CN112464455B - Impact load calculation method suitable for concave welding seam of seamless steel rail - Google Patents

Impact load calculation method suitable for concave welding seam of seamless steel rail Download PDF

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CN112464455B
CN112464455B CN202011304707.3A CN202011304707A CN112464455B CN 112464455 B CN112464455 B CN 112464455B CN 202011304707 A CN202011304707 A CN 202011304707A CN 112464455 B CN112464455 B CN 112464455B
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董捷
张壮
董少华
王志岗
李冉
郑英豪
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Hebei University of Architecture
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Abstract

The invention discloses a method for calculating impact load at a concave welding seam of a seamless steel rail, which comprises the following steps of: collecting and calculating corresponding parameters of wheel-rail impact load; obtaining a critical speed expression and a specific numerical value according to the time relation; judging whether the train speed is greater than a critical speed or not; calculating by adopting a high-frequency transient impact force and medium-low frequency response force correction formula deduced in high-speed operation; and calculating by adopting a high-frequency transient impact force and a medium-low frequency response stress correction formula deduced in low-speed operation. The invention takes the discontinuity of train wheels at the joint to deeply research the impact load when a heavy-duty train passes through a concave weld joint, and takes a driving wheel unit model with a single wheel attached with secondary spring damping as a research object to research the algorithm of the impact load generated by a train-track coupling system at a steel rail weld joint.

Description

Impact load calculation method suitable for concave welding seam of seamless steel rail
Technical Field
The invention belongs to the field of railway track foundation engineering design, and particularly relates to an impact load calculation method suitable for a concave welding seam of a seamless steel rail.
Background
With the increase of the axle weight and speed of the truck, the dynamic performance of the truck and the rail is further deteriorated, particularly when a large axle weight truck passes through an unsmooth area of a steel rail welding joint, the interaction between a wheel and a rail is aggravated, the rail condition is deteriorated, and the geometric and rigidity irregularity of a line and the damage of the steel rail are caused.
In order to reduce the influence of vibration load generated by the wavy abrasion of the rail surface on the rail and the surrounding environment, the rail maintenance department mostly adopts a rail grinding wagon to grind the rail structure, thereby not only ensuring the flatness of the rail surface on the rail structure, but also eliminating the convex welding seam joint formed after the welding of the seamless steel rail joint is finished.
However, the prior grinding measures do not have a significant effect on saddle-type wear in the weld region of the rail. If the train running speed reaches a certain critical speed, the wheels can be separated from the track temporarily when passing through the area, impact loads which are several times of wheel loads can be generated when the wheels are contacted with the track again, and then frequent impact loads generated during the running of a long-marshalling and high-density heavy-duty train seriously weaken the safety and reliability of the track structure during service, aggravate the damage degree of the wheel-track structure, generate huge potential threats to the safe running of the heavy-duty train, even lead to the derailment and overturn of the train seriously, and bring huge economic losses to railway transportation and economy.
Disclosure of Invention
The invention is provided for solving the problems in the prior art, and aims to provide a method for calculating the impact load at the concave welding seam of the seamless steel rail.
The technical scheme of the invention is as follows: a method for calculating an impact load at a concave welding seam of a seamless steel rail comprises the following steps:
collecting and calculating corresponding parameters of wheel-rail impact load
Establishing a vertical model of the train and the track, and acquiring relevant parameters of wheel-track impact load;
ii, obtaining the critical speed expression and the specific value according to the time relation
Obtaining a critical speed expression according to the time relation, and obtaining a critical speed by combining relevant parameters of the wheel-rail impact load;
iii, judging whether the train speed is greater than the critical speed
Judging the speed of the train according to the critical speed, wherein the train runs at a high speed when the speed is higher than the critical speed, and runs at a low speed when the speed is lower than the critical speed;
iv, calculating by adopting a high-frequency transient impact force and medium-low frequency response force correction formula deduced in high-speed operation
Establishing a mechanical model in high-speed operation to obtain an impact speed in high-speed operation and obtain a corrected impact force calculation formula;
v, calculating by using a high-frequency transient impact force and a medium-low frequency response force correction formula deduced in low-speed operation
And establishing a mechanical model during low-speed operation to obtain the impact speed during low-speed operation and obtain a corrected impact force calculation formula.
