Railway axle inclination angle acceleration calculation method and corresponding easement curve linear condition

Abstract

According to the railway axle inclination angle acceleration calculation method and the corresponding easement curve linear condition, a train axle inclination angle acceleration calculation formula and the corresponding easement curve linear condition are determined through re-correction, and the railway axle inclination angle acceleration calculation method and the corresponding easement curve linear condition can be used for construction, maintenance and theoretical research of railways or various wheel track type rail traffics. The linear condition of the railway and wheel track traffic easement curve is that when a train runs, the starting point and the end point of the easement curve are required to meet the condition that the # imgabs 0 # value is zero, and the # imgabs 1 # value between the starting point and the end point of the easement curve continuously changes; when the rotation line serves as the easement curve, the inclination angle angular acceleration is constantly zero, namely when the cubic parabola serves as the easement curve of # imgabs2 #, the calculation formula of the inclination angle angular acceleration is # imgabs3 #

Description

Technical Field

[0001] The present invention relates to railways and wheel-rail type rail transit, and in particular to a method for calculating railway axle inclination angular acceleration and corresponding transition curve linear conditions, which redefines a train axle inclination angular acceleration calculation formula within the transition curve range of railways and wheel-rail type rail transit, and corrects the transition curve linear conditions related to the axle inclination angular acceleration. Background Art

[0002] Railway or wheel-rail transit lines consist of three parts: straight sections, circular curve sections and transition curve sections. The angle formed by the train axle and the horizontal plane is the axle inclination angle. When the train is running on a straight section, the inclination angle is zero, and it is a constant value in the circular curve section. When the train is running on a transition curve, the axle inclination angle changes continuously, causing the body to roll. In order to meet the requirements of train driving safety and riding comfort, it is required that the force of the rails in the transition curve range on the wheel tilting of the running train cannot suddenly appear or disappear, that is, the angular acceleration of the inclination angle is zero at the start and end of the transition curve, and the angular acceleration of the inclination angle changes continuously and evenly between the start and end of the transition curve.

[0003] According to Railway Engineering, the traditional formula for calculating the angular acceleration of the axle inclination angle when the train is traveling on a gentle curve is: Therefore, the "Railway Engineering" and "Railway Curve Surveying and Design Table" use "at the start and end of the transition curve" Between start and end The value should change continuously and evenly" is one of the basic linear conditions of railway transition curves; the calculation formula and linear requirements of the acceleration of the outer rail rising speed and the angular velocity of the inclination angle are consistent. According to the acceleration requirements of the outer rail rising speed, "Railway Curves and Their Maintenance" is derived as " The same requirement that the value should not suddenly appear or disappear at the straight-slow point or the slow-straight point, the slow-round point or the round-slow point, and should change continuously and evenly on the transition curve is one of the basic linear conditions of railway transition curves. However, through mathematical calculation and analysis, it is found that the above book formula derivation will Mistakenly However, erroneous deduction results occurred and were used as one of the basic linear conditions for railway and rail transit transition curves for a long time.

[0004] Considering that the angular acceleration of the train axle inclination angle or the acceleration of the outer rail rise speed directly affects the safety and comfort of the train, with the research and construction of high-speed railways and ultra-high-speed railways, the correctness and accuracy of its calculation is very important. Cloonets and cubic parabolas are often used in transition curves of transportation projects. Researching and proposing the corresponding correct calculation method and the corresponding transition curve linear conditions are the focus of the present invention. Summary of the invention

[0005] The technical problem to be solved by the present invention is to provide a method for calculating the angular acceleration of a railway axle inclination angle and the corresponding linear conditions of a transition curve, and to re-correct and determine the calculation formula for the angular acceleration of a train axle inclination angle and the corresponding linear conditions of a transition curve, which can be used for the construction, maintenance and theoretical research of railways or various types of wheel-rail rail transit.

