| The spindle,a critical functional component of machining centers,undergoes reliability bench testing,a primary means for acquiring spindle failure data and analyzing spindle failure mechanisms to enhance the overall reliability of the machining center.The load spectrum is a prerequisite for conducting reliability bench tests on spindle components.Therefore,investigating methods for compiling spindle load spectra holds significant importance.Challenges arise in selecting typical working conditions to ensure the authenticity and effectiveness of load spectrum data sources.The impact loads during tool Cutting in and out stages can accumulate spindle damage more easily,making it a crucial factor in load spectrum compilation.Traditional time-domain extrapolation methods cannot accurately identify large cycle loads in the load-time history and neglect interactions between different directions and types of loads during the extrapolation process,leading to distorted results.To address these issues,this paper systematically explores methods for compiling dynamic loads considering the characteristics of different cutting stages.A multi-criteria decision-making mixed model is proposed for selecting typical working conditions.The paper analyzes and reconstructs non-stationary dynamic loads during tool Cutting in and out stages in the time-frequency domain.For steady-state machining stages,a stable cutting phase load time-domain extrapolation method based on the Time Series Rainflow Load Cycle(TSRLC)is employed,incorporating load extreme value extrapolation.A distribution model for equivalent load amplitude and torque mean is established,resulting in the compilation of the spindle dynamic random loading spectrum.The main research contributions are as follows:(1)Proposal of a method for selecting typical working conditions based on a multi-criteria decision-making mixed model.This involves establishing a dynamic load model based on characteristic features of a large amount of process data,using empirical formulas,creating a frequency distribution chart of equivalent loads according to the time proportion of each working condition,constructing a mixed distribution model,and applying a multi-criteria decision-making technique to optimize the model combination.Ultimately,12 milling,9 drilling,and 9 boring processes are selected as typical working conditions for numerical control machining centers.(2)Proposal of a Cutting in and out stage load spectrum editing method based on Time-Frequency Domain Mixing(TFDM).This involves segmenting the load signal into cutting-in,stable cutting,and cutting-out stages using Mann-Kendall(M-K)and Spearman’s-Rho(S-R)trend tests.A TFDM-based editing method is proposed to address the limitations of traditional methods,ensuring that the load spectrum applied to spindle durability tests accurately reproduces the working load characteristics of critical components.A universal load model describing the frequency characteristics of milling,drilling,and boring processes is established.The feasibility of the bench test and the specific characteristics of the load(load frequency analysis model)are considered,reconstructing the loads for the Cutting in and out stages and providing a theoretical basis for compiling the load spectrum.(3)Proposal of a time-domain extrapolation method for stable cutting stages based on TSRLC.Traditional extreme value extrapolation methods such as Load Extrapolation in Rainflow Domain(LERD)and Load Extremes Time Domain(LETD)suffer from limitations,including loss of time-domain information and inaccurate identification of large load cycles,leading to distorted extrapolation results.A TSRLC-based multi-axis dynamic load time-domain extrapolation method is proposed to overcome these limitations,considering the interaction between multipleaxis loads and their impact on life.(4)Proposal of a dual-component mixed distribution function modeling method based on Linear Moment Ratio Diagram(L-MRD)for load frequency extrapolation.Given the variety of cutting load types and the challenges in rapidly and accurately selecting the most suitable mixed model,a modeling method based on L-MRD for dual-component mixed distribution functions is proposed to achieve quick modeling and load frequency extrapolation.Taking into account the randomness of load frequency distribution for milling,drilling,and boring load spectra,a random extraction is performed using the mixed congruence method to establish the spindle random program load spectrum.This research presents a load spectrum compiling method of bachining center spindle reliability test considering cutting in and out dynamic load in machining centers,providing technical support for subsequent spindle system reliability testing. |