# Characteristic Analysis and Co-Validation of Hydro-Mechanical Continuously Variable Transmission Based on the Wheel Loader

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## Abstract

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## 1. Introduction

## 2. Analysis of the Wheel Loader Characteristics

#### 2.1. Force Characteristics

#### 2.2. Velocity Characteristics

#### 2.2.1. Types of HMCVT

- H range, where the transmission has only hydrostatic power.
- HM range, with forward transmission of the PG.
- HM’ range, with reverse transmission of the PG.

#### 2.2.2. Velocity Characteristics

#### 2.3. Power Characteristics

## 3. The Factors Influencing the Proportion of Hydrostatic Power

- To realize the same speed shift connection between the H range and hydro-mechanical range, as you can see from Equation (23) and Figure 9, when ${i}_{p}=1$, $\left|{i}_{oeM}\right|$ increases with the increase of $\left|{i}_{CVTM}\right|$ and decreases with the increase of $\left|{i}_{1}\right|$.
- As can be seen from Equation (19), under certain conditions of ${T}_{M}$, $\left|{T}_{o}\right|$ increases with the increase of $\left|{i}_{1}\right|$ and decreases with the increase of $\left|{i}_{PG}\right|$. So, matching patterns a and b have better torque characteristics than matching patterns c and d in Table 2.
- From Equation (28) and Figure 10, the range of transmission ratio, $\alpha ,$ increases with the increase of ${i}_{PG}$, and Schemes 2, 4, and 6 exist as ${i}_{oe}=0$ because of $\alpha <0$.
- From the Equations (26), (27), (29), and Figure 11, ${\rho}_{M}$ and ${\rho}_{m}$ are independent of ${i}_{CVTM}$, and only related to ${i}_{PG}$. Schemes 2, 4, and 6 exist as the work condition with the lowest transmission efficiency because mechanical transmission occurs in backward power recirculation, i.e., $\rho <-1$, as shown in Figure 6. The transmission efficiency of matching patterns b, c, and d are lower than matching pattern a because $\left|{\rho}_{M}\right|>0.6$ and mechanical transmission occurs even in backward power recirculation, as shown in Figure 6. Therefore, the efficiency of HMCVT is significantly reduced.

