Xiangdong Ni and Mingxi Bao

（1. College of Mechanical and Electrical Engineering, Shihezi University, Shihezi 832003, Xinjiang,China；2. Key Laboratory of Northwest Agricultural Equipment, Ministry of Agriculture, Shihezi University, Shihezi 832003, Xinjiang, China）

Abstract: With a transmission system suitable for a medium or large self-propelled cotton picker as the object of the study, the following work focuses on the influence law of an independently designed hydro-mechanical continuously variable transmission(HMCVT) in the process of changing sections. An HMCVT simulation model was established using the multibody dynamics Simulation X software. The accuracy of the simulation model was verified by comparing the numerical values of the output speed of the HMCVT with model predictions. The HMCVT test bench was built independently using a John Deere 4045HYC11 diesel engine as power input. The engine speed, load torque, oil pressure, and flow of speed regulating valve were considered the influencing factors. The sliding friction power was the response index for the segment change process test. We analysed the reasons for the decrease in output speed during the shifting process, and proposed to effectively reduce the stable speed difference before and after the output shaft shifting by shifting the stage ahead (with displacement ratio of –0.96). This study provides a reference value for the smoothness of the HMCVT of the self-propelled cotton picker, and is relevant in promoting the use of the cotton picker.

Key words: transmission scheme；shifting process；test analysis；dynamic characteristics

The hydro-mechanical continuously variable transmission(HMCVT) is a device that combines hydraulic stepless transmission with a mechanical gear high-efficiency transmission. HMCVT characteristically has high transmission power and efficiency[1-4]. The transmission device uses a small displacement hydraulic element to achieve a wide range of speed adjustments, which can greatly reduce the operational complexity and improve the fuel economy and power of the vehicle.

Extensive research has been conducted on HMCVT. However, in most studies, the research focus is mainly in wind-power generation systems, tractors and other working machines,whereas few studies have been conducted on the cotton picker transmission system. Huang et al.developed a variable-speed input and constantspeed output HMCVT for wind-power generation systems and simulated its dynamics[5]. Yoo et al. designed an HMCVT power transmission system with a combination of helical gears and planetary gears for 8-ton medium-sized forklifts,calculated the specifications of complex helical gears and planetary gear transmissions, analysed the bending and compression stresses of the gears, and optimised structural parameters[6].Zhang et al. established the characteristic equations for speed, torque, power, and efficiency of an HMCVT according to the basic principle of power distribution, which meets the requirements of tractors[7]. A corresponding HMCVT developed by Xi’an University of Technology and Henan University of Science and Technology in China is intended for various tractor operations(such as sowing, weeding, and harvesting); it uses 8 clutches and 6 + 3 gears to achieve stepless speed change[8-11]. An HMCVT developed by Nanjing Agricultural University was also mainly designed for high-power tractors, and uses a WP6T180E21 engine as the power source. This HMCVT has 5 clutches and 4 sections. Related research has been conducted on its efficiency and the process of changing sections[12–15]. Beijing Institute of Technology proposed a starting process control strategy and corresponding solenoid valve dead-zone processing method related to the position of the brake pedal for trucks, designing and implementing an incremental PID closedloop control system[16–18].

As the cotton planting area is extensive, the demand for cotton pickers is high, the working environment is harsh, and the load changes frequently. In this study, we independently designed a hydraulic mechanical continuously variable transmission to meet the operational requirements of the cotton picker and studied its shifting process.

1 Transmission Characteristics

1.1 HMCVT transmission scheme

For the medium- and high-power cotton pickers, we independently designed a differential clutch HMCVT with fewer clutches and gears[19–24]. The designed operating speed range of HMCVT adjustment is 0–25 km/h. The power input is a John Deere 4045HYC11 diesel engine,which requires an engine power of 100 kW and output rated speed of 2 200 r/min. According to the different speed requirements of the cotton picker under initial and re-harvesting conditions,a transmission with three forward sections and one reverse section is designed, as shown in Fig.1.

Fig.1 HMCVT principle diagram

The forward section of the transmission is divided into three sections: pure hydraulic H section, hydraulic machine HM1 section, and hydraulic machine HM2 section[25-27]. The reverse section includes the R section, which is controlled by two wet clutches C1, C2and brake B.The clutch and brake joint site diagram is shown in Tab.1. i1, i2, i3are the transmission ratios of each gear pair; k1, k2are the characteristic parameters of the compound planetary gear system,and the ratio of the number of ring-gear teeth to the number of sun-gear teeth. The relationship of the transmission ratio of each gear pair in the HMCVT transmission scheme is as follows: i1=0.585 4, i2= 1.345 2, i3= 0.377 6, k1= 3.56, and k2= 2.56.

