Method for inversely designing wheel tread profile by using difference in contact angle and difference in rolling circle radius

Abstract

A method for inversely deriving and designing the wheel tread profile using the difference in contact angle and the difference in rolling circle radius, which relates to a method for designing the wheel tread profile. Select a wheel tread profile that meets the basic parameters; set the origin of the wheel tread coordinate system as the point where the rolling circle is located, and the origin of the rail head coordinate system as the common tangent point of the rail surface; change the lateral displacement of the wheel set, and use the trace method to obtain the wheel-rail contact point, contact angle, and tread profile; based on the contact angle data, obtain the difference in contact angle; take the wheel-rail contact point when the lateral displacement of the wheel set is 0 as the initial value of integration, and integrate the tangent value of the difference in contact angle in the positive and negative directions of the lateral displacement respectively to obtain the curve of the difference in rolling circle radius; compare the curve of the difference in rolling circle radius of the wheel set obtained by using the trace method, and the inversely derived tread profile meets the requirements; obtain a partial wheel tread profile, check its curve of the difference in rolling circle radius, and obtain the wheel tread profile. It takes into account the combined action of the left and right wheels of the entire wheel set, has higher design accuracy, reduces wheel-rail wear, and extends the service life.

Description

Technical Field

[0001] The present invention relates to a method for designing the profile of a wheel tread, specifically a method for inversely designing the profile of a wheel tread using the contact angle difference and the rolling circle radius difference. Background Art

[0002] The design of railway wheel treads has important theoretical significance and practical value in the field of rail transit, and is directly related to the safety, stability and economy of train operation. The wheel tread is the core component of the wheel-rail system. It not only bears the weight of the train, but also undertakes the lateral and longitudinal forces generated during the driving and braking processes. With the development of railway transportation towards high-speed and heavy-haul directions, the design of wheel treads faces a more complex operating environment and higher performance requirements. Traditional wheel tread design methods usually rely on the combination of geometric characteristics and mechanical properties, based on engineering experience or simplified models, and are designed by optimizing a single performance index, such as curve negotiation performance, vehicle running stability or wear characteristics. These methods show high effectiveness under relatively simplified working conditions, but in modern high-speed and heavy-haul railway operations, their limitations are becoming increasingly prominent. The wheel-rail contact behavior is the core issue in the design of wheel treads. The contact state between the wheel tread and the rail surface will affect the dynamic characteristics of the train, and the contact angle difference and the rolling circle radius difference are two key parameters. The contact angle difference reflects the relative angular change between the wheel and the rail surface during wheel-rail contact, and has an important impact on the curve negotiation ability and running stability of the train; the rolling circle radius difference describes the change in the rolling circle radius at the wheel-rail contact point during the lateral movement of the wheel set, and has a significant effect on the wear distribution and traction performance of the wheel. Optimizing these two parameters can not only improve the matching performance of the wheel-rail system, but also improve the dynamic performance of train operation, reduce wear and extend the service life of wheels and rails. However, in traditional design methods, due to the insufficient understanding of the complexity of wheel-rail contact behavior, it is often difficult to effectively control the contact angle difference and the rolling circle radius difference, thus limiting the overall performance of wheel tread design.

[0003] Related patent document: CN105512397A discloses a method for designing the tread profile of independent wheels and independent wheels. The method for designing the tread profile includes the following steps: 1) determining the left and right wheel contact angle difference curve according to vehicle parameters, track parameters, and desired vehicle dynamic performance indicators; 2) specifying the initial distribution area of wheel-rail contact points; 3) taking the left and right wheel contact angle difference curve in step 1) and the distribution area of wheel-rail contact points in step 2) as the design objectives of the wheel tread profile, and inversely deducing the wheel tread profile that meets the requirements according to the mutual relationship between the rail profile, rail bottom slope, wheel tread profile, left and right wheel contact angle difference curve, and the distribution area of wheel-rail contact points; 4) calculating the wheel-rail contact stress according to the designed tread profile; 5) determining whether the wheel-rail contact stress is optimal, otherwise returning to step 2) to readjust the distribution area of wheel-rail contact points until the wheel-rail contact stress converges to the minimum value.

[0004] The design accuracy of the above technology is generally average and still needs to be improved. Summary of the Invention

[0005] The purpose of the present invention is to provide a method for inversely deducing and designing the wheel tread profile using the contact angle difference and rolling circle radius difference, which can take into account the combined action of the left and right wheels of the entire wheel set, has higher design accuracy, effectively reduces wheel-rail wear, extends the service life of wheels and rails, obtains good wheel-rail contact geometry, and thus improves the running stability of the train and the riding comfort of passengers.

