. The axle is perpendicular to the wheelset axis and points vertically upwards. The axis coincides with the wheelset axis and its direction is determined by the right-hand screw rule. In the global coordinate system, the origin is located on the track centerline at the initial position during dynamic calculations. The X-axis is along the direction of train movement, the Z-axis is vertically upward, and the Y-axis is determined according to the right-hand screw rule.

[0040] Then, based on the wheel set roll angle and yaw angle, a transformation matrix is ​​constructed from the local coordinate system of the wheelset to the global coordinate system, and its formula is:

[0041] in, For the transformation matrix, The rotation matrix is ​​determined by the roll angle. The rotation matrix is ​​determined by the wheel yaw angle. For wheelset roll angle, The wheel's head-shaking angle.

[0042] Then, the contour line of the wheel bottom satisfying the projection contour condition in the global coordinate system is solved. In the local coordinate system of the wheelset, the points on the contour line of the wheel bottom satisfying the projection contour condition... The expression is shown as:

[0043] In the formula For the local coordinate system of the wheelset, the point is... The Y-coordinate of the intersection point of the rolling circle and the generatrix. Let Z be the Z coordinate of the intersection point. For point The deflection angle relative to the intersection point; point The expression for the corresponding point in the global coordinate system is:

[0044] In the formula , These represent the translations of the local coordinate system of the wheelset along the Y-axis and Z-axis, respectively. Point in the global coordinate system Coordinates on the X, Y, and Z axes.

[0045] Deflection angle The solution formula is:

[0046] Substitution point By finding the expression for the corresponding point in the global coordinate system, the point at the bottom of the wheelset that satisfies the projected profile condition can be obtained. Coordinates form the potential contact line.

[0047] It should be noted that in the local coordinate system of the wheelset, the contour line of the bottom of the wheel that satisfies the projection contour condition can be calculated using existing methods, which will not be elaborated here.

[0048] Then, wheel-rail contact is determined, such as... Figure 4 The diagram shown is a schematic diagram of wheel-rail contact determination in an embodiment of this specification. It utilizes the principle that the contact point of the wheel has a projection point on the rail along the outer normal vector when in contact. Through rigorous mathematical derivation, the coordinates of the corresponding contact point on the rail are obtained analytically.

[0049] Any point on the potential contact line The expression for the tangent vector is:

[0050] The derivative in the above formula is solved as follows:

[0051] The formula for calculating the outward normal vector of a point on the potential contact line is:

[0052] In the formula Let be the external normal vector of the i-th point on the potential contact line. Let be the coordinates of the (i+1)th point on the potential contact line in the global coordinate system on the Z-axis. Let be the coordinates of the (i-1)th point on the potential contact line in the global coordinate system along the Z-axis. Let be the coordinates of the (i+1)th point on the potential contact line in the global coordinate system on the Y-axis. Let be the coordinates of the (i-1)th point on the potential contact line in the global coordinate system on the Y-axis.

[0053] When the distance from the walk distance is sufficiently short, the unit formed by two adjacent points on the track It can be approximated as a straight line segment, where, Let j be the j-th point on the track. For the (j+1)th point on the track, the normal vector With rail profile unit There is an intersection It satisfies:

[0054] In the formula The expression is:

[0055] like Then the decision point In the rail profile unit There is a projection point. .point The expression is:

[0056] Projection point With point The gap value between potential contact point pairs The calculation formula is:

[0057] in, , The projection point in the global coordinate system In the X-axis coordinate, The projection point in the global coordinate system In the Y-axis coordinate, The projection point in the global coordinate system The coordinates on the Z-axis.

[0058] The set is obtained by calculating the gap values ​​at all points on the potential contact line of the wheel. , where n represents the number of points on the potential contact line of the wheel. This represents the gap value corresponding to the i-th point on the potential contact line of the wheel.

[0059] Figure 5 The diagram shown is a schematic diagram of the selection of contact point gap values ​​in the embodiments of this specification. Figure 5 Therefore, setting a tolerance value is necessary. If any gap value in the set satisfy:

[0060] but Contact gap value ,and Corresponding point and Forming potential contact point pairs, This represents the minimum gap value.

[0061] Then, based on the coordinates of the projected points in the potential contact point pair, the rolling circle radius corresponding to the points in the potential contact point pair, and the gap value corresponding to the potential contact point pair, the boundary points of the potential contact area between the wheel and rail are determined, and the formula is as follows:

[0062] in, Let j be the gap value corresponding to the j-th potential contact point pair. Represents the projection point in the j-th potential contact point pair Coordinates on the X-axis This represents the point in the j-th potential contact point pair. The corresponding rolling circle radius, Let be the coordinates of the boundary point corresponding to the j-th potential contact point pair on the X-axis.

