AU2018200145B2

AU2018200145B2 - Method for optimizing a track position

Info

Publication number: AU2018200145B2
Application number: AU2018200145A
Authority: AU
Inventors: Bernhard Lichtberger
Original assignee: HP3 Real GmbH
Current assignee: HP3 Real GmbH
Priority date: 2017-02-06
Filing date: 2018-01-08
Publication date: 2019-09-12
Anticipated expiration: 2038-01-08
Also published as: AU2018200145A1; EP3358079B1; JP2018127882A; ES2775756T3; AT520036A1; AT519218A4; JP7037948B2; AT520036B1; AT519218B1; EP3358079A1

Abstract

Method for optimizing a track position The invention relates to a method for optimizing a track position and for guiding a track-mounted track construction machine after a measuring drive with a track mounted track measuring carriage (A) having at least two wheel axles supported on a machine frame (21), a navigation unit, a device (7, 6, 9, 10) for pressing the wheels (1) against the rail (12) and an odometer (24) for measuring an arc length (s) of the rail (12). In order to create advantageous measuring conditions, a measuring drive is first carried out with the track-mounted track measuring car riage (A) equipped with an inertial navigation unit (INS, 5), the wheels (1) of which are pressed against the rails (12), wherein the length of the arc is meas ured with the odometer (24), the angular position (AL, AO, AG) of the inertial navigation unit (INS, IMU, 5) is measured against a Cartesian reference coordi nate system (x, y, z) and stored, and that after the measuring drive coordinate points (Pi) of the track (A, e, Pi) of the navigation unit (INS, 5) are calculated in space from the stored angular positions (A, AO, AO) by means of compensa tion calculation and from the thus optimized coordinate points (P) of the track(A, e, Pi) a locus image (1) is formed by zeroing the z-components and a longitudi nal section (2) by zeroing the x-components, after which a curve determined by means of mathematical connection functions is laid through the coordinate points (Pi). (Fig. 7) ly A Rs Rs -T-L %B -o V =R -R R. R t s R't y ARs t2 ' ti dp d

Description

Method for optimizing a track position

The invention relates to a method for optimizing a track position and guiding a track-mounted track construction machine after a measuring drive with a trackmounted track measuring carriage, comprising at least two wheel axles supported on a machine frame, a navigation unit, a device for pressing the wheels to the rail and an odometer for measuring an arc length of the rail.

Most tracks for railways are arranged as ballasted tracks. The sleepers lie in the ballast. Irregular subsidence in the ballast and displacements in the lateral positional geometry of the track are caused by the acting wheel forces of the trains that travel over said ballast. The subsidence in the ballast bed causes errors in the longitudinal level, the superelevation (in the arc), and the track lining position If specific limit of comfort values of these geometric quantities are exceeded, maintenance work is planned and performed.

The repair and correction of these geometric track faults is mostly currently carried out by means of track construction machines. In order to ensure that the track can be released for operation again after such track geometry repair work, the railway permanent-way machines are equipped with so-called approval measuring systems and acceptance recording systems. Acceptance tolerances are determined for the quality of the track position after the improvement by the permanent-way machines or other methods. They represent the minimum requirements placed on the quality of the produced geometric improvements. They are proven by acceptance measuring systems and acceptance recording systems.

2018200145 23 Aug 2019

The important quantities to be mentioned, corrected and recorded in this case are the twisting of the track, longitudinal level of the track, direction or lateral position of the track, and the transverse inclination or superelevation of the track. A railway permanent-way machine such as a track tamping machine rebuilds the track geometry which was adversely affected by loading by trains. For this purpose, the track is lifted and lined to the target position by means of lifting and lining devices controlled in an electrohydraulic manner.

The lower the residual errors after maintenance work of a permanent-way machine, the lower the interacting forces of the train traffic, the slower the track geometry deteriorates under the train traffic, the greater the durability of the track system. It is therefore desirable to ideally bring the track geometry to the target position, as subsequently considerable costs and effort can be saved. The faster the trains travel, the smaller the permissible tolerance values. For moving trains, the correction of errors (error wavelength typically from 3 m to 70 m) is essential. The error wavelengths to be considered are based on the line speed.