[0006] To solve the above technical problems, the technical solution adopted by the present invention is as follows:

[0007] A method for inversely deducing and designing the wheel tread profile using the contact angle difference and rolling circle radius difference (or a method for inversely deducing and designing the railway wheel tread profile using the contact angle difference and rolling circle radius difference), the technical solution thereof lies in that it includes the following steps:

[0008] S1. Obtain the rail head profile of the railway rail and the rail bottom slope, and select a wheel tread profile that meets the basic parameters, where the basic parameters include gauge, wheel set inner distance, flange height, flange thickness, hub width, tread width, distance from the point where the rolling circle is located to the wheel back, distance from the flange thickness measurement point to the point where the rolling circle is located, and vertical distance from the gauge measurement point to the top surface;

[0009] S2. Set the origin of the wheel tread coordinate system as the point where the rolling circle is located, and the origin of the rail head coordinate system as the common tangent point of the left and right rail surfaces;

[0010] S3. Considering the influence of the wheel set roll angle, change the lateral displacement of the wheel set, and use the trace method to obtain the wheel-rail contact points, contact angles, and wheel tread profile when the lateral displacement of the wheel set varies within the range of -12.5 mm to 12.5 mm;

[0011] S4. Obtain the contact angle difference based on the left and right wheel-rail contact angle data;

[0012] S5. Taking the wheel-rail contact point when the wheel set lateral displacement is 0 as the integral initial value, integrate the tangent value of the contact angle difference in the positive and negative directions of the lateral displacement respectively to obtain the rolling circle radius difference curve based on the contact angle difference;

[0013] S6. Compare the wheel set rolling circle radius difference curve obtained by using the trace method and the wheel set rolling circle radius difference curve based on the contact angle difference. When the numerical difference between the two under the same lateral displacement is less than the set value, it is determined that the rolling circle radius difference value based on the contact angle difference is within an acceptable range, that is, the tread profile obtained by back-calculation meets the requirements of engineering design. Otherwise, the tread profile needs to be adjusted and redesigned;

[0014] S7. Obtain the tread profile of part of the wheels, check the rolling circle radius difference curve (that is, check the rolling circle radius difference curve of the tread profile of part of the wheels), and obtain the wheel tread profile that meets the requirements of a certain contact angle difference curve and rolling circle radius difference curve;

[0015] S8. For the newly obtained wheel tread profile (based on), conduct contact characteristic calculation and contact stress analysis, and perform smoothing and other treatments as needed.

[0016] In the above technical solution, the preferred technical solution may be that in step S1, the following method is used for setting: both the wheels and rails included in the above wheel-rail are rigid, that is, the elastic deformation of wheel-rail contact is ignored; the shape of the rail head is convex upward, that is, the tangent slope of each point changes monotonically; the shape of the rail head and the designed wheel tread profile are symmetrical left and right; the given flange height, flange thickness, and tread width remain unchanged. In step S3, the following method is used to obtain the wheel-rail contact point, contact angle, and wheel tread profile:

[0017] S31. Given the rail head profile and the target tread profile (i.e., the "seed" tread profile), considering the effect of the wheel set roll angle, the condition for calculating the contact angle is:

[0018] ;

[0019] ; ;

[0020] ;

[0021] ;

[0022] ;

[0023] ;

[0024] ;

[0025] ;

[0026] ;

[0027] Among them, is the rail head profile; is the target tread profile; is the roll angle of the wheel set; is the lateral displacement of the wheel set; the contact point coordinates of the left wheel tread and the rail surface are and respectively, and the contact point coordinates of the right wheel tread and the rail surface are and ; and are the left and right contact angles respectively.

[0028] S32. Calculate the ordinate of the tread profile using the contact angle. After obtaining the contact angle, there is the following expression through transformation:

[0029] ;

[0030] ;

[0031] Among them, is the ordinate of the tread profile; represents the ordinate of the tread contact point when the lateral displacement is 0.

[0032] In the above technical solution, the preferred technical solution can also be that in step S4, the formula for calculating the contact angle difference is as follows: ; Among them, is the contact angle difference.

[0033] In the above technical solution, the preferred technical solution can also be that in step S5, the formula for calculating the rolling circle radius difference based on the contact angle difference is as follows:

[0034] ;

[0035] Among them, is the rolling circle radius difference calculated based on the contact angle difference; when the lateral displacement of the wheel set is 0, there is .

