Turnout switch area steel rail polishing profile design method based on wheel diameter difference function

Abstract

The invention discloses a turnout switch area steel rail grinding profile design method based on a wheel diameter difference function. The turnout switch area steel rail grinding profile design method comprises the following steps: (1) collecting profile data of a wheel tread and a turnout switch area steel rail key section; (2) calculating characteristic parameters such as a turnout zone wheel-rail contact point position and a wheel diameter difference, and determining a design area and a non-design area of a turnout switch zone steel rail polishing profile; (3) defining and optimizing a wheel diameter difference deviation function to obtain a design objective function; steel rail grinding profile constraint conditions and boundary conditions are introduced, and a turnout switch area steel rail grinding profile design mathematical model with optimization of wheel-rail contact features as a target is established; (4) splicing the obtained profile and the profile of the non-design area to obtain a complete turnout switch area steel rail polishing profile; and (5) analyzing whether parameters such as the wheel-rail contact point position, the wheel diameter difference and the equivalent taper of the grinding profile are optimized or not. The complete turnout switch area steel rail grinding profile design method is established, and the method is suitable for grinding profile design of various types of turnout switch area steel rails.

Description

Technical Field

[0001] The invention relates to a method for designing a rail grinding profile in a turnout switching area based on a wheel diameter difference function, and belongs to the technical field of rail grinding for turnouts in rail transportation. Background Art

[0002] Turnouts are the main equipment for guiding locomotives to change or cross the track they are on. They have a complex structure, low driving safety, short service life, and high maintenance investment. They are one of the weakest components in the rail transit track structure. When a locomotive passes through a turnout, the top width and height of the point rail are constantly changing, and the wheel-rail contact state in the switch area also changes accordingly. The wheel-rail contact point in the switch area will be transferred from the point rail to the base rail (forward switch) or from the base rail to the point rail (reverse switch). Due to the jumping of the contact point and the continuous change of the wheel-rail contact state, a large dynamic interaction force between the wheel and the rail will be generated when the locomotive passes through the turnout, and these forces are the main cause of the defects of the turnout rails.

[0003] Rails in turnout areas are more susceptible to damage than those in section lines, and require more costs to maintain. Rail profile grinding refers to grinding the profile based on the actual conditions of the line and running vehicles, starting from improving the mechanical properties of wheel-rail contact and the vehicle dynamics performance during wheel-rail matching. Based on the profile measured on site, a targeted grinding profile is designed to correct the rail profile, thereby improving the wheel-rail contact relationship, eliminating abnormal vibration of locomotives and vehicles caused by poor rail profiles, eliminating and suppressing rail surface damage, improving train operation safety, and extending the service life of rails, ensuring the safety and economy of rail transit operations.

[0004] The grinding profiles of rails in the turnout area are mostly designed based on experience. The grinding profiles designed based on experience lack theoretical basis, and the profiles designed based on experience can no longer meet the operational needs of rail transportation such as higher-speed trains and heavy-load trains. Due to the unique structural characteristics of the rails in the turnout area (the hidden-tip structure formed by the point rail attached to the base rail), the profiles designed by conventional methods are continuous and linear, which is difficult to meet the unique close-fitting structural characteristics. Therefore, it is necessary to design the grinding profile based on a design method that coexists theory and experience. Summary of the invention

[0005] The purpose of the present invention is to solve the above problems existing in the existing turnout switch area rail profile grinding and to propose a turnout switch area rail grinding profile design method based on the wheel diameter difference function.

[0006] The technical solution implemented by the present invention is as follows: a method for designing the grinding profile of a rail in a turnout switching area based on a wheel diameter difference function, comprising the following steps:

[0007] (1) Record the basic parameters of the turnout, the wear area of ​​the rail, and the form of damage; collect and count the key cross-sectional profile data of the wheel tread and the rail in the turnout switch area, and use them as matching items for wheel-rail contact feature calculation; the basic parameters of the turnout include the type of turnout, the geometric dimensions of the switch area, the gauge of each part of the switch area, and the overall structural layout of the switch area.