[0006] The technical solution adopted by the present invention to solve the technical problem is as follows:

[0007] The railway axle inclination angle acceleration calculation method and the corresponding transition curve linear condition of the present invention are characterized by:

[0008] The linear condition of the transition curve of railway and wheel-rail transportation is: when the train is running, the starting and ending points of the transition curve are required to meet The value is zero, and the transition curve is between the start and end points. The value changes continuously;

[0009] Cloak curves and cubic parabolas are commonly used transition curves in railways or wheel-rail transportation. The axle inclination angle acceleration is calculated according to the following formula:

[0010] When the clothoid is used as the transition curve, the angular acceleration of the inclination angle is always zero, that is,

[0011] When the cubic parabola is used as the transition curve, the calculation formula of the inclination angle angular acceleration is:

[0012] Where: is the inclination angle of the train axle at any point on the transition curve, measured in radians; t is the running time of the train in the range of the transition curve; K is the curvature of any point on the transition curve; a is the linear acceleration of the train during travel; g is the local acceleration of gravity; v is the running speed of the train at any point on the transition curve; C is the transition curve constant, which is the product of the design radius and the design length of the transition curve.

[0013] The beneficial effects of the present invention are that the traditional calculation formula for the inclination angle and angular acceleration and the corresponding linear condition of the transition curve when the train is traveling in the range of the transition curve are corrected; a new calculation formula for the inclination angle and angular acceleration and the corresponding linear condition of the transition curve are determined, which are applicable to all railways and wheel-rail type rail transit, have good practicality and versatility, and can provide an important theoretical basis for the design, maintenance and theoretical research of railway and wheel-rail type rail transit projects. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] This specification includes the following drawing:

[0015] Figure 1 It is a schematic diagram of the inclination angle of the axle to the horizontal plane. DETAILED DESCRIPTION

[0016] The present invention is further described below in conjunction with the accompanying drawings and embodiments.

[0017] The railways and wheel-rail type rail transit mentioned in this specification refer to all railways or wheel-rail type rail transit that realize the support, guidance and drive of the train through the interaction between the train wheels and the rails.

[0018] Reference Figure 1 , the inclination angle between the train axle and the horizontal plane is:

[0019]

[0020] Where: h is the inclination angle between the axle and the horizontal plane and the superelevation value of the outer rail at any point on the transition curve; S1 is the distance between the wheel-rail contact points on the two rails of the track, which is a constant.

[0021] In order to balance the centrifugal force during driving, the radius of curvature at any point on the transition curve should match the superelevation value of the outer rail. The balance relationship between speed and superelevation value is:

[0022]

[0023] Where: g is the local gravitational acceleration; v, ρ, l are the train running speed, curvature radius and running length at any point on the transition curve.

[0024] According to formulas (1) and (2), when the centrifugal force is balanced at any point, the calculation formula for the inclination angle of the easement curve range is:

[0025]

[0026] Where: K is the curvature of any point on the transition curve, t is the time the train runs within the transition curve. From formula (2), the linear acceleration of the train is By importing it into formula (3), we can deduce as follows:

[0027]

[0028] When the clothoid is used as a transition curve, The curvature of any point on the transition curve is as follows.

[0029]

[0030] Where: C is the constant parameter of the clothoid, which is the product of the radius of curvature of any point on the transition curve and the length of the transition curve.

[0031] According to formula (5), when the clothoid is used as a transition curve, the transition curve range always exists According to formula (4), when the clothoid is used as a relaxation curve, its inclination angle and angular acceleration are always zero, that is, Then the angular acceleration of the inclination angle at the starting point and end point of the transition curve and between the starting point and the end point are all always zero. Considering that being always zero is also a continuous and uniform change, when the spiral line is used as a transition curve, no matter what driving state the train is in, it satisfies the linear conditions that the angular acceleration of the inclination angle at the starting point and the end point of the transition curve is zero, and the linear conditions between the starting point and the end point change continuously and uniformly.

[0032] When the cubic parabola is used as the transition curve, the calculation formula of the inclination angle angular acceleration is derived as follows.