[0036] In the above technical solution, the preferred technical solution can also be that step S6 includes:

[0037] S61. Use the trace method to obtain the rolling circle radius difference curve of the wheel set through the left and right wheel side tread profile curves;

[0038] S62. Obtain the curve of the difference in the rolling circle radius of the wheel set based on the difference in contact angles;

[0039] S63. Compare the above two curves and check the following formula: ;

[0040] where, is the difference in the rolling circle radius of the wheel set obtained by the trace method; is the difference in the rolling circle radius of the wheel set obtained by the trace method; is the set error value, .

[0041] If the above formula does not hold, adjust the designed tread surface according to . The part with a lateral shift amount less than 0 is allocated to the left wheel, and the rest is allocated to the right wheel, and compared with the original tread surface parameter, i.e., the difference in the rolling circle radius.

[0042] In the above technical solution, the preferred technical solution may also be that the redesign in step S6 refers to repeating step S6 and comparing it with the original wheel tread parameters.

[0043] In the above technical solution, the preferred technical solution may also be that step S7 includes:

[0044] S71. Obtain the outer shape of part of the wheel tread. Based on the obtained outer shape of part of the wheel tread, check whether the curve of the difference in the rolling circle radius (of the part of the wheel tread) differs from the expected curve by value, is the set error value, . If so, expand the newly obtained outer shape of part of the wheel tread according to the original wheel tread outer shape, and the expansion principle is to ensure that the basic parameters of the wheel tread remain unchanged;

[0045] S72. Refine the step size of the change in the lateral shift amount of the wheel set to improve the calculation accuracy;

[0046] S73. Directly change the local line shape of the curve and deduce the new tread outer shape to obtain a wheel tread outer shape that meets the requirements of a certain contact angle difference curve and rolling circle radius difference curve;

[0047] S74. The new tread outer shape needs to be merged to obtain a complete wheel tread outer shape.

[0048] In the modern railway operating environment, the running speed of trains increases, the load increases, and the curve radius decreases. These factors cause the wheel-rail contact behavior to exhibit obvious non-linearity and complex dynamic characteristics. Based on the inverse design method using the contact angle difference and the rolling circle radius difference, the optimization design of the wheel tread profile is realized through geometric and mechanical calculations of the wheel set. Different from the traditional design path, this method directly integrates the optimization goal of the left-right wheel-rail contact relationship of the entire wheel set into the design process, and uses the mapping relationship between the contact parameters and the tread geometry to inversely solve the tread profile that meets the target performance. The inverse design considering the wheel set structure provides a new technical path for the rail transit field, which helps to promote the transformation of the wheel tread design theory from the geometric and mechanical static design based on a single wheel-rail to the dynamic optimization based on the comprehensive contact behavior of the wheel set-rail. Therefore, at the present stage of the rapid development of rail transit technology, studying and promoting the inverse design technology of the wheel tread not only has important significance for improving the comprehensive performance of the wheel-rail system, but also provides strong technical support for the continuous improvement of the rail transit equipment manufacturing level. In view of this, the present invention proposes a method for inversely designing the rail wheel tread profile using the contact angle difference and the rolling circle radius difference to design and optimize the wheel tread profile curve, thereby improving the train running stability and the passenger riding comfort.

[0049] The beneficial effects produced by the present invention adopting the above technical solutions are as follows:

[0050] By optimizing the contact behavior of the wheel set as a whole rather than a single wheel, the present invention can more comprehensively consider the dynamic coordination of the left and right wheels, thereby improving the stability of the wheel set during curve negotiation. The coordinated optimization of the contact angle difference and the rolling circle radius difference between the left and right wheels effectively reduces the asymmetric force distribution between the wheel and the rail, avoiding lateral offset and potential safety hazards during vehicle operation.

[0051] Based on the design of the entire wheel set, the dynamic offset of the wheel-rail contact point and its adaptability to the gauge change can be more accurately controlled, reducing the excitation phenomenon and vehicle body vibration during vehicle operation. By coordinating the rolling circle radius difference between the left and right wheels, the asymmetric torque during wheel operation is reduced, significantly improving the running smoothness of the train and the comfort experience of passengers.

[0052] The traditional method only considers a single wheel and cannot avoid the difference in contact conditions between the left and right wheels during operation, resulting in uneven wheel-rail wear and shortened service life. By considering the contact behavior of the entire wheel set, the present invention effectively balances the friction force distribution between the wheel and the rail, reduces local wear, extends the service life of the wheel and the rail, and thus significantly reduces the maintenance cost and the track maintenance frequency.

