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Horizontal and vertical positions of points for the control assessment of crane rails are classically determined separately. The procedure is time consuming and causes non-homogenous accuracy of the horizontal and vertical position of control points. The proposed alternative approach is based on polar measurements using a high accuracy total station instrument and a special platform with two precise surveying prisms fixed on it. Measurements are carried out from a single station thus ensuring a common coordinate system and homogenous accuracy. The position of the characteristic point of a rail is derived from the measured positions of both prisms with known geometry of the platform. The influence of platform non-horizontality is defined, along with its elimination procedure. Accuracy assessment is ensured with redundant measurements. Result of the proposed procedure is a numerical and graphical presentation of characteristic points. The control parameters required in international Eurocode standards are easily determined from them.

In order to ensure safe operation of bridge cranes it is necessary to control the adequacy of crane rails. According to Eurocode 3 standards [

Some alternative methods provided for specific tasks have been published. Kyrinovič and Kopáčik in [

The proposed approach provides simultaneous determination of horizontal and vertical positions of rails from a single instrument station. It is based on the polar surveying method. A precise total station is used along with a special L-shaped platform. Two precise measuring prisms are attached to the platform. We place the platform on the rail at the desired profile points.

The measured polar coordinates are transformed into the Cartesian coordinate system, while the coordinate system is chosen in such a way as to be aligned with the rails. The local Cartesian right-handed coordinate system is used. The obtained coordinates represent a relative relation between the rails.

The proposed approach is better than the classical methods due to its cability for faster measurement of profile points. Higher density of points can be achieved with no effort. Using redundant measurements the precision of the measurements as well as the precision of the results can be assessed. The method ensures homogenous position accuracy of point determination in terms of both horizontal and vertical position. Despite the large number of measurements, the proposed method is still faster and more economical than the conventional approach.

The national standard for crane rails from the Eurocode 3 standards [

The span between rails;

The elevation difference between rails in each profile.

The actual span can deviate from the projected one by a maximum of 10 mm. The maximum elevation difference must not exceed the value determined by equation. Δ_{max}= s/600

The crane rail is measured using a classical polar surveying method for detail points. Characteristic points are determined indirectly by measuring the position of the “L” platform. According to the required precision and the principles of the method, the proposed approach may be used if two conditions are met:

A total station providing adequate basic measurement precision of at least 1 mm must be used.

A target point can be unambiguously signalized in a way that ensures sub millimeter accuracy of centering.

The homogeneity of the measurement precision is maintained by measuring all points from a single instrument station. The instrument must be set in a stable position which enables the visibility of all desired detail points of the rail.

According to the required measurement precision derived from standard [

Cartesian coordinates of a single detail point are calculated from the measured polar coordinates (

Using error propagation law, the precision of coordinate determination can be calculated according to the measurements precisions:

Matrix

We are mainly interested in differences between coordinates. The rail span is the difference between the

When we try to use the inversed error propagation law in

According to the desired coordinate difference precisions, we calculate the required precisions of measurements. They are represented in

Simulation results (

A special platform (

The position of the characteristical point, representing the upper inner edge of the rail, can be derived from the measured positions of both precise prisms. Accurate dimensions of the platform need to be known,

Each setting of the platform onto a crane rail provides us with two prism center points. We want to represent each setting with one characteristical point. The position of a characteristic point is shown in

Indexes 1 and 2 will hereafter represent the upper (5) and the side (6) prism, respectively. Two computation modes provide us the control and accuracy evaluation of the characteristical point. For such computation parameters, _{1}, _{1}, _{2}, _{2} defining the geometry of the platform have to be known. Using an indirect approach we determined the values for all four parameters: _{1} = 58.94 mm, _{1} = 110.89 mm, _{2} = 110.52 mm and _{2} = 15.39 mm. The accuracy of parameter determination is in the order of a tenth of a millimeter. Hereafter they can be assumed to be exact.

The influence of the non-horizontality of the platform on the determination of prism position was investigated. We propose a computation procedure which minimizes the influence of non-horizontality to the largest possible extent. In order to achieve maximal accuracy, the circular level fixed on the edge of the platform has to be rectified before each use. However, due to limited precision of the circular level, errors of non-horizontality will still appear in the measurements. Effects of non-horizontality should be excluded from the procedure to the greatest extent possible. Rotation of the platform around the given point displaces the upper prism in horizontal direction by:

The side prism moves contrary in the horizontal direction by:

_{1} = 0.3673 mm, _{1} = 0.0005 mm, _{2} = 0.0007 mm and _{2} = 0.4929 mm.