[0008] (2) Analyze the wheel-rail contact characteristics. Based on the collected wheel tread and key cross-section profile data of the turnout area, use the wheel-rail contact characteristic numerical iteration method to calculate characteristic parameters such as the wheel-rail contact point position and wheel diameter difference in the turnout area, and determine the design area and non-design area of ​​the rail grinding profile in the turnout area.

[0009] (3) A general mathematical description of the rail profile in the turnout switch area is made in combination with the rail geometry of the turnout switch area, and the wheel diameter difference obtained in step (2) is optimized, that is, the optimized wheel diameter difference function is taken as the design target, and the design target function is obtained by defining the optimized wheel diameter difference deviation function; and the rail grinding profile constraint conditions and boundary conditions are introduced to establish a mathematical model for the design of the rail grinding profile in the turnout switch area with the optimization of the wheel-rail contact characteristics as the main target.

[0010] (4) The rail profile of the design area is iteratively calculated using the numerical integration method, and the obtained profile is combined with the profile of the non-design area to obtain the complete rail grinding profile of the turnout switch area.

[0011] (5) The wheel-rail contact calculation is performed on the grinding profile obtained in step (4) by using the wheel-rail contact characteristic numerical iteration method. Compared with the initial profile, the parameters such as the wheel-rail contact point position, wheel diameter difference, and equivalent taper of the grinding profile are analyzed to see whether they are optimized and meet the requirements. If the requirements are not met, the process returns to step (2). If the requirements are met, the grinding profile of the rail in the turnout area is output.

[0012] The key cross-sectional profile data of the rail in the turnout switching area is obtained by scanning the turnout switching area with a non-contact laser measuring instrument.

[0013] The specific steps of step (2) include:

[0014] Unify the data coordinates of the wheel and track into the same coordinate system, and input the measured wheel tread profile, rail profile and track parameters on both sides of the turnout area;

[0015] The lateral displacement y of a given wheelset relative to the track centerline w , move the left and right wheel tread profiles parallel to each other by y w ;

[0016] The translated wheelset is moved upward along the Z axis by a distance △Z to separate the wheelset from the track.

[0017] Calculate the minimum vertical spacing between the left and right wheel rail profiles and compare the left and right minimum spacing values. If ΔZ rmin -ΔZ lmin(s / b) ≤ε, ε is the set accuracy (10 -6 ~10 -4 mm), the left and right wheels are considered to be in contact with the track at the minimum spacing position, and the coordinates of the wheel-rail contact point are obtained at this time; if ΔZ rmin -ΔZ lmin(s / b) >ε, rotate the wheelset around the center in a clockwise direction (ΔZ rmin <ΔZ lmin(s / b) ) or in the counterclockwise direction (ΔZ rmin <ΔZ lmin(s / b) )Rotation Angle, calculated Adjust the left and right wheel tread profiles by angle; repeatedly calculate the minimum vertical distance between the left and right wheel rail profiles and compare the left and right minimum distance values, so that the left and right minimum distances meet the set accuracy requirements, and output the wheel set lateral displacement y w The coordinates of the wheel-rail contact point are obtained when the wheel-rail contact point position is determined; when the wheel-rail contact point position is determined, the main wheel-rail contact characteristic parameters such as the roll angle, wheel-rail contact angle, the curvature radius of the contour line at the tread contact point, the curvature radius of the contour line at the rail contact point, and the wheel diameter difference can be obtained, and the wheel-rail contact point distribution area is taken as the design area, and the other areas are taken as the non-design area.

[0018] The mathematical model for the design of the rail grinding profile in the turnout switching area is as follows:

[0019] Take multiple control points for the wheel diameter difference curve, based on the wheel diameter difference curve optimization criterion: when the wheelset lateral displacement is small, the wheel diameter difference should be small, when the wheelset lateral displacement is large, the wheel diameter difference should be large, and the wheel diameter difference curve needs to remain monotonic, the first-order derivative of the wheel diameter difference curve is continuous, and the second-order derivative is as continuous as possible.

