Development of a model for the optimization of the main factors influencing a 162kW wheeled tractor driver’s whole body vibration

Abstract

The vibration tests were carried out using a 162kW wheeled tractor to evaluate the Whole-body vibration while the tractor working in the field, driving on concrete road and in-parking state. The tractor ride comfort was analyzed using the joint weighted acceleration of seat surface vibration from 1 to 80 Hz as the evaluation indicator, according to ISO2631 standard suggestions. During field work, the combined acceleration of the driver’s whole body vibration is 1.39, and the subjective feeling is extremely uncomfortable. Based on the multi-body dynamics analysis software, a tractor dynamics simulation model including the seat, cab mounts, chassis, tyre and road coupling system was established. By changing the model parameters, the influence of the tractor driver’s whole body vibration under the condition of the artificial test track was further analyzed. The analysis shows that the factors that have a greater impact on the driver’s whole body vibration when driving on the artificial runway are the vertical stiffness of the tyre, the vertical stiffness of the seat suspension, and the damping coefficient of the tyre.

Keywords

Agricultural tractor whole-body vibration filed tests artificial track multi-body dynamic model

Introduction

Tractors are widely used in agricultural production activities, its working environment is very harsh. The severe vibration generated by the tractor during operation affects the physical and mental health of the driver and the efficiency of operation. Therefore, reducing tractor vibration has always been the focus of research by designers.¹ During the actual operation of the tractor, its vibration performance depends on many variables, including soil type, type of operation, tyre pressure, tractor mass distribution, forward speed, etc.^2–7 The vibration generated by road excitation needs to be transmitted to the human body through three vibration isolation elements, namely tires, cab suspension, and seats, and relevant vibration research has focused on these three areas. Gomez-Gil et al.⁸ studied the effect of seat-mounted ground clearance on the driver’s lateral vibration characteristics. Roberto studied the vibration transmission characteristics of the tractor seat in three directions on different road surfaces. The test results showed that the seat has good isolation against vertical vibration and poor vibration isolation in the horizontal direction, suggesting that the influence of transverse and longitudinal rocking motion should be minimized when the tractor is manufactured.³ Maciejewski⁹ developed a model of the horizontal seat suspension and human coupling system, optimizing the vibration isolation performance of the seat suspension. Zhu designed a six-legged parallel suspension for tractor cab damping and used the sensitivity method to optimize the design of the system.¹⁰ Tong studied the vibration characteristics of tractor cabs and suspension isolation. The root-mean-square (RMS) values of acceleration in all directions of the cab center of mass were reduced by rubber suspension isolation, with the greatest reduction in the RMS value in the lateral tilt direction.¹¹ Mehdizadeh et al.¹² matched the stiffness and damping of the cab suspension system using the seat surface vibration weighted acceleration as the optimization objective. Xue investigated the effect of tyre pressure on the driver’s lateral ride vibration characteristics illustrating that changes in front tyre pressure had little effect on the root mean square value of lateral acceleration at the seat, while increasing rear tyre pressure resulted in a gradual increase in the root mean square value of lateral acceleration.¹³

A large number of theoretical and experimental studies have been carried out on the vibration characteristics of tractors, but most of the tests are carried out for specific types of operation and several combinations of tests, and the extensiveness of the test findings is insufficient. The research on vibration damping components is also mostly directed at a certain aspect of the seat, cab mounts and tyres, lacking systematic and comprehensive analysis. During the actual operation of the tractor, the vibration of the seat, cab, chassis and tyre-road system are coupled to each other. In this paper, a variety of tractor use scenarios are tested and driving smoothness analysis is carried out around the test data. A multi-system coupled dynamics model of tractor component interaction is developed to provide a comprehensive analysis of the factors influencing tractor smoothness.

Smoothness evaluation methods

The tractor’s smoothness is mainly evaluated according to the driver’s comfort. As shown in Figure 1, In the analysis of tractor smoothness, the root mean square value of the weighted vibration along the x, y and z directions at the seating surface is used as the evaluation index. According to the international standard ISO 2631-1 “Mechanical vibration and shock- Evaluation of human exposure to whole-body vibration -- Part 1: General requirements,” the relationship between the subjective perception of the human body is shown in Table 1. Vibration model of the human body in the seated position seen Figure 1. x,y,z refer to the direction of translational vibration. For rotational vibration, they refer to the axis of rotation, r. (Rotation about x-,y-,and z-axes is designated roll, pitch and yaw, respectively.)¹⁴

Figure 1.

