# A Simplified Methodology to Evaluate the Design Specifications of Hydraulic Components
## 2 Pressure: Load History and Damage Factor  
Our main example for measuring time-load history and then performing statistical analysis is a front loader. In practice, a long-term load spectrum contains complete load information, but this is difficult to directly measure due to the restrictions of testing technology, as well as time and cost. Therefore, obtaining long-term load spectrum information based on short-term data was necessary. Until now, engineers have used traditional methods to obtain long-term load spectrum data, basically consisting of multiplying a short-term load spectrum by a constant proportionality coefficient. The disadvantages of traditional methods are that only the data measured in a finite time are repeated, extreme loads cannot be measured, and their impact on damage is ignored. Load extrapolation methods can overcome the above limitations. With the development of statistics and computer software, although difficult, it is possible to apply load extrapolation methods. [PERSON] et al. [9] provided a selection guidance and several load extrapolation methods that can be applied. In this paper, an approach inspired by traditional methods is presented to overcome these challenges, consisting of (i) evaluating the damage produced in the hydraulic component for each short-term spectra (damage factor); (ii) considering each short-term spectra and its damage index as statistical samples of the total damage produced by complete load information; and (iii) the laboratory specifications are estimated from the damage factors of different machine tasks, which produce the same damage the component suffers during its lifespan. For illustrative purposes, two front loader tasks were considered: loading and transport. Pressure histories (traces) for all hydraulic cylinders can be obtained by pressure transducers installed in cylinder's ports. Current design methods use cycle counting in order to interpret the varying pressure range of the varying loads. The following two methods are the most commonly applied methods in the field of fatigue studies: reservoir and rain-flow. In our case, the obtained data (pressure vs. time) from every pressure trace were treated with the reservoir cycle counting method recommended in EN 13445-3 standard--Unfired pressure vessels Part 3: Design [10]. Also, this algorithm was standardised according to ASTM E 1049-85, Cycle Counting in Fatigue Analysis [8]. Once the cycles were identified, the damage for all the cycles in the loading history were combined to obtain the damage for the entire loading history. A number of deterministic damage accumulation models have been developed since the late 1990, that can be mainly classified into two categories: linear damage cumulative theories [11] and nonlinear damage cumulative theories [12]. The first models have some shortcomings: (i) they fail to consider load history; (ii) cumulative damage has no relationship with load sequence effects; and (iii) effects of load interaction are not taken into account. Therefore, to address the above-mentioned disadvantages, nonlinear cumulative damage theories were suggested, which were classified into six groups by [PERSON] [13]. Although we are aware that the linear method of mining is non-conservative, it was used because Miner's rule [14] is probably the simplest and conceptual cumulative damage model that can be used to didactically explain our approach. Miner's rule states that if there are \(q\) different pressure levels (with linear damage hypothesis), the fraction of life consumed (damage) \(D\) by exposure to the cycles at the different pressure levels is  
\[\sum_{i=1}^{q}\frac{n_{i}}{N_{i}}=D \tag{1}\]  
where \(n_{i}\) is the number of cycles accumulated at pressure \(P_{i}\) and \(N_{i}\) is the number of cycles to failure at pressure \(P_{i}\). Fatigue damage for an individual cycle is the reciprocal of the fatigue life, \(N_{i}\) Fatigue lives for a cycle are computed using constant amplitude methods with the appropriate pressure or stress ranges, mean stresses, and material properties.