[0063] Finally, all potential contact points of the wheel are plotted against their corresponding boundary points on the XY plane and connected sequentially to obtain the projected profile of the potential contact area. This projected profile is used to predict the wheel-rail wear of the wheel.

[0064] In practice, the above steps can be performed on each wheel of the train to obtain the projected profile of the potential contact area of ​​each wheel, thereby further analyzing the degree of wheel-rail wear of each wheel.

[0065] For example, this embodiment uses the condition of conformal contact between the LMA wheel and the TB60 rail under the influence of the head-up angle for testing, such as... Figure 6 and Figure 7 The diagram shows the potential contact area of ​​the left wheel calculated using the existing 2D simplification method, node search method, and the fully analytical method of the embodiments in this specification. Figures 6-7 It is evident that the computational error of the 2D simplification method causes the left boundary of the potential contact area obtained by it to shift in the negative Y-axis direction compared to the left boundary of the potential contact area obtained by the other three methods. The fully analytical method uses the normal vector as the basis for contact determination, correctly reflecting the influence of changes in the wheel yaw angle and wheel wear, and obtains a continuous conformal potential contact area located on the wheel tread and rim portion that is similar to that obtained by the node search method.

[0066] As shown in Table 1, the average computation time of the semi-analytical method is 1.10 times that of the 2D simplified method, the average computation time of the fully analytical method is 1.28 times that of the 2D simplified method, and the average computation time of the node search method is 78.17 times that of the 2D simplified method. The computation time of the fully analytical method is only 1.63% of that of the node search method, achieving conformal contact determination under the condition of wear vehicle contour participating in contact under the influence of head-shaking angle, and the calculation accuracy is consistent with that of the node search method.

[0067] Table 1 Comparison of computation time

[0068] Based on the same inventive concept, embodiments of this specification also provide a fully analytical device for the conformal contact geometry of wheel and rail considering the head-up angle, such as... Figure 8 The diagram shown is a structural schematic of a fully analytical device for wheel-rail conformal contact geometry considering the head-up angle, according to an embodiment of this specification. The device includes: The potential contact line projection unit 1001 is used to calculate the potential contact line of the wheel from the local coordinates of the wheelset using the projection profile method based on the wheelset roll angle and yaw angle. The potential contact point pair screening unit 1002 is used to construct adjacent discrete points on the track into track units, calculate the projection points of points on the potential contact line onto the track units, and calculate the gap value between the points on the potential contact line and their corresponding projection points, and form potential contact point pairs with the gap values ​​that meet the requirements and the projection points. Boundary point determination unit 1003 determines the boundary points of the potential contact area of ​​the wheel and rail based on the coordinates of the projection points in the potential contact point pair, the rolling circle radius corresponding to the points in the potential contact point pair, and the gap value corresponding to the potential contact point pair. The potential contact area forming unit 1004 is used to form the region outline of the potential contact area based on the boundary points of the potential contact area.

[0069] The beneficial effects obtained by the above-described device are the same as those obtained by the above-described method, and will not be described in detail in the embodiments of this specification.

[0070] like Figure 9 The diagram shown is a structural schematic of a computer device according to an embodiment of this specification. The methods described in this specification can be applied to the computer device of this embodiment.

[0071] Computer device 1102 may include one or more processing devices 1104, such as one or more central processing units (CPUs), each of which may implement one or more hardware threads.

[0072] Computer device 1102 may also include any storage resource 1106 for storing information of any kind, such as code, settings, data, etc. Without limitation, storage resource 1106 may include any one or more combinations of the following: any type of RAM, any type of ROM, flash memory device, hard disk, optical disk, etc.

[0073] More generally, any storage resource can use any technology to store information.

[0074] Furthermore, any storage resource can provide volatile or non-volatile retention of information.

[0075] Furthermore, any storage resource can represent a fixed or removable component of computer device 1102.

[0076] In one scenario, when processing device 1104 executes associated instructions stored in any storage resource or combination of storage resources, computer device 1102 may perform any operation of the associated instructions.

[0077] The computer device 1102 also includes one or more drive mechanisms 1108 for interacting with any storage resource, such as hard disk drive mechanism, optical disk drive mechanism, etc.

[0078] The computer device 1102 may also include an input / output module 1110 (I / O) for receiving various inputs (via input device 1112) and providing various outputs (via output device 1114).

[0079] A specific output mechanism may include a presentation device 1116 and an associated graphical user interface (GUI) 1118.

[0080] In other embodiments, the input / output module 1110 (I / O), input device 1112, and output device 1114 may be omitted, and the device may simply function as a computer device in the network.