Tab. 1 Clutch and brake joint site diagram

1.2 Speed ratio characteristics

One reason for the speed stepless change of the HMCVT is to allow for the HMCVT to switch between pure hydraulic H section and the HM1 and HM2 sections by adjusting the separation and combination of clutch and brake. Another reason is to change the swing angle of the variable mechanism in the closed high-pressure two-way variable pump to the pure hydraulic H section and the HM1 and HM2 sections. In combining the step switching, which is controlled by the clutch and stepless speed change regulated by the variable pump as well as the transmission ratios of the pure hydraulic H section, the HM1 and HM2 sections are connected end-to-end to achieve continuous speed change of the hydraulic transmission. The speed ratio characteristics of each gear of the HMCVT are shown in Tab. 2.The speed ratio of the HMCV is shown in Fig.2.

Tab. 2 Speed ratio characteristics of each gear of HMCVT

Fig.2 Curve of HMCVT speed ratio and displacement ratio

In the speed ratio equations, ninis the transmission input speed, represented in r/min; noHis the output speed of pure hydraulic H gear, represented in r/min; noHM1is the output speed of hydraulic machinery HM1 gear, represented in r/min; noHM2is the output speed of HM2 gear,represented in r/min; ε is the displacement ratio that motor ratio with pump speed.

1.3 Power split ratio characteristics

When the HMCVT is in the pure hydraulic H section, the transmission schematic shows that the clutches C1and C2are in the disengaged state, the bidirectional variable pump-controlled quantitative motor hydraulic speed control system transmits all the power. Thus, the power split ratio ρ is always 1. Tab. 3 shows the HMCVT power split ratio when –1≤ε≤1.

Tab. 3 Characteristics of power split ratio and displacement ratio of HMCVT

The characteristic curve of the power split ratio of each gear of HMCVT is shown in Fig.3.The power split ratio of each gear of the HMCVT indicates that the ratio of the power delivered by the hydraulic speed control system to the total output power of the HMCVT changes with the change in the displacement ratio of the bidirectional variable pump. When the hydraulic speed control system transfers less power and the mechanical variable speed system transfers more power, the HMCVT power split has a lower value and the HMCVT transfer efficiency is higher. When ρ = 1, the output power of the HMCVT is transferred by the hydraulic speed control system. When ρ = 0, the HMCVT power is completely transmitted by the mechanical transmission system, and the system transmission efficiency is highest.

Fig.3 Characteristic curves of power split ratio

2 Model Simulation and Analysis

The HMCVT simulation model includes mechanical and hydraulic parts and is a highly nonlinear multi-input multi-output complex system. The secondary factors in the system are ignored, while factors such as temperature, friction,elastic deformation, and vibration of the HMCVT system affect the output characteristics.

2.1 Kinetic model

To build an effective and practical simulation model, we propose the equivalent rotational inertia model to reduce the complexity of building a simulation model. The HMCVT characteristically exhibits little deformation and large damping. Therefore, when modelling the HMCVT dynamic model, the system can be simplified as inertial damping, and the elastic deformation of the components can be ignored. The mathematical model of the HMCVT dynamics is shown in Fig.4.

6.Gold in plenty and all the joys of the world as well:The Devil offers material gain but the focus is on money and physical (non-spiritual) enjoyment20. Basically, the Devil is offering a version of his traditional pact21.Return to place in story.

Fig.4 HMCVT dynamic model

2.2 Model of hydraulic volume speed regulation system of pump control motor

The variable pump-controlled quantitative motor system is divided into four parts: electromechanical conversion elements, electro-hydraulic proportional servo valve-controlled double-acting symmetric hydraulic cylinders, variable piston-bidirectional variable pump swash plate swing angle, and the pump control motor circuit.The bidirectional variable pump is a swash-plate axial piston variable pump used in a closed hydraulic drive system. The variable mechanism of the two-way variable pump controls the three-position four-way electro-hydraulic proportional servo valve by inputting the current of the proportional solenoid in order to change the displacement of the double-acting symmetrical hydraulic cylinder. The variable pump swash plate inclination is determined by the displacement of the hydraulic cylinder to control the output speed of the quantitative motor. The principle diagram of the two-way variable pump-controlled quantitative motor system is shown in Fig.5.