Various track lining methods have emerged for correcting track errors. On the one hand, there are relative methods that only smooth the track position and, on the other hand, absolute methods. In the absolute methods, the track positions are corrected according to predetermined target geometries. The target geometries of the railway tracks are available as track plans and can be used after input to the control computer of the permanent-way machine to calculate the systematic errors with knowledge of the behavior of the measuring systems. If the absolute correction values for the front end of the machine measuring device are known, then the front end of the machine measuring device is guided on the setpoint curve and the rear end is guided on the already corrected track. The lining process is carried out at the workplace. The position of the tamping machine in the track longitudinal axis is usually determined by an odometer.

If the target geometry is unknown, then the track position is usually measured with the known methods with a chord system for the direction and a chord system for the longitudinal height before work. The actual transverse inclination is

2018200145 23 Aug 2019 measured with a pendulum. Pendulums depend on the accelerations occurring during the measuring drive. In particular, the centrifugal acceleration during the measuring drive in the arc leads to large errors. This typically limits the measurement speed to a range of about 5 km/h. The measurement of the track position via chord systems is associated with a transfer function, i.e. the measured signal deviates from the actual track error with respect to its shape, gain, and phase position. The measured values are proportional to the curvatures of the track. The measurement of the height position of the track by means of a chord measurement system also provides curvature-proportional signals having a transfer function. Changes in inclination (transition from one inclination to another) cannot be determined from the measured data, since it cannot be distinguished between curvature errors of the track position and between inclination transitions which also manifest themselves as curvature differences. In addition, from the curvature measurements of the height no conclusion on the actual inclination is possible (the machine is in a certain inclination, but is unable to derive said inclination from the measurements, since the entire measuring system is inclined and performs only a relative measurement).

For the optimization of the track position according to the known conventional methods, the measured curvatures are smoothed to a target curvature curve. Then, the difference between the measured and the smoothed target curvature image is formed. An approximate inverse transfer function is formed by means of digital filters (see, for example, DE 103 37 976 B4). This inverse transfer function is now applied to the difference between the measured and the smoothed target positional curvature image. The track error is thus obtained by approximation. If the error to be corrected exceeds permissible maximum correction values then the target positional curvature image must be modified accordingly by means of complicated methods. The situation is similar with constraints or positions of constraints. A position of constraint such as a bridge may require that lateral shifts are not permitted, for example. With respect to longitudinal height, a further processing step is necessary in contrast to the direction, since it is only possible to lift but not to lower. The lifting and lowering progression arising from the optimization must be positively definite. For this purpose, the lifting correc4

2018200145 23 Aug 2019 tions are raised so that no negative (lowerings) occur any more. These calculations are difficult and inaccurate for the reason that curvature images are assumed. Errors correspond approximately to a two-fold integration of the curvature differences, but these also contain a transfer function.

The prior art is defined by chord measuring systems and pendulums or inclinometers for measuring the longitudinal height, the direction and the transverse inclination. The prior art is also defined by odometers for determining the position of the measuring system on the track. Also known in the art are satellite navigation systems (such as GPS, Navstar or Galileo). Inertial navigation systems (INS) or inertial navigation systems which consist of a central sensor unit with mostly three acceleration and rotation rate sensors are also state of the art. The spatial movement of the vehicle and therefrom the respective geographical position in an INS are determined continuously in an INS by integration of the accelerations and rotation rates measured by the IMU (inertial measurement unit). INS systems operate at data rates of about 100-1000 Hz and high precisions and low drift (<0.01° to 0.05°/hour). They calibrate themselves automatically in breaks when they are not moved. The main advantage of an INS is that it can be operated without reference. The acceleration can be measured by means of vehiclefixed acceleration sensors (strap-down). Of course, the use of only one IMU is possible in principle, in this case the absolute roll angle must be measured by an independent inclinometer. Advantages of these measuring systems are roll angles which can be measured independently of the centrifuge acceleration, a widely applicable transfer function of the system of = 1, i.e. the actual track of the vehicle is measured in space without distortion of the form, the amplification or the phase position of the track errors. From this three-dimensional track of the vehicle in space and an equidistant measurement via odometer, 3D coordinates are obtained. By projection onto the xy-plane, one obtains the locus image of the track and the projection onto the yz-plane yields the vertical section. In addition, satellite navigation data can be recorded (e.g. via GPS). State of the art are also so-called North-based INS systems that provide absolute angular deviations of the roll, yaw and pitch angle relative to a north-facing system. The x-unit vector points to the north, the z-unit vector in the direction of gravity and the y-unit vec5

2018200145 23 Aug 2019 tor is then aligned so that an orthonormal system is formed. The absolute angle deviations represent a unit vector which shows the direction of the measuring carriage on which the INS system is located.