[0020] The two-point cubic interpolation in Hermite interpolation is used to interpolate the values ​​between adjacent control points to obtain a complete optimized wheel diameter difference curve, and the design objective function is obtained by defining the optimized wheel diameter difference deviation function:

[0021]

[0022] Among them, ΔR opt (y w ) is the target wheel diameter difference, i.e. the wheel diameter difference after optimization using the Hermite interpolation method; ΔR real (y w ) is the actual wheel diameter difference; y w is the lateral displacement of the wheelset.

[0023] Based on the rail geometry, the general mathematical description of the rail profile in the turnout area can be as follows:

[0024]

[0025] Among them, φ w is the roll angle; y rl(s / b) 、z rl(s / b) is the coordinate of the wheel-rail contact point on the switch point side in the track coordinate system; wl(s / b) 、z wl(s / b) is the coordinate of the wheel-rail contact point on the switch point side in the wheelset coordinate system; rr 、z rr is the coordinate of the wheel-rail contact point on the basic rail side of the turnout switch area in the track coordinate system; wr 、z wr are the coordinates of the wheel-rail contact point on the basic rail side of the turnout switching area in the wheelset coordinate system; s / b are the rails on the point rail side of the turnout switching area.

[0026] Combined with the principle that "the shape of the polishing profile design area and its derivative function should remain monotonous", the constraints of the polishing profile design are as follows:

[0027]

[0028] On the basis of the above, additional constraints specific to the grinding profile of the turnout switch area are as follows:

[0029]

[0030] The above equations (1), (2), (3) and (4) constitute a complete mathematical model for the design of rail grinding profile in the turnout switching area.

[0031] The iterative calculation method for the rail grinding profile of the turnout switching area is as follows:

[0032] The unknown variables in the general mathematical description of the rail profile of the turnout switching area are separated and formed into column vectors. Formula (2) can be transformed into a matrix form:

[0033] A·u=b; (5)

[0034]

[0035] u=[y rl(s / b) 'z rl(s / b) 'y rr 'z rr 'y wl(s / b) 'φ w '] T ; (7)

[0036]

[0037] Transform equation (5): u = A-1 b; (9)

[0038] Let y = [y rl(s / b) z rl(s / b) y rr z rr y wl(s / b) φ w ] T , x=y w , we can transform equation (9) into a standard ordinary differential equation: y'=f(x,y); (10)

[0039] In the formula, f is the derivative of y with respect to x. Combining formula (10), we have: f:A -1 b; (11)

[0040] Given the initial value: y(x0) = y0; (12)

[0041] Combining equations (10) and (12), the complete set of ordinary differential equations for the rail grinding profile design problem in the turnout switch area is established:

[0042]

[0043] The Euler method in numerical integration is used to solve the ordinary differential equations. The initial value of the integral y0 needs to be given, that is, the value of the independent unknown variable when the wheelset lateral displacement is 0 mm:

[0044] y0=[y rl0(s / b) z rl0(s / b) y rr0 z rr0 y wl0(s / b) φ w0 ] T ; (14)

[0045] When the wheelset lateral displacement is 0 mm, y rl0(s / b) 、z rl0(s / b) ,y rro 、z rr0 ,y wl0(s / b) ,φ w0 From the wheel-rail contact calculation in step (2), φ w0 =0.

[0046] Among them, φ w0 is the lateral displacement of the wheelset y w =Roll angle at 0mm; y rl0(s / b) 、z rl0(s / b) is the coordinate of the wheel-rail contact point on the switch point side in the track coordinate system; wl0(s / b) is the coordinate of the wheel-rail contact point on the basic rail side of the turnout switch area in the track coordinate system; rro 、z rr0It is the coordinate of the wheel-rail contact point on the basic rail side of the turnout switching area in the track coordinate system.

[0047] In the process of numerical integration solution, under the premise of ensuring the solution accuracy, the efficiency of the integral solution is taken into account. The integral step size adopted by the method is 0.1 mm. The initial value and integral step size of the Euler method have been determined, and the grinding profile of the rail in the turnout switch area can be obtained by iterative calculation.

[0048] The wheel-rail contact characteristic numerical iteration method described in step (2) is used to calculate the wheel-rail contact of the polished profile obtained by solving step (4). Compared with the initial profile, the parameters such as the wheel-rail contact point position, wheel diameter difference, and equivalent taper of the polished profile are analyzed to see whether they are optimized and meet the requirements. If the requirements are not met, the process returns to step (2). If the requirements are met, the polished profile of the rail in the turnout switching area is output.