Fig.5 Schematic of two-way variable pump-controlled quantitative motor system

2.3 Clutch model

As the shifting mechanism of the HMCVT system, the clutch has different parameters and settings for the hydraulic oil circuit, both of which greatly influence the analysis of its overall dynamic performance. The clutch transmits torque through the frictional force between the friction plates, and its mechanism is divided into complete separation and complete coupling, characterized as a stable state and slippage in an unstable state. In the process from the sliding friction state to full engagement of the clutch, the dynamic friction torque is in a time-variant state,and the transmitted torque is a combination of the diaphragm spring-pressing force and clutch input torque. The dynamics of the clutch model are shown in Fig.6.

Fig.6 Clutch dynamics model

When the master and driven discs are in the sliding state, the dynamic friction torque Thiis

where s is the number of friction plates of the clutch; A is the working area of the friction in m2; R is the radius of action of the friction plate in m; w1is the angular speed of the friction plate active plate in rad/s; w2is the friction plate angular velocity of the passive plate in rad/s; and phis the pressure acting on the friction plate in Pa.

2.4 HMCVT simulation model

The HMCVT model and simulation is based on its transmission design scheme and mathematical model of HMCVT transmission components(which include the engine, two-way variable pump-controlled quantitative motor hydraulic speed control system, planetary gear train mechanism, and clutch/brake hydraulic system). The HMCVT speed characteristics, response characteristics of the two-way variable pump-controlled quantitative motor system, oil filling characteristics of the clutch/brake hydraulic system,and smoothness of the shift can be studied in the constructed HMCVT system simulation. The HMCVT simulation system is shown in Fig.7.

Given an engine output speed of 900 r/min,1 500 r/min, and 2 200 r/min, the relationship between the output speed of the HMCVT and the transmission ratio is shown in Fig.8. The simulation value of the HMCVT output speed in purely hydraulic H gear and hydraulic mechanical HM1 gear is close to the experimental value.Due to oil leakage, the simulated value at high speeds has a certain deviation from the experimental values. Additionally, during the shifting periods, the actual output speed of the HMCVT drops by a large margin. Thus, the HMCVT simulation model is reasonable.

Fig.7 Hydro-mechanical CVT transmission simulation system

Fig.8 HMCVT output speed

3 Shifting Process Test

3.1 Test conditions

This test was completed in the hydraulic transmission laboratory of Shihezi University.The test process was conducted on a custommade hydraulic mechanical continuously variable transmission test bench constructed by the research group. The structure of the test bench is presented in Fig.9.

Fig.9 HMCVT test bench

3.2 HMCVT measurement and control system and test instrument

The diesel engine parameters are displayed by the Moffi meter and control panel. The speed and torque sensor is connected to the engine,HMCVT, and the magnetic power brake to detect the input and output shaft parameters. The specific parameters of the HMCVT test bench are shown in Tab. 4.

The main interface of the measurement and control system of the hydraulic mechanical continuously variable test bed is mainly used for setting, adjusting, and detecting the basic parameters of HMCVT. The basic parameter control and display area of the HMCVT is shown in Fig.10.The main interface includes port settings and basic parameter settings. The speed and torque sensor 1-2, TCU lower machine, magnetic powder brake, and other ports are connected and set in the port settings. The basic parameter settings include engine throttle adjustment, magnetic powder brake current adjustment and engine speed torque, HMCVT output speed torque parameter display area, monitoring pure hydraulic H gear, and HM1 and HM2 gear status.

4 Analysis of Test Results

For the shift process, the process of switching from HM1 to HM2 is the most complex, asthe working time of HM1 and HM2 is the longest. Therefore, this test uses HM1 to switch to HM2. The main influencing factors include engine speed, clutch oil pressure, flow valve flow,and load torque. A gear shift test was conducted on the transmission system of medium and large cotton pickers, and the dynamic characteristics of the gearbox during the gear shift process were analysed to provide a basis for the next installation test. The load torque values are 75 N·m,100 N·m, and 125 N·m; the oil pressure values are 3 MPa, 4 MPa, and 5 MPa; the engine speeds are 1 000 r/min, 1 550 r/min, and 2 000 r/min;and the flow rates of the governing valve are 3 L/min, 4 L/min, and 5 L/min. Response indicators include jerk, sliding power, HMCVT output speed, and torque.

