Processing of stress dataset with rain-flow counting method

In this contribution we are dealing with application of rain-flow method to processing the experimental stress data. Vibration of agricultural plough on duty was measured by sensor of acceleration ADXL345 Inertial Sensor mounted on the Pottinger Plough frame. Measured acceleration data was transformed to the stress on the frame. The mathematical algorithm of rain-flow method was based on the recommendation of ASTM code. The simple mathematical model was developed and the algorithm was implemented to the environment of PTC® Mathcad Prime® 4. Processing of experimental data was realized with MicrosoftTM Excel® format table importing to the Mathcad Prime® software. The results from raw data and filtered data were compared.


INTRODUCTION
In many application of constructions life analysis were used the strain gauges to measure the stress in the materials under the random loading.The measurement is complicated because the gauges must be glued to the whole construction in the certain points and directions.Data recording and processing must be provided with the very wide skills [10].The time-domain approach was defined by [1,2] in which the response time history is calculated by static stress analysis by superimposing all stress influences from the applied loads at each time step, lacks the dynamics of the structure especially for vibration-based problems when a loading excites the natural frequencies of the structure.The use of strain gauges is possible for limited locations only and moreover requires early knowledge of critical fatigue locations.On the other hand, using the sensors of acceleration is very useful in measurement of vibrations of beams, where the beams are the components of the framed structures.Mathematical definition of Rain Flow Cycle (RFC) was first time defined by [8].The method presented by [8] attaches to each maximum of the strain function the amplitude of a corresponding cycle or two half cycles, which are evaluated independently from each other.
Algorithm of RFC was analyzed by [3,9].Practical application of RFC in fatigue life prediction was published by many authors.We can include to major works [4,5,6,7].

Measurement system and object
Object for measurement was a plough Pottinger depicted on Figure 1.The basic parameters of plough are listed in the Table 1 [11].Measurement on plough was realized on deep plow.The plowed ground was planar without rough parts.The plough was mounted on tractor Fendt Vario 930.

Mathematical model
As mentioned below, the measured vibration data were transformed to the stress data set.For the transformation we designed the simple mathematical model based on the theory of cantilever beam design theory.We substituted the real plough with model as depicted on Figure 4.For utilizing the designed model we set up the basic assumption as follows: • three-point linkage stiffness is similar as a fixed connection of the cantilever beam, • for bending moment is used the effective length of plough, • plough support wheel damping is contained in the acceleration data, • used loading is the weight of the plough, • neutral axis of the beam lay to the beam axis of symmetry, • neglecting the shear deformation.( ) . .
For purpose of processing the experimental data we transformed acceleration dataset to the stress data set.Finally we get a formula for stress of beam with Equation 3. . .
We processed the raw accelerations data set and filtered data set.Stress dataset from raw data is depicted on Figure 5.The raw accelerations data was filtered with Butterworth maximally flat magnitude filter (see Equations 4).The transformed data from filtered dataset is depicted on Figure 6.

Rain flow counting cycle (RFC)
For processing the transformed data we used the Mathcad Prime® 4 software.Rain flow counting method is used to decomposition of the load signal.The load signal is represented by maxims and minima.Increasing and decreasing parts are counted as half cycles.Initial and final extreme do not have to follow behind, other half cycles can run between them.The name of the method is based on the idea, that after recording the load drops of water flow and drain as from the roof.Our algorithm is based on the [3,5] descriptions.For method we set up basic rules for half cycle identification with respect the Figure 7, as follows: 1) In every local extreme begins a half cycle, 2) half cycle ends if the edge of the outermost roof is reached(1-4, 2-3, 4-5, 5-8, 6-7), 3) half cycle ends if the drop strikes the dripping drop from the higher roof (3-4, 7-8).

RESULTS AND DISCUSSION
Applying the RFC to the raw and filtered data we get the significant results about the both datasets.The values are solved by Equations 5, 6.For the raw data we set the results to the Table 2. Tables 2 and 3

CONCLUSIONS
In this paper we are dealing with stress data processing by rain-flow counting algorithm.Data was obtained from experimental measurement of vibration of plough beam.The accelerations were converted to the stress time series.For signal processing we used the Butterworth maximally flat magnitude filter.In software Mathcad Prime 4 we designed the algorithm for establishing the relevant stress dataset by rain-flow counting algorithm.We processed the raw and filtered data.Result of RFC is rain-flow histogram matrix.From analysis we get the result that the raw data gives more irrelevant range of values than filtered data.The distribution of filtered data is more evenly distributed.

M
-bending moment of the plough beam, P m -plough mass, ( ) i ac -measured acceleration array, ef L -effective length of plough 6m = .

Figure 5 Figure 6
Figure 5 Stress from raw data

Figure 7 8
Figure 7 Rain flow method, where B σ is stress directly correspond with Figures 9, 10.Bin in the Tables 2, 3 means interval width of histogram.

Figure 8
Figure 8 Flowchart of RFC

Figure 9
Figure 9 Stress raw data amplitudes and means layout

Figure 10
Figure 10 Stress filtered data amplitudes and means layout

Figure 11
Figure 11 Rain-flow matrix histogram from raw data Figure 12 Rain-flow matrix histogram from filtered data

Table 2
Results from rain-flow matrix histogram from raw data

Table 3
Results from rain-flow matrix histogram from filtered data