The machining accuracy of CNC machine tools is significantly affected by the thermal deformation of the feed system. The ball screw feed system is extensively used as a transmission component in precise CNC machine tools, responsible for converting rotational motion into linear motion or converting torque into repetitive axial force. This study presents a multi-physical coupling analysis model for the ball screw feed system, considering internal thermal generation, intending to reduce the influence of screw-induced thermal deformation on machining accuracy. This model utilizes the Fourier thermal conduction law and the principle of energy conservation. By performing calculations, the thermal source and thermal transfer coefficient of the ball screw feed system are determined. Moreover, the thermal characteristics of the ball screw feed system are effectively analyzed through the utilization of finite element analysis. To validate the proposed analysis model for the ball screw feed system, a dedicated test platform is designed and constructed specifically to investigate the thermal characteristics of the ball screw feed system in CNC machine tools. By selecting specific CNC machine tools as the subjects of investigation, a comprehensive study is conducted on the thermal characteristics of the ball screw feed system. The analysis entails evaluating parameters like temperature field distribution, thermal deformation, thermal stress, and thermal equilibrium state of the ball screw feed system. By comparing the simulation results from the analysis model with the experimental test results, the study yields the following findings: The maximum absolute error between the simulated and experimental temperatures at each measuring point of the feed system components is 2.4◦C, with a maximum relative error of 8.7%. The maximum absolute error between the simulated and experimental temperatures at the measuring point on the lead screw is 2.0◦C, with a maximum relative error of 6.8%. The thermal characteristics obtained from the steady-state thermal analysis model of the feed system exhibit a prominent level of agreement with the experimental results. The research outcomes presented in this paper provide valuable insights for the development of ball screw feed systems and offer guidance for the thermal design of machine tools.

The paper deals with bifurcation and/or non-bifurcation post-buckling curves of composite plates under biaxial compression. For different lay-up sequences, a coupling, i.e. extension-bending (EB) is considered. The current investigations present distinct equilibrium paths describing when they have bifurcation-type and/or non-bifurcation-type responses. The novel parameter (i.e. EB coupling imperfection) is calculated to show the amount of non-bifurcation in the equilibrium path as a quantitative parameter. For the case of non-square plates, a novel mixed-mode analysis is conducted. The effects of different characters in laminated composites such as layer arrangement, loading ratio, aspect ratio, and boundary conditions are investigated. A novel result concluded in the numerical examples where there are some possibilities to have different mode shapes in linear and non-linear buckling analysis. FEM results of ANSYS software verify the results of analytical equations.

This paper aims to develop new highly efficient PSC-algorithms (algorithms that contain a polynomial-time sub-algorithm with sufficient conditions for the optimality of the solutions obtained) for several interrelated problems involving identical parallel machine scheduling. These problems share common basic theoretical positions and common principles of their solving. Two main intractable scheduling problems are considered: (“Minimization of the total tardiness of jobs on parallel machines with machine release times and a common due date” (TTPR) and “Minimising the total tardiness of parallel machines completion times with respect to the common due date with machine release times” (TTCR)) and an auxiliary one (“Minimising the difference between the maximal and the minimal completion times of the machines” (MDMM)). The latter is used to efficiently solve the first two ones. For the TTPR problem and its generalisation in the case when there are machines with release times that extend past the common due date (TTPRE problem), new theoretical properties are given, which were obtained on the basis of the previously published ones. Based on the new theoretical results and computational experiments the PSC-algorithm solving these two problems is modified (sub-algorithms A1, A2). Then the auxiliary problem MDMM is considered and Algorithm A0 is proposed for its solving. Based on the analysis of computational experiments, A0 is included in the PSC-algorithm for solving the problems TTPR, TTPRE as its polynomial component for constructing a schedule with zero tardiness of jobs if such a schedule exists (a new third sufficient condition of optimality). Next, the second intractable combinatorial optimization problem TTCR is considered, deducing its sufficient conditions of optimality, and it is shown that Algorithm A0 is also an efficient polynomial component of the PSC-algorithm solving the TTCR problem. Next, the case of a schedule structure is analysed (partially tardy), in which the functionals of the TTPR and TTCR problems become identical. This facilitates the use of Algorithm A1 for the TTPR problem in this case of the TTCR problem. For Algorithm A1, in addition to the possibility of obtaining a better solution, there exists a theoretically proven estimate of the deviation of the solution from the optimum. Thus, the second PSC-algorithm solving the TTCR problem finds an exact solution or an approximate solution with a strict upper bound for its deviation from the optimum. The practicability of solving the problems under consideration is substantiated.