Furthermore, the heavy-duty train in the step i is simplified into a two-system spring mass system model.
Furthermore, in the step i, a half structure is taken to perform dynamic analysis in consideration of the symmetry of the train and the track model.
Furthermore, in the step i, the transverse vibration load generated by the snake-shaped motion of the train and the like is ignored, and only the vertical vibration effect of the wheel-track system is considered.
Further, in step i, the steel rail is a Euler beam model based on a Winkler elastic foundation beam.
Further, in step ii, the time relationship yields the critical velocity expression:
Figure GDA0003681620730000031
furthermore, the calculation formula of the impact speed and the corrected impact force during high-speed operation in step iv is specifically as follows:
when the running speed of the heavy-load train is higher than v 0 When the wheel passes through the point A, the wheel starts to make horizontal projectile motion, as shown in the figure, the time of the wheel passing through the concave part is determined by the horizontal speed of the wheel, and the impact speed when the wheel runs to the point B mainly comprises the speed of the wheel making free-falling body motion to contact with the track
Figure GDA0003681620730000032
And the vertical component v generated by wheel rotation y2 (v y2 ＝γv 1 sinβ≈γv 1 Beta) is prepared from two parts.
Solved by the geometrical relationship:
Figure GDA0003681620730000033
the impact velocity at the seamless rail joint is:
Figure GDA0003681620730000034
calculating to obtain:
Figure GDA0003681620730000035
the rotation angle alpha is:
Figure GDA0003681620730000036
the correction formula is as follows:
Figure GDA0003681620730000041
Figure GDA0003681620730000042
wherein v is 1 -the running speed of the wheel before it enters the rail joint; v. of 2 -speed of wheel rail joint point B; l 0 -length of the rail joint recess; m 1 ，M 2 Kg for the sprung mass and the unsprung mass of the heavy-duty train; gamma-coefficient of converting the rotational inertia of the wheel into reciprocating inertia; α — wheel angle; h is the descending height of the axle center of the wheel; p st -static wheel load of heavy load train, kN; k H -linear wheel-rail contact stiffness; m is a unit of e -the effective track mass, kg, typically 0.4m, where m is the distributed track mass of an equivalent elastic foundation beam,
m＝m r +m s a, wherein m r The mass per unit length of the steel rail is kg/m, m s Weighing half of sleepers, wherein kg and a are sleeper intervals, and taking 0.6m; m is u Unsprung mass of vehicleAn amount; m is t -the mass of the track concentration, kg,
Figure GDA0003681620730000043
wherein k is the distribution rigidity of the steel rail, E is the elastic modulus of the steel rail, and J is the section inertia moment of the steel rail; k is a radical of t -the track concentration stiffness, N/m,
Figure GDA0003681620730000044
C t concentrated damping of the track, N.s.m -1 ，
Figure GDA0003681620730000045
Wherein C is track distributed damping, N.s.m -1 。
Further, in step v, the calculation formula of the impact speed and the corrected impact force at the low speed operation is specifically as follows:
when the running speed of the heavy-duty train is lower than v 0 When the wheel is vertically sunk to a maximum height h at the joint of the seamless steel rail, the speed of the wheel at the point B mainly comprises a vertical downward speed component v 0 (wherein
Figure GDA0003681620730000051
) And a transient impact component v which is opposite to the direction of the vertical speed of the wheel center when rotating around the point B B (wherein
Figure GDA0003681620730000052
) And (4) forming.