[0033] According to the results of the national "Eighth Five-Year Plan" scientific and technological project "Research on the Selection of Design Parameters of Bridges and Tunnels for High-Speed ​​Railway Lines" "Preliminary Study on the Parameters of Horizontal and Vertical Curves of High-Speed ​​Railways" and the requirements of railway and rail transit design specifications, the rectangular coordinate equation of the cubic parabola transition curve is as follows.

[0034]

[0035] Where: C is a constant parameter, which is the product of the designed circular curve radius R and the length of the transition curve l0.

[0036] According to formula (6), my country's railway adopts straight superelevation along the slope. Using calculus analysis, the length of the small segment on the transition curve is taken as dl, then the first-order derivative of the length of the small segment and the length of the transition curve with respect to x is:

[0037]

[0038] For the rectangular coordinate system, let the straight-slow point or the slow-straight point of the transition curve be the origin, and the curvature formula of any point on the line transition curve is:

[0039]

[0040] According to formula (2) and formula (9), when a cubic parabola transition curve is used, the superelevation value of any point on the transition curve when the centrifugal force is balanced is calculated as:

[0041]

[0042] Let equation (10) be the first derivative with respect to x, and let Then equation (10) and equation (8) can be expressed as follows:

[0043]

[0044] Divide the above equation of equation (11) by the following equation; take the first-order derivative of equation (9) with respect to x and then divide it by the following equation of equation (11). The superelevation slope rate and curvature slope rate of the balanced centrifugal force at any point on the cubic parabola transition curve are expressed as:

[0045]

[0046] According to the following formula (2) and formula (12), when the cubic parabola is used as a transition curve, the curvature time-varying rate is expressed as:

[0047]

[0048] According to the current design specifications, the design radius of a high-speed railway with a design speed of 350km / h is generally 12,000 to 5,500 meters. This range of values ​​is the straight-slow point or the slow-straight point of the transition curve. The calculated value is the largest and is located in the interval [1.0004763,1.0078392], which is approximately equal to 1. Similarly, The calculated value is in [3.22×10 -10 ,6.28×10 -9 ] interval, can be regarded as zero consideration. At the same time, considering that the length of the transition curve of high-speed railway in the current design specifications is much longer than that of the transition curve of intercity, conventional railway or rail transit, then when the design radius is the same, the straightening point or the straightening point of the transition curve of intercity and conventional railway or rail transit is The calculated value will be much smaller than the corresponding value of the high-speed railway transition curve and can be regarded as zero. It is also approximately equal to 1. Therefore, from the perspective of engineering accuracy requirements, when a cubic parabola transition curve is used, when the centrifugal force of the train is balanced at any point on the transition curve, equation (13) can be derived as follows:

[0049]

[0050] Where: a is the acceleration of the train during travel.

[0051] When formula (14) is introduced into formula (3), and the cubic parabola is used as the transition curve, the angular acceleration calculation formula of the inclination angle is:

[0052]

[0053] It can be seen that when the clothoid and cubic parabola are used as transition curves, under the same design parameters, the calculation formula and calculated value of the train inclination angle angular acceleration are different. When the train acceleration is zero, the inclination angle angular acceleration within the range of the cubic parabola transition curve is zero. For the dynamic characteristics of the inclination angle angular acceleration, theoretically, the clothoid and cubic parabola cannot be replaced by each other as transition curves.

[0054] In summary, the corresponding traditional angular acceleration formula is and "At the beginning and end of the relaxation curve, due Between start and end The linear condition of the transition curve that "the value changes continuously and evenly" is wrong.

[0055] The present invention corrects the traditional calculation formula of the inclination angle and angular acceleration and the corresponding linear condition of the transition curve when the train travels in the range of the transition curve; it redefines the calculation formula of the inclination angle and angular acceleration of the train axle and the corresponding linear condition of the transition curve, is applicable to all railways and wheel-rail type rail transit, has good practicality and versatility, and can provide an important theoretical basis for the design, maintenance and theoretical research of railway and wheel-rail type rail transit projects.

