doi: 10.1111/j.1460-2695.2008.01221.x Load spectra analysis and reconstruction for hydraulic pump components M. CARBONI 1 , A. CERRINI 1 , P. JOHANNESSON 2 , M. GUIDETTI 3 and S. BERETTA 1 1 Department of Mechanical Engineering, Politecnico di Milano, Via La Masa 34, I-20156 Milano, Italy, 2 Fraunhofer-Chalmers Institute for Industrial Mathematics, Chalmers Science Park SE-412 88, G¨ oteborg, Sweden and 3 Casappa SpA, Via Balestrieri 1, I-43044 Cavalli di Collecchio (PR), Italy Received in final form 27 June 2007 ABSTRACT Hydraulic pumps are used as operating components in many mechanical systems (e.g. actuators in machines for moving materials) and, consequently, during their work- ing life they are subjected to variable amplitude loadings. As this is the case, a thorough analysis of their load histories may be highly useful as it would help to determine an equivalent constant amplitude signal which could be easily applied to a test bench for the homologation of pumps. In the present paper, a novel methodology for the analysis of hydraulic pumps is suggested. The proposed methodology accounts for the different dam- aging processes of fixed and rotating parts of hydraulic pumps and applies both statistics of extreme values and the analysis of signals in the Markov domain. The results consist of block loadings, to be applied at the test bench, which represent extrapolated experimental signals measured on pumps during their service in different applications. Keywords extreme values; fatigue; hydraulic pumps; load spectra; Markov chains. INTRODUCTION Hydraulic pumps are components adopted in several mechanical systems: typically, they supply power to the linear and rotating actuators in agricultural machines or machines for moving materials. Due to their particu- lar working cycles, in which stationary phases alternate with loading and unloading movement phases, hydraulic pumps undergo pressure which varies over time. The availability of pressure signals which are representative of a pump’s normal activity and acquired during a pump’s working lifetime along with the analysis of these signals is therefore very important for the homologation and veri- fication of products and prototypes. In generic mechanical components, measurements can be carried out following one (or both) of the two dis- tinct approaches: (i) the time domain, where the acquired signals are temporal sequences of signal levels, each com- bined with other relevant instantaneous quantities of in- terest and (ii) the Markov domain, where the acquired signal is stored in a 2D Markov matrix 1 defined as the collection of all the observed transitions from a ‘max’ to ‘min’ level and from a ‘min’ to ‘max’ level together with Correspondence: M. Carboni. E-mail: michele.carboni@polimi.it the relative number of cycles. The latter approach has the advantage of producing a more compact, space-saving output, but it also has the disadvantage of losing the time sequence of the signal levels. This means that if only time histories are acquired during service, the Markov matrix can be built from them during a post-processing stage, but if only Markov matrixes are collected, the original ac- quired time signal is lost and cannot be reconstructed in exactly the same way. Although the approaches produce outputs with differing available information, both permit further elaboration of the signals that could be utilized to better design the me- chanical components. For example, statistics of extreme values 2,3 can be applied, in acquired time histories, in or- der to extrapolate load histories for working times longer than the acquisition time (see 4 ). On the other hand, for acquired or derived Markov matrices, the Markov chain statistical process 1 allows simulated load time histories (equivalent, from the statistical point of view, to the orig- inal experimental ones, with the advantage of having the possibility to apply opportune elaborations to the matrixes in order to get simulated load time histories with specific characteristics) to be calculated. The present study analyses and elaborates the pressure time histories registered during the working time of the pumps with an aim to determine an equivalent damaging c  2008 The Authors. Journal compilation c  2008 Blackwell Publishing Ltd. Fatigue Fract Engng Mater Struct 31, 251–261 251 Fatigue & Fracture of Engineering Materials & Structures