## 1 Introduction  
The worm-type distributor, comprising a hopper, a screw shell, and a rotating screw, stands as a typical distribution mechanism that is extensively employed in agricultural machinery for fertilization [1, 2]. Fertilization, aimed at providing an appropriate amount of nutrients to crops, encounters challenges with existing worm-type distributors due to flow fluctuations--a key factor influencing crop quality and yield [3]. Flow fluctuation correlates closely with the physical properties of particles (e.g., particle size [4] and shape [5, 6]),the helical structure (e.g., screw pitch [7] and blade diameter [8]), and operational conditions (e.g., rotational speed [9; 10]). Dynamic simulation methods using the discrete element method (DEM) have recently proven effective in studying the motion laws of particles [11]. Consequently, numerous researchers have employed the DEM to address the flow fluctuation issue in worm-type distributors by focusing on these aspects.  
For instance, [PERSON] et al. studied the effect of particle size on flow fluctuation and found that the reduction of particle size gradually improved the stability and accuracy of spiral transportation [12]. [PERSON] et al. found, through the DEM, that particle shape significantly influences mass flow rate under screw conveyance at high rotational speeds [13]. [PERSON] et al. reduced flow fluctuation by altering the screw pitch at the feed inlet, conveying section, and outlet [14]. [PERSON] et al. studied the effects of six types of helical structures on flow fluctuation based on the DEM [15]. [PERSON] et al. simulated helical transportation under different helical rotational speeds and angles of inclination through the DEM, finding that flow fluctuation decreases with the increase in the helical rotational speed and angle of inclination [16]. [PERSON] et al. explored the influences of a shaft helix and shaftless helix on flow fluctuation under different rotational speeds, observing a decrease in flow fluctuation with an increasing rotational speed [17].  
Despite successful proposals of various methods to decrease flow fluctuation, the underlying causes still warrant deeper exploration. Flow fluctuation in the helical fertilization process is a macroscopic phenomenon that is essentially driven by changes in the particle swarm movement, induced by external stresses. Analyzing the stress characteristics of particle swarms at the microscopic level can offer a novel perspective to elucidate flow fluctuation. The rotational speed, a crucial operational parameter of the worm-type distributor, significantly affects both macroscopic flow fluctuation and microscopic force and energy transmission among particle swarms. Although scholars have emphasized the importance of the spiral rotational speed on flow fluctuation [18; 19; 20], the influence of the stress characteristics of particle swarms on the flow fluctuation from the meso-scale remains largely unexplored. Therefore, this study investigates the causes of flow fluctuation by employing the rotational speed as a variable, aiming to reveal the action mechanism of particle swarm force and energy on the meso-scale.  
In this study, a numerical simulation of the fertilization process of a worm-type distributor was conducted through the DEM. The qualitative and quantitative exploration of the internal relations between the flow fluctuation and contact force fluctuation among particles paved the way for a deep analysis of the influences of the helical rotational speed on contact forces (including the axial coefficient of variation and the circumferential uniformity index) among particles. The ultimate goal is to elucidate the internal mechanism of flow fluctuation and provide theoretical guidance for the stable fertilization of worm-type distributors.