In general the rotation point is not the intersection of lines through prism centers. The actual rotation point is the point where the platform leans on the rail. This point is not defined due to imperfections of the rail shape. However, values of _{1} and _{2} are negligible even for greater rotation angles according to the size of the platform. On the other hand, values of _{2} and _{1} are noticeable despite the low inclination of the platform and they should not be neglected. To conclude, the vertical component of the position is well defined for the upper prism and the horizontal component is well defined for the side prism. Therefore, to determine the characteristic point

The proposed method was tested practically in November 2011. The task was to determine the geometry of the crane rail in one of the industrial buildings of the Brestanica thermal power plant (TEB).

To measure the geometry of the crane rails we used a uniform method for determining the positions of the rails in the horizontal and vertical sense. The characteristic points of the crane rail were determined indirectly by measuring the position of the prisms on the “L” platform. We used the classical polar method of surveying, in which we measure the horizontal direction, zenith angle and slope distance to the point. All points were measured from a single station of the instrument. This provides a unique coordinate system for all measured points.

We used the Leica Geosystems TS30 total station, with the technical characteristics given in

The instrument was stabilized with a tripod on a stationary crane. The platform was set on the rail every 1.4 m and put in a horizontal position using the circular level. The prisms were pointed towards the instrument.

The positions of both prisms were measured twice using the ATR function, which provides homogenous sighting precision for each measuring point on the rail. The platform was placed on each rail 38 times. For each stabilization of the platform each prism was measured twice. As a result we got 304 measured points with the polar coordinates [

The results of the polar surveying method (_{ijkl}_{ijkl}_{ijkl}

For the presentation of the positions of characteristical points on each rail we chose a rectangular Cartesian coordinate system with the following properties:

the coordinate system unit is the meter,

the

the

the

the origin of the coordinate system is arbitrary, but provides the coordinates of all points to be both positive and less than 100.

The computation of point coordinates in the chosen coordinate system can be achieved using the following steps:

The transformation of points from polar to Cartesian coordinates in the local coordinate system of the instrument can be performed using

The _{L}_{L}

Azimuth angle for each set is computed from slope coefficient

The value of orientational direction

The coordinates of the measured points in the chosen local coordinate system were computed in the same way as in the first step. The only difference was that orientational directions were subtracted from all horizontal directions and that the coordinate system origin was translated 10 meters to the left (the

Twofold measurements of each prism are averaged. Measurement control has already been performed during the computation of the coordinates in the local coordinate system. The results are Cartesian coordinates of all the measured prisms in the desired coordinate system.

According to _{1}_{t}_{1}_{t}_{1}, _{t}_{1}] and _{1}_{t}_{2}_{t}_{2}, _{t}_{2}]. The positional difference between them is computed as:

According to differences _{δt}

Given the coordinates of the prism centres and the constants of the platform, the coordinates of the characteristic points for each position of the platform are computed using _{δ}

We assume that the differences between the computed values of the coordinates of characteristical point from both prisms on the platform are small enough. The definite values of coordinates are computed from

The precision estimation of the characteristical points follows from the precision of the measured prism centres (_{1}, _{2}, _{1}, and _{2}. Based on the error propagation law (propagation of variances and covariances) using

It can be noted that the measurement precision is very high. The standard deviations of all three coordinates are far below 1 mm. These values are comparable with the precision of orthogonal measuring method and the method of geometrical levelling.

