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The staircase effect and support structure under overhanging geometry are two inherent weaknesses that reduces the surface quality and induces material waste. This paper aims to design a five-axis fused deposition modeling system with interference-free nozzle to solve the problems.

To facilitate the application of five-axis printing machine, three new printing methods are proposed according to different geometries and application requirements, which include tangential direction printing, normal sculpture printing and compatible printing.

The static flow beading characteristic is researched to establish the criterion for switching the mode between three-axis printing and five-axis printing. Experiment proves the critical point existing and 51° is the critical point at the given parameters. The concept of dynamic flow beading is proposed. The relationship between equivalent volume and roughness is established based on elaborate experiments, which helps to figure out the boundary between safe area and beading area under different parameters of layer thickness and nozzle diameter.

Three new printing methods are proposed according to different geometries and application requirements, which include tangential direction printing, normal sculpture printing and compatible printing. Considering the special movement situation during five-axis printing process, the dynamic flow beading issue is proposed. The relationship between equivalent volume and roughness is established based on elaborate experiments, which helps to figure out the boundary between safe area and beading area under different parameters of layer thickness and nozzle diameter.

Grey modeling technique is an important element of grey system theory, and academic articles applied to agricultural science research have been published since 1985, proving the broad applicability and effectiveness of the technique from different aspects and providing a new means to solve agricultural science problems. The analysis of the connotation and trend of the application of grey modeling technique in agricultural science research contributes to the enrichment of grey technique and the development of agricultural science in multiple dimensions.

Based on the relevant literature selected from China National Knowledge Infrastructure, the Web of Science, SpiScholar and other databases in the past 37 years (1985–2021), this paper firstly applied the bibliometric method to quantitatively visualize and systematically analyze the trend of publication, productive author, productive institution, and highly cited literature. Then, the literature is combed by the application of different grey modeling techniques in agricultural science research, and the literature research progress is systematically analyzed.

The results show that grey model technology has broad prospects in the field of agricultural science research. Agricultural universities and research institutes are the main research forces in the application of grey model technology in agricultural science research, and have certain inheritance. The application of grey model technology in agricultural science research has wide applicability and precise practicability.

By analyzing and summarizing the application trend of grey model technology in agricultural science research, the research hotspot, research frontier and valuable research directions of grey model technology in agricultural science research can be more clearly grasped.