Disadvantages of the known method for track position optimization and calculation of the track errors from a measuring drive are measured values subject to a transfer function, the inverse transfer function of chord measuring systems which are to be depicted only approximately, the negative influence of inclinometers by externally acting accelerations, the difficult to meet boundary conditions such positions of constraints, constraints or maximum allowable correction values in the optimization calculation. Disadvantageous is also the low measuring speed which is permissible during a measuring drive. A further disadvantage is that chord measuring systems have a local propagation in the longitudinal direction of the machine of 10-20 m. Frequently, permanent-way machines are therefore equipped with trailers under which the measuring system is housed. This increases the cost and length of the machines. If additional work units such as a sweeping brush, ballast silo or dynamic track stabilizer are attached to the trailer, the use of chord measuring systems is impossible. A disadvantage of the known methods for track position optimization is that the absolute inclination of the track and the inclination changes cannot to be determined from the measured data. The unknown position of the inclination changes according to the known methods leads in these areas to a faulty track position correction by the permanentway machines. Another drawback with the known methods is that, because of the digital non-recursive filters used and their necessary settling path, it is necessary to measure approximately 13 times of the short chord section in front of the track actually to be corrected (typically a lies in the range of 4-7 m - this provides pre- and post-measurement lengths of 50 to 90 m). At the low measuring speeds of the known methods a corresponding amount of time is required. The known chord methods also have the disadvantage of an offset (e.g. by wear of the measuring wheel, inaccuracies of the encoder, the driver in which the chord runs, the vibrations of the chord, etc.), which must be checked regularly. The recalibration of the chord measurement systems is complex and costly.

2018200145 23 Aug 2019

Some embodiments of the present disclosure, therefore, are aimed at further developing, after a measuring drive, a method for optimizing a track position by taking into account boundary conditions such as positions of constraints, constraints and maximum allowable track position corrections by means of an inertial navigation system (INS) or an inertial measurement system (IMU) and an odometer in such a way that the disadvantages of the known systems such as influencing by externally acting accelerations, limited measuring speed, influence of a transfer function of the chord measuring system, offsets of the chord measuring system to be calibrated, boundary conditions in the optimization that are difficult to meet and the construction of an additional trailer are avoided.

Any discussion of documents, acts, materials, devices, articles or the like which has been included in the present specification is not to be taken as an admission that any or all of these matters form part of the prior art base or were common general knowledge in the field relevant to the present disclosure as it existed before the priority date of each of the appended claims.

Throughout this specification the word comprise, or variations such as comprises or comprising, will be understood to imply the inclusion of a stated element, integer or step, or group of elements, integers or steps, but not the exclusion of any other element, integer or step, or group of elements, integers or steps.

According to one aspect, there is provided a method for optimizing a track position and for guiding a track-mounted track construction machine after a measuring drive with a track-mounted track measuring carriage, having at least two wheel axles supported on a machine frame, a navigation unit, a device for pressing the wheels to the rail and an odometer for measuring an arc length of the rail, wherein first a measuring drive is carried out with a track-mounted track measuring carriage which is equipped with an inertial navigation unit, the wheels of which are pressed against the rails, wherein the arc length is measured with the odometer, the angular position of the inertial navigation unit is measured and stored relative to a Cartesian reference coordinate system, and wherein after the

2018200145 23 Aug 2019 measuring drive coordinate points of the track of the navigation unit are calculated in space from the stored angular positions by means of compensation calculation and from the thus optimized coordinate points of the track a locus image is formed by zeroing the z-components and a longitudinal section by zeroing the xcomponents, after which a curve determined by means of mathematical connection functions is laid through the coordinate points.

According to another aspect, there is provided a device for optimizing a track position and for guiding a track-mounted track construction machine with a trackmounted track measuring carriage having at least two wheel axles supported on a machine frame, a navigation unit, a device for pressing the wheels to a track with two rails and an odometer for measuring an arc length of the rail, wherein the track measuring carriage, in the region of opposite longitudinal sides, comprises at least two wheel groups having wheels which are each associated with rails and which are mutually rotatably mounted about a track measuring carriage transverse axis, and wherein the track measuring carriage is equipped with an inertial navigation unit, a device for pressing the wheels to the rail and an odometer for measuring an arc length of the rail.