[0056] The present invention corrects the linear condition of the railway and wheel-rail track traffic transition curve to: when the train is running, the starting and ending points of the transition curve are required to meet The value is zero, and the transition curve is between the start and end points. The value changes continuously.

[0057] Cloak curves and cubic parabolas are commonly used transition curves in railways or wheel-rail transportation. The axle inclination angle acceleration is calculated according to the following formula:

[0058] 1. When the clothoid is used as the transition curve, the angular acceleration of the inclination angle is always zero, that is,

[0059] 2. When the cubic parabola is used as the transition curve, the calculation formula of the inclination angle angular acceleration is:

[0060]

[0061] Where: is the inclination angle of the train axle at any point on the transition curve, measured in radians; t is the running time of the train in the range of the transition curve; K is the curvature of any point on the transition curve; a is the linear acceleration of the train during travel; g is the local acceleration of gravity; v is the running speed of the train at any point on the transition curve; C is the transition curve constant, which is the product of the design radius and the design length of the transition curve.

[0062] When a roundabout is used as a transition curve for railway or wheel-rail transportation, the transition curve range always exists. Then according to the inclination angle acceleration calculation formula It can be seen that when the clothoid is used as a transition curve, its inclination angle acceleration is always zero, that is, it always exists Then the starting point and end point of the transition curve, and the inclination angular acceleration between the starting point and the end point are always zero. Considering that it is always zero is also a continuous and uniform change. Therefore, when the spiral line is used as a transition curve, no matter what kind of driving state the train is in, it satisfies the linear conditions that the starting point and end point of the transition curve are zero, and the inclination angular acceleration changes continuously and uniformly between the starting point and the end point.

[0063] When a cubic parabola is used as a transition curve for railway or wheel-rail transit, the cubic parabola transition curve inclination acceleration calculation formula shows that theoretically, only when the linear acceleration of the train is zero can the linear conditions of zero inclination acceleration at the start and end of the transition curve and continuous and uniform change between the start and end points be met. For high-speed railways, the transition curve is long and the design radius is large, so the calculated inclination acceleration value is very small and can be regarded as zero; however, for low-speed railways, subways and other wheel-rail transit, the transition curve is small and the design radius is small, so the calculated inclination acceleration value is large, which will greatly affect passenger comfort and increase wheel-rail wear, which is consistent with the poor comfort of riding conventional railways, subways and other wheel-rail transit.

[0064] When a clothoid or cubic parabola is used as a transition curve, the calculated values ​​of the train axle inclination angle acceleration are different at the same design parameters and driving speed. When the linear acceleration of the train is zero, the inclination angle acceleration within the range of the cubic parabola transition curve is zero. For dynamic characteristics, theoretically, the clothoid and cubic parabola cannot be interchanged as transition curves.

Claims

1. A method for calculating the acceleration of the railway axle inclination angle and the corresponding transition curve linear conditions, which are characterized by: The linear condition of the transition curve of railway and wheel-rail transportation is: when the train is running, the starting and ending points of the transition curve are required to meet The value is zero, and the transition curve starts and ends The value changes continuously; Cloak curves and cubic parabolas are commonly used transition curves in railways or wheel-rail transportation. The axle inclination angle acceleration is calculated according to the following formula: When the clothoid is used as the transition curve, the angular acceleration of the inclination angle is always zero, that is, When the cubic parabola is used as the transition curve, the calculation formula of the inclination angle angular acceleration is: Where: is the inclination angle of the train axle at any point on the transition curve, measured in radians; t is the running time of the train in the range of the transition curve; K is the curvature of any point on the transition curve; a is the linear acceleration of the train during travel; g is the local acceleration of gravity; v is the running speed of the train at any point on the transition curve; C is the transition curve constant, which is the product of the design radius and the design length of the transition curve.

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