The impact velocity is calculated as follows:
Figure GDA0003681620730000053
calculating to obtain:
Figure GDA0003681620730000054
the rotation angle alpha is:
Figure GDA0003681620730000055
the correction formula is as follows:
Figure GDA0003681620730000056
Figure GDA0003681620730000057
wherein v is 1 -the running speed of the wheel before entering the rail joint; v. of 2 -speed at point B of the wheel rail joint; l 0 -length of the rail joint recess; m 1 ，M 2 -weight, kg, on and off the spring of the heavy-duty train vehicle; gamma-coefficient of the wheel rotation inertia converted into reciprocating inertia; α — wheel angle; h is the descending height of the axle center of the wheel; p st -static wheel load, kN, of the heavy-duty train; k H -linear wheel-rail contact stiffness; m is a unit of e -an effective track mass, kg, typically 0.4m, where m is the distributed track mass of an equivalent elastic foundation beam,
m＝m r +m s a, wherein m r The mass per unit length of the steel rail is kg/m, m s Weighing half of sleepers, wherein kg and a are sleeper intervals, and taking 0.6m; m is u -a vehicle unsprung mass; m is a unit of t -the mass of the track concentration, kg,
Figure GDA0003681620730000061
wherein k is the distribution rigidity of the steel rail, E-the elastic modulus of the steel rail, and J-is the section inertia moment of the steel rail; k is a radical of t -the track concentration stiffness, N/m,
Figure GDA0003681620730000062
C t -central damping of the track, N.s.m -1 ，
Figure GDA0003681620730000063
Wherein C is track distributed damping, N.s.m -1 。
The invention takes the discontinuity of train wheels at the joint to deeply research the impact load of a heavy-duty train passing through a concave weld joint, takes a driving wheel unit model with single wheel and secondary spring damping as a research object, and researches the algorithm of the train-track coupling system generating the impact load at the steel rail weld joint.
Drawings
FIG. 1 is a flow chart of the method of the present invention;
FIG. 2 is a vertical model of a train and track of the present invention;
FIG. 3 is a mechanical model of the present invention operating at low speed;
FIG. 4 is a mechanical model of the present invention operating at high speed;
Detailed Description
The present invention is described in detail below with reference to the accompanying drawings and examples:
as shown in fig. 1 to 4, a method for calculating an impact load applied to a concave weld of a seamless steel rail comprises the following steps:
i, collecting and calculating corresponding parameters of wheel track impact load
Establishing a vertical model of the train and the track, and acquiring relevant parameters of wheel-track impact load;
ii, obtaining the critical speed expression and the specific value according to the time relation
Obtaining a critical speed expression according to the time relation, and obtaining a critical speed by combining relevant parameters of the wheel-rail impact load;
iii, judging whether the train speed is greater than the critical speed
Judging the speed of the train according to the critical speed, wherein the train runs at a high speed when the speed is higher than the critical speed, and runs at a low speed when the speed is lower than the critical speed;
iv, calculating by adopting a high-frequency transient impact force and medium-low frequency response force correction formula deduced in high-speed operation
Establishing a mechanical model in high-speed operation to obtain the impact speed in high-speed operation and obtain a corrected impact force calculation formula;
v, calculating by using a high-frequency transient impact force and a medium-low frequency response stress correction formula deduced in low-speed operation
And establishing a mechanical model during low-speed operation to obtain the impact speed during low-speed operation and obtain a corrected impact force calculation formula.
Furthermore, the heavy-load train in the step i is simplified into a two-series spring mass system model.
Furthermore, in the step i, a half structure is taken to perform dynamic analysis in consideration of the symmetry of the train and the track model.
Furthermore, in the step i, the transverse vibration load generated by the snake-shaped motion of the train and the like is ignored, and only the vertical vibration effect of the wheel-track system is considered.
Further, the steel rail in step i is an Euler beam model on the basis of a Winkler elastic foundation beam.