[0053] The present invention is applicable to the optimization of wheel-rail contact under complex working conditions such as high speed, heavy load and small curve radius. By dynamically optimizing the entire wheel set, comprehensive adaptation to multiple working conditions can be achieved, improving the operation reliability and performance stability of the rail transit system under harsh conditions. The design method provided by the present invention takes into account the combined action of the left and right wheels of the entire wheel set, with higher design accuracy, effectively enhancing the stability during the operation of the wheels, and improving the performance and operation economy of the rail transit system.

[0054] In addition, the present invention breaks through the traditional idea of single-wheel optimization and provides a new technical path for the overall design of the wheel set. This method can not only be directly applied to the design of the wheel tread, but also provide theoretical and method support for the dynamic analysis and optimization of more complex wheel-rail systems.

[0055] The present invention provides a method for inversely designing the profile of the wheel tread by using the contact angle difference and the rolling circle radius difference. This method takes into account the combined action of the left and right wheels of the entire wheel set, with higher design accuracy, effectively reducing wheel-rail wear and extending the service life of the wheels and rails, obtaining good wheel-rail contact geometry, thereby improving the stability of train operation and the riding comfort of passengers. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Figure 1 It is a schematic flow chart for the inverse design of the profile of the railway wheel tread in the present invention.

[0057] Figure 2 、 Figure 3 It is a schematic diagram of the wheel-rail contact point pair, Figure 2 It is a schematic diagram of the left wheel-rail contact point pair, Figure 3 It is a schematic diagram of the right wheel-rail contact point pair.

[0058] Figure 4 、 Figure 5 They are curves of the wheel-rail contact parameters on the left and right sides varying with the lateral displacement, Figure 4 They are curves of the contact angle difference between the left and right wheel-rails varying with the lateral displacement, Figure 5 They are curves of the rolling circle radius difference between the left and right wheel-rails varying with the lateral displacement.

[0059] Figure 6 、 Figure 7 They are curves of the integral of the tangent value of the contact angle varying with the lateral displacement, Figure 6 They are the corresponding curves of the left wheel-rail, Figure 7 They are the corresponding curves of the right wheel-rail.

[0060] Figure 8 They are curves of the rolling circle radius difference between the left and right wheel-rails varying with the lateral displacement, including the original tread and the designed tread 1.

[0061] Figure 9To design the curve of the relative error value of the difference in rolling circle radius between the designed tread 1 and the original tread varying with the lateral displacement.

[0062] Figure 10 、 Figure 11 Is the curve of the integral of the tangent value of the contact angle corrected according to the relative error value of the difference in rolling circle radius varying with the lateral displacement, Figure 10 Is the corresponding curve for the left wheel-rail, Figure 11 Is the corresponding curve for the right wheel-rail.

[0063] Figure 12 Is the curve of the difference in rolling circle radius between the left and right wheel-rails after correction varying with the lateral displacement, including the original tread and the designed tread 2.

[0064] Figure 13 Is the curve of the relative error value of the difference in rolling circle radius between the designed tread 2 and the original tread varying with the lateral displacement after correction.

[0065] Figure 14 、 Figure 15 Is the curve of the integral of the tangent value of the contact angle after secondary correction according to the relative error value of the difference in rolling circle radius varying with the lateral displacement, Figure 14 Is the corresponding curve for the left wheel-rail, Figure 15 Is the corresponding curve for the right wheel-rail.

[0066] Figure 16 Is the curve of the difference in rolling circle radius between the left and right wheel-rails after secondary correction varying with the lateral displacement, including the original tread and the designed tread 3 (the two curves almost coincide).

[0067] Figure 17 Is the curve of the relative error value of the difference in rolling circle radius between the designed tread 3 and the original tread varying with the lateral displacement after secondary correction.

[0068] Figure 18 、 Figure 19 Is the curve of the integral of the tangent value of the contact angle after secondary correction and smoothing varying with the lateral displacement, Figure 18 Is the corresponding curve for the left wheel-rail (the two curves almost coincide), Figure 19 Is the corresponding curve for the right wheel-rail (the two curves almost coincide).

[0069] Figure 20 、 Figure 21 Is the comparison diagram of the final designed wheel tread profile and the original wheel tread profile, Figure 20 Is the corresponding curve for the left wheel-rail, Figure 21 Is the corresponding curve for the right wheel-rail. Specific implementation method

[0070] To make the objectives, technical solutions and advantages of the present invention clearer, the technical solutions of the present invention will be clearly and completely described below in conjunction with the embodiments. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention. Based on these embodiments, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the scope of the present invention.