All characteristic points of rails were divided into two groups, each representing its own rail. For each rail we have 38 points. Although the position of points (

In the horizontal sense we control the parallelism of the crane rails. In the chosen coordinate system it means a difference of the

A possible way of representing the result of surveying in the horizontal sense is shown in

It is evident that the deviations are within the tolerances prescribed by the standard (10 mm). Results can be represented graphically as shown in

In the vertical sense it is appropriate to represent the vertical deviation of the rail from its reference horizontal line. The reference horizontal line belongs to an average height of all characteristical points of both rails. In

It is evident that the height differences between the left and the right rail are within the tolerances prescribed by the standard (). (Δ_{max} = 32.2mm) Results can be represented graphically as shown in

The described method simplifies the process of control measurements of crane rails. It also allows the accuracy assessment from redundant measurements, which was not possible in the conventional way. The method is significantly faster than the classical method. Instead of using two theodolite stations, providing connectivity between both stations, and the use of geometrical levelling, the proposed method allows us to do all measurements from one station with the use of just one instrument (one surveying method). A particular requirement of the method is the use of precise instruments and a calibrated platform with two precise prisms, which allows redundant identification of target points with high precision. The method is based on the simultaneous determination of points in the horizontal and vertical sense that ensures homogeneous precision. The method allows us to obtain data on the exact position of profiles, which ensures detailed modeling of the rail. Knowing the longitudinal position of the characteristical points allows us to perform a Fast Fourier Transformation (FFT) of the data, which provides a deeper insight into the deformation of the rails.

The authors would like to thank the management of TEB–Brestanica power stations, who allowed measurements and publication of results.

European Standard EN 1993–6: 2004. Eurocode 3: Design of Steel Structures–6. Part: Crane rails.

“L” platform for point signalization and its constants.

Left: stabilization of instrument; right: stabilization of the “L” platform on the rail.

Schematic illustration of measurements.

Graphical representation of deviations in horizontal sense (red—left rail, blue—right rail).

Graphical representation of deviations in vertical sense (red—left rail, blue—right rail).

Calculation of the required measurement precisions for the cases of two profiles (in the beginning and at the end of rail).

| ||||
---|---|---|---|---|

in the beginning of the rail | at the end of the rail | |||

T_{left} |
T_{right} |
T_{left} |
T_{right} | |

horizontal direction | 209° | 359° | 292° | 315° |

zenith distance | 129° | 115° | 104° | 103° |

slope distance | 7 m | 13 m | 53 m | 55 m |

_{s} |
53.4″ | 14.6″ | 3.5″ | 3.4″ |

_{z} |
62.5″ | 20.6″ | 3.4″ | 3.4″ |

_{d} |
1.8 mm | 1.3 mm | 0.9 mm | 0.9 mm |

Main technical characteristics of the Leica Geosystems TS30 total station.

operation interval | −20 ^{°}C to +50 ^{°}C |

resolution of electronic level | 2″ |

minimum distance | 1.7 m |

standard deviation _{iso−THEO} |
0.5″ |

precision of system ATR _{iso−THEO} |
1″ or 1 mm |

reference conditions: _{0}, _{0}, _{0} |
1.0002863, 1013.25 hPa, 12 °C |

range | 3.5 km /1 prism, 5.4 km /3 prisms |

standard deviation _{iso−EDM} |
0.6 mm; 1 ppm |

Statistics of differences between two repeated measurements.

0.033 | 0.002 | 0.016 | |

_{δt} |
0.22 | 0.17 | 0.10 |

max|_{t}| |
1.00 | 0.86 | 0.49 |

Precision parameters of the coordinates of characteristical points.

0.33 | 0.00 | |

_{δ} |
0.37 | 0.55 |

max| |
1.00 | 1.76 |

Representation of numerical results in horizontal sense.

1 | 0.4 | 19.2000 | 0.5 |

2 | 3.0 | 19.1963 | –0.7 |

3 | 0.7 | 19.1976 | –1.7 |

4 | –0.1 | 19.1981 | –1.9 |

5 | –1.2 | 19.1978 | –3.4 |

⋮ | ⋮ | ⋮ | ⋮ |

| |||

3.0 | 6.3 mm | 4.3 | |

–3.6 | –3.7 mm | –3.4 |

Representation of numerical results of surveying in vertical direction.

1 | 12.7 | 5.0 | 7.7 |

2 | 10.0 | 3.0 | 7.0 |

3 | 7.5 | 1.3 | 6.2 |

4 | 5.6 | 1.2 | 4.4 |

5 | 4.8 | 1.9 | 2.9 |

⋮ | ⋮ | ⋮ | ⋮ |

| |||

12.7 | 9.0 | 7.7 | |

–4.5 | –1.7 | –0.8 |