Further, in step ii, the time relationship may be used to obtain the critical speed expression:
Figure GDA0003681620730000081
furthermore, the calculation formula of the impact speed and the corrected impact force during high-speed operation in step iv is specifically as follows:
when the running speed of the heavy-load train is higher than v 0 When the wheel passes through the point A, the wheel starts to make horizontal projectile motion, as shown in the figure, the time of the wheel passing through the concave part is determined by the horizontal speed of the wheel, and the impact speed when the wheel runs to the point B mainly comprises the speed of the wheel making free-falling body motion to contact with the track
Figure GDA0003681620730000082
And the vertical component v generated by wheel rotation y2 (v y2 ＝γv 1 sinβ≈γv 1 Beta) is prepared from two parts.
Solved by the geometrical relationship:
Figure GDA0003681620730000083
the impact velocity at the seamless rail joint is:
Figure GDA0003681620730000084
calculating to obtain:
Figure GDA0003681620730000085
the rotation angle alpha is:
Figure GDA0003681620730000086
the correction formula is as follows:
Figure GDA0003681620730000087
Figure GDA0003681620730000091
Figure GDA0003681620730000092
wherein v is 1 -the running speed of the wheel before it enters the rail joint; v. of 2 -speed of wheel rail joint B; l 0 -length of the rail joint recess; m 1 ，M 2 Kg for the sprung mass and the unsprung mass of the heavy-duty train; gamma-coefficient of the wheel rotation inertia converted into reciprocating inertia; α -wheel angle; h is the descending height of the wheel axle center; p is st -static wheel load, kN, of the heavy-duty train; k is H -linear wheel-rail contact stiffness; m is e -the effective track quality is determined by the track quality,kg, typically 0.4m, where m is the distributed track mass of an equivalent elastic foundation beam,
m＝m r +m s a, wherein m r The mass per unit length of the steel rail is kg/m, m s Weighing half of sleepers, wherein kg and a are sleeper intervals, and taking 0.6m; m is u -vehicle unsprung mass; m is a unit of t -the mass of the track concentration, kg,
Figure GDA0003681620730000093
wherein k is the distribution rigidity of the steel rail, E is the elastic modulus of the steel rail, and J is the section inertia moment of the steel rail; k is a radical of t -the track concentration stiffness, N/m,
Figure GDA0003681620730000094
C t concentrated damping of the track, N.s.m -1 ，
Figure GDA0003681620730000095
Wherein C is track distributed damping, N.s.m -1 。
Further, in step v, the calculation formula of the impact velocity and the corrected impact force at the low-speed operation is specifically as follows:
when the running speed of the heavy-load train is lower than v 0 When the vertical sinking height of the wheel reaches the maximum value h at the joint of the seamless steel rail, the speed of the wheel at the point B mainly consists of a vertical downward speed component v 0 (wherein
Figure GDA0003681620730000101
) And a transient impact component v which is opposite to the direction of the vertical speed of the wheel center when rotating around the point B B (wherein
Figure GDA0003681620730000102
) And (4) forming.
