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Abstract

This article focuses on the shift strategy of hydro-mechanical infinitely variable transmission. A computer simulation is carried out to investigate the shift strategy, and the simulation results are verified by the test data. There are four typical working conditions in the continuous shift process, among which the shift process from F₂(N) to F₃(P) plays a decisive role in shift quality. The shift strategy based on the physical parameters from F₂(N) to F₃(P) is lower engine rotating speed, smaller load torque, lower main circuit pressure, and larger speed valve flow rate. The shift strategy based on the shift time from F₂(N) to F₃(P) is to switch the third group of clutches first, then disengage the first group of clutches, and engage the second group of clutches at last. The results show that the shift quality of hydro-mechanical infinitely variable transmission can be improved greatly by the optimization of physical parameters and shift time.

Keywords

Hydro-mechanical infinitely variable transmission shift strategy physical parameters shift time optimization

Introduction

Hydro-mechanical infinitely variable transmission (HMIVT) is a combined stepless speed change device, which is mainly composed of the hydraulic speed regulation mechanism and the mechanical speed variation mechanism.^1–3 Because of the stepless speed change in hydraulic transmission and the high efficiency of mechanical transmission, HMIVT has attracted more and more attention.^4–8 In a long period, however, the research on HMIVT has focused on the construction design and performance study.^9–12 With the increasing requirements of vehicle ride, more and more importance has been attached to the research on the shift strategy. So this article focuses on the shift strategy from the perspective of physical parameters and shift time.

The shift process of HMIVT is a sophisticated dynamics process. There are many factors affecting the shift quality, such as external factors (e.g. power source and load), self-factors of HMIVT (e.g. hydraulic system and transmission system), and control system of clutches (e.g. main circuit pressure and speed valve flow rate). As mentioned above, self-factor is related to the design scheme of HMIVT; the physical parameters discussed in this article mainly involve four factors: engine rotating speed, load torque, main circuit pressure, and speed valve flow rate.^13,14 Studying on the shift strategy usually does not involve shift time, because most of the shift process in the same ranges only involve two clutches, in which shift time plays a limited role in providing shift quality. However, the shift quality involving multi-group clutches is not only related to the design parameters of the clutch itself but also affected by the shock of other clutches, which makes the modeling, simulation, and test more and more difficult. Since tractors often work under extreme conditions, the study on the shift shock is very important.

This article aims to solve the optimal shift strategy problem of transmission involving multi-group clutches and build the simulation model of HMIVT based on Simulation X, using output shaft speed drop amplitude, output shaft dynamic load coefficient, output shaft maximum degree of shock, and shift time as evaluation indexes to analyze transmission involving multi-group clutches. Based on the continuous shift process analysis of transmission, the typical working conditions that influence the shift quality of transmission can be concluded, and the simulation study and experimental validation of the shift strategy based on the physical parameters and the shift strategy based on the shift time are also conducted.

Construction of HMIVT and evaluation index for shift quality

Construction of HMIVT

To optimize the shift strategy, an HMIVT is selected as the research object. The construction of HMIVT is shown in Figure 1.¹⁵Table 1 shows the engagement conditions of HMIVT components.

Figure 1.

Construction of HMIVT.

Table 1.

Engagement conditions of HMIVT components.

Range		Engagement conditions
Range		S₁	S₂	C₁	C₂	C₃	C₄	C₅	C₆	C₇	C₈
Forward	F₃(N)	√		√		√				√
	F₃(P)	√			√		√			√
	F₂(N)	√		√		√			√
	F₂(P)	√			√		√		√
	F₂(N)	√		√		√		√
	F₂(P)	√			√		√	√
	F(H)	√									√
Reverse	R(H)		√								√
	R₂(P)		√		√		√		√
	R₂(N)		√	√		√			√

Simulation model of HMIVT

According to the construction of HMIVT in Figure 1, the simulation model of HMIVT based on Simulation X is shown in Figure 2. The simulation model of HMIVT consists of five parts: (1) engine speed and load torque, (2) hydraulic speed regulation system, (3) mechanical transmission system, (4) gear trains and shafting, and (5) hydraulic control system of clutches. Among them, the hydraulic control system of clutches is the core module for the research of shift strategy, which is shown in Figure 3.

