1. When designing gears, you might have come across this notion: the number of teeth on a pair of meshing gears should be as prime numbers as possible, meaning they have no common factors and cannot be divided evenly. For example, z1=14 and z2 = 79. What are the benefits of having prime numbers for the number of teeth? Is it necessary to have them be prime? Today, let's take a look together. First, let's see the benefits.

2.When the number of teeth is coprime, it can lead to uniform wear between the teeth of two gears. If there is a common factor in the number of teeth on both gears, a tooth from the smaller gear will repeatedly engage with several fixed teeth on the larger gear, which can easily cause localized wear, especially when individual gears have defects. However, if the number of teeth is coprime, the contact points of tooth engagement will be distributed across all teeth, thus extending the life of the gears.

3.The number of teeth is mutually prime to reduce vibration and noise. The number of teeth is mutually prime to avoid the generation of periodic excitation force and reduce vibration and noise in transmission. If the number of teeth is in a multiple relationship, the periodic superposition of error or load may cause resonance.

4.The impact of manufacturing errors in gear distribution. The number of teeth that are mutually prime helps to mitigate the effects of machining errors on transmission smoothness, thereby improving overall transmission accuracy. Given these benefits, must the tooth count meet the requirement of being mutually prime? In fact, it doesn't have to; in some cases, the principle of mutual prime can be relaxed. For example, in gearboxes where gears need to engage frequently, uniform wear is less critical, so the principle of mutual prime does not have to be strictly followed. Or in applications with strict requirements for transmission ratios, such as i=4, non-prime tooth counts (e.g., z1=14, z2=56) may be necessary, but in such cases, good lubrication must be ensured, and high-precision hard-faced gear designs should be used whenever possible. Another scenario is when the number of teeth on a gear is too high (usually exceeding 100). To improve machinability and accuracy (considering differential gears or indexing gears), prime numbers are often avoided. When gears cannot be mutually prime, possible uneven loads can be compensated for through shaping or optimized design. In summary: mutual prime tooth counts are a conventional design principle for optimizing transmission performance. If conditions permit, prime tooth counts should be chosen whenever possible. If mutual prime is not feasible, the decimal places of the tooth count divisor should be as many as possible. In specific scenarios, adjustments can be made flexibly based on requirements. When designing, wear, noise, manufacturing cost, and transmission ratio accuracy should all be considered comprehensively. The table below summarizes these points for your reference.