[0071] Embodiment 1: As Figure 1 , Figure 2 , Figure 3 , Figure 4 , Figure 5 , Figure 6 , Figure 7 , Figure 8 , Figure 9 , Figure 10 , Figure 11 , Figure 12 , Figure 13 , Figure 14 , Figure 15 , Figure 16 , Figure 17 , Figure 18 , Figure 19 , Figure 20 , Figure 21 shown, the method for inversely designing the wheel tread profile using the contact angle difference and the rolling circle radius difference of the present invention includes the following steps:

[0072] S1. Obtain the head profile of the railway rail and the rail bottom slope, and select a wheel tread profile that meets the basic parameters, where the basic parameters include the gauge, the inner distance between wheel pairs, the flange height, the flange thickness, the hub width, the tread width, the distance from the point where the rolling circle is located to the wheel back, the distance from the flange thickness measurement point to the point where the rolling circle is located, and the vertical distance from the gauge measurement point to the top surface. In step S1, the following method is used for setting: both the wheel and the rail included in the above wheel-rail are rigid, that is, the elastic deformation of the wheel-rail contact is ignored; the head profile is convex upward, that is, the tangent slope of each point changes monotonically; the head profile and the designed wheel tread profile are symmetric about the left and right; the given flange height, flange thickness, and tread width remain unchanged. The head profile of the selected railway rail is CN60, the rail bottom slope is 1 / 40, the gauge is 1435 mm; the wheel tread profile is LM, the nominal rolling circle radius of the wheel is 420 mm, the inner distance between the wheel backs is 1353 mm, the step size of the wheel pair lateral displacement is 0.05 mm, and the calculation range of the wheel pair lateral displacement is -12.5 to 12.5 mm.

[0073] S2. Set the origin of the wheel tread coordinate system as the point where the rolling circle is located, and the origin of the rail head coordinate system as the common tangent point of the left and right rail surfaces.

[0074] S3. Consider the influence of the wheelset roll angle, change the lateral displacement of the wheelset, and use the trace method to obtain the wheel-rail contact point, contact angle, and wheel tread profile when the lateral displacement of the wheelset varies within the range of -12.5 mm to 12.5 mm. That is, in step S3, the following method is used to obtain the wheel-rail contact point, contact angle, and wheel tread profile:

[0075] S31. Given the rail head profile and the target tread profile (i.e., the "seed" tread profile), that is, for the CN60 rail head profile and the LM wheel tread profile, considering the effect of the wheelset roll angle, the conditions for calculating the contact angle are:

[0076] ;

[0077] ; ;

[0078] ;

[0079] ;

[0080] ;

[0081] ;

[0082] ;

[0083] ;

[0084] ;

[0085] Among them, is the rail head profile; is the target tread profile; is the roll angle of the wheelset; is the lateral displacement of the wheelset; the contact point coordinates of the left wheel tread and the rail surface are respectively and , and the contact point coordinates of the right wheel tread and the rail surface are respectively and ; and are the left and right contact angles respectively.

[0086] S32. Calculate the ordinate of the tread profile using the contact angle. After obtaining the contact angle, there are the following expressions through transformation:

[0087] ;

[0088] ;

[0089] Among them, is the vertical coordinate of the tread profile; represents the vertical coordinate of the tread contact point when the lateral displacement is 0, which is 420 mm.

[0090] S4. Obtain the contact angle difference based on the left and right wheel-rail contact angle data. In step S4, the formula for calculating the contact angle difference is as follows:

[0091] ; where is the contact angle difference.

[0092] S5. Taking the wheel-rail contact point when the wheel set lateral displacement is 0 as the integral initial value, integrate the tangent value of the contact angle difference in the positive and negative directions of the lateral displacement respectively to obtain the rolling circle radius difference curve based on the contact angle difference.

[0093] In step S5, the formula for calculating the rolling circle radius difference based on the contact angle difference is as follows: ;

[0094] where is the rolling circle radius difference calculated based on the contact angle difference; when the wheel set lateral displacement is 0, there is . During the calculation process, the integration step size is set to 0.05 mm.

[0095] S6. Compare the wheel set rolling circle radius difference curve obtained by using the trace method and the wheel set rolling circle radius difference curve based on the contact angle difference. When the numerical difference between the two at the same lateral displacement is less than the set value, it is considered that the rolling circle radius difference value based on the contact angle difference is within an acceptable range, that is, the tread profile obtained by back-calculation meets the requirements of the engineering design. Otherwise, the tread profile needs to be adjusted and redesigned; the redesign in step S6 refers to repeating step S6 and comparing it with the original wheel tread parameters. Step S6 includes:

[0096] S61. Using the trace method, obtain the wheel set rolling circle radius difference curve through the left and right wheel side tread profile curves;

[0097] S62. Obtain the wheel set rolling circle radius difference curve obtained based on the contact angle difference;

[0098] S63. Compare the above two curves and check the following formula:

[0099] ; where is the wheel set rolling circle radius difference obtained by the trace method; is the set error value, .