The impact velocity is calculated as follows:
Figure GDA0003681620730000103
calculating to obtain:
Figure GDA0003681620730000104
the rotation angle alpha is:
Figure GDA0003681620730000105
the correction formula is as follows:
Figure GDA0003681620730000106
Figure GDA0003681620730000107
wherein v is 1 -the running speed of the wheel before entering the rail joint; v. of 2 -speed at point B of the wheel rail joint; l 0 -length of the rail joint recess; m 1 ，M 2 Kg for the sprung mass and the unsprung mass of the heavy-duty train; gamma-coefficient of converting the rotational inertia of the wheel into reciprocating inertia; α — wheel angle; h is the descending height of the wheel axle center; p st -static wheel load, kN, of the heavy-duty train; k H -linear wheel-rail contact stiffness; m is e -effective track mass, kg, 0.4m according to relevant railway codes and papers, where m is the distributed track mass of an equivalent elastic foundation beam, m = m r +m s A, wherein m r The mass per unit length of the steel rail is kg/m, m s Weighing half of sleepers, wherein kg and a are sleeper intervals, and taking 0.6m; m is u -a vehicle unsprung mass; m is t -the mass of the track concentration, kg,
Figure GDA0003681620730000111
wherein k is the distribution rigidity of the rail, E-the elastic modulus of the rail, and J-is the railA cross-sectional moment of inertia; k is a radical of t -the track concentration stiffness, N/m,
Figure GDA0003681620730000112
C t concentrated damping of the track, N.s.m -1 ，
Figure GDA0003681620730000113
Wherein C is track distributed damping, N.s.m -1 。
The train-track vertical system model is based on the analysis of train-track vertical coupling dynamics and serves as a theoretical tool of the invention, and the train model completely reflects the mass (M) of a train body and a bogie frame c 、M n ) And its nodding inertia (J) c 、J n ) Sinking and floating of vehicle body and bogie (Z) Ci 、Z ni ) And nodding (phi) thereof ci 、Φ ni ) Movement while taking into account a series of suspension stiffness (K) 1 ) And damping (C) 1 ) Stiffness of secondary suspension (K) 2 ) And damping (C) 2 )。
The track model completely reflects the sinking and floating (Z) of the steel rail, the sleeper and the track bed r 、Z s 、Z b ) The steel rail is regarded as an infinite beam (Euler beam) on a continuous elastic scattered point support, the base under the rail is scattered along the longitudinal direction, the scattering takes each sleeper supporting point as an element, each supporting unit adopts a three-layer (steel rail-sleeper-railway bed-roadbed) spring-damping vibration model, m r 、EI y Respectively representing the unit length mass of the steel rail and the bending rigidity of the steel rail; k is a radical of r 、k s 、k b And C r 、C s 、C b Respectively showing the rigidity and the damping under the steel rail, the sleeper and the track bed corresponding to each supporting unit.
Example one
The following are examples for determining the seamless rail impact loads P1 and P2.
In a certain heavy-load line in actual operation, a concave welding seam exists at a steel rail welding joint, and the width l of a concave part is actually measured on site 0 4mm, the maximum vertical sinking height of the wheel is 0.002mm, the radius of the wheel is 420mm, and the running speed is 160km/h, neglecting transverse vibration load generated by snake motion of the train and the like in the process that the train passes through the concave part of the steel rail joint, and only considering the vertical vibration effect of the wheel rail system.
S1, collecting corresponding parameters of wheel rail impact load, wherein specific numerical values are shown in the following table
Name (R) (symbol) Unit of Numerical value
Sprung mass of vehicle M 1 Kg 1500
Vehicle unsprung mass M 2 kg 900
Speed of train v Km·h -1 160
Static wheel load Pst KN 75
Rail joint angle α rad 0.01
Modulus of elasticity of rail E N·m -2 2.058·10 11
Moment of inertia of rail section J m 4 3.227·10 -5
Track centralized damping C t N·s·m -1 25000
Wheel rail contact stiffness K H N·m -1 1600
Distributed rigidity of rail K N·m -1 1.25·10 8
Wheel set unsprung mass m u kg 1000
Mass per unit length of rail m r kg·m -1 60
Mass of track centralization m t kg 305
Distributing track mass m kg 300
Track central stiffness k t N·m -1 8.49*10 7
Distance between sleepers a m 0.54
Quality of half sleeper m s kg 130
Effective track mass m e kg 120
S2, obtaining a critical speed expression and a specific numerical value according to the time relation and the proportional relation
Figure GDA0003681620730000121
Calculating to obtain the critical speed v 0 ＝132.8km/h。
S3, judging whether the train speed is greater than the critical speed or not
In an actual operation of a certain heavy-load line, the train speed is 160Km/h and is greater than the critical speed 132.8160Km/h, so that the high-frequency transient impact force and the medium-low frequency response stress correction formula deduced in high-speed operation are adopted for calculation.