This is provided in that a measuring carriage with 2 sets of wheels that are designed to be rotatable relative to one another produces an INS system. In addition, the measuring carriage can be constructed so that the rotation device of the wheel sets is provided with a track gauge measurement. Thus, the geometric position of both rails can be determined in one measurement process. The wheel contact points can be determined with precise knowledge of the track gauge, thus increasing the precision of the superelevation determination. Connected to the measuring carriage is an odometer which measures the distance traveled by the measuring carriage on the track. The measuring carriage is placed laterally against a rail during measurement or pressed on both sides via the track gauging measurement. Therefore, the INS measures the tangent to the track direction and the longitudinal inclination as well as the transverse inclination of the measuring carriage on the track (the superelevation). In equidistant steps for example (typically 0.25; 0.5 or 1m - also a quasi-continuous recording is possible because

2018200145 23 Aug 2019 of the high measurement rates of the INS) the measured data of the INS are stored at the appropriate place. For each measuring point, apart from the INS data, the exact arc length traveled (or the track kilometer) is also stored.

The method according to the present disclosure provides an optimized target track position in height and direction and the associated correction values on the arc length measured with odometer. A further advantage in addition to the higher measuring speed is the robustness of the INS or IMU generally against external disturbing accelerations. The compaction of the ballast bed is carried out with 35 Hz. Permanent-way machines run on diesel engines and therefore show disturbing vibration and acceleration levels. The additional advantage of the method according to the present disclosure is that the position of the inclination changes and the absolute inclinations can be determined exactly and thereby qualitatively considerably more accurate correction values for the track construction machine can be predefined. Greater achieved track position accuracy extends the geometrical durability of the track and significantly reduces the cost of maintenance. Another advantage is the limitation of the pre- and post-measuring lengths to about a machine length (typically 10-20m). It is equally advantageous that exact curvature images and longitudinal inclination images can be determined with the method according to the present disclosure, which correspond to the usual representation of the railway. This target data can thus be used in subsequent processing. They also provide an excellent basis for the surveying service of the railway for a determination of the target geometry of the hitherto unknown track geometry of the track. Since the target arrow heights and target longitudinal heights are determined mathematically from the target locus images and the target inclination images, advantageously no offset of the measuring system occurs in the method according to the present disclosure. This eliminates expensive calibration methods.

After completion of the measuring drive, the track of the measuring carriage in space is calculated from the absolute angle differences to the north-based coordinate system of the recorded INS values for each measuring point (roll, yaw and pitch angle). As an initial condition, the initial angle vector is favorably placed in

2018200145 23 Aug 2019 the initial direction of the measuring carriage at the beginning of the measuring drive. The integration of the track (calculation of the 3D coordinates of the measurement travel positions) is carried out according to:

By setting z = 0 in the 3D coordinates, one obtains the so-called locus image f(xy). By setting x = 0, the longitudinal section g(y, z) is formed. The longitudinal section shows the course of altitude and also the inclination changes (transition from one inclination to another). Depending on the route class, base lengths are defined. The locus image is divided by a base length into sections, which base length is predetermined by track type. The smoothing occurs for example by means of cubic splines according to the method of least squares sum of the deviations. These splines are joined to a smoothed target locus curve. The correction values are then trimmed by the maximum allowable correction values. Constraints are connected by a steady continuous mathematical function passing through the transition points and the constraints. The previous target locus is converted to a new modified one by overlay. Minor changes remain without impact on the vehicle. The same procedure is used in the case of positions of constraints. The modified and applicable target locus are thus obtained. The differences to the target curve of the direction are the lining correction values that are passed to the permanent-way machine. In order for the permanent-way machine to be able to process the target curve of the direction with its chord system, the target curve must yet be converted to the chord measurement system values (arrow height for the direction). This is done mathematically by calculating a chord continuously into the target curve of the direction. The target arrow height calculated therefrom is transferred to the permanent-way machine controller. Thus, the permanent-way machine can perform the track correction in the direction.

