# Dynamic Characteristic Analysis and Clutch Engagement Test of HMCVT in the High-Power Tractor

Authors: Yuan Chen; Yu Qian; Zhixiong Lu; Shuang Zhou; Maohua Xiao; Petr Bartos; Yeping Xiong; Guanghu Jin; Wei Zhang
Journal: Complexity
 (2021)

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## Abstract

Hydromechanical continuously variable transmission (HMCVT) is capable of bearing large torque and has wide transmission range, which is suitable for high-power tractors. Dynamic characteristics could influence the tractor life, especially in a high-power tractor. Wet clutch is the crucial component in the HMCVT, which could smooth and soft power transmission. Therefore, it is important to study the dynamic characteristics and implement the wet clutch test of HMCVT. In this paper, AMESim is used to establish virtual models of gearbox, pump-controlled hydraulic motor system, and shifting hydraulic system. Then, a simulation study of tractor operation under working condition is carried out. The internal and external meshing forces of the planetary row are analyzed. Finally, the wet clutch engagement process of HMCVT  in the high-power tractor is tested to verify the oil pressure. The simulation results show that the values of internal and external meshing force become larger as the throttle opening increases. At the moment of shifting change, the meshing forces of the planetary gear have great impact. The clutch test shows that the trend of the oil filling curve obtained from the bench test is similar to that obtained from the theoretical curve, which verifies the simulation results.


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## Body

## 1. Introduction

The main function of the tractor is to be used in conjunction with various traction and driving machines to complete agricultural field operations, earthwork engineering operations, transportation operations, and stationary operations [1]. The transmission performance of the gearbox will have an important impact on the tractor and its transmission system. The hydromechanical continuously variable transmission (HMCVT) has attracted extensive attention in recent years [2–5]. In order to meet the requirements of tractors working under multiple working conditions, at present, high-power tractor gearboxes are set with more gears. The increase of gears in gearboxes not only makes its structure complex and error prone to operate, but also the dynamic characteristics of the tractor are difficult to guarantee [6].Scholars have carried out a lot of research on HMCVT. The German company ZF [7] produced the S-Matic series of hydraulic mechanical transmissions, which used dual-row planetary row confluence to output power for the first time. The Japanese Company Komatsu [8] successfully developed a stepless speed change device suitable for construction machinery and applied it to the D155AX-3 bulldozer and WA380-3 loader. In recent years, various well-known gearbox manufacturers have launched HMCVT with independent intellectual property rights, such as John Deere, Caterpillar of the United States, and Valtra of Finland [9]. The typical HMCVT model is shown in Figure 1.Figure 1
The HMCVT S-Matic.Regarding mechanical characteristic analysis for HMCVT, Xia et al. [10] proposed an optimized design method for the selection of the structural parameters of the PCHMCVT to ensure competent overall performance. Zheng and Sun [11] used AMESim to establish a physical model of an HMCVT and simulated and analyzed the speed regulation characteristics, output torque characteristics, and acceleration characteristics of the pure hydraulic section of it. Zhang [12] and He et al. [13] have, respectively, optimized the design of the hydraulic mechanical stepless gearbox. Li et al. [14] analyzed the working principle of HMCVT and successfully developed a hydraulic mechanical stepless gearbox suitable for high-power tractors for both water and drought. Zhai et al. [15] introduced a two-stage planetary row device for the final transmission of a wheeled tractor, which is compact in structure, reliable in operation, and easy to install. Wang et al. [16] proposed a new type of compound planetary row transmission new hydraulic mechanical continuously variable transmission scheme based on the traditional single-row planetary and double planetary row. Guo et al. [17] established the conditions for synchronous shifting of multistage HMCVT and verified the high efficiency characteristics of it. Wang et al. [18] used the basic principles of dynamics to establish a tractor dynamic model and verified its good dynamic characteristics under ploughing condition. Xiao et al. [19, 20] studied the dynamic characteristics of the hydraulic circuit in HMCVT, and a fast system identification method was proposed. Cheng et al. [21–26] improved the genetic algorithm to implement the HMCVT  parameter optimization, and the new proposed model can improve the HMCVT transmission efficiently and flexibly.From the analysis above, we can see that scholars’ research on HMCVT is focused on the structure characteristics or the shifting strategy, but there is little research on the dynamic characteristics and clutch engagement. In this paper, the HMCVT scheme and simulation model was proposed, the dynamic meshing forces were calculated, and the wet clutch engagement characteristics were tested for a high-power tractor.


