# Study of a Small Robot for Mine Hole Detection
## 2 Functional Analysis and Mechanical Modeling
### Shaft Strength Calibration Calculation  
The shaft, a crucial transmission component of the robot, is tasked with supporting the rotating parts and facilitating motion and power transfer. To achieve the design goals, it is necessary to consider both the structural dimensions and the operational capacity. The precise structural dimensions of the shaft are defined by its specific mounting position and its designated function. The operational capacity of the shaft is calculated taking into account factors such as strength, stiffness, and vibration stability. Typically, the operational capacity of the shaft relies primarily on its strength, particularly with regard to the conditions of torsional strength. Based on the mechanical design manual, it is known that the torsional strength of the shaft should be satisfied:  
\[\tau_{T}=\frac{T}{W_{T}}\approx\frac{9,550,000\frac{P}{n}}{0.2d^{3}}\leq[\tau _{T}] \tag{8}\]  
In Equation (8), \(\tau_{T}\) is the torsional shear stress, MPa; \(T\) is the torque applied to the shaft, Nmm; \(W_{T}\) is the torsional shear factor of the shaft, mm; \(n\) is the speed of the shaft, r/min; \(P\) is the transmission efficiency of the shaft, kW; \(d\) is the diameter of the shaft at the calculated section, mm; and \([\tau_{T}]\) is the allowable torsional shear stress, MPa.  
We limit the output power of the motor to 8 W, so the power allocated to a single-driven level gear is 4 W. Then, taking \(P=4\) W, the traction force required by the mine hole-inspection robot is 150 N. Then, taking \(F=200\) N, based on \(P=FV\), it can be deduced that the robot's moving speed is 0.06 m/s. The crawling wheel radius is 22.5 mm, as calculated using Equation (9):  
\[1\;\mathrm{m/s}=\frac{30}{\pi R}\;\mathrm{r/min} \tag{9}\]  
It can be deduced that the speed of the shaft is 25.5 r/min, and the shaft diameter condition can be obtained using the torsional strength condition of the shaft:  
\[d\geq\sqrt[3]{\frac{9550,000}{0.2[\tau_{T}]}}\sqrt[3]{\frac{P}{n}}=A_{0}\sqrt [3]{\frac{P}{n}} \tag{10}\]  
where 45 steel is chosen as the material of the shaft. Then, \([\tau_{T}]\) is taken as 30 and \(A_{0}\) is taken as 110. Substituting into Equation (10), we obtain \(d\geq 5.93\), and thus, the design dimension of the shaft should be 6 mm.  
Finite element simulation software (Abaqus 2021) can effectively verify the force of the components in the limit state. When the robot is obstructed and the crawler wheel stops, the motor's output torque reaches its maximum, and at this time, the drive shaft will be subjected to a considerable load and reach the limit state.  
The gear motor's maximum output torque is 8.8 Nm, and the level gear ratio is 1. Neglecting unfavorable factors such as friction, i.e., the maximum torque the drive shaft is subjected to is also 8.8 Nm, the post is modeled in finite element software, the torque is added at the right end of the stick, and the constraints are fixed at the left end to simulate the case of a blocked stop of the crawler wheel.  
Figure 3 shows the strain cloud on the left side and the stress cloud on the right. The analysis results show that the portion where the maximum strain and the maximum stress appear is near the end where the load is added. In addition, the shaft holes on the level gears should not be oversized during subsequent machining and assembly to improve the tightness and stiffness of the mounting area and reduce deformation.