Abstract This paper studies the basic rated dynamic load of ball screw pairs using graphs, intuitively illustrating the influence of lead, ball diameter, and nominal diameter of the ball screw pair on the basic rated dynamic load in the calculation of the rated dynamic load, providing a reference for the engineering application of ball screw pairs. Keywords Ball screw pair, basic rated dynamic load, lead, ball diameter, nominal diameter Introduction The ball screw pair is a ball screw transmission mechanism with unique mechanical characteristics. It is a screw transmission element with balls (steel balls) as rolling elements between a screw and a nut. Therefore, the relative motion between the screw and the nut can be transformed into rolling. Due to its high efficiency (generally >90%), high precision and high speed characteristics, wear resistance, and reversible motion, the ball screw pair, as a highly efficient (energy-saving) and precise advanced transmission mechanism, has attracted widespread interest and attention both domestically and internationally, and has been widely applied. my country has been researching ball screw pairs for over 40 years, primarily focusing on the transmission stiffness of the ball screw, the contact deformation and contact angle between the steel balls and raceways, the return angle of the nut and return mechanism, and error compensation and control during actual machining. However, research on the load-bearing capacity of ball screw pairs has been minimal. This paper studies the calculation formula for rated dynamic load and, based on the relationship between load and its key factors, proposes some suggestions (a) to improve the load-bearing capacity of ball screw pairs, aiming to enhance their performance. 1. Four Commonly Used Ball Screw Pair Structures Currently, there are four commonly used ball screw pair structures both domestically and internationally: Internal circulation structure (represented by circular and elliptical reversers), where the reversers form a ball circulation loop, with each reverser forming one turn of the ball chain. This structure has low load capacity and is suitable for miniature and general ball screw pairs. External circulation structure (represented by the insert type), where the inserts form a ball circulation loop, with each insert having at least 1.5 turns of the ball chain. This structure has high load capacity and a wide range of applications. End cap structure, where the end caps at both ends of the nut form a ball circulation loop, with each loop having at least one turn of the ball chain. This structure has a relatively high load capacity and is suitable for multi-start, large-lead ball screw pairs. Cover plate structure, where the cover plates form the ball screw circulation loop, with one cover plate per nut, and each cover plate forming at least 1.5 turns of the ball chain. This structure is mostly suitable for miniature ball screw pairs. The first two structures are the most commonly used… A simplified diagram of these four commonly used structures is shown in Figure 1. 2. Definition and Calculation Formula of Rated Dynamic Load The basic rated dynamic load is defined as the pure axial load that a batch of ball screw pairs of the same specifications can withstand after operating for 1 million revolutions under the same conditions, without fatigue spalling (or pitting) occurring on 90% of the screw pairs (thread raceway surface or ball surface). [align=center] Figure 1: Simplified structural diagram of 4 commonly used ball screw pairs Figure 2: Relationship between basic rated dynamic load and lead[/align] Calculation of the rated dynamic load C of the ball screw pair (Note: In the following calculation formula, r[sub]s[/sub] and r[sub]n[/sub] are the raceway curvature radii of the screw and nut, respectively. In the formula, frs and frn are the compatibility of the screw and ball nut of the ball screw pair; Dω is the ball diameter; Dωp is the pitch circle diameter of the ball screw; fu is the working stroke coefficient; z is the number of steel balls in one thread raceway; i is the total number of working turns of the nut; Ph is the lead; lu is the effective working stroke; fc is the rated dynamic load characteristic value, which is related to the geometry of the raceway and the properties of the material. In this formula, fc is obtained when the raceway hardness is greater than 60HRC and the thread helix angle is less than 10 degrees. 3 Factors Affecting Rated Dynamic Load From the above formula for rated dynamic load, it can be seen that to discuss rated dynamic load, we should start with the ball diameter, the nominal diameter of the ball screw helix, and the lead, and discuss the relationship between them. The following analysis uses an external circulation ball screw assembly produced by a certain ball screw manufacturer as an example. With a load ball rotation count of 3.5 turns and an effective working stroke of 1000 mm, the basic rated dynamic load of the ball screw is analyzed using the formula described above in two cases, with graphical data. ① As shown in Figure 2, the curve of the basic rated dynamic load changes when the lead increases from 4 mm to 8 mm when the nominal diameter of the ball screw is 32 mm and the ball diameter is 3.969 mm. From the curve shown in Figure 2, it can be seen that under a single-line configuration, when the lead increases from 4.0 mm to 7.9 mm in steps of 0.1 mm, the rated dynamic load decreases from 18.4388 kN to 18.1723 kN. The change in lead has little effect on the rated dynamic load, and the trend of the curve is almost a straight line. From the curve's variation, it can be seen that in the multi-line configuration, the influence of the lead on the rated dynamic load is also not significant. However, since multi-line configurations can greatly increase the transmission speed, the influence of the lead on the speed of the ball screw transmission is amplified in the multi-line configuration. ② Figure 3 shows the variation curve of the basic rated dynamic load corresponding to the increase of the ball (steel ball) diameter from 3.169 mm to 4.169 mm when the lead of the single-lead ball screw increases from 6 mm to 25 mm to 59 mm. [align=center] Figure 3: Variation curve of basic rated dynamic load, ball diameter and nominal diameter[/align] From the curve, it can be seen that the rated dynamic load generally increases with the increase of the ball screw diameter, and the dynamic load value increases faster with the increase of the ball diameter. It is evident that, within a certain range, the combined effect of the ball diameter and the nominal screw diameter on the rated dynamic load is a wave-like fluctuation, and the larger the nominal screw diameter, the more obvious the fluctuation of the rated dynamic load. Table 1 also clearly shows the difference in rated dynamic load corresponding to the nominal diameter from 25 mm to 59 mm when the ball diameter increases from 3.169 mm to 4.169 mm. 4 Conclusion As can be seen from the above discussion, among the three main influencing factors of the basic rated dynamic load of the ball screw pair, the lead has a relatively small influence on the rated dynamic load, and it changes inversely with the lead and the rated dynamic load; the ball diameter and the nominal diameter of the screw have an amplifying effect on the rated dynamic load, and it is worth noting that the wave-like undulation shown in Figure 2 is rising, which is also the focus of future research. At the same time, the research work in this paper has certain reference value for the production and selection of ball screw pairs and the theoretical research of ball screws in engineering applications. References 1 Xiao Zhengyi. Development trend of ball screw pairs. Beijing: Manufacturing Technology and Machine Tool, 2000 (4): 11-13 2 Xu Hao. Mechanical Design Handbook (4). Beijing: Machinery Industry Press, 2000