## 2. Modeling

### 2.1. Gearbox Dynamic Model

This paper puts forward the HMCVT scheme, which is shown in Figure2. This transmission scheme is a constant-ratio split-moment converging speed type. The engine power is divided into two power transmissions through the fixed-axis gear pair i1 or i2i3 (i2i3 works in forward gear) and the hydraulic power distribution gear pair ip. One power is transmitted to the common sun gear shafts of planetary rows K1 and K2 through the variable displacement pump-fix displacement motor, which is a hydraulic flow, and the other power is transmitted to the planet carrier K1 and the ring gear K2 through the fixed shaft gear pair (the planet carrier of K1 and the gear ring of K2 are firmly connected), which is the mechanical flow. The hydraulic flow and mechanical flow converge in the planetary rows K1 and K2, and then the combined flow force is transmitted to the ring gear of K1 or planet carrier K2. Finally, by separately controlling the engagement of wet clutches C1, C2, and C3, the power can be transmitted to the output shaft. In this process, stepless speed regulation can be realized in each section by controlling the displacement ratio of the variable pump.Figure 2
HMCVT scheme.AMESim has been widely used in aerospace, vehicles, construction machinery, ships, and other multidisciplinary fields and has become a platform for modeling and simulation of complex systems such as liquid, mechanical, electrical, electromagnetic, thermal analysis, and control. AMESim software is more and more widely used in modeling, simulation, and analysis of complex systems. AMESim is applied to the modeling process of HMCVT in this paper.The planetary gear mechanism model is shown in Figure3(a), and its mathematical model is shown as follows [27]:(1)v1a=−Rad1+Rad2Rad1⋅vca−Rad2Rad1⋅v2a,v0=Rad2⋅v2b−Rad1⋅v1aRad2−Rad1+vca,T2b=facteff×Rad2Rad1×T1b−T1a+T2b,Tca=T1b−T1a+T2b−T2b+Tcb,where v1a is the rotational speed of Port 1A, vca is the rotational speed of Port 2A, v2b is the rotational speed of Port 4B, v0 is the rotational speed of the carrier, Rad1 is the number of the sun gear, Rad2 is the number of the ring gear, T2a and T2b are the input and output torque of the ring gear, and Tca and Tcb are the input and output torque of the carrier.Figure 3
The model of the HMCVT component. (a) Planet gear. (b) Variable pump. (c) Shifting hydraulic system.
(a)(b)(c)The variable pump model (PU003 C) is selected from the Hydraulic library, as shown in Figure3(b). The opening range of the variable pump model is −1≤ swash ≤1. When turning forward, port 3 is the oil outlet; when turning backward, port 3 is the oil inlet. The mathematical model of a variable pump is shown as follows:(2)qp=e⋅vp⋅swash1000,Tp=pAP−pBP⋅e⋅swash20⋅π,where qp is the flow of the variable pump, e is the displacement of the pump, swash is the throttle opening of the pump, Tp is the shaft torque of the pump, and pAP and pBP are the inlet and outlet oil pressure.The quantitative motor model (M0001 C) is selected from the Hydraulic library, and the mathematical model is shown as follows:(3)qm=e⋅vm1000,Tm=pAm−pBm⋅e⋅swash20⋅π,where qm is the flow of motor, vm is the motor speed, Tm is the torque of the motor, and pAm and pBm are the inlet and outlet oil pressure of the motor.Based on the models of various parts, like the wet clutch, the oil circuit, the corresponding signal control elements, and the torque output elements, the simulation model of the shifting hydraulic system could be obtained, as shown in Figure3(c).According to the gearbox model, hydrostatic circuit, shifting system model, and tractor model, the simulation model of HMCVT is obtained, as shown in Figure4.Figure 4
The simulation model of HMCVT.