Figure 2.

Simulation model of HMIVT.

Figure 3.

Simulation model of hydraulic control system of clutches.

HMIVT efficiently realizes stepless speed change by mechanical transmission and hydraulic transmission. Clutches are controlled by the solenoid directional control valves during the shift. Because of the smaller flow requirement of main circuit, a small displacement fixed pump is used as the oil driving device. The main circuit pressure is controlled by the pressure valve; meanwhile, the speed control valve flow rate is controlled by the corresponding directional control valve.

Evaluation index for shift quality

In this article, the output shaft speed drop amplitude, output shaft dynamic load coefficient, output shaft maximum degree of shock, and shift time are selected as the evaluation indexes of shift quality.

Output shaft speed drop amplitude

The output shaft speed drop amplitude reflects the rotating speed fluctuation during shifting, which can be expressed as

δ = \frac{| n_{o} - n_{o \min} |}{n_{o}}

(1)

where δ is the output shaft speed drop amplitude, n_o is the output shaft steady speed, and n_o_min is the output shaft minimum speed.

Output shaft dynamic load coefficient

The output shaft dynamic load coefficient reflects the torque fluctuation during shifting, which can be expressed as

γ = \frac{T_{o \max}}{T_{o}}

(2)

where γ is the output shaft dynamic load coefficient, T_o is the output shaft steady torque, and T_o_max is the output shaft maximum torque.

Output shaft/intermediate shaft maximum degree of shock

The degree of shock reflects the vibration and shock of shaft. The output shaft maximum degree of shock and intermediate shaft maximum degree of shock are applied to analyze the different actions of clutches during shifting. The output shaft maximum degree of shock can be expressed as

j_{\max} = {| \frac{r_{q}}{i_{o} i_{LB}} \frac{d^{2}}{d t^{2}} (\frac{π n_{o}}{30}) |}_{\max}

(3)

where j_max is the output shaft maximum degree of shock, r_q is the driving wheel radius, i_o is the main reducer transmission ratio, and i_LB is the wheel-side transmission ratio.

Shift time

The shift process involves two clutches experiencing four stages: before switching, torque phase, inertial phase, and after switching, so the shift process involving more clutches will be much complicated; this article holds that the shifting is finished when the output shaft rotating speed reaches 99% of the steady rotating speed.

Continuous shift process of HMIVT

According to the simulation model in Figure 2, the conditions of clutches and the displacement of variable pump are controlled at every 10 s. The simulation curves of continuous shift process are shown in Figure 4.

Figure 4.

Simulation curves of continuous shift process.

The rotating speed curves reflect the speed change in shafts, and the angular acceleration curves reflect the torque fluctuation of shafts. We can conclude that the shift process from F₂(N) to F₃(P) plays a decisive role in improving the shift quality during the whole process.

Shock is caused by the switch time difference of clutches during shifting. Load torque leads to a rapid decrease in the output shaft rotating speed, and the output shaft rotating speed will reach the minimum value, when its transmission torque realizes the balance between the most related clutch and the load. This article takes the shift process from F₂(N) to F₃(P) for example to study shift control strategy based on the physical parameters and shift time.

Analysis on the shift strategy based on the physical parameters

Simulation analysis

The study on shift quality based on the physical parameters is actually solving a optimization problem, which involves multi-factor and multi-evaluation index, so this article chooses the L₉(3⁴) orthogonal table as a research method. Range method is used to analyze the simulation results due to the uniqueness of simulation data, and variance analysis method is applied to analyze the test results due to the existence of test error. According to the comparison between the sum of squares and error square sum, F-test is used to draw the conclusions concerning the variance analysis.