[0100] If the above formula does not hold, according to Adjust the designed tread surface. The part corresponding to a lateral displacement less than 0 is allocated to the left wheel, and the remaining part is allocated to the right wheel, and it is compared with the original tread parameters, i.e., the difference in rolling circle radius.

[0101] S7. Obtain the tread profile of some wheels, check the curve of the difference in rolling circle radius (of the tread profile of some wheels), and obtain the tread profile of the wheels that meets the requirements of a certain contact angle difference curve and rolling circle radius difference curve. Step S7 includes:

[0102] S71. Obtain the tread profile of some wheels. According to the obtained tread profile of some wheels, check whether the curve of the difference in rolling circle radius (of the tread profile of some wheels) differs from the expected curve by a value which is a set error value. If so, expand the newly obtained tread profile of some wheels according to the original wheel tread profile. The expansion principle is to ensure that the basic parameters of the wheel tread remain unchanged;

[0103] S72. Refine the step size of the change in the lateral displacement of the wheel set to improve the calculation accuracy;

[0104] S73. Directly change the local line shape of the curve, and deduce a new tread profile to obtain the tread profile of the wheels that meets the requirements of a certain contact angle difference curve and rolling circle radius difference curve;

[0105] S74. The new tread profile needs to be merged to obtain a complete wheel tread profile.

[0106] Since there are some sections of the new tread profile that do not contact the rail surface, when performing reverse tread design using the method based on the contact angle difference and rolling circle radius difference, the non-contact area of the tread cannot be designed. Therefore, it needs to be combined with the reference tread to form a complete wheel tread profile. The tread designed by reverse design consists of a reference tread, a designed tread, and a transition section between the two.

[0107] S8. For the newly obtained wheel tread profile, conduct contact characteristic calculation and contact stress analysis, and perform smoothing and other treatments as needed.

[0108] The present invention makes a comparison between the newly designed tread surface and the original LM tread surface:

[0109] The present invention compares the standard LM wheel tread surface with the wheel tread surface (defined as Design Treads 1 - 3) reverse-designed by the method based on the contact angle difference and rolling circle radius difference to verify the effectiveness of the design method. The curves of the difference in the rolling circle radius between the left and right sides of the standard LM wheel tread surface and the wheel tread surface reverse-designed are as Figure 8 , Figure 12 and Figure 16As shown, it can be seen that within the range of lateral displacement from -12.5 to 12.5 mm, the curve of the difference in rolling circle radii between the left and right sides of the wheel tread designed by reverse design coincides with the corresponding curve of the standard LM wheel tread after two corrections, indicating that the designed wheel tread meets the design requirements after two corrections.

[0110] Furthermore, according to Figure 9 and Figure 13 the curves of the relative error of the difference in rolling circle radii between the left and right sides varying with the lateral displacement, the curves of the integral of the tangent value of the contact angle between the left and right sides varying with the lateral displacement after the first and second corrections (design tread 2 and design tread 3) are obtained, as shown in Figure 10 、 Figure 11 、 Figure 14 and Figure 15 By comparing the difference in rolling circle radii between the left and right sides of design tread 3 and the original tread, as shown in Figure 16 and plotting the corresponding relative error curve of the difference in rolling circle radii between the left and right sides, as shown in Figure 17 it can be obtained that the relative error is less than 10 -6 Therefore, the profile of design tread 3 meets the requirements of engineering design. Figure 18 、 Figure 19 are the integral curves of the tangent value of the contact angle between the left and right sides after smoothing, that is, the curve of the profile of design tread 3 varying with the lateral displacement. Figure 20 、 Figure 21 are the comparison diagrams of the profiles of the final designed left and right wheel treads and the original left and right wheel treads.

[0111] Comparing Figure 2 、 Figure 3 and Figure 14 、 Figure 15 it can be obtained that the error of design tread 3 relative to the original tread in the vertical coordinate direction is less than 0.0035 mm; at the same time, from Figure 20 、 Figure 21 it can be obtained that the profile of the finally designed wheel tread is very close to the profile of the original wheel tread; thus, it shows that the reverse design method of the wheel tread proposed by the present invention meets the requirements of engineering design. If further improvement in accuracy is required, it can be obtained by adjusting the above lateral displacement calculation step size.

