COMPARATIVE ANALYSIS OF INERTIAL–ENERGY AND KINEMATIC CHARACTERISTICS OF NEEDLE MECHANISMS IN CHAIN-STITCH SEWING MACHINES

Abstract

The article presents findings from a comparative study of kinematic and inertia-energy traits of needle mechanisms in six-bar and four-bar stitch-forming systems utilized in 164-class chain stitch sewing equipment from the Rimoldi firm and the MF-7923D model from Juki. The investigation involved juxtaposing normalized motion S(φ), v(φ), a(φ)  with unitary harmonic functions, assessing their impact on the mechanism's inertial load. Calculations encompassed simulation modeling in SolidWorks Motion for kinematic and inertia-energy parameters (M_кр(φ), P_eq(φ), T_eq(φ), Jeq(φ)), determining mass-and-inertia specifications of the links (J_s,i, m, S(x, y)), and analytical computations of the equivalent reduced moment function Jeq(φ)  and its decomposition into the reduced moments of inertia J_eq,i(φ) for each link in the Assur groups, performed within the Mathcad environment.

Kinematic results showed the six-bar needle mechanism possesses motion laws closer to harmonic compared to the four-bar needle mechanism. Deviation ranges for the six-bar mechanism’s motion laws are 2.1–12.8% versus 3.6–18.5% for the four-bar one. The magnitudes ΔS(j), Δv(j), Δa(j)  for the six-bar needle mechanism exhibit smaller absolute deviations, particularly outside the ranges φ ≈ 0, π, 2π.

Inertial indicators for the six-bar mechanism feature a higher average value for the reduced moment of inertia Jeq(φ)  —by approximately ≈36%—and a peak by about ≈38.2%, with a range between J_max та J_min that is 1.78 times greater (about ≈78%) when compared to the four-bar mechanism. The relative oscillation amplitude of J_eq(φ) is 8.2% in the four-bar and 10.7% in the six-bar system. Such characteristics necessitate greater inertial demands during startup and braking, increase instantaneous stresses on the drive, and require more precise flywheel balancing. Furthermore, maximum torsional loads under identical operating conditions in the 164-class mechanism were higher, M_кр,max ≈ 0,27 N·m versus 0.16 N·m in the MF-7923D, while peak values of equivalent power P_eq(φ) increased in the MF-7923D machine to ≈ 24$ W against ≈17$ W in the 164-class machine, ≈42$% difference, corresponding to lower J_eq(φ).

It was determined that mass-and-inertia specifications of the links in the first coupler group of the Assur mechanism (links 2-3) in the six-bar needle system of the 164-class machine significantly affect the magnitude of the reduced moment of inertia J_eq(φ). The discrepancy between computer simulation modeling and analytical calculations does not exceed 2–6%, confirming the veracity of the derived outcomes.

The obtained results advance research in balancing theory and can be applied to select optimal control profiles (S S-start/stop, dM/dt limitation) and for mass-inertial optimization of structural components within the mechanism.