For the height (x = 0 is set), the height profile (g(y, z) is obtained according to the present disclosure in absolute height values. The transition from an inclination to the next indicates a change of the inclination in the data (which is easily determinable after filtering of the actual height profile with a digital filter which permits only long wavelength changes (e.g. > 50m) (e.g. the second derivative of the filtered height profile makes the change of inclination clearly determinable). If the

2018200145 23 Aug 2019 inclination changes are thus determined, regression functions are calculated between them (e.g. regression lines). The connection between these individual regression curves is made by compensation curves of higher order, e.g. cubical splines (with certain typical rounding-off length e.g. 6 m). The result is a steady continuous mathematical function as the target height profile. Subsequently, the differences between the measured actual height position and the target height position are formed. The differences correspond to the corrections to be made and are raised so that no negative values occur and pure positive lifting values result. In order to ensure that the permanent-way machine can process the target height profile with its chord system, this has yet to be converted to the chord measurement system values (longitudinal height). This is done mathematically by continuously calculating a chord into the target curve of the height position. The resulting calculated target longitudinal height and the lifting values are transferred to the permanent-way machine controller. Thus, the permanent-way machine can perform the track correction in the longitudinal height.

In the case of perfect work, the corrected track positions are obtained which correspond to the course of the smoothed target locus curve and the target height profile, while maintaining the boundary conditions such as positions of constraint, constraints or maximum correction values.

It is understood that the system described here can also be used as a separate measuring system for generating an acceptance record, with the advantage that no spatially extended measuring system is present and thus a trailer would not be necessary. This method obviously includes the advantage of performing the measuring recording at speeds of up to 80km/h. This results in enormous time savings for the measuring drive compared to the current systems, which are typically carried out at only about 5 km/h. If the locus image is differentiated twice mathematically by arc length, the curvature is obtained. The curvature image is the common representation in the railway. Another advantage is that certain changes in position of the track (e.g. a pivoting in the station area) can be superimposed directly to the desired locus image. The permanent-way machine then simply converts this after transferring the control data obtained from the desired

2018200145 23 Aug 2019 locus image. Such defaults are not possible in a curvature. The result of the method according to the present disclosure is, in addition, the advantage that the position of the inclination changes and the absolute inclinations can be determined exactly, and thus qualitatively considerably more accurate correction values for the track-construction machine can be predefined.

The subject matter of the present disclosure is schematically shown in the drawing by way of example, wherein:

Fig. 1 shows a plan view and elevation of a track measuring carriage according to an embodiment of the present disclosure with INS unit,

Fig. 2 shows a schematic diagram of a chord-based precision track correction method,

Fig. 3 shows a diagram of north-based 3D track coordinates,

Fig. 4 shows a diagram of 3D track coordinates - determination of the locus image and the longitudinal inclination image,

Fig. 5 shows a diagram of the formation of the optimized target track position with the aid of cubic compensation splines,

Fig. 6 shows a detailed representation of the smooth connection between compensation splines,

Fig. 7 shows a schematic representation of the formation of a target track position taking into account a single constraint,

Fig. 8 shows a schematic representation of the formation of a target track position taking into account a position of constraint,

Fig. 9 shows a longitudinal height section with balanced target height position and inclination change and height correction values.

Fig. 1 shows a track measuring carriage A according to the present disclosure with an INS unit 5 which is arranged on the connecting measuring carriage frame 8. The measuring carriage A runs on four wheels 1 on the rails 12. The wheels 1 of one side are each rigidly connected to each other 2, 3. The two opposite wheel sides are rotatably mounted to each other via an axle 4. Thus, the track measuring carriage A can occupy a defined position in twisted tracks. The axle 4 is designed to be displaceable in the axial direction. The displacement is per12

2018200145 23 Aug 2019 formed by an air cylinder 6, 14 so that both pairs of wheels 2, 3 run left and right at the rail edge 12. By means of a distance sensor 7, the actual track width SPW is measured. The wheelbase width RAW is calculated as follows :

RAP = SPW + b_k bk... Rail head width

The pairs of wheels 1, 2 and 1, 3 are applied with a vertical force and a horizontal force via two inclined cylinders 10. This ensures the start of the wheels 1 on the rails 12 and prevents the derailment. Vertical cylinders 9 are used to raise in the locked position and the railing of the measuring carriage at the start of work or end of work. 11 schematically illustrates a sliding bearing in which the torsion axis 4 can be both twisted and transversely displaced 6. 21 illustrates the machine frame of the permanent-way machine. At the measuring carriage A, an odometer (distance measuring device) 24 is attached which measures the arc length of the track.

