As an important component in mechanical transmission systems, gears need to follow many principles and standards in their design and manufacturing to ensure their normal operation and long-term durability. In gear design, the selection of the number of teeth is a key factor. The limitation that the number of teeth in a gear cannot be less than 17 is closely related to the following reasons: avoiding undercutting, improving gear strength, manufacturing process limitations, meshing smoothness, and other related factors. The following is a detailed explanation of these reasons.
1 Avoid root cutting phenomenon
Root cutting refers to the process in which the root of a gear is cut off due to a small number of teeth, resulting in an incomplete tooth shape. This phenomenon will affect the normal meshing of gears, reduce their strength and service life.
The phenomenon of root cutting usually occurs on gears with fewer teeth. For standard involute gears, root cutting is prone to occur when the number of teeth is less than 17. Root cutting not only causes the actual tooth shape of the gear to deviate from the designed tooth shape, but also creates an unstable phenomenon during the transmission process. One of the methods to avoid root cutting is to increase the number of teeth, which is generally believed to be at least 17 or more.
II Improve gear strength
The strength of gears is a key factor in ensuring their normal operation. During the transmission process of gears, each tooth will bear a certain load. If the number of teeth is too small, the load borne by each tooth will relatively increase, leading to stress concentration and fatigue failure of the gear.
Increasing the number of teeth in a gear can effectively distribute the load on the gear, reducing the relative load on each tooth, thereby improving the strength and durability of the gear. Especially in high load and high-speed working environments, the strength of gears is particularly important. Therefore, the number of teeth in the gear should not be too small, at least 17 or more should be maintained to ensure its strength.
III Limitations of manufacturing processes
The manufacturing process of gears also has a certain impact on the requirements for the number of teeth. The machining of gears requires high-precision manufacturing equipment and processes. If the number of teeth is too small, the tooth profile of the gear will become more complex and the machining difficulty will increase.
In traditional gear machining methods, such as milling and gear planning, gears with too few teeth are prone to machining errors, which not only affects the meshing accuracy of the gears but also increases manufacturing costs. Although modern gear machining uses CNC machine tools and high-precision cutting tools, gears with too few teeth still struggle to ensure high accuracy. Therefore, when designing gears, it is common to choose gears with a larger number of teeth to reduce manufacturing difficulty and errors.
IV Meshing stability
The smoothness of gear transmission is one of the important indicators in gear design. During the meshing process of gears with fewer teeth, due to the large spacing between each tooth and the significant variation in transmission ratio, the transmission becomes unstable, resulting in noise and vibration.
Increasing the number of teeth can effectively improve the smoothness of gear transmission. Gears with more teeth have more teeth in each meshing process, resulting in less variation in transmission ratio, ensuring smooth transmission and reducing noise and vibration. Especially in high-speed transmission systems, the smoothness of gears has a significant impact on the performance and lifespan of the entire system, so the number of teeth in the gears cannot be too small.
V Other related factors
In addition to the main reasons mentioned above, the selection of gear teeth also involves other related factors, such as module, gear size, and weight.
1. The relationship between modulus and number of teeth
Module is an important parameter in gear design, representing the size of the gear tooth profile. The relationship between modulus and tooth number is close, and the larger the modulus, the larger the tooth profile of the gear. The larger the module of a gear with the same number of teeth, the larger the diameter of the gear. If the number of teeth is too small and the modulus is large, the size of the gear will become unreasonable, affecting the assembly and use of the gear.
2. Gear size and weight
The size and weight of gears are also factors that need to be considered during design. A gear with too few teeth will have a larger tooth shape, resulting in an increase in overall size and weight of the gear, which will have an impact on the layout and load capacity of the mechanical system. Especially in some lightweight designs, the size and weight of gears are key factors. Therefore, selecting the appropriate number of teeth and keeping the size and weight of the gear within a reasonable range is also an important consideration in gear design.
3. Exceptions in practical applications
Although in general, the number of teeth in a gear should not be less than 17, there may be different design requirements in certain special applications. For example, in some low-speed, low load transmission systems, gears with fewer teeth can be used. In this case, designers need to consider various factors comprehensively to carry out reasonable design and optimization.
In addition, in non-standard gear or special gear designs, such as non involute gears, helical gears, etc., the limit on the number of teeth may vary. At this point, specialized design and calculations need to be carried out based on specific application scenarios and requirements.
6、 Summary
In summary, the limitation that the number of teeth in a gear cannot be less than 17 is mainly to avoid undercutting, improve gear strength, reduce manufacturing difficulty and errors, ensure transmission stability, and consider various factors such as gear size and weight. Although there may be exceptions in special applications, following this design principle generally helps to ensure the normal operation and long-term durability of gears. Designers need to consider various factors comprehensively in the actual design process, and carry out reasonable design and optimization to meet the requirements of specific applications.