## 2.1. Gearbox Dynamic Model

This paper puts forward the HMCVT scheme, which is shown in Figure2. This transmission scheme is a constant-ratio split-moment converging speed type. The engine power is divided into two power transmissions through the fixed-axis gear pair i1 or i2i3 (i2i3 works in forward gear) and the hydraulic power distribution gear pair ip. One power is transmitted to the common sun gear shafts of planetary rows K1 and K2 through the variable displacement pump-fix displacement motor, which is a hydraulic flow, and the other power is transmitted to the planet carrier K1 and the ring gear K2 through the fixed shaft gear pair (the planet carrier of K1 and the gear ring of K2 are firmly connected), which is the mechanical flow. The hydraulic flow and mechanical flow converge in the planetary rows K1 and K2, and then the combined flow force is transmitted to the ring gear of K1 or planet carrier K2. Finally, by separately controlling the engagement of wet clutches C1, C2, and C3, the power can be transmitted to the output shaft. In this process, stepless speed regulation can be realized in each section by controlling the displacement ratio of the variable pump.Figure 2
HMCVT scheme.AMESim has been widely used in aerospace, vehicles, construction machinery, ships, and other multidisciplinary fields and has become a platform for modeling and simulation of complex systems such as liquid, mechanical, electrical, electromagnetic, thermal analysis, and control. AMESim software is more and more widely used in modeling, simulation, and analysis of complex systems. AMESim is applied to the modeling process of HMCVT in this paper.The planetary gear mechanism model is shown in Figure3(a), and its mathematical model is shown as follows [27]:(1)v1a=−Rad1+Rad2Rad1⋅vca−Rad2Rad1⋅v2a,v0=Rad2⋅v2b−Rad1⋅v1aRad2−Rad1+vca,T2b=facteff×Rad2Rad1×T1b−T1a+T2b,Tca=T1b−T1a+T2b−T2b+Tcb,where v1a is the rotational speed of Port 1A, vca is the rotational speed of Port 2A, v2b is the rotational speed of Port 4B, v0 is the rotational speed of the carrier, Rad1 is the number of the sun gear, Rad2 is the number of the ring gear, T2a and T2b are the input and output torque of the ring gear, and Tca and Tcb are the input and output torque of the carrier.Figure 3
The model of the HMCVT component. (a) Planet gear. (b) Variable pump. (c) Shifting hydraulic system.
(a)(b)(c)The variable pump model (PU003 C) is selected from the Hydraulic library, as shown in Figure3(b). The opening range of the variable pump model is −1≤ swash ≤1. When turning forward, port 3 is the oil outlet; when turning backward, port 3 is the oil inlet. The mathematical model of a variable pump is shown as follows:(2)qp=e⋅vp⋅swash1000,Tp=pAP−pBP⋅e⋅swash20⋅π,where qp is the flow of the variable pump, e is the displacement of the pump, swash is the throttle opening of the pump, Tp is the shaft torque of the pump, and pAP and pBP are the inlet and outlet oil pressure.The quantitative motor model (M0001 C) is selected from the Hydraulic library, and the mathematical model is shown as follows:(3)qm=e⋅vm1000,Tm=pAm−pBm⋅e⋅swash20⋅π,where qm is the flow of motor, vm is the motor speed, Tm is the torque of the motor, and pAm and pBm are the inlet and outlet oil pressure of the motor.Based on the models of various parts, like the wet clutch, the oil circuit, the corresponding signal control elements, and the torque output elements, the simulation model of the shifting hydraulic system could be obtained, as shown in Figure3(c).According to the gearbox model, hydrostatic circuit, shifting system model, and tractor model, the simulation model of HMCVT is obtained, as shown in Figure4.Figure 4
The simulation model of HMCVT.