## 4. The Efficiency Analysis of the Matching Pattern A

#### Theoretical Calculation

## 5. Co-Validation of Simulation and Test

#### 5.1. The Method of Co-Validation

#### 5.2. The Application of Test and Validation

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

HMCVT | Hydro-Mechanical Continuously Variable Transmission |

CVT | Continuously Variable Transmission |

PSD | Power-Split Device |

PJD | Power Junction Device |

FT | Final Transmission |

PG | Planetary Gear train |

VP | Variable Displacement Hydraulic Pump |

FM | Fixed Displacement Hydraulic Motor |

${F}_{K}$ | Driving force of the wheel loader |

${F}_{f}$ | Rolling resistance of the wheel loader |

${F}_{\omega}$ | Air resistance of the wheel loader |

${F}_{i}$ | Ramp resistance of the wheel loader |

${F}_{a}$ | Inertia force of the wheel loader |

${m}_{t}$ | Total weight of the wheel loader |

${i}_{t}$ | Transmission ratio of the whole transmission system. |

${i}_{e}$ | The transmission ratio between engine and shaft e |

${i}_{p}$ | The transmission ratio between shaft e and pump |

${i}_{1}$ | Transmission ratio between motor and shaft 1 of PG |

${i}_{2}$ | Transmission ratio between shaft e and shaft 2 of PG |

${i}_{PG}$ | Transmission ratio between output shaft and shaft 1 |

${i}_{CVT}$ | Transmission ratio of Hydrostatic CVT |

${i}_{oe}$ | Transmission ratio of HMCVT |

${i}_{f}$ | Transmission ratio between PG output shaft and the wheel |

${n}_{E}$ | Engine speed |

${n}_{e}$ | Shaft e speed |

${n}_{P}$ | Pump shaft speed |

${n}_{M}$ | Motor shaft speed |

${n}_{1}$ | Shaft 1 speed of PG |

${n}_{2}$ | Shaft 2 speed of PG |

${n}_{o}$ | Output shaft speed of PG |

${n}_{K}$ | Wheel speed |

${V}_{P}$ | Pump displacement |

${V}_{M}$ | Motor displacement |

${T}_{1}$ | Shaft 1 torque of PG |

${T}_{2}$ | Shaft 2 torque of PG |

${T}_{o}$ | Output shaft torque of PG |

${T}_{M}$ | Motor shaft torque |

${T}_{K}$ | Driving torque of wheel loader |

${T}_{E}$ | Engine torque |

$\alpha $ | The range of transmission ratio, ${i}_{oe}$ |

$\beta $ | The range of ${i}_{CVT}$ |

$v$ | Wheel loader velocity |

${r}_{K}$ | Radius of wheel |

$\rho $ | Proportion of hydrostatic power in total power |

${P}_{o}$ | Output power of HMCVT |

${P}_{K}$ | Driving power |

${P}_{CVT}$ | Hydrostatic CVT power |

${P}_{MT}$ | Mechanical Transmission power |

$k$ | PG characteristic coefficient |

${\eta}_{I}$ | Efficiency of mode Ⅰ |

${\eta}_{\mathit{II}}$ | Efficiency of mode Ⅱ |

${\eta}_{CVT}^{v}$ | Volumetric efficiency of Hydrostatic CVT |

${\eta}_{CVT}^{m}$ | Mechanical efficiency of Hydrostatic CVT |

${\eta}_{P}^{v}$ | Volumetric efficiency of VP |

${\eta}_{P}^{m}$ | Mechanical efficiency of VP |

${\eta}_{P}^{t}$ | Total efficiency of VP |

${\eta}_{M}^{v}$ | Volumetric efficiency of FM |

${\eta}_{M}^{m}$ | Mechanical efficiency of FM |

${\eta}_{M}^{t}$ | Total efficiency of FM |

${\eta}_{CVT}$ | Hydrostatic CVT efficiency |

${\eta}_{1}$ | Efficiency of gear set 1 |

${\eta}_{2}$ | Efficiency of gear set 2 |

${\eta}_{p}$ | Efficiency of gear set p |

${\eta}_{21}^{o}$ | Efficiency between shaft 2 and shaft 1 of PG |

${\eta}_{1o}^{2}$ | Efficiency between shaft 1 and output shaft of PG |

${\eta}_{2o}^{1}$ | Efficiency between shaft 2 and output shaft of PG |

${\eta}_{s1}$ | HMCVT efficiency of scheme 1 |

${\eta}_{s3}$ | HMCVT efficiency of scheme 3 |

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**Figure 10.**The range of transmission ratio, ${i}_{oe},$ in four matching patterns. (

**a**) The transmission range $\alpha $ of pattern a; (

**b**) The transmission range $\alpha $ of pattern b; (

**c**) The transmission range $\alpha $ of pattern c; (

**d**) The transmission range $\alpha $ of pattern d.

**Figure 11.**The hydrostatic power proportion, $\rho $, in four matching patterns. (

**a**) The hydrostatic power proportion pattern a; (

**b**) The hydrostatic power proportion pattern b; (

**c**) The hydrostatic power proportion pattern c; (

**d**) The hydrostatic power proportion pattern d.

**Figure 12.**The range of transmission ratio, ${i}_{oe},$ in the matching pattern a. (

**a**) The transmission range $\alpha $ of scheme 1; (

**b**) The transmission range $\alpha $ of scheme 3.

**Figure 13.**$\rho $ of the matching pattern a. (

**a**) ${\rho}_{M},$ and ${\rho}_{m}$ of scheme 1; (

**b**) ${\rho}_{M},$ and ${\rho}_{m}$ of scheme 3.

**Figure 18.**The structural scheme and transmission ratio, ${i}_{oe},$ of the multi-range HMCVT: (

**a**) The structural scheme of multi-range HMCVT; (

**b**) The curve of transmission ratio ${i}_{oe}$.

**Figure 20.**HMCVT efficiency under different working conditions: (

**a**) Vehicle full load; (

**b**) Vehicle no-load; (

**c**) Engine rated power (162 kW); (

**d**) Engine maximum torque (853 N·m); (

**e**) Engine medium torque (400 N·m); (

**f**) Comprehensive comparison of efficiency.

Scheme | Transmission Sketch | ${\mathit{i}}_{\mathit{P}\mathit{G}}$ | Range of Values |
---|---|---|---|

1 | $\frac{1}{k+1}$ | 0.2 to 0.4 | |

2 | $\frac{k}{k+1}$ | 0.6 to 0.8 | |

3 | $-\frac{1}{k}$ | −0.67 to −0.25 | |

4 | $\frac{k+1}{k}$ | 1.25 to 1.67 | |

5 | $-k$ | −4 to −1.5 | |

6 | $k+1$ | 2.5 to 5 |

Pattern | Scheme | Sketch | Property | ${\mathit{i}}_{\mathit{P}\mathit{G}}$ | $\mathit{k}$$\mathit{k},\text{}{\mathit{k}}^{\prime}$ |
---|---|---|---|---|---|

a | 1 | Forward deceleration | 0.25 to 0.4 | ${k}^{\prime}=k+1$ | |

3 | Reverse deceleration | −0.25 to −0.4 | |||

b | 2 | Forward deceleration | 0.6 to 0.67 | ${k}^{\prime}=\frac{1}{k}+1$ | |

3 | Reverse deceleration | −0.6 to −0.67 | |||

c | 4 | Forward acceleration | 1.5 to 1.67 | ${k}^{\prime}=\frac{1}{k}+1$ | |

5 | Reverse acceleration | −1.5 to −1.67 | |||

d | 6 | Forward acceleration | 2.5 to 4 | ${k}^{\prime}=k+1$ | |

5 | Reverse acceleration | −2.5 to −4 |

Parameters | Value |
---|---|

Rated power, ${P}_{E}$/Rated speed, ${n}_{E}$ | 162 kW/2000 rpm |

Maximum torque, ${T}_{ETMax}$/Engine speed | 853 N·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 |

Working Condition | Power (kW)/Torque (N·m) | Speed (rpm) |
---|---|---|

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 |

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## Share and Cite

**MDPI and ACS Style**

Wan, L.; Dai, H.; Zeng, Q.; Sun, Z.; Tian, M.
Characteristic Analysis and Co-Validation of Hydro-Mechanical Continuously Variable Transmission Based on the Wheel Loader. *Appl. Sci.* **2020**, *10*, 5900.
https://doi.org/10.3390/app10175900

**AMA Style**

Wan L, Dai H, Zeng Q, Sun Z, Tian M.
Characteristic Analysis and Co-Validation of Hydro-Mechanical Continuously Variable Transmission Based on the Wheel Loader. *Applied Sciences*. 2020; 10(17):5900.
https://doi.org/10.3390/app10175900

**Chicago/Turabian Style**

Wan, Lirong, Hanzheng Dai, Qingliang Zeng, Zhiyuan Sun, and Mingqian Tian.
2020. "Characteristic Analysis and Co-Validation of Hydro-Mechanical Continuously Variable Transmission Based on the Wheel Loader" *Applied Sciences* 10, no. 17: 5900.
https://doi.org/10.3390/app10175900