Factor A represents the engine rotating speed, the three levels of which are, respectively, 900, 1200, and 1500 r/min; Factor B represents the load torque, the three levels of which are, respectively, 75, 100, and 125 N m; Factor C represents the main circuit pressure, the three levels of which are, respectively, 3, 4, and 5 MPa; Factor D represents the speed valve flow rate, the three levels of which are, respectively, 3, 4, and 5 L/min. The output shaft speed drop amplitude, dynamic load coefficient, maximum degree of shock, and shift time are expected to be used as evaluation indexes I, II, III, and IV. Each index should be tested nine times; the conclusions of range analysis of shift quality based on the physical parameters are shown in Table 2.

Table 2.

Range analysis table of shift quality based on the physical parameters.

Evaluation index	Range				Optimal scheme
Evaluation index	A	B	C	D	Optimal scheme
I	7.74%	7.50%	0.97%	3.26%	A₃B₁D₃C₁
II	0.07	0.98	0.29	0.02	B₃C₁A₁D₁₍₃₎
III	1.09	2.55	1.38	0.66	B₁C₁A₂D₂
IV	0.03	0.19	0.10	0.67	D₃B₁C₁A₁

There is some difference among the optimal schemes in Table 2, so the principal aspect of contradiction should be emphatically solved according to the data above. The scheme A₃B₁D₃C₁ can be substituted by the scheme A₃B₁D₃ for evaluation index I, the range of which is changed from (9.91%, 29.38%) (all schemes) to (9.91%, 10.88%) (scheme A₃B₁D₃); the scheme B₃C₁A₁D₁₍₃₎ can be substituted by the scheme B₃C₁ for evaluation index II, the range of which is changed from (1.88, 3.24) (all schemes) to (1.88, 1.97) (scheme B₃C₁); the scheme B₁C₁A₂D₂ can be substituted by the scheme B₁C₁A₂ for evaluation index III, the range of which is changed from (7.95, 13.63) (all schemes) to (7.95, 8.61) (scheme B₁C₁A₂); the scheme D₃B₁C₁A₁ can be substituted by the scheme D₃B₁ for evaluation index IV, the range of which is changed from (1.24, 2.23) (all schemes) to (1.24, 1.37) (scheme D₃B₁).

HMIVT test bench

HMIVT test bench includes mechanical transmission system and computer measurement and control system. The mechanical transmission system mainly includes engine, torque–speed transducers, HMIVT, valve assembly, and dynamometer. The computer measurement and control system, which is shown in Figure 5, is composed of an upper machine and two lower machines. The upper machine exchanges data with serial ports and data acquisition cards, and the lower machines perform data acquisition. The upper machine and the lower machines are communicated by the CAN interface cards, and the LabVIEW is used as the software development platform.^16–19

Figure 5.

Computer measurement and control system.

Test verification

The variance analysis method of orthogonal test should be used to study the shift quality based on the physical parameters. Test schemes for each evaluation index should be divided into nine groups, while each group should be tested four times. We choose F-test to draw the significant conclusions; the comparison of the simulation results and test results is shown in Table 3.

Table 3.

Comparison of simulation results and test results.

Contrastive analysis	Evaluation index	I	II	III	IV
Simulation results	Optimal scheme	A₃B₁D₃C₁	B₃C₁A₁D₁₍₃₎	B₁C₁A₂D₂	D₃B₁C₁A₁
Simulation results	Primary and secondary factor	AB(*) D() C	B(**) C() AD	B(**) C() AD	D(**) BC() A
Test results	Optimal scheme	B₁A₃D₃C₁	B₃C₁A₁D₂	B₁C₁D₂A₂	D₃B₁C₁A₁
Test results	Primary and secondary factor	BA(*) D() C	B(**) C() AD	B(**) C() DA	D(*) B() C(*) A

F_α(2,27) > 5.49(***), 5.49 ≥ F_α(2,27) > 3.47(**), 53.47 ≥ F_α(2,27) > 2.51(*).

There are some differences in the simulation results and test results, which are caused by the model simplification and test error. However, the results of the test basically tally with the simulation results. That is to say, engine rotating speed and load torque play major roles in evaluation index I, followed by speed valve flow rate; load torque plays a major role in evaluation indexes II and III, followed by main circuit pressure; speed valve flow rate plays a major role in evaluation index IV, followed by load torque and main circuit pressure.