[0081] Computer device 1102 may also include one or more network interfaces 1120 for exchanging data with other devices via one or more communication links 1122. One or more communication buses 1124 couple the components described above together.

[0082] The communication link 1122 can be implemented in any way, such as through a local area network, a wide area network (e.g., the Internet), a point-to-point connection, or any combination thereof.

[0083] Communication link 1122 may include any combination of hardwired links, wireless links, routers, gateway functions, name servers, etc., governed by any protocol or combination of protocols.

[0084] This specification also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the above-described method.

[0085] This specification also provides computer-readable instructions, wherein when a processor executes the instructions, the program therein causes the processor to perform the above-described method.

[0086] It should be understood that in the various embodiments of this specification, the sequence number of each process does not imply the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of this specification.

[0087] It should also be understood that, in the embodiments of this specification, the term "and / or" is merely a description of the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A existing alone, A and B existing simultaneously, and B existing alone. Furthermore, in the embodiments of this specification, the character " / " generally indicates that the preceding and following related objects have an "or" relationship.

[0088] Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed in this specification can be implemented in electronic hardware, computer software, or a combination of both. To clearly illustrate the interchangeability of hardware and software, the components and steps of each example have been generally described in terms of functionality in the foregoing description. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementations should not be considered beyond the scope of the embodiments in this specification.

[0089] Those skilled in the art will understand that, for the sake of convenience and brevity, the specific working processes of the systems, devices, and units described above can be referred to the corresponding processes in the foregoing method embodiments, and will not be repeated here.

[0090] In the embodiments provided in this specification, it should be understood that the disclosed systems, apparatuses, and methods can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the couplings or direct couplings or communication connections shown or discussed may be indirect couplings or communication connections through some interfaces, devices, or units, or they may be electrical, mechanical, or other forms of connection.

[0091] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of the embodiments described in this specification, depending on actual needs.

[0092] Furthermore, the functional units in the various embodiments of this specification can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0093] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solutions of the embodiments of this specification, in essence, or the parts that contribute to the prior art, or all or part of the technical solutions, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this specification. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0094] This specification describes the principles and implementation methods of the embodiments using specific examples. The above descriptions of the embodiments are only for the purpose of helping to understand the methods and core ideas of the embodiments in this specification. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of the embodiments in this specification. Therefore, the content of this specification should not be construed as a limitation on the embodiments in this specification.

Claims

1. A fully analytical method for the conformal contact geometry of wheel and rail considering head-off angle, characterized in that, The method includes: Based on the wheel roll angle and yaw angle, the potential contact line of the wheel is calculated from the local coordinates of the wheel set using the projection profile method. Adjacent discrete points on the track are constructed into track units. The projection points of points on the potential contact line on the track units are calculated, and the gap value between the points on the potential contact line and their corresponding projection points is calculated. Points and projection points that meet the requirements of the gap value are used to form potential contact point pairs. Based on the coordinates of the projection points in the potential contact point pair, the rolling circle radius corresponding to the point in the potential contact point pair, and the gap value corresponding to the potential contact point pair, the boundary points of the potential contact area of ​​the wheel and rail are determined. The region outline of the potential contact area is formed based on the boundary points of the potential contact area.

2. The method according to claim 1, characterized in that, Based on the wheelset roll angle and yaw angle, the potential contact line of the wheel is calculated from the local coordinates of the wheelset using the projection profile method, including: Based on the wheel-rail profile data, establish the local and global coordinate systems for the wheelset; Construct a transformation matrix from the local coordinates of the wheelset to the global coordinate system based on the wheelset roll angle and yaw angle. The potential contact line is obtained by transforming the contour line of the bottom of the wheel that satisfies the projection contour condition from the local coordinate system of the wheelset to the global coordinate system using the transformation matrix.

3. The method according to claim 2, characterized in that, The formula for constructing the transformation matrix from the local coordinate system of the wheelset to the global coordinate system based on the wheelset roll angle and yaw angle is as follows: in, For the transformation matrix, The rotation matrix is ​​determined by the roll angle. The rotation matrix is ​​determined by the wheel yaw angle. For wheelset roll angle, The wheel's head-shaking angle.

4. The method according to claim 3, characterized in that, The potential contact line is obtained by transforming the contour line of the wheel bottom that satisfies the projection contour condition from the local coordinate system of the wheelset to the global coordinate system using the transformation matrix, including: In the local coordinate system of the wheelset, the points on the contour line of the bottom of the wheel that satisfy the projection contour condition are... The expression is shown as: In the formula For the local coordinate system of the wheelset, the point is... The Y-coordinate of the intersection point of the rolling circle and the generatrix. Let Z be the intersection point. For point The deflection angle relative to the intersection point; Using the transformation matrix to transform the points The points on the potential contact line are obtained by transforming the local coordinate system of the wheelset to the global coordinate system. The expression is: Deflection angle The solution formula is: In the formula , These represent the translations of the local coordinate system of the wheelset along the Y-axis and Z-axis, respectively. Point in the global coordinate system Coordinates on the X, Y, and Z axes.