## 3. Simulation Analysis of Tractor under Working Conditions

Figure5 and Table 1 show the change of the internal and external meshing forces of the planetary row under working condition.Figure 5
Meshing force of the planet gear. (a) Internal meshing force and (b) external meshing force.
(a)(b)Table 1
Internal and external meshing force in working condition.
Working conditionExternal meshing force (N)Internal meshing force (N)MaximumMinimumMaximumMinimum—2.20 × 1077.33 × 1062.00 × 1073.33 × 106As can be seen from Figures5(a) and 5(b), the internal and external meshing forces of the planetary row both have great impacts at the moment of the engine throttle opening change. The maximum and minimum values of internal meshing force are 3.33 × 106 N and 2.00 × 107N, respectively. The maximum and minimum values of external meshing force are 2.20 × 107N and 7.33 × 106 N, respectively.They all become larger as the throttle opening increases. At the moment of shifting change, the internal and external meshing forces of the planetary gear have great impact at 2.5s–3.5 s. Then, the magnitudes of the meshing force change decrease, and the trend tends to be stable.


## 4. Clutch Engagement Characteristic Test of HMCVT

### 4.1. Power Drive Module

DEUTZ TCD2013L062 V engine was selected for the test. The accelerator control system of it is a dual-sensor control loop system, which is mainly composed of displacement sensor, current sensor, accelerator pedal, and stepping motor. The test sent an electric signal of speed adjustment to the engine by changing the pedal angle of the accelerator pedal. After the ECU got the control signal and then the stepper motor could be controlled by output current, the throttle opening can be changed.The engine throttle opening was collected by displacement sensors, and ECU output current was collected by current sensors. The signals were compared with the original value in the input controller and realized the rapid adjustment of the engine speed controller according to the control algorithm.This HMCVT test bench selected and designed the accelerator pedal according to the engine type and ECU, as is shown in Figure6.Figure 6
Accelerator pedal of the engine.The bolt adjusting device was installed on the accelerator pedal, and the length of it was related to the change of the position of the accelerator pedal. The corresponding scale line was drawn on the bolt in direct proportion to the speed of the engine.


### 4.2. HMCVT Load Module

The dynamometer loaded the gearbox by outputting different quantities and can simulate the working state of the vehicle in different working conditions. The test bench selected the Lanlin DW250 (Figure7) type eddy current dynamometer to match the rotation speed and power of the engine.Figure 7
Eddy current dynamometer.


### 4.3. Oil Pressure Sensor

The JM-801 pressure sensor with a ceramic core was selected for the test bench. When the pressure was applied to the ceramic membrane, the surface of the membrane will undergo subtle deformation.The resistance was printed on the back of the ceramic diaphragm, and the Wheatstone bridge can be formed. The Wheatstone bridge will generate a voltage signal due to voltage sensitive effect. The signal is proportional to the pressure and excitation current. The oil pressure value of C0, C1, C2, and lubrication main oil line in the platform can be read directly through the pressure indicator table (Figure8).Figure 8
Oil pressure gauge.


### 4.4. Test Bench

The overall structure diagram of the test bench is shown in Figure9. The test bench was mainly composed of diesel engine, speed rising transmission, and support device. In the test bench, the diesel engine was used as the power source.Figure 9
The HMCVT test bench.


### 4.5. Clutch Oil Filling Test

The structure of C0, C1, and C2 was basically the same, and this paper took C0 as an example to carry out the bench test research on oil filling process. Test steps were as follows.First, the engine was started to adjust the accelerator pedal and stabilize the output speed of the engine to 1295 r/min.Secondly, the engagement button of C0 was pressed in the measurement platform. The oil pressure of the main oil relief valve was set at 2.8 MPa.After receiving the electrical signal, the proportional directional valve of C0 pumped the filtered oil from the tank and sent to the clutch. The oil filling process of C0 is shown in Figure10.Figure 10
Oil filling characteristic curve of the wet clutch.


#### 4.5.1. 0-a Section

This section was mainly to eliminate the gap between the friction plates. The oil pressure raised from 0 MPa to 0.03 MPa rapidly. The slope of the variation of the curve in this section is 0.6.