The shift strategy based on the physical parameters is lower engine rotating speed, smaller load torque, lower main circuit pressure, and larger speed valve flow rate. It is noteworthy that the shift strategy discussed above is the whole control strategy. If there are some special requirements on the evaluation index, the corresponding control strategies will be changed. Single-factor loading tests can be used to analyze shift strategy based on the physical parameters, the results which are shown in Table 4. The test results of shift strategy based on the physical parameters are shown in Figure 6. According to the test comparison diagrams based on the physical parameters, the shift quality in Test 3 is superior to that in Tests 1 and 2.

Table 4.

Test schemes of shift strategy based on the physical parameters.

	Physical parameters
	Engine rotating speed (r/min)	Load torque (N m)	Main circuit pressure (MPa)	Speed valve flow rate (L/min)
Test 1	1500	150	5	3
Test 2	1200	120	4	4
Test 3	900	90	3	5
Assumed conditions	Switch time of clutches: 10.00 s

Figure 6.

Test comparison diagrams based on the physical parameters.

Analysis on the shift strategy based on the shift time

Simulation analysis

According to the analysis above, the shift process from F₂(N) to F₃(P) involves six clutches, which can be divided into three groups: Group 1(C₁, C₃), Group 2(C₂, C₄), and Group 3(C₆, C₇). The longer the switch time, the larger the shaft speed fluctuation amplitude; the shorter the switch time, the tighter the clutches’ engagement conditions, so the switch time of clutches in the same group does not show distinctive difference, while the shift time difference exists in the different groups of clutches, which provides theoretical basis by grouping study.

Switch strategy of clutches between groups

Factors A, B, and C, respectively, represent the first, the second, and the third groups of clutches, and Factor D is the blank column. Levels 1, 2, and 3, respectively, represent the different switch time of clutches (9.50, 10.00, 10.50 s). The output shaft speed drop amplitude, output shaft dynamic load coefficient, intermediate shaft maximum degree of shock, and output shaft maximum degree of shock are expected to be used as evaluation indexes I, II, III, and IV. Test schemes for each evaluation index can be divided into nine groups; the conclusions of range analysis based on the shift time are shown in Table 5.

Table 5.

Range analysis table of shift quality based on the shift time between groups.

Evaluation index	Range				Optimal scheme
Evaluation index	A	B	C	D	Optimal scheme
I	1.67%	17.90%	26.16%	4.64%	C₁B₃A₃
II	0.12	0.37	0.37	0.20	B₃C₂(C₂B₃)A₃
III	11.31	14.04	3.23	16.31	B₃A₃C₃
IV	7.27	1.29	6.09	1.69	A₃C₂B₂

According to the range analysis data in Table 5, the scheme C₁B₃A₃ can be substituted by the scheme C₁B₃ for evaluation index I, the range of which is changed from (−1.30%, 49.07%) (all schemes) to (−1.30%, 5.01%) (scheme C₁B₃); the scheme B₃C₂(C₂B₃)A₃ can be substituted by the scheme B₃C₂(C₂B₃) for evaluation index II, the range of which is changed from (2.02, 3.08) (all schemes) to (2.02, 2.34) (scheme B₃C₂(C₂B₃)); the scheme B₃A₃C₃ can be substituted by the scheme B₃A₃ for evaluation index III, the range of which is changed from (9.19, 54.08) (all schemes) to (9.19, 25.50) (scheme B₃A₃); the scheme A₃C₂B₂ can be substituted by the scheme A₃C₂ for evaluation index IV, the range of which is changed from (4.56, 21.02) (all schemes) to (4.56, 6.25) (scheme A₃C₂). The shift strategy of clutches among groups is that clutches in Group 3 should be switched earlier than that in Group 1 and Group 2, which provides theoretical basis for the discussion below.

Switch strategy of clutches in Group 3

Single-factor loading test can be used to analyze switch strategy of clutches in Group 3. The switch time of clutches is shown in Table 6. The shift quality simulation results of clutches in Group 3 are shown in Figure 7.