5. The method according to claim 1, characterized in that, Calculating the projection points of points on the potential contact line onto the track unit includes: Calculate the outward normal vector of the point on the potential contact line; Two adjacent points on the track and Comprising orbital units, in which, Let j be the j-th point on the track. Let j be the (j+1)th point on the track; Calculate the intersection point between the external normal vector and the track unit, and use it as the projection point of that point on the potential contact line onto the track unit.

6. The method according to claim 5, characterized in that, The coordinates of the i-th point on the potential contact line are: , Let be the coordinates of the i-th point on the potential contact line in the global coordinate system on the X-axis. Let be the Y-coordinate of the i-th point on the potential contact line in the global coordinate system. Let be the coordinates of the i-th point on the potential contact line in the global coordinate system on the Z-axis; The formula for calculating the outward normal vector of a point on the potential contact line is: In the formula Let be the external normal vector of the i-th point on the potential contact line. Let be the coordinates of the (i+1)th point on the potential contact line in the global coordinate system on the Z-axis. Let be the coordinates of the (i-1)th point on the potential contact line in the global coordinate system along the Z-axis. Let be the coordinates of the (i+1)th point on the potential contact line in the global coordinate system on the Y-axis. Let be the coordinates of the (i-1)th point on the potential contact line in the global coordinate system on the Y-axis.

7. The method according to claim 6, characterized in that, Calculating the intersection point between the external normal vector and the track element, as the projection point of that point on the potential contact line onto the track element, includes: calculate ,like This indicates that there is an intersection point between the outer normal vector and the orbital unit. , The intersection That is, the projection point of the i-th point on the potential contact line onto the track unit, where, Let be the tangent vector at the i-th point on the potential contact line. .

8. The method according to claim 6, characterized in that, Calculate the gap value between a point on the potential contact line and its corresponding projected point. The formula is: in, , The projection point in the global coordinate system In the X-axis coordinate, The projection point in the global coordinate system In the Y-axis coordinate, The projection point in the global coordinate system The coordinates on the Z-axis.

9. The method according to claim 8, characterized in that, The points corresponding to the required gap values ​​and the projected points constitute potential contact point pairs, including: Determine the minimum clearance value from all clearance values ​​for this wheel; The following conditions will be met: The point corresponding to the gap value and projection point Forming a potential contact point pair, To predetermine the tolerance value, , where n represents the number of points on the potential contact line of the wheel. This represents the clearance value corresponding to the i-th point on the potential contact line of the wheel. This represents the minimum gap value.

10. The method according to claim 8, characterized in that, The formula for determining the boundary points of the potential contact area of ​​the wheel and rail, based on the coordinates of the projected points in the potential contact point pair, the rolling circle radius corresponding to the points in the potential contact point pair, and the gap value corresponding to the potential contact point pair, is as follows: in, Let j be the gap value corresponding to the j-th potential contact point pair. Represents the projection point in the j-th potential contact point pair Coordinates on the X-axis This represents the point in the j-th potential contact point pair. The corresponding rolling circle radius, Let be the coordinates of the boundary point corresponding to the j-th potential contact point pair on the X-axis.

11. A fully analytical device for the conformal contact geometry of wheel and rail considering the head-off angle, characterized in that, The device includes: The potential contact line projection unit is used to calculate the potential contact line of the wheel from the local coordinates of the wheelset using the projection profile method based on the wheelset roll angle and yaw angle. The potential contact point pair screening unit is used to construct adjacent discrete points on the track into track units, calculate the projection points of points on the potential contact line onto the track units, and calculate the gap value between the points on the potential contact line and their corresponding projection points, and form potential contact point pairs with the gap values ​​that meet the requirements and the projection points. The boundary point determination unit determines the boundary points of the potential contact area between the wheel and rail based on the coordinates of the projection points in the potential contact point pair, the rolling circle radius corresponding to the points in the potential contact point pair, and the gap value corresponding to the potential contact point pair. A potential contact area forming unit is used to form the region outline of the potential contact area based on the boundary points of the potential contact area.

12. A computer device comprising a memory, a processor, and a computer program stored in the memory, characterized in that, When the processor executes the computer program, it implements the method according to any one of claims 1 to 10.

13. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, implements the method of any one of claims 1 to 10.

14. A computer program product, characterized in that, The computer program product includes a computer program that, when executed by a processor, implements the method of any one of claims 1 to 10.

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