Fig.10 Main interface of measurement and control system of HMCVT test bench

4.1 Analysis of HMCVT output speed influence

As shown in Fig.11a, the output shaft speed decreases with different engine speeds. As the engine speed continues to increase, the speed decreases by 260.73 r/min, 347.06 r/min, and 408.61 r/min. The output speed before and after the shift is basically unchanged, but a certain decrease still occurs. As shown in Fig.11b, although the drop range of theload torque and output shaft speed varies slightly, the difference is not large. However, as the load torque continues to increase, the output shaft speed decline range and rise time advance slightly. The speed drops were 312.57 r/min, 352.08 r/min, and 383.02 r/min,respectively. As shown in Fig.11c, the output shaft speed drop range does not change for different main oil circuit pressures, but as the main oil circuit pressure increases, the HMCVT output shaft speed rise time decreases greatly. The peak time is 30.2 s, 27.6 s, and 27.3 s. As shown in Fig.11d, the output shaft speed drop range varies greatly with different flow rates of the governing valve. As the flow rate of the governor valve increases, the speed of the output shaft decreases to a lesser extent. The speed drops are 498.7 r/min,374.7 r/min, and 301.7 r/min, respectively. The HMCVT output shaft speed rise time improves greatly, and the peak time is 28.1 s, 27.9 s, and 27.5 s.

The greater the engine speed, the greater the speed drop. The greater the flow of the governor valve, the smaller the speed decrease and the smaller the speed rise time. From these results,we observe that the engine speed and flow rate of the governor valve have a greater influence on the speed reduction. The oil pressure of the main oil circuit and flow rate of the governor valve have a greater influence on the speed rise time.The greater the oil pressure, the smaller the rise time of the HMCVT output shaft speed.

Fig.11 Effect of influencing factors on HMCVT output speed

4.2 Analysis of HMCVT output torque influence

As shown in Fig.12a, the trend in the output torque is inconsequential for various engine speeds. As the engine speed increases, the maximum torque of the HMCVT reaches 323.4 N·m at 26.7 s, 289.4 N·m at 26.8 s, and 253.4 N·m at 26.9 s. The peak value of the output torque occurs at the moment when clutch C2is engaged.As shown in Fig.12b, the output torque varies with the same load torque but the peak value is different. As the load torque increases, the maximum torque of the HMCVT reaches 306.8 N·m,290.3 N·m, and 273 N·m at 26.8 s. The peak value of the output torque occurs at the moment when C2is engaged. The peak output torque decreases slightly with an increasing load. As shown in Fig.12c, the trending change of the output torque varies greatly with different main oil circuit pressures. The maximum torque of HMCVT is –216.7 N·m, 276.8 N·m, and 467.4 N·m at 25.1 s ,26.8 s, and 26.6 s, respectively. The peak value of the output torque occurs at the moment when C2is engaged. The peak value of the output torque increases with an increase of oil pressure in the main oil circuit. As shown in Fig.12d, the output torque variation trend is subtle for different flow rates of the governor valve. However, as the flow of the governor valve increases, the timing in the torque change is improved, and the maximum torque of the HMCVT reaches 268.5 N·m,276.9 N·m, and 282.1 N·m at 27.3 s, 26.5 s, and 26.57 s, respectively. The peak value of the output torque occurs at the moment when C2is engaged.

Fig.12 Effects of influencing factors on HMCVT output torque

The preceding results show that the main oil circuit pressure and flow rate of the governor valve have a greater effect on the output torque,while the engine speed and load torque have a reduced effect on the output torque. The greater the oil pressure, the greater the maximum output torque. The greater the flow of the governor valve, the shorter the time to reach the maximum torque.

4.3 Analysis of jerk influence

As shown in Fig.13a, with the increase in the engine speed, the maximum jerk simultaneously occurs at approximately 26.5 s, reaching 17.68 m/s3, 20.35 m/s3, and 20.16 m/s3. As shown in Fig.13b, with the increase of the load torque,the maximum jerk simultaneously occurs around 26.5 s, reaching 19.6 m/s3, 20 m/s3, and 20.3 m/s3.The maximum jerk increases slightly with the increase in the load torque. As shown in Fig.13c,as the oil pressure of the main oil circuit increases, the maximum jerk also occurs at approximately 26.5 s, reaching 10.7 m/s3, 20.4 m/s3, and 25.1 m/s3. The maximum jerk decreases slightly with the increase of the oil pressure. As shown in Fig.13d, with the increase of the flow rate of the governor valve, the maximum impact occurrence time varies, reaching 20.3 m/s3at approximately 27.1 s, 20.6 m/s3at approximately 26.5 s, and 16.5 m/s3at approximately 26.2 s. The maximum jerk decreases slightly as the flow of the governor valve increases.

The preceding results show that the main oil circuit pressure and the flow rate of the governor valve have a greater impact on the jerk,and the engine speed and load torque have a smaller effect. The greater the oil pressure, the greater the maximum peak. The greater the flow rate of the governor valve, the smaller the maximum peak time of jerk.

