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The reliability data from the front driven axle of a four-wheel drive tractor exhibits a multi-peak distribution because of the complex field environment. The aim of this study was to establish an accurate statistical model for the dynamic stress spectrum with mixed distributions. Using rain-flow counting, the stress-time history of the tractor was transformed into the rain-flow matrix with two parameters. The mean and range of the stress data in the rain-flow domain was modelled with the mixed Gaussian and Weibull distributions, respectively. The identification of unknown parameters is an important and here a novel parameter identification method that adopts a genetic algorithm (GA) for rapid searching was proposed with the generalised reduced gradient (GRG) method was applied for accurate identification. The results of finite element analysis (FEA) provide reference for the selection of the measured points. To obtain the dynamic strain signal, a real-time test system was built and a field experiment was carried out. The calculation and evaluation results confirmed that this approach precisely estimated parameters and established a highly accurate mixed model. For the mixed Gaussian and Weibull distributions, the determination coefficients R2 exceed 0.98 and the maximum KS test values were not more than 0.2. Furthermore, this study provided accurate model parameters to determine the stress spectrum for the full-life cycle for use in future research.

The fatigue load spectrum is one of the most important parts in accelerated durability testing of agricultural machinery; however, the traditional editing approach just focuses on influence of load amplitude on mechanical components, which is not suitable for the agricultural machinery, the loads of which are broad in frequency bandwidth and time-varying in stress amplitude. Therefore, considering the comprehensive influence of load amplitude and frequency on the fatigue life of materials, a power-density-based fatigue load spectrum editing (PD-LSD) approach for accelerated durability testing is proposed ensuring that fatigue load spectrum for accelerated durability testing of tractor components can reproduce operation load characteristics of components. The concept of power density is introduced, and a fatigue analysis method based on power density and short-time Fourier transform (STFT) is discussed. For the approach of this study, STFT and stress-life (S–N) curve were used to derive accumulative power density (AccPD) of the load signal. The AccPD identified and extracted high fatigue damage segments of original load signal and obtained reduced accelerated load spectrum of components. Based on the load signal of the 88-kW tractor front axle, this approach and the time damage editing approach were applied to edit the load signal. The results show that, the accelerated load Signal Ⅰ based on the PD-LSD approach with a shorter length of time contained almost same damage of the original load signal, and the statistical parameters (mean value, root mean square and kurtosis coefficient) and the signal amplitude domain of the accelerated load Signal Ⅰ were more consistent with the original load signal, which verifies the acceleration, accuracy and effectiveness of the approach. This research supports fatigue testing and durability analysis for a key component of agricultural machinery.

Vibration cementing is a new technique that can significantly improve the bond strength of cementing interface. To popularize this technique, it is necessary to solve the key problem of how to make cementing string generate downhole radial vibration in the WOC stage. For this purpose, an electric vibrator was developed. With this vibrator, electric energy is converted into mechanical energy by means of a high-temperature motor vibration unit. The motor vibration unit rotates the eccentric block through an output shaft to generate an exciting source, which produces an axial-rotating exciting force at the bottom of the casing string. Then, the vibration characteristics of vertical well casing string under the exciting force were analyzed by using the principal coordinate analysis method, and the response model of casing string to an electric vibrator was developed. Finally, the effects of casing string length, exciting force and vibration frequency on the vibration amplitude at the lowermost of the casing string were analyzed based on a certain casing program. It is indicated that the casing string length and the square of vibration frequency are inversely proportional to the vibration amplitude at the lowermost of the casing string, and the exciting force is proportional to the vibration amplitude at the lowermost of the casing string. These research results provide a theoretical support for the application of vibration cementing technology to the cementing sites with different requirements on well depth and amplitude.