MATHEMATICAL MODEL AND ANSYS ANALYSIS OF THE LEAD SCREW–NUT MECHANISM OF THE RT117 MACHINE TOOL
Keywords:
lead screw, nut, machine tool feed drive, ANSYS Mechanical, Rigid Dynamics, Motion Loads, Lagrange equations, inertia relief, von Mises stress, finite element methodAbstract
This article presents a mathematical model and a sequential ANSYS Mechanical 2024 R2 analysis of the lead screw–nut drive of the RT117 machine tool (Rigid Dynamics followed by Static Structural). The relevance of the work is determined by the need to estimate inertial loads and the elastic response of a long, slender screw in machine-tool feed drives before experimental testing. A kinematic relation between the screw and the nut–apron system was derived, and a reduced two-coordinate Lagrangian model was constructed to interpret the numerical time series. The mechanism consisted of a steel screw 60 mm in diameter and 2000 mm long, a nut and a 400 kg apron, with a total translating mass of 446.849 kg. A constant angular velocity of 144 rad/s, a lead of 9 mm per revolution and a cam displacement law of 59 points over 1.12 s were specified. The most loaded dynamic instant was transferred to an elastic model of the screw by the Motion Loads procedure, and Inertia Relief was used to balance the resultant axial load. The peak cam force was 21.163 kN, the peak force transmitted through the nut was 19.169 kN, and the largest torque modulus in the motor joint was 27.457 N·m. In the elastic stage the maximum von Mises stress was 17.597 MPa and the maximum total deformation was 0.0379 mm. The analytical relations agreed with the ANSYS results at all 1169 time points up to numerical rounding. Thread friction, working load and experimental verification remain for further study.
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