[0049] The beneficial effects of the present invention are that the present invention establishes a complete mathematical model for the design of the rail grinding profile in the turnout switching area, specifically involving objective functions, constraints and boundary conditions, and the model has high accuracy and is applicable to the design of the rail grinding profile in the turnout switching area of ​​various models; the present invention adopts a wheel-rail contact characteristic numerical iteration method to calculate other characteristic parameters such as the wheel-rail contact point position and wheel diameter difference in the turnout area, determines the design area and the non-design area according to the distribution position of the wheel-rail contact point, and can accurately design the area where the rail needs to be optimized and improve the design efficiency.

[0050] The present invention constructs a target curve by a data fitting method, and the obtained target curve is smoothly connected and very consistent with the requirements of the grinding profile design. The present invention solves the grinding profile by numerical integration, and by calculating the wheel-rail contact characteristic parameters of the grinding profile, analyzes whether the optimization effect of the relevant wheel-rail contact characteristic parameters meets the requirements. If not, it returns to step 2. If it meets the requirements, it outputs the grinding profile of the rail in the turnout switching area, and the obtained grinding profile has higher accuracy, smaller error, and better wheel-rail contact performance.

[0051] The invention discloses a method for designing the grinding profile of rails in a turnout switching area based on a wheel diameter difference function, establishes a complete method for designing the grinding profile of rails in a turnout switching area from collection-analysis-design-verification, and is applicable to the design of grinding profiles of rails in various turnout switching areas. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] Figure 1 It is a flow chart of a method for designing a rail grinding profile in a turnout switching area based on a wheel diameter difference function according to the present invention;

[0053] Figure 2 Flow chart for calculating wheel-rail contact characteristics in the turnout switching area;

[0054] Figure 3 It is a diagram describing the wheel-rail contact characteristics in the turnout switching area;

[0055] Figure 4 This is a schematic diagram of the distribution of wheel-rail contact points between the measured rail profile and the measured wheel tread in the turnout area with a point rail top width of 35mm;

[0056] Figure 5 It is a schematic diagram of the difference in wheel diameter between the measured rail profile and the measured wheel tread in the turnout area with a point rail top width of 35mm;

[0057] Figure 6 Schematic diagram of the design area and non-design area for the grinding profile of a 35mm rail with a point rail top width in the turnout area;

[0058] Figure 7 Schematic diagram of the optimization method for the wheel diameter difference of 35mm top width of the point rail in the turnout switching area. DETAILED DESCRIPTION

[0059] The following is a further detailed description of a rail grinding profile design method for a turnout switching area based on a wheel diameter difference function proposed by the present invention in conjunction with the accompanying drawings and specific embodiments.

[0060] like Figure 1 As shown in FIG. 1 , a flow chart of a method for designing a rail grinding profile in a turnout switching area based on a wheel diameter difference function is shown. The specific implementation steps are as follows:

[0061] Step 1: In this embodiment, a non-contact laser measuring instrument is used to scan the switch section to obtain the rail profile data of the turnout switch area, and the key cross-section profile of the rail is selected as the design object.

[0062] Step 2: Figure 2 As shown, the wheel-rail contact characteristics are analyzed, and according to the collected rail switch area profile coordinate data, the wheel-rail contact characteristic numerical iteration method is used to calculate the characteristic parameters such as the wheel-rail contact point position and wheel diameter difference in the turnout area to determine the design area and the non-design area.

[0063] Figure 3 The figure shows the wheel-rail contact characteristic description diagram of the turnout. The data coordinates of the wheel and the track are unified into the same coordinate system, and the track parameters such as the measured rail profiles on both sides of the turnout switching area, the wheel tread profiles and the rail bottom slope are input.

[0064] The lateral displacement y of a given wheelset relative to the track w , move the left and right wheel tread profiles parallel to each other by y w .