S4, calculating the impact load during high-speed operation, and performing working condition calculation analysis on an impact load calculation formula to obtain the following results:
when the running speed of the heavy-load train is higher than v 0 When the wheel passes through the point A, the wheel begins to do horizontal projectile motion
v 1 ＝v＝160Km·h -1
Calculating the impact load in high-speed operation to obtain a calculation result
Figure GDA0003681620730000131
Figure GDA0003681620730000132
The invention takes the discontinuity of train wheels at the joint to deeply research the impact load of a heavy-duty train passing through a concave weld joint, takes a driving wheel unit model with single wheel and secondary spring damping as a research object, and researches the algorithm of the train-track coupling system generating the impact load at the steel rail weld joint.

Claims (7)

1. The impact load calculation method suitable for the concave welding seam of the seamless steel rail is characterized by comprising the following steps of: the method comprises the following steps:
collecting and calculating corresponding parameters of wheel-rail impact load
Establishing a vertical model of the train and the track, and acquiring relevant parameters of wheel-track impact load;
(ii) obtaining the expression of the critical speed and the specific value according to the time relationship
Obtaining a critical speed expression according to the time relation, and obtaining a critical speed by combining relevant parameters of the wheel-rail impact load;
(iii) judging whether the train speed is greater than the critical speed
Judging the speed of the train according to the critical speed, wherein the train runs at a high speed when the speed is higher than the critical speed, and runs at a low speed when the speed is lower than the critical speed;
(iv) calculating by using a high-frequency transient impact force and medium-low frequency response force correction formula deduced in high-speed operation
Establishing a mechanical model in high-speed operation to obtain an impact speed in high-speed operation and obtain a corrected impact force calculation formula;
(v) calculating by using a high frequency transient impact force and a medium-low frequency response force correction formula derived during low-speed operation
Establishing a mechanical model during low-speed operation to obtain the impact speed during low-speed operation and obtain a corrected impact force calculation formula;
the impact velocity and the impact force formula after correction calculation during high-speed operation in the step (iv) are specifically as follows:
when the running speed of the heavy-load train is higher than v 0 When the wheel passes through the point A, the wheel starts to make horizontal projectile motion, the time of the wheel passing through the concave part is determined by the horizontal speed of the wheel, and the impact speed when the wheel runs to the point B mainly comprises the speed of the wheel making free-falling body motion to contact with the track
Figure FDA0003799943050000011
Figure FDA0003799943050000021
And the vertical component v generated by wheel rotation y2 (v y2 ＝γv 1 sinβ≈γv 1 Beta) is adopted as the basis of the train body, wherein mu is a train mechanical parameter ratio, specifically is the ratio of the sum of the unsprung mass and the unsprung mass of the train to the gravity acceleration,
solved by the geometrical relationship:
Figure FDA0003799943050000022
the impact velocity at the seamless rail joint is:
Figure FDA0003799943050000023
calculating to obtain:
Figure FDA0003799943050000024
the rotation angle alpha is:
Figure FDA0003799943050000025
the correction formula is as follows:
Figure FDA0003799943050000026
Figure FDA0003799943050000027
Figure FDA0003799943050000031
wherein v is 1 -the running speed of the wheel before it enters the rail joint; v. of 2 -speed of wheel rail joint point B; l 0 -length of the rail joint recess; m 1 ，M 2 Kg for the sprung mass and the unsprung mass of the heavy-duty train; r-wheel radius; gamma-coefficient of the wheel rotation inertia converted into reciprocating inertia; α — wheel angle; h is the descending height of the axle center of the wheel; p st -static wheel load, kN, of the heavy-duty train; k H -linear wheel-rail contact stiffness; m is e -effective track mass, kg, taken as 0.4m, where m is the distributed track mass of an equivalent elastic foundation beam, m = m r +m s A, wherein m r The mass per unit length of the steel rail is kg/m, m s Weighing half of sleepers, wherein kg and a are sleeper intervals, and taking 0.6m; m is u -vehicle unsprung mass; m is t -the mass of the track concentration, kg,
Figure FDA0003799943050000032
wherein k is the distribution rigidity of the steel rail, E is the elastic modulus of the steel rail, and J is the section inertia moment of the steel rail; k is a radical of formula t -the track concentration stiffness, N/m,
Figure FDA0003799943050000033
C t concentrated damping of the track, N.s.m -1 ，
Figure FDA0003799943050000034
Wherein C is track distributed damping, N.s.m -1 。
2. The method for calculating the impact load at the concave welding line of the seamless steel rail according to claim 1, which is characterized in that: and (3) simplifying the heavy-load train in the step (i) into a two-system spring mass system model.