Table 6.

Switch time of clutches (switch strategy of clutches in Group 3).

		Disengagement time	Engagement time
Assumed conditions	Group 1	C₁, C₃(10.00 s)
Assumed conditions	Group 2		C₂, C₄(10.00 s)
Group 3	Scheme 1	C₆(9.00 s)	C₇(9.50 s)
	Scheme 2	C₆(9.00 s)	C₇(9.50 s)
	Scheme 3	C₆(9.50 s)	C₇(9.00 s)

Figure 7.

Shift quality simulation results of clutches in Group 3.

The output shaft lowest speed, respectively, reaches 1066.27, 1021.80, and 1059.50 r/min in 10.94,11.05, and 10.85 s, so the output shaft speed drop amplitude is, respectively, 7.15%, 6.39%, and 7.74%, which shows that the switch time has little effect on evaluation index I. The output shaft maximum torque, respectively, reaches 187.90, 189.59, and 203.11 N m in 11.21, 11.35, and 11.09 s, so the output shaft dynamic load coefficient is, respectively, 1.88, 1.89, and 2.03, which shows that there is little difference on evaluation index II when the switch time of C₆ is no later than that of C₇. The intermediate shaft maximum degree of shock, respectively, reaches 27.40, 19.76, and 20.32 in 11.13, 11.13, and 11.09 s, which shows that evaluation index III has excellent performance when the switch time of C₆ is not earlier than that of C₇.

The output shaft maximum degree of shock, respectively, reaches 8.24, 8.48, and 13.03 in 11.23, 11.36, and 10.99 s, which shows that evaluation index IV has excellent performance when the switch time of C₆ is not later than that of C₇. According to the analyses above, the control strategy of clutches in Group 3 is that clutches C₆ and C₇ are switched at the same time.

Switch strategy of clutches in Groups 1 and 2

The range analysis can be used to analyze the switch strategy of clutches in Groups 1 and 2. The switch time of clutches is shown in Table 7.

Table 7.

Switch time of clutches (switch strategy of clutches in Groups 1 and 2).

	Switch time
Assumed conditions	Group 3	Disengagement time C₆ (10.00 s)	Engagement time C₇ (10.00 s)
Group 1 and Group 2	Three levels	Switch time: 10.50, 11.00, 11.50 s
Group 1 and Group 2	Four factors	A(clutch C₁), B(clutch C₂), C(clutch C₃), D(clutch C₄)

According to the L₉(3⁴) orthogonal tables related to the evaluation indexes of shift quality, the range analysis conclusions for the clutches of planet gear mechanism based on the shift time are shown in Table 8.

Table 8.

Range analysis table of shift quality based on the shift time in Groups 1 and 2.

Evaluation index	Range				Optimal scheme
Evaluation index	A	B	C	D	Optimal scheme
I	3.20%	1.87%	1.81%	0.56%	A₃B₃C₃D₂₍₃₎
II	0.29	0.19	0.22	0.07	A₁C₁B₁D₁
III	1.94	6.63	9.51	9.65	D₃C₁B₁A₁
IV	24.27	12.14	14.58	6.55	A₁C₁B₂D₃

According to the range analysis data in Table 8, the scheme A₃B₃C₃D₂₍₃₎ can be substituted by the scheme A₃B₃C₃ for evaluation index I, the range of which is changed from (3.58%, 11.02%) (all schemes) to (3.58%, 4.14%) (scheme A₃B₃C₃); the scheme A₁C₁B₁D₁ can be substituted by the scheme A₁C₁B₁ for evaluation index II, the range of which is changed from (1.91, 2.68) (all schemes) to (1.91, 2.17) (scheme A₁C₁B₁); the scheme D₃C₁B₁A₁ can be substituted by the scheme D₃C₁B₁ for evaluation index III, the range of which is changed from (11.7, 39.43) (all schemes) to (11.7, 13.64) (scheme D₃C₁B₁); the scheme A₁C₁B₂D₃ can be substituted by the scheme A₁C₁B₂ for evaluation index IV, the range of which is changed from (−3.99, 53.55) (all schemes) to (−3.99, 2.56) (scheme A₁C₁B₂). The proportion of factor based on the shift time in Groups 1 and 2 is shown in Table 9.