[0065] Move the translated wheelset upward along the Z axis for a distance △Z to separate the wheelset from the track. Calculate the minimum vertical spacing between the left and right wheel-rail profiles and compare the left and right minimum spacing values. If △Z rmin -ΔZ lmin(s / b) ≤ε, ε is the set accuracy (10-6 ~10 -4 mm), it is considered that the left and right wheels are in contact with the track at the minimum spacing position. At this time, the coordinates of the wheel-rail contact point are obtained. If ΔZ rmin -ΔZ lmin(s / b) >ε, rotate the wheelset around the center in a clockwise direction (ΔZ rmin >ΔZ lmin(s / b) ) or in the counterclockwise direction (ΔZ rmin <ΔZ lmin(s / b) )Rotation angle.

[0066] By calculated The left and right wheel tread profiles are adjusted by angle, the minimum vertical spacing between the left and right wheel rail profiles is calculated repeatedly, and the left and right minimum spacing values ​​are compared to make the left and right minimum spacing meet the set accuracy requirements. The output wheel set lateral displacement y w The coordinates of the wheel-rail contact point.

[0067] Once the position of the wheel-rail contact point is determined, the main wheel-rail contact characteristic parameters such as the roll angle, wheel-rail contact angle, curvature radius of the contour line at the tread contact point, curvature radius of the contour line at the rail contact point, and wheel diameter difference can be obtained. The area where the wheel-rail contact point is distributed is taken as the design area, and other areas are taken as non-design areas.

[0068] like Figure 4 and Figure 5 As shown, Figure 4 This is a schematic diagram of the distribution of wheel-rail contact points between the measured rail profile and the measured wheel tread in the turnout area with a point rail top width of 35mm; Figure 5 The figure is a schematic diagram of the difference between the measured rail profile and the measured wheel tread when the top width of the point rail is 35 mm in the turnout area. The design area and the non-design area can be determined based on the distribution of wheel-rail contact points, such as Figure 6 The figure shows the design area and non-design area of ​​the rail grinding profile with a top width of 35mm in the turnout area.

[0069] Step 3: A general mathematical description of the rail profile is made in combination with the rail geometry, and the wheel diameter difference obtained in step 2 is optimized. The optimized wheel diameter difference function is taken as the design goal. The design objective function is obtained by defining the optimized wheel diameter difference deviation function, and the rail grinding profile constraints and boundary conditions are introduced to establish a mathematical model for the rail grinding profile design in the turnout switch area with the optimization of wheel-rail contact characteristics as the main goal.

[0070] The specific steps of step 3 are:

[0071] Take multiple control points for the wheel diameter difference curve, based on the wheel diameter difference curve optimization criteria: when the wheelset lateral displacement is small, the wheel diameter difference should be small, when the wheelset lateral displacement is large, the wheel diameter difference should be large, and the wheel diameter difference curve needs to remain monotonic, the first-order derivative of the wheel diameter difference curve is continuous, and the second-order derivative is as continuous as possible. Use the two-point cubic interpolation in the Hermite interpolation to interpolate the values ​​between adjacent control points to obtain a complete optimized wheel diameter difference curve, and define the optimized wheel diameter difference deviation function to obtain the design objective function:

[0072]

[0073] Where: ΔR opt (y w ) is the target wheel diameter difference, i.e. the wheel diameter difference after optimization using the Hermite interpolation method; ΔR real (y w ) is the actual wheel diameter difference.

[0074] Based on the rail geometry, the general mathematical description of the rail profile in the turnout area can be as follows:

[0075]

[0076] Among them, φ w is the roll angle; y rl(s / b) 、z rl(s / b) is the coordinate of the wheel-rail contact point on the switch point side in the track coordinate system; wl(s / b) 、z wl(s / b) is the coordinate of the wheel-rail contact point on the switch point side in the wheelset coordinate system; rr 、z rr is the coordinate of the wheel-rail contact point on the basic rail side of the turnout switch area in the track coordinate system; wr 、z wr are the coordinates of the wheel-rail contact point on the basic rail side of the turnout switching area in the wheelset coordinate system; s / b are the rails on the point rail side of the turnout switching area.