Fig. 2 schematically shows the operation of a precision track correction system B. This consists of a chord of length L with chord sections a and b. The permanent-way machine with the chord-based correction system works in the direction of AR. 21 represents the track position to be corrected and R_s the optimized track target position. In the illustrated drawing, one assumes that the track behind the chord has already been corrected. In this case, the rear point of the chord is on the corrected track. The front point would be on the actual track position 21 at the front however. For the method, it is therefore necessary first to determine the correction value v. The front end of the chord must be guided on the track target position R_s. This can be achieved in such a way that the chord is guided on the front of a transverse adjusting device which is adjusted exactly by the difference v at each step. Another condition for the proper functioning of the method is the specification of the target arrow height fs. As a result, the necessary reference value is obtained in order to achieve the track target position f_swith

2018200145 23 Aug 2019 ί?Μ/ = Λ-/,

RW ... Reference value

For perfect function, therefore, the arrow heights f_s and the correction values v must therefore be determined by a corresponding method.

Fig. 3 schematically shows a north-based coordinate system. The x axis points to the north N, the z axis is parallel to the gravitational axis g. Rotations about the x axis are measured by the roll angle Φ (superelevation angle), rotations about the z axis correspond to the heading angle (heading or also gear angle or yaw angle) Ψ, and rotations about the y axis provide the inclination angle (pitch or pitch angle) Θ. At the beginning of the measurement, the three differential angles ΔΦ, ΔΨ and ΔΘ which form the direction of the vehicle to the north-based coordinate system are measured and delivered by the INS. The unit vector in the machine direction then results in:

COS-ψ COS0 εϊηΨ cos& είηΘ

The measurement of the INS is read in over the measured arc length in equidistant sections λ (typically 0.25 -1 m). The first data point Pi is then simply calculated as follows:

P, = λ-ef

At the next measurement, the new point Pi +1 is formed by vector addition.

Λ+1 — F] + A e_I+1

2018200145 23 Aug 2019

This procedure is thus carried out with all measured data points. The distance traveled (the arc length s) is measured with an odometer and co-recorded and then results in:

Sj ⁼ Z A i ... Number of read data points

Since the equidistant measurement rate λ is very short, the error that results from the secant formation can be neglected. The rail can be assumed to be straight within the typical measuring rate of 0.25-1 m. The wave length of the error to be taken into account is typically up to 100 m, so a possibly cumulative error can also be neglected.

Fig. 4 shows schematically in a north-based system the previously described 3D coordinate line 3 with coordinate triplets Pi(xi, yi, Zi). By setting z to zero, one obtains the projection of this 3D coordinate line on the xy plane, i.e. the so-called locus image 1. By setting x to zero, one obtains the projection of this 3D coordinate line on the yz plane, i.e. the so-called inclination image 2. The locus image 1 shows the course of the track, the straight sections, the transition arcs or the position of the full arcs. Track direction errors are superimposed on this geometry. The longitudinal height image shows absolute inclinations, the inclination changes and superimposed height errors. For each of the measured and recorded coordinate triplets Pi, the current arc length Si (track km) is co-stored as a parameter.

Fig. 5 shows schematically a locus image (z = 0). To construct a target locus curve Rs, the actual locus curve 3 is subdivided into uniform sections D by way of example within the terms of the present disclosure. For each section D, for example a balancing cubic regression spline or any other mathematical regression curve of higher order (according to the method of the smallest square sum of the deviations) SPL1, SPL2 is calculated in a first step. In the following, the procedure for cubic regression splines will be described by way of example. A

2018200145 23 Aug 2019 third-order cubic regression spline is used for example so that a turning point in the track geometry can be displayed correctly (arc changes for example from a left-hand arc to a right-hand arc). The length of the section D is selected according to the route class. The faster one drives, the larger the radii and the lower the track errors. Longer sections D are therefore selected at higher route classes. In the next step, the xi, X2 transition lengths L_u are selected whose length is also selected according to the route class. The regression curves are now to be interconnected in such a way that a steady course results under boundary conditions. These connecting curves SPL3 can be made with mathematical compensation curves of higher order. By way of example, a cubic compensation polynomial SPL3 is described here, but other mathematical equations are possible. With xi or X2, the points on the calculated compensation spline (P1 from spline equation SPL1 and P2 from spline equation SPL2) are calculated. Between the points Pi and P2, cubic polynomials SPL3 are now calculated under the initial conditions as shown enlarged in Fig. 6. For a cubic transition polynomial, the points P1 and P2 are known and the inclines ti, t2 at these points of the cubic regression splines. These steps result in a consistent smooth target locus Rs which is mathematically clearly described. If one differentiates this target locus Rs twice, then one obtains the curvature k = 1/R of the target position as used in the railway. This is a great advantage because one thereby determines a target geometry which can be used again in the next track maintenance work. In Fig. 6, the curvature image k(s) for the target geometry curve y(x) is also shown schematically by way of example. If the following approach is taken as a cubic polynomial:

y = a-x³-|-h-x:²-|-c-% + i/ and for the tangents in the endpoints t = 3 a -x² + 2 b x + c and for the points P1 = (xi , yi); P2 = (X2, y2)

2018200145 23 Aug 2019 then the parameters a, b, c and d can be calculated analytically as follows:

(y₂ - >'i) - 0*2 - *i) (tz + ti) jT = •^1 ^{— X}2 + 2 ^X2 ‘ C^x2 — ^1.) _ό _ t₂ ~ ~ 3~ g-O₂ ~*i) (A₂ - *i) c = d = - a xf - b xf - c χχ

The least squares method for a regression with a cubic spline leads to the follow ing four normal equations:

n

M-yt

n

i = l

n ... Number of data points

In order to determine the coefficients ao, a2, a3 and a4, the equation system is to be solved for example with the Gaussian algorithm or Cramer's rule.

2018200145 23 Aug 2019

The cubic regression spline obtained according to the least squares method has the form:

y = + - jc + a₂ ' *² + ^fi3 ' X³

The schematic representation also shows the position of a chord with the chord length L and the chord sections a and b. The target arrow height f_s is determined by calculation.

Fig. 7 shows schematically how the target locus curve Rs can be adjusted with respect to a constraint Zp. First, as shown above, the target locus curve Rs is calculated from the points of the actual locus curve Ri. One moves backwards or forwards a distance dp from the constraint and superimposes a transitional spline with the boundary conditions Pi, ti and Zp, t2'. The tangent t2' is selected parallel to the tangent t2. The connection to the front is calculated similarly.

Thereby, the target locus curve is modified so that it passes continuously through the constraint Zp. The displacement v is then calculated as Rs - Ri.

Fig. 8 shows schematically a procedure of adaptation of the target locus curve Rs when a position of constraint W must be met. The example shows a switch (of length Lw) into which the target locus curve enters (Wa) and from which it exits (We) tangentially. For this purpose, the points of the previously calculated target locus curve Pa and Pe are determined. Here, as above, a cubic spline is calculated whose initial (tA, tw) and end tangents (tE, tw) and initial (Pa, We) and end points (Wa, Pe) are specified. Lra and Lke are chosen so that between the new target locus curve (Rs') only steady deviations from the previous target locus curve (Rs) are present which do not noticeably influence the vehicle. The chord of the permanent-way machine is then numerically moved over the resulting final target locus curve (Rs') - this results in the target arrow height course. The deviations between target (Rs') and actual locus curve (Ri) provide the correction values for the direction.

Fig. 9 shows schematically the actual height image (x = 0) 15. Inclination changes NW can be recognized by kinks in the course of the height. For example, re18

2018200145 23 Aug 2019 gression functions are calculated (e.g. linear regression line) between the inclination changes (constant slope or gradient). Other regression functions can also be used. The method is described by way of example below based on linear regression lines. In order to determine the position of the inclination changes more precisely, first the height image 15 is filtered with a digital filter so that the shortwave components are filtered away (up to 50 m wavelength for example). This results in a smooth height profile 17. This filtered height profile 17 is numerically differentiated twice. Due to the double differentiation, the inclination changes produce a clear peak that is easy to detect. The maximum value (maximum slope in the center of inclination change) indicates the position of the inclination change.

From the position of the inclination changes NW thus determined, the points NWa and NWe lying on the regression lines are determined left and right at a distance of radii of curvature (length typically 6 m). These points are then connected by cubic splines 18, for example. The boundary conditions for these cubic splines 18 are tangents of the regression line at the points NWa and NWe and the points NWa and NWe themselves. As a result, a target longitudinal height image Hs is obtained. The chord L, a, b of the permanent-way machine is then moved numerically along the curve on the target longitudinal height image Hs this then provides as a result the target longitudinal heights fi_. The deviations between the target and the actual longitudinal height image provide the correction values for the height Δζ.