#### 4.5.2. a-b Section

The slope of the variation of the curve in this section is 0.52. At this stage, the piston compressed the spring under the action of the oil pressure, and the oil pressure increased with compression of the return spring. The oil pressure pf C0 rose slowly from 0.03 MPa to 0.42 MPa. The variation of oil pressure was related to the torque transferred by the clutch and piston stroke.


#### 4.5.3. b-c Section

The slope of the variation of the curve in this section is 7.8. In this stage, the oil pressure of C0 rose rapidly from 0.42 MPa to 2.8 MPa, which was set by the relief valve in order to ensure the torque.


#### 4.5.4. c-d Section

This section was the pressure holding stage. The oil pressure of C0 was maintained at 2.8 MPa.


### 4.6. Test Discussion

The oil filling process can be divided according to the slope of the oil pressure change in each section. The oil filling time was short at 0–0.5 s, and the range of oil pressure change is 0.03 MPa. This section was the stage of rapid oil filling.The oil filling duration of 0.05–0.8 s was 0.75 s, accounting for 68% of the total oil filling time. And, the variation range of oil pressure was 0.39 MPa, accounting for 14% of the set oil filling pressure. Therefore, this stage was the slow booster stage.The oil filling duration of 0.8–1.1 s was 0.3 s, accounting for 27% of the total oil filling time. And, the variation range of oil pressure was 2.38 MPa, accounting for 85% of the set oil filling pressure. In a short time, the oil pressure showed a step rise. Therefore, the stage was the step booster stage.During 1.1–1.4 s, the oil filling pressure reached the set value of 2.8 MPa and remained as such. Therefore, the stage was the pressure holding stage.According to analysis, the oil filling curve obtained from the test bench had a similar trend to the theoretical curve. It verified the oil filling characteristics of the wet clutch and proved the accuracy of the HMCVT test bench.


## 4.1. Power Drive Module

DEUTZ TCD2013L062 V engine was selected for the test. The accelerator control system of it is a dual-sensor control loop system, which is mainly composed of displacement sensor, current sensor, accelerator pedal, and stepping motor. The test sent an electric signal of speed adjustment to the engine by changing the pedal angle of the accelerator pedal. After the ECU got the control signal and then the stepper motor could be controlled by output current, the throttle opening can be changed.The engine throttle opening was collected by displacement sensors, and ECU output current was collected by current sensors. The signals were compared with the original value in the input controller and realized the rapid adjustment of the engine speed controller according to the control algorithm.This HMCVT test bench selected and designed the accelerator pedal according to the engine type and ECU, as is shown in Figure6.Figure 6
Accelerator pedal of the engine.The bolt adjusting device was installed on the accelerator pedal, and the length of it was related to the change of the position of the accelerator pedal. The corresponding scale line was drawn on the bolt in direct proportion to the speed of the engine.


## 4.2. HMCVT Load Module

The dynamometer loaded the gearbox by outputting different quantities and can simulate the working state of the vehicle in different working conditions. The test bench selected the Lanlin DW250 (Figure7) type eddy current dynamometer to match the rotation speed and power of the engine.Figure 7
Eddy current dynamometer.


## 4.3. Oil Pressure Sensor

The JM-801 pressure sensor with a ceramic core was selected for the test bench. When the pressure was applied to the ceramic membrane, the surface of the membrane will undergo subtle deformation.The resistance was printed on the back of the ceramic diaphragm, and the Wheatstone bridge can be formed. The Wheatstone bridge will generate a voltage signal due to voltage sensitive effect. The signal is proportional to the pressure and excitation current. The oil pressure value of C0, C1, C2, and lubrication main oil line in the platform can be read directly through the pressure indicator table (Figure8).Figure 8
Oil pressure gauge.


## 4.4. Test Bench

The overall structure diagram of the test bench is shown in Figure9. The test bench was mainly composed of diesel engine, speed rising transmission, and support device. In the test bench, the diesel engine was used as the power source.Figure 9
The HMCVT test bench.