Fig.13 Effects of influencing factors on jerk

4.4 Analysis of sliding work influence

As shown in Fig.14a, with the engine speed increasing continuously, the stable sliding and grinding work of the clutch is 2 029.8 J, 5 049.9 J,and 12 418.5 J. As shown in Fig.14b, with the continuous increase in load torque, the stable sliding wear work of the clutch is 3 331.7 J, 5 056.3 J,and 7 252.8 J. As shown in Fig.14c, with the continuous increase in the oil pressure in the main oil circuit, the stable sliding wear work of the clutch is 22 264.7 J, 6 769.5 J, and 3 722.5 J.As shown in Fig.14d, as the flow rate of the speed control valve increases, the sliding friction work generation time varies slightly because the clutch combination time becomes shorter as the flow rate of the flow valve increases. The steady sliding work of the clutch is 15 401.2 J, 6 777.1 J,and 3 113.5 J.

The above results show that the engine speed, load torque, oil pressure in the main oil circuit, and flow rate of the governor valve all have obvious effects on the sliding work. The greater the engine speed and load torque, the greater the sliding friction work. The greater the oil pressure is in the main oil circuit and the greater the flow rate of the governor valve, the smaller the friction work.

5 Analysis of Output Speed at Shifting Time

Fig.14 Effects of influencing factors on sliding friction work

As shown in Fig.11, the stable speed for the input and output shafts of the HMCVT are different before and after shifting. The main factors that affect the speed drop are as follows: ① when C1is disconnected and C2is not engaged, the speed of transmission is due to the hydraulic transmission, resulting in a certain drop in power output. ② The transmission ratios before and after shifting are different. According to the structural design parameters of the HMCVT, the shift process of HM1 and HM2 is realized when the displacement ratio is –1. The maximum transmission ratio of HM1 and the minimum transmission ratio of HM2 are shown in Tab. 5.

Therefore, to avoid the excessive speed difference in the shift process, it is possible to shift in advance when the displacement ratio is less than –1, which can improve the smoothness of the shift process in the HMCVT.

When the engine speed is 1 550 r/min, the corresponding load torque is 100 N·m, the flow rate of the governor valve is 4 L/min, the oil pressure is 4 MPa, and the displacement ratio is shifted at –1, –0.96, and –0.93. The HMCVT out-put speed during the shifting process is shown in Fig.15. When the displacement ratio is –1, the stable speed before clutch engagement is 2 226.6 r/min, the stable speed after clutch engagement is 2 156.5 r/min, and the difference in stable speed is 70.1 r/min. When the displacement ratio is –0.96, the stable speed before clutch engagement is 2 196.4 r/min, and the stable speed after clutch engagement is 2 187.3 r/min,with the difference in stable speed being 9.1 r/min.When the displacement ratio is –0.93, the stable speed before clutch engagement is 2 173.7 r/min,and the stable speed after clutch engagement is 2 210.5 r/min, with the difference in stable speed being 36.8 r/min. Therefore, the shift time is optimal when the displacement ratio is –0.96, effectively reducing the stable speed difference before and after the output shaft is shifted.

Tab. 5 Transmission ratio of HM1 and HM2

Fig.15 Shift speed output curve for different displacement ratios

6 Conclusions

① The speed of the engine and flow of the governor valve have a great influence on speed reduction. The oil pressure of the main oil circuit and flow rate of the governor valve have a greater influence on the speed rise time. The oil pressure of the main oil circuit and flow rate of the governor valve have a greater effect on the output torque. Whereas, the engine speed and load torque have a smaller effect on the output torque.

② The oil pressure in the main oil circuit and the flow rate of the governor valve have a greater effect on the jerk, while the engine speed and load torque have a smaller effect. The greater the oil pressure, the greater the maximum peak of the jerk. The greater the flow rate of the governor valve, the smaller the maximum peak time of jerk. The influence of engine speed, load torque, oil pressure in the main oil circuit, and flow rate of the governor valve on sliding work is obvious. The greater the engine speed and load torque, the greater the slipping power. The greater the oil pressure in the main oil circuit is and the greater the flow rate in the governor valve is the smaller the sliding work.

③ The shift is performed when the HMCVT displacement ratio is –0.96. The stable speed before clutch engagement is 2 196.4 r/min,and the stable speed after clutch engagement is 2 187.3 r/min. The difference in stable speed is 9.1 r/min, effectively reducing the stable speed of the output shaft difference before and after the shift.