The lower diagram shows how Δζ lift values are determined from the deviations. The permanent-way machine can only perform lifting and no settlements (negative sign of the correction values) 20. Therefore, in the region of the linear regression line, the largest negative correction |H| is determined. This value is added to all determined correction values. The result is a new zero line Nl. Thus, all correction values H l become positive and can be carried out by the permanent-way machine. If the thus determined lifting correction values (25) exceed the maximum permissible lifting Hmax, then the range of exceeding is simply limited to the maximum lifting value (hatched area).

Claims

1. A method for optimizing a track position and for guiding a track-mounted track construction machine after a measuring drive with a track-mounted track measuring carriage, having at least two wheel axles supported on a machine frame, a navigation unit, a device for pressing the wheels to the rail and an odometer for measuring an arc length of the rail, wherein first a measuring drive is carried out with a track-mounted track measuring carriage which is equipped with an inertial navigation unit, the wheels of which are pressed against the rails, wherein the arc length is measured with the odometer, the angular position of the inertial navigation unit is measured and stored relative to a Cartesian reference coordinate system, and wherein after the measuring drive coordinate points of the track of the navigation unit are calculated in space from the stored angular positions by means of compensation calculation and from the thus optimized coordinate points of the track a locus image is formed by zeroing the z-components and a longitudinal section by zeroing the x-components, after which a curve determined by means of mathematical connection functions is laid through the coordinate points.

2. A method according to claim 1, wherein higher-order regression functions are placed through the coordinate points and the adjoining regression functions within a range are connected with a higher-order mathematical connection function in such a way in that this mathematical connection function passes through the end points of the regression functions and their end tangents, after which a target locus curve is fitted at boundary-condition-forming constraints by superimposition of an angle correction and boundary-condition-forming positions of constraint at the beginning and end are fitted by means of higher-order mathematical connection functions over a transition length.

2018200145 23 Aug 2019

3. A method according to claim 1 or 2, wherein tolerances are specified for boundary-condition-forming positions of constraint and constraints.

4. A method according to any one of claims 1 to 3, wherein inclination changes are determined in the longitudinal section, namely the height image, and regression functions are calculated for sections between the inclination changes, wherein for a target height curve the inclination change transitions are formed by mathematical transition functions, and wherein, in order for the lifting corrections to be positively definite, the entire correction line is raised by the largest value of the setting or the absolute value is added thereto, wherein values which exceed the maximum permissible lift value are cut off and not executed.

5. A method according to any one of claims 1 to 4, wherein a working chord of a permanent-way machine is mathematically moved over a target locus curve and a target height profile and thereby a target arrow height is calculated for the direction and a target longitudinal height, wherein the differences between the target locus curve and the actual locus curve yield the correction values for the direction and the differences between the target height profile and the actual height profile yield the corrections for the lifting, whereby the control signals required for controlling the permanent-way machine according to a 3-point precision method are transferred to the control system of the permanent-way machine.

6. A method according to any one of claims 1 to 5, wherein the analytical mathematical representation of a target locus curve is differentiated twice and wherein the resulting curvature depending on the arc length as a conventional curvature image and the target height is also differentiated twice and is displayed as a height curvature image depending on the arc length.

2018200145 23 Aug 2019

7. A method according to any one of claims 1 to 6, wherein a track measuring carriage with inertial navigation system or inertial measuring system is pulled behind the permanent-way machine and the track position errors the superelevation error and the gauge error are recorded in an acceptance record as remaining residual error after work.

8. Device for optimizing a track position and for guiding a track-mounted track construction machine with a track-mounted track measuring carriage having at least two wheel axles supported on a machine frame, a navigation unit, a device for pressing the wheels to a track with two rails and an odometer for measuring an arc length of the rail, wherein the track measuring carriage, in the region of opposite longitudinal sides, comprises at least two wheel groups having wheels which are each associated with rails and which are mutually rotatably mounted about a track measuring carriage transverse axis, wherein the track measuring carriage is equipped with an inertial navigation unit, a device for pressing the wheels to the rail and an odometer for measuring an arc length of the rail, and wherein the device for pressing the wheels to the rail comprises an actuating drive with which the wheel groups are displaceable in the direction of the track measuring carriage transverse axis for pressing wheel rims of the wheels to inner flanks of the rail heads.

9. A device according to claim 8, wherein a sensor associated with the track measuring carriage transverse axis is provided for measuring the track width.