## 4.5. Clutch Oil Filling Test

The structure of C0, C1, and C2 was basically the same, and this paper took C0 as an example to carry out the bench test research on oil filling process. Test steps were as follows.First, the engine was started to adjust the accelerator pedal and stabilize the output speed of the engine to 1295 r/min.Secondly, the engagement button of C0 was pressed in the measurement platform. The oil pressure of the main oil relief valve was set at 2.8 MPa.After receiving the electrical signal, the proportional directional valve of C0 pumped the filtered oil from the tank and sent to the clutch. The oil filling process of C0 is shown in Figure10.Figure 10
Oil filling characteristic curve of the wet clutch.


### 4.5.1. 0-a Section

This section was mainly to eliminate the gap between the friction plates. The oil pressure raised from 0 MPa to 0.03 MPa rapidly. The slope of the variation of the curve in this section is 0.6.


### 4.5.2. a-b Section

The slope of the variation of the curve in this section is 0.52. At this stage, the piston compressed the spring under the action of the oil pressure, and the oil pressure increased with compression of the return spring. The oil pressure pf C0 rose slowly from 0.03 MPa to 0.42 MPa. The variation of oil pressure was related to the torque transferred by the clutch and piston stroke.


### 4.5.3. b-c Section

The slope of the variation of the curve in this section is 7.8. In this stage, the oil pressure of C0 rose rapidly from 0.42 MPa to 2.8 MPa, which was set by the relief valve in order to ensure the torque.


### 4.5.4. c-d Section

This section was the pressure holding stage. The oil pressure of C0 was maintained at 2.8 MPa.


## 4.5.1. 0-a Section

This section was mainly to eliminate the gap between the friction plates. The oil pressure raised from 0 MPa to 0.03 MPa rapidly. The slope of the variation of the curve in this section is 0.6.


## 4.5.2. a-b Section

The slope of the variation of the curve in this section is 0.52. At this stage, the piston compressed the spring under the action of the oil pressure, and the oil pressure increased with compression of the return spring. The oil pressure pf C0 rose slowly from 0.03 MPa to 0.42 MPa. The variation of oil pressure was related to the torque transferred by the clutch and piston stroke.


## 4.5.3. b-c Section

The slope of the variation of the curve in this section is 7.8. In this stage, the oil pressure of C0 rose rapidly from 0.42 MPa to 2.8 MPa, which was set by the relief valve in order to ensure the torque.


## 4.5.4. c-d Section

This section was the pressure holding stage. The oil pressure of C0 was maintained at 2.8 MPa.


## 4.6. Test Discussion

The oil filling process can be divided according to the slope of the oil pressure change in each section. The oil filling time was short at 0–0.5 s, and the range of oil pressure change is 0.03 MPa. This section was the stage of rapid oil filling.The oil filling duration of 0.05–0.8 s was 0.75 s, accounting for 68% of the total oil filling time. And, the variation range of oil pressure was 0.39 MPa, accounting for 14% of the set oil filling pressure. Therefore, this stage was the slow booster stage.The oil filling duration of 0.8–1.1 s was 0.3 s, accounting for 27% of the total oil filling time. And, the variation range of oil pressure was 2.38 MPa, accounting for 85% of the set oil filling pressure. In a short time, the oil pressure showed a step rise. Therefore, the stage was the step booster stage.During 1.1–1.4 s, the oil filling pressure reached the set value of 2.8 MPa and remained as such. Therefore, the stage was the pressure holding stage.According to analysis, the oil filling curve obtained from the test bench had a similar trend to the theoretical curve. It verified the oil filling characteristics of the wet clutch and proved the accuracy of the HMCVT test bench.


## 5. Conclusions

In this paper, the dynamic characteristics of HMCVT were analyzed. The wet clutch engagement characteristics were tested. The analysis could be reference for the design of a high-power tractor. The conclusions can be made as follows:(1)
The values of internal and external meshing force become larger as the throttle opening increases.(2)
At the moment of shifting change, the meshing forces of the planetary gear have great impact.(3)
The magnitudes of the meshing force change decrease, and the trend tends to be stable after shifting change.(4)
The clutch test shows that the trend of oil filling is similar to the theoretical curve. The simulation model is reliable.



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