# Study on the Influence of Gear Spoke Hole Numbers on Meshing Noise
## 1 Introduction  
Nowadays, the meshing noise of the gear systems, which are widely used power and motion transmission devices, has attracted widespread attention from experts in the field. With the development of machinery manufacturing and processing technology, especially the emergence of new technologies such as additive manufacturing [1; 2; 3], machinery processing accuracy can be guaranteed [4]. Then, the structure optimization of gears, such as spoke hole structures, can provide a new idea for reducing meshing noise.  
The meshing noise of the gears is mainly caused by meshing stiffness shock and meshing error without considering the bending deformation of the gear shaft. This paper mainly discusses the previous influencing factor.  
The changes in the meshing teeth numbers during the transmission process will result in the changes of the contact line length. Then, stiffness shock occurs during the periodic meshing of gears. The periodic vibration of the gears along the meshing line caused by the stiffness shock will promote the generation of noise. To control the meshing stiffness and the stiffness fluctuation during gear transmission is an effective way to restrain the periodic vibration.  
The meshing stiffness is related to many parameters of the gear, including the number of teeth, modulus, displacement factor, etc. It has been studied by previous scholars that the meshing performance of the gears can be improved by optimizing the structural parameters [5].  
Significant efforts have been devoted to studying gear meshing. Based on the finite element method, the accuracy of gear meshing calculations is achieved by Coy [6]. Then, the meshing stiffness can be obtained by the numerical calculation method [7] and the finite element method [8]. In addition, the influencing factors of meshing stiffness, such as the profile errors [9], the tooth tip radius [10], and the rotation speed [11], were verified.  
For gear meshing noise, the mapping relationship between mesh stiffness and noise is established by considering the gear rim thickness [12], pressure angle and helix angle [13], bearing load [14], and other parameters.  
However, research on the influence of the gear spoke structure on gear meshing noise has rarely been reported. The spoke is an important structure of the gear, and it will affect the gear meshing noise. The spoke hole structure was proposed to solve the above problems. This paper aims to analyze the influence of the gear spoke hole numbers on the meshing stiffness and noise under the condition of constant speed and resistance moment. The results show that more spoke holes lead to less meshing stiffness and less stiffness fluctuation. In addition, it was observed from the BEM acoustic simulation that the meshing stiffness is the dominate factor for noise. Less meshing stiffness will result in louder noise according to the correspondence between the gear spoke hole numbers, stiffness, and noise. The experiment shows the same trend through measuring the vibration of the reducer outer box caused by the change in spoke hole numbers. In summary, more spoke holes result in louder noise, and the growth trend will decrease slightly with the increase in spoke hole numbers, which agrees with the simulation. The results represent a reasonable method to design the gear spoke structure for reducing the meshing noise.