Table 9.

Proportion of factor based on the shift time in Groups 1 and 2.

Evaluation index	Optimal scheme (the proportion of factor)
I	C₁ disengaging time delay (43.01%), C₂ engaging time delay (25.13%)
I	C₃ disengaging time delay (24.33%); cumulative proportion (92.47%)
II	C₁ disengaging time advance (37.66%), C₃ disengaging time advance (28.57%)
II	C₂ engaging time advance (24.68%); cumulative proportion (90.91%)
III	C₄ engaging time delay (34.80%), C₃ disengaging time advance (34.30%)
III	C₂ engaging time advance (23.91%); cumulative proportion (93.01%)
IV	C₁ disengaging time advance (42.18%), C₃ disengaging time advance (25.34%)
IV	C₂ engagement in time (21.10%); cumulative proportion (88.62%)

The simulation results show that the shift strategy based on the shift time is to switch the third group of clutches first, then disengage the first group of clutches, engage the second group of clutches at last.

Test verification

Single-factor loading tests can be used to analyze the shift strategy based on the shift time, the results which are shown in Table 10. The test results of shift strategy based on the shift time are shown in Figure 8.

Table 10.

Test schemes of shift strategy based on the shift time.

	Switch time
	9.50 s	10.00 s	10.50 s
Test 1	Group 1	Group 2	Group 3
Test 2	Group 2	Group 3	Group 1
Test 3	Group 3	Group 1	Group 2
Assumed conditions	Engine rotating speed: 1200 r/min; load torque: 120 N m; main circuit pressure: 4 MPa; speed valve flow rate: 4 L/min

Figure 8.

Test comparison diagrams based on the shift time.

According to the test comparison diagrams in Figure 8, the shift quality in Test 3 is superior to that in Tests 1 and 2. The study on the shift strategy based on shift time is on the premise of the fixed physical parameters, and vice versa. We often set switch time of clutches according to the physical parameters in the practical application, and the engagement conditions of clutches are controlled by the pulse-width modulation (PWM) modulator. The controllers locate the time frame from the structural body databases and then control the switch time of clutches according to the databases.

Conclusion

The shift process from F₂(N) to F₃(P) plays a decisive role in improving shift quality during whole shift process. Shift quality can be improved greatly by optimizing the physical parameters and the shift time of HMIVT involving multi-group clutches.

In the shift process from F₂(N) to F₃(P), the shift strategy based on the physical parameters is lower engine rotating speed, smaller load torque, lower main circuit pressure, and larger speed valve flow rate.

In the shift process from F₂(N) to F₃(P), the shift strategy based on the shift time is to switch the third group of clutches first, then disengage the first group of clutches, engage the second group of clutches at last.

Footnotes

Academic Editor: Mario L Ferrari

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This article was financially supported by National Natural Science Foundation Project (51575001) and Scientific Research Innovation Project of Jiangsu University (KYXX-0008).

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Analysis on the shift strategy of hydro-mechanical infinitely variable transmission based on the orthogonal test

Abstract

Keywords

Introduction

Construction of HMIVT and evaluation index for shift quality

Construction of HMIVT

Simulation model of HMIVT

Evaluation index for shift quality

Output shaft speed drop amplitude

Output shaft dynamic load coefficient

Output shaft/intermediate shaft maximum degree of shock

Shift time

Continuous shift process of HMIVT

Analysis on the shift strategy based on the physical parameters

Simulation analysis

HMIVT test bench

Test verification

Analysis on the shift strategy based on the shift time

Simulation analysis

Switch strategy of clutches between groups

Switch strategy of clutches in Group 3

Switch strategy of clutches in Groups 1 and 2

Test verification

Conclusion

Footnotes

Declaration of conflicting interests

Funding

References