[0112] Traditional wheel tread design methods often take a single wheel as the research object, ignoring the dynamic interaction of the entire wheel set as a system during the operation on the track. This limitation makes it difficult to coordinate the contact behaviors of the left and right wheels, thus affecting the stability and safety of the train. The use of the overall wheel set optimization design technology can comprehensively consider the cooperative relationship between the left and right wheels. By optimizing the contact angle difference and the rolling circle radius difference, the contact behavior of the entire wheel set becomes more balanced. This optimization can not only improve the curve negotiation performance of the train, enhance the anti-roll stability, but also improve the adaptability of the train under complex operating conditions such as high speed, heavy load, and small curve radius, significantly enhancing the safety and reliability of train operation.

[0113] The development of rail transit is facing increasing demands for energy conservation, consumption reduction, and sustainable development. The uneven wear of the wheel-rail system not only shortens the service life of wheels and rails, but also significantly increases the maintenance cost and operation burden. The technical solution of the present invention can effectively reduce local wear and wear differences and extend the service life of the wheel-rail system by overall optimizing the contact behavior of the wheel set, thereby reducing the maintenance and replacement frequency and directly reducing the operation cost. In addition, this technical solution can also improve the wheel-rail matching, reduce the wheel-rail friction energy consumption, and provide technical support for energy conservation and consumption reduction in rail transit.

[0114] In terms of theoretical research, the technical solution of the present invention breaks the traditional idea based on single-wheel optimization by introducing the inverse design of overall wheel set optimization in the tread design. This not only deepens the understanding of wheel-rail contact behavior, but also provides new technical support for multi-objective dynamic optimization problems, and can be further applied to multi-scale dynamics analysis, intelligent optimization design, and research and development of rail transit equipment in the field of rail transit.

[0115] The present invention is compared with the technical solution (Comparative Document 1) disclosed in CN105512397A: Comparative Document 1 uses the contact angle difference curve and the wheel-rail contact distribution function as the design objective function, and thus uses the wheel-rail geometric constraint model to inversely deduce the tread profile of the contact section. The present invention first obtains the rolling circle radius difference curve using the contact angle difference curve, and then compares the rolling circle radius difference curve obtained by the trace method and the rolling circle radius difference curve based on the contact angle difference. When the numerical difference between the two at the same lateral displacement is less than the set value, it is considered that the rolling circle radius difference value based on the contact angle difference is within the acceptable range, that is, the inversely deduced tread profile meets the requirements. Therefore, the difference lies in that the objective function of the present invention is the rolling circle radius difference curve (that is, the present invention also considers the rolling circle radius difference verification). Compared with Comparative Document 1, the technical effect produced by the present invention is that since the rolling circle radius difference calculation is added on the basis of inversely deducing the tread profile using the contact angle difference, the design accuracy of the present invention is higher, the design accuracy is increased by more than 10%, and the stability during the operation of the wheel is effectively improved.

[0116] In summary, the above embodiments of the present invention provide a method for inversely designing the wheel tread profile by using the difference in contact angle and the difference in rolling circle radius. This method takes into account the combined action of the wheels on both sides of the entire wheel set, has higher design accuracy, effectively reduces wheel-rail wear, extends the service life of wheels and rails, obtains a good wheel-rail contact geometry relationship, and thus improves the running stability of the train and the riding comfort of passengers.

Claims

1. A method for designing the wheel tread profile by reverse calculation using the contact angle difference and the rolling circle radius difference, characterized in that: It includes the following steps: S1. Obtain the rail head shape and rail bottom slope of the railway rail, and select the wheel tread shape that meets the basic parameters, wherein the basic parameters include track gauge, inner distance of wheelset, wheel flange height, wheel flange thickness, wheel hub width, tread width, distance from the rolling circle point to the wheel back, distance from the wheel flange thickness measurement point to the rolling circle point, and vertical distance from the track gauge measurement point to the top surface; S2. Set the origin of the wheel tread coordinate system as the point where the rolling circle is located, and the origin of the rail head coordinate system as the common tangent point of the left and right rail surfaces; S3. Considering the influence of the wheelset roll angle, change the lateral displacement of the wheelset, and use the trace method to obtain the wheel-rail contact point, contact angle and wheel tread shape when the lateral displacement of the wheelset changes within the range of -12.5mm to 12.5mm; S4. Obtaining the contact angle difference based on the wheel-rail contact angle data on the left and right sides; S5, taking the wheel-rail contact point when the wheelset lateral displacement is 0 as the initial value of integration, integrating the tangent value of the contact angle difference in the positive and negative directions of the lateral displacement respectively, and obtaining a rolling circle radius difference curve based on the contact angle difference; S6. Compare the wheelset rolling circle radius difference curve obtained by the trace method with the wheelset rolling circle radius difference curve based on the contact angle difference. When the difference between the two values ​​under the same lateral displacement is less than the set value, it is determined that the rolling circle radius difference value based on the contact angle difference is within an acceptable range, that is, the tread shape obtained by reverse deduction meets the requirements of the engineering design. Otherwise, the tread shape needs to be adjusted and redesigned. S7, obtaining a part of the wheel tread profile, checking the rolling circle radius difference curve, and obtaining a wheel tread profile that meets certain contact angle difference curve and rolling circle radius difference curve requirements; S8. For the newly obtained wheel tread shape, perform contact characteristic calculation and contact stress analysis, and perform smoothing as needed.