3. The method for calculating the impact load at the concave welding seam of the seamless steel rail according to claim 2, which is characterized in that: and (4) taking a half structure for dynamic analysis in consideration of the symmetry of the train and the track model in the step (i).
4. The method for calculating the impact load at the concave welding line of the seamless steel rail according to claim 3, wherein the method comprises the following steps: and (3) neglecting transverse vibration loads generated by snake-shaped movement of the train and the like in the step (i), and only considering the vertical vibration effect of the wheel track system.
5. The method for calculating the impact load at the concave welding seam of the seamless steel rail according to claim 4, wherein the method comprises the following steps: the steel rail in the step (i) is an Euler beam model based on a Winkler elastic foundation beam.
6. The method for calculating the impact load at the concave welding line of the seamless steel rail according to claim 1, which is characterized in that: the expression for the critical velocity in step (ii) from the time relationship is:
Figure FDA0003799943050000041
wherein v is 0 -a critical speed; l 0 -length of the rail joint recess; m is a group of 1 -the sprung mass of the heavy-duty train vehicle, kg; m 2 -unsprung mass, kg, of a heavy-duty train vehicle; h is the descending height of the axle center of the wheel; g is the acceleration of gravity.
7. The method for calculating the impact load at the concave welding line of the seamless steel rail according to claim 1, which is characterized in that: in the step (v), the calculation formulas of the impact velocity and the corrected impact force during the low-speed operation are as follows:
when the running speed of the heavy-load train is lower than v 0 When the wheel is vertically sunk to a maximum height h at the joint of the seamless steel rail, the speed of the wheel at the point B mainly comprises a vertical downward speed component v 0 (wherein
Figure FDA0003799943050000042
) And a transient impact component v which is opposite to the direction of the vertical speed of the wheel center when rotating around the point B B (wherein
Figure FDA0003799943050000043
) Composition is carried out;
the impact velocity is calculated as follows:
Figure FDA0003799943050000044
calculating to obtain:
Figure FDA0003799943050000045
the rotation angle alpha is:
Figure FDA0003799943050000051
the correction formula is as follows:
Figure FDA0003799943050000052
Figure FDA0003799943050000053
wherein v is 1 -the running speed of the wheel before entering the rail joint; v. of 2 -speed at point B of the wheel rail joint; l 0 -length of the rail joint recess; m is a group of 1 ，M 2 Kg for the sprung mass and the unsprung mass of the heavy-duty train; gamma-coefficient of the wheel rotation inertia converted into reciprocating inertia; α — wheel angle; h is the descending height of the axle center of the wheel; p st Heavy-load trainStatic wheel load, kN; k is H -linear wheel-rail contact stiffness; m is a unit of e -effective track mass, kg, taken as 0.4m, where m is the distributed track mass of an equivalent elastic foundation beam, m = m r +m s A, wherein m r The mass per unit length of the steel rail is kg/m, m s Weighing half of sleepers, wherein kg and a are sleeper intervals, and taking 0.6m; m is u -vehicle unsprung mass; m is t -the mass of the track concentration, kg,
Figure FDA0003799943050000054
wherein k is the distribution rigidity of the steel rail, E-the elastic modulus of the steel rail, and J-is the section inertia moment of the steel rail; k is a radical of t -the track concentration stiffness, N/m,
Figure FDA0003799943050000055
C t concentrated damping of the track, N.s.m -1 ，
Figure FDA0003799943050000056
Wherein C is track distributed damping, N.s.m -1 。
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