[0077] Combined with the principle that "the shape of the polishing profile design area and its derivative function should remain monotonic", the constraints for the polishing profile design can be given as:

[0078]

[0079] On the basis of the above, additional constraints specific to the grinding profile of the turnout switch area are added:

[0080]

[0081] Combining equations (1), (2), (3) and (4) can form a complete mathematical model for the design of rail grinding profile in the turnout switching area.

[0082] Step 4: Use the numerical integration method to iteratively calculate the rail profile of the design area, and splice the obtained profile with the profile of the non-design area to obtain the complete rail grinding profile of the turnout switch area.

[0083] The specific steps of step 4 are:

[0084] The unknown variables in equation (2) are separated and formed into column vectors, and equation (2) is transformed into a matrix form as follows:

[0085] A·u=b (5)

[0086] in:

[0087]

[0088] u=[y rl(s / b) 'z rl(s / b) 'y rr 'z rr 'y wl(s / b) 'φ w '] T ; (7)

[0089]

[0090] Transform equation (5): u = A -1 b; (9)

[0091] Let y = [y rl(s / b) z rl(s / b) y rr z rr y wl(s / b) φ w ] T , x=y w , we can transform equation (9) into a standard set of ordinary differential equations: y'=f(x,y); (10)

[0092] Where f is the derivative of y with respect to x, combined with formula (10), we have:

[0093] f:A -1 b; (11)

[0094] Given the initial value: y(x0) = y0; (12)

[0095] Combining equations (10) and (12), the complete set of ordinary differential equations for the design of the grinding profile of the turnout switch area is established:

[0096] The Euler method in numerical integration is used to solve the ordinary differential equations. The initial value of the integral y0 needs to be given, that is, the value of the independent unknown variable when the wheelset lateral displacement is 0 mm:

[0097] y0=[y rl0(s / b) z rl0(s / b) y rr0 z rr0 y wl0(s / b) φ w0 ] T ; (14)

[0098] When the wheelset lateral displacement is 0 mm, y rl0(s / b) 、z rl0(s / b) ,y rro 、z rr0 ,y wl0(s / b) ,φ w0 It can be obtained by calculating the wheel-rail contact in step 2, where φ w0 =0.

[0099] φ w0 is the lateral displacement of the wheelset y w =Roll angle at 0mm; y rl0(s / b) 、z rl0(s / b) is the coordinate of the wheel-rail contact point on the switch point side in the track coordinate system; wl0(s / b) is the coordinate of the wheel-rail contact point on the basic rail side of the turnout switch area in the track coordinate system; rro 、z rr0 It is the coordinate of the wheel-rail contact point on the basic rail side of the turnout switching area in the track coordinate system.

[0100] In the process of numerical integration solution, under the premise of ensuring the solution accuracy, taking into account the efficiency of the integral solution, the integral step length adopted by the present invention is 0.1 mm. The integral initial value and integral step length of the Euler method have been determined, and the grinding profile of the rail in the turnout switch area can be obtained by iterative calculation.

[0101] Step 5, using the wheel-rail contact characteristic numerical iteration method described in step 2 to perform wheel-rail contact calculation on the polished profile obtained by iterative calculation in step 4, and comparing it with the initial profile, analyzing whether the parameters such as the wheel-rail contact point position, wheel diameter difference, and equivalent taper of the polished profile are optimized and meet the requirements; if not, return to step 2; if it meets the requirements, output the polished profile of the turnout switch area rail.

