## 5 Co-Validation of Simulation and Test
### The Application of Test and Validation  
In order to validate the correctness of the above analysis, in this paper, an example is given to verify the validity of the method. Take a wheel loader as an example, the parameters are shown in Table 3.  
According to the parameters of a wheel loader, the structural scheme of the multi-range HMCVT is designed and the transmission ratio, \(i_{\text{\emph{e}}}\), is analyzed, as shown in Figure 18.  
Where i0, i1, i2, i3, i4, and i5 are the transmission ratio of gear sets, S1, S2, and S3 are synchronizers, C is clutch, PG1 is the Scheme 1 of PG, and PG3 is the Scheme 3 of PG. The table is the engagement state of synchronizers or clutch, in which positive is coupled and negative is uncoupled. It can be seen from Figure 18 that the forward direction of a multi-range HMCVT consists of a pure hydrostatic range (H range) and three hydrostatic and mechanical transmission ranges (HM1, HM2, and HM3 range). The backward direction consists of a pure hydrostatic range (H range) and two hydrostatic and mechanical transmission ranges (HM1 and HM2 range). The performance of each range can be tested and analyzed in the same method of co-validation; therefore, this paper takes one range to carry out co-validation. Figure 17: Hydrostatic CVT efficiency test bed. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Value** \\ \hline Rated power, \(P_{E}\)/Rated speed, \(n_{E}\) & 162 kW/2000 rpm \\ Maximum torque, \(T_{ETMax}\)/Engine speed & 853 N\textbackslash{}m /1500 rpm \\ Vehicle mass & 16,500 kg \\ Rated load & 50 kN \\ VP Maximum displacement & 80 mL/r \\ FM displacement & 80 mL/r \\ Maximum pressure & 42 MPa \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The parameters of a wheel loader. The HM1 range is a commonly used range in the working process of the loader and takes Scheme 3 in Table 1 as PJD. During the HM1 range, the load of the wheel loader has a large range of changes, and the largest traction force also occurs in this range. Therefore, this paper takes the HM1 range as the research object to analyze under five typical working conditions, as shown in Table 4.  
Under the working condition of engine maximum torque, the engine speed is 1500 rpm and the vehicle speed is 1.125-1.857 m/s during the HM1 range; under the others, the engine speed is 2000 rpm \begin{table}
\begin{tabular}{c c c} \hline \hline
**Working Condition** & **Power (kW)/Torque (N-m)** & **Speed (rpm)** \\ \hline Engine rated power, \(P_{E}\) & 162/- & 2000 \\ Engine maximum torque & -/853 & 1500 \\ Engine medium torque & -/400 & 2000 \\ Vehicle full load, \(T_{K}\) & -/16,480 & 2000 \\ Vehicle no-load, \(T_{K}\) & -/11,880 & 2000 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Working conditions of the wheel loader. Figure 18: The structural scheme and transmission ratio, \(i_{ee}\), of the multi-range HMCVT: (**a**) The structural scheme of multi-range HMCVT; (**b**) The curve of transmission ratio \(i_{ee}\). and the vehicle speed is 1.5-2.5 m/s. The HM1 range transmission system simulation model is built by using AMESim software, and the simulation model is shown in Figure 19.  
Through the co-validation method of simulation and test, the analysis results are shown in Figure 18.  
As can be seen from Figure 20a-e, the efficiency of the hydrostatic CVT is significantly reduced with the reduction of \(i_{CVT}\), and reaches the lowest value when approaching zero. At this time, the inclination of the VP swash plate is near zero, which results in the FM output speed approaching zero. Therefore, the mechanical efficiency is greatly reduced, and causes the efficiency of hydrostatic CVT to reach the lowest. However, the proportion of hydrostatic power in total power, \(\rho\), is also close to zero, hence it has little effect on the efficiency of HMCVT, and the highest efficiency of HMCVT is at \(i_{CVT}=0\). Figure 19: Simulation model of HM1 range.