In order to study the unbalanced response of the main shaft system of the carpet tufting machine, the mathematic model of the ground tufting machine shaft system by the moment method is used. The transfer matrix method mainly discretizes the continuously distributed elastic system into a multi-degree-of-freedom system composed of concentrated mass points, shaft segments and elastic supports, that is, the mass of the rotor is concentrated on several nodes along the axis. The node and the shaft segment are formed into a unit, and the relationship between the left state vector and the right state vector is established, and then the transfer matrix is extracted, and the state equations of the arbitrary section and the initial section of the rotor are established by continuous conditions.
Among them, the node is a number of mass points discrete according to the actual situation of the shaft system, used to connect the massless shaft section. The setting of the node follows the following rules:
(1) Nodes need to be set at the hinge joints between the shaft and other parts;
(2) Nodes need to be set at the support;
(3) Nodes need to be set at the sudden change of the cross-section.
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