Claims

1. A method for designing the rail grinding profile of a turnout switch area based on a wheel diameter difference function, characterized in that: The method steps are as follows: (1) Record the basic parameters of the turnout, the wear area of ​​the rails, and the forms of damage; collect and count the key cross-sectional profile data of the wheel tread and the rails in the turnout switch area, and use them as matching items for wheel-rail contact feature calculation; (2) Based on the collected wheel tread and key cross-section profile data of the turnout area, the wheel-rail contact point position and wheel diameter difference characteristic parameters of the turnout area are calculated using the wheel-rail contact characteristic numerical iteration method to determine the design area and non-design area of ​​the rail grinding profile of the turnout area; (3) Optimizing the wheel diameter difference obtained in step (2), that is, taking the optimized wheel diameter difference function as the design target, and obtaining the design target function by defining the optimized wheel diameter difference deviation function; and introducing the rail grinding profile constraint conditions and boundary conditions, and establishing a mathematical model for the rail grinding profile design in the turnout switch area with the optimization of wheel-rail contact characteristics as the main target; (4) The rail profile of the design area is iteratively calculated using the numerical integration method, and the obtained profile is spliced ​​with the profile of the non-design area to obtain the grinding profile of the rail in the complete turnout switch area; (5) The wheel-rail contact calculation is performed on the grinding profile obtained in step (4) by using the wheel-rail contact characteristic numerical iteration method. Compared with the initial profile, the wheel-rail contact point position, wheel diameter difference, and equivalent taper parameters of the grinding profile are analyzed to see whether they are optimized and meet the requirements. If not, return to step (2). If it meets the requirements, output the grinding profile of the turnout rail.

2. The method for designing the rail grinding profile of a turnout switch area based on a wheel diameter difference function according to claim 1, characterized in that: The key cross-sectional profile data of the rail in the turnout switching area is obtained by scanning the turnout switching area with a non-contact laser measuring instrument.

3. The method for designing the rail grinding profile of a turnout switch area based on a wheel diameter difference function according to claim 1, characterized in that: The basic parameters of the turnout include the type of turnout, the geometric dimensions of the switch area, the gauges of each part of the switch area, and the overall structural layout of the switch area.

4. The method for designing the rail grinding profile of a turnout switch area based on a wheel diameter difference function according to claim 1, characterized in that: The specific steps of step (2) include: Unify the data coordinates of the wheel and track into the same coordinate system, and input the measured wheel tread profile, rail profile and track parameters on both sides of the turnout area; The lateral displacement y of a given wheelset relative to the track centerline w , move the left and right wheel tread profiles parallel to each other by y w ; The translated wheelset is moved upward along the Z axis by a distance △Z to separate the wheelset from the track; Calculate the minimum vertical spacing between the left and right wheel rail profiles and compare the left and right minimum spacing values. If ΔZ rmin -ΔZ lmin(s / b) ≤ε, ε is the set accuracy (10 -6 ~10 -4 mm), the left and right wheels are considered to be in contact with the track at the minimum spacing position, and the coordinates of the wheel-rail contact point are obtained at this time; if ΔZ rmin -ΔZ lmin(s / b) >ε, rotate the wheelset around the center in a clockwise direction (ΔZ rmin <ΔZ lmin(s / b) ) or in the counterclockwise direction (ΔZ rmin <ΔZ lmin(s / b) )Rotation Angle, calculated Adjust the left and right wheel tread profiles by angle; repeatedly calculate the minimum vertical distance between the left and right wheel rail profiles and compare the left and right minimum distance values, so that the left and right minimum distances meet the set accuracy requirements, and output the wheel set lateral displacement y w The coordinates of the wheel-rail contact point are obtained when the wheel-rail contact point position is determined; when the wheel-rail contact point position is determined, the main wheel-rail contact characteristic parameters such as the roll angle, wheel-rail contact angle, the curvature radius of the contour line at the tread contact point, the curvature radius of the contour line at the rail contact point, and the wheel diameter difference can be obtained, and the wheel-rail contact point distribution area is taken as the design area, and other areas are taken as non-design areas.