2. The method for reversely designing the wheel tread profile by using the contact angle difference and the rolling circle radius difference according to claim 1, characterized in that: In step S1, the following method is used to set: The wheels and rails included in the above-mentioned wheel-rail are rigid, that is, the elastic deformation of the wheel-rail contact is negligible; the rail head shape is convex, that is, the tangent slope of each point changes monotonically; the rail head shape and the designed wheel tread shape are symmetrical on the left and right; the given wheel flange height, wheel flange thickness and tread width remain unchanged.

3. The method for reversely designing the wheel tread profile by using the contact angle difference and the rolling circle radius difference according to claim 1, characterized in that: In step S3, the wheel-rail contact point, contact angle and wheel tread profile are obtained in the following manner: S31. Given the rail head shape and target tread shape, considering the effect of the wheelset roll angle, the condition for calculating the contact angle is: ； ； ； ； ； ； ； ； ; ;in, The rail head shape; is the target tread profile; is the rolling angle of the wheelset; is the lateral displacement of the wheelset; the coordinates of the contact points between the left wheel tread and the rail surface are and , the coordinates of the contact points between the right wheel tread and the rail surface are and ; and The left and right contact angles, respectively; S32. Calculate the ordinate of the tread shape using the contact angle. After obtaining the contact angle, the following expression is obtained through transformation: ； ； in, is the ordinate of the tread shape; Indicates the vertical coordinate of the tread contact point when the lateral displacement is 0.

4. The method for reversely designing the wheel tread profile by using the contact angle difference and the rolling circle radius difference according to claim 1, characterized in that: In step S4, the contact angle difference is calculated as follows: ;in, is the contact angle difference.

5. The method for reversely designing the wheel tread profile by using the contact angle difference and the rolling circle radius difference according to claim 1, characterized in that: In step S5, the rolling circle radius difference calculation formula based on the contact angle difference is as follows: ;in, is the rolling circle radius difference calculated based on the contact angle difference; when the wheelset lateral displacement is 0, .

6. The method for reversely designing the wheel tread profile by using the contact angle difference and the rolling circle radius difference according to claim 1, characterized in that: Step S6 includes: S61, using a trace method, obtaining a wheelset rolling circle radius difference curve through the side tread profile curves of the left and right wheels; S62, obtaining a wheelset rolling circle radius difference curve based on the contact angle difference; S63. Compare the two above curves and calculate the following formula: ； in, is the wheelset rolling circle radius difference obtained by the trace method; is the set error value, ; If the above formula does not hold, according to Adjust the designed tread, distribute the corresponding part of the lateral displacement less than 0 to the left wheel, and the rest to the right wheel, and compare it with the original tread parameter, that is, the rolling circle radius difference.

7. The method for reversely designing the wheel tread profile by using the contact angle difference and the rolling circle radius difference according to claim 1, characterized in that: The redesign in step S6 refers to repeating step S6 and comparing with the original wheel tread parameters.

8. The method for reversely designing the wheel tread profile by using the contact angle difference and the rolling circle radius difference according to claim 1, characterized in that: Step S7 includes: S71, obtaining a partial wheel tread profile, and checking whether the absolute value of the difference between the rolling circle radius difference curve and the wheel pair rolling circle radius difference obtained by the trace method is less than value, is the set error value, , then the newly obtained part of the wheel tread shape is expanded according to the original wheel tread shape, and the expansion principle is to ensure that the basic parameters of the wheel tread remain unchanged; S72, refining the step length of the wheelset lateral displacement change; S73, directly changing the shape of the local lines of the curve to deduce the new tread shape; S74. The new tread shape needs to be merged to obtain a complete wheel tread shape.

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