5. The method for designing the rail grinding profile of a turnout switch area based on a wheel diameter difference function according to claim 1, characterized in that: The mathematical model for the design of the rail grinding profile in the turnout switching area is as follows: Take multiple control points for the wheel diameter difference curve, based on the wheel diameter difference curve optimization criteria: when the wheelset lateral displacement is small, the wheel diameter difference should be small, when the wheelset lateral displacement is large, the wheel diameter difference should be large, and the wheel diameter difference curve needs to be monotonic, the first-order derivative of the wheel diameter difference curve is continuous, and the second-order derivative is as continuous as possible; The two-point cubic interpolation in Hermite interpolation is used to interpolate the values ​​between adjacent control points to obtain a complete optimized wheel diameter difference curve, and the design objective function is obtained by defining the optimized wheel diameter difference deviation function: Among them, ΔR opt (y w ) is the target wheel diameter difference, i.e. the wheel diameter difference after optimization using the Hermite interpolation method; ΔR real (y w ) is the actual wheel diameter difference; y w is the lateral displacement of the wheelset; Based on the rail geometry, the general mathematical description of the rail profile in the turnout area can be as follows: Among them, φ w is the roll angle; y rl(s / b) 、z rl(s / b) is the coordinate of the wheel-rail contact point on the switch point side in the track coordinate system; wl(s / b) 、z wl(s / b) is the coordinate of the wheel-rail contact point on the switch point side in the wheelset coordinate system; rr 、z rr is the coordinate of the wheel-rail contact point on the basic rail side of the turnout switch area in the track coordinate system; wr 、z wr is the coordinate of the wheel-rail contact point on the basic rail side of the turnout switching area in the wheelset coordinate system; s / b is the rail on the point rail side of the turnout switching area; Combined with the principle that "the shape of the polishing profile design area and its derivative function should remain monotonous", the constraints of the polishing profile design are as follows: On the basis of the above, additional constraints specific to the grinding profile of the turnout switch area are as follows: The above equations (1), (2), (3) and (4) constitute a complete mathematical model for the design of rail grinding profile in the turnout switching area.

6. The method for designing the rail grinding profile of a turnout switch area based on a wheel diameter difference function according to claim 1, characterized in that: The iterative calculation method for the rail grinding profile of the turnout switching area is as follows: The unknown variables in the general mathematical description of the rail profile of the turnout switching area are separated and formed into column vectors. Formula (2) can be transformed into a matrix form: A·u=b; (5) u=[y rl(s / b) 'z rl(s / b) 'y rr 'z rr 'y wl(s / b) 'φ w '] T (7) Transform equation (5): u = A -1 b; (9) Let y = [y rl(s / b) z rl(s / b) y rr z rr y wl(s / b) φ w ] T , x=y w , we can transform equation (9) into a standard ordinary differential equation: y'=f(x,y); (10) In the formula, f is the derivative of y with respect to x. Combining formula (10), we have: f:A -1 b; (11) Given the initial value: y(x0) = y0; (12) Combining equations (10) and (12), the complete set of ordinary differential equations for the rail grinding profile design problem in the turnout switch area is established: The Euler method in numerical integration is used to solve the ordinary differential equations. The initial value of the integral y0 needs to be given, that is, the value of the independent unknown variable when the wheelset lateral displacement is 0 mm: y0=[y rl0(s / b) z rl0(s / b) y rr0 z rr0 y wl0(s / b) φ w0 ] T ; (14) When the wheelset lateral displacement is 0 mm, y rl0(s / b) 、z rl0(s / b) ,y rro 、z rr0 ,y wl0(s / b) ,φ w0 It is obtained by calculating the wheel-rail contact in step (2), where φ w0 =0;φ w0 is the lateral displacement of the wheelset y w =Roll angle at 0mm; Among them, y rl0(s / b) 、z rl0(s / b) is the coordinate of the wheel-rail contact point on the switch point side in the track coordinate system; wl0(s / b) is the coordinate of the wheel-rail contact point on the basic rail side of the turnout switch area in the track coordinate system; rro 、z rr0 The coordinates of the wheel-rail contact point on the basic rail side of the turnout switching area in the track coordinate system; In the process of numerical integration solution, under the premise of ensuring the solution accuracy, the efficiency of the integral solution is taken into account. The integral step size adopted by the method is 0.1 mm. The initial value and integral step size of the Euler method have been determined, and the grinding profile of the rail in the turnout switch area can be obtained by iterative calculation.

7. The method for designing the rail grinding profile of a turnout switch area based on a wheel diameter difference function according to claim 1, characterized in that: The wheel-rail contact characteristic numerical iteration method described in step (2) is used to calculate the wheel-rail contact of the polished profile obtained by solving step (4). Compared with the initial profile, the wheel-rail contact point position, wheel diameter difference, and equivalent taper parameters of the polished profile are analyzed to see whether they are optimized and meet the requirements. If not, the process returns to step (2). If it meets the requirements, the polished profile of the rail in the turnout switching area is output.

Images