Vibration model of the human body in the seated position.

Table 1.

Classification of human subjective feelings.

Root mean square value of the frequency- weighted acceleration	Subjective feelings
Less than 0.315 m/s²	Not uncomfortable
0.315 m/s² to 0.63 m/s²	A little uncomfortable
0.63 m/s² to 1.25 m/s²	Uncomfortable
Greater than 1.25 m/s²	Extremely uncomfortable

A frequency weighting function is constructed using the 1/3 octave bandwidth method in accordance with ISO 2631-1, multiplying each 1/3 octave component from 1 to 80 Hz by a weighting factor shown in Table 2 to calculate the root mean square value of the weighted acceleration in each axial direction. The joint weighted acceleration at the seat surface is calculated as shown in equation (1).

a_{w} = \sqrt{{(1.4 a_{w x})}^{2} + {(1.4 a_{w y})}^{2} + {a_{w z}}^{2}}

(1)

Where: a_wx, a_wy, a_wz are the frequency-weighted RMS values of acceleration in the direction, direction and direction respectively. The units are m/s².

Table 2.

Main frequency weights for one-third octave.

Frequency (Hz)	z-direction weighting factor	x and y directions weighting factors
1	0.482	1.011
1.25	0.484	1.008
1.6	0.494	0.968
2	0.531	0.89
2.5	0.631	0.776
3.15	0.804	0.642
4	0.967	0.512
5	1.039	0.409
6.3	1.054	0.323
8	1.036	0.253
10	0.988	0.212
12.5	0.902	0.161
16	0.768	0.125
20	0.636	0.1
25	0.513	0.08
31.5	0.405	0.0632
40	0.314	0.0494
50	0.246	0.0388
63	0.186	0.0295
80	0.132	0.0211

Driver whole-body vibration test analysis

Test subjects and test conditions

The main parameters of the test subjects in this paper are shown in Table 3.

Table 3.

Tractor characteristics.

Item	Unit	Value
Tractor power	kW	162
Tractor dimensions (lengthwidthheight)	mm	555025003240
Wheelbase	mm	2950
Front- rear wheelbase	mm	1923-1940
Minimum usable mass	kg	8583
Ballast weight (front-rear)	kg	800-400
Tyres dimensions (front-rear)	—	16.9R30-520/85R42
Tyres pressure	bar	1.7
Front axle suspension	—	N/A
Cab suspension	—	Four silent-block
Driver’s seat	—	Pneumatic suspension

The test conditions include: (1) ploughing operation in the field with a four-share plough at approx. the vehicle speed is about 8 km/h; (2) driving in the field with a four-share plough (lifted state) at approx. 8 km/h; (3) driving with a four-share plough (lifted state) on a concrete road transit at approx. 25 km/h; (4) parking in place with the throttle fully open and the engine at a maximum speed of 2320 r/min. The tractor driver is a male, weighing 72 kg and standing 177 cm tall (Figures 2–5).

Figure 2.

Seat surface measurement point.

Figure 3.

Seat rail measurement point.

Figure 4.

Parking measurement scene.

Figure 5.

Field operations measurement scene.

The driver’s whole-body vibration was measured using a BK-4515B accelerometer with a sensitivity of 100 mV/g. The data acquisition system was a LAN-XI module from BK with a high-pass filter set at 0.7 Hz. For further vibration characterization, vibration signals from the seat rails, cab mounts and other locations were also acquired (Table 4).

Table 4.

Results of vibration measurements at the seat surface under different test conditions (m/s²).

	a_x		a_y		a_z
	Mean	SD	Mean	SD	Mean	SD
Field operations	1.04	0.13	0.63	0.10	0.79	0.09
Field driving	0.86	0.08	1.10	0.13	0.53	0.08
Driving on concrete	0.82	0.06	1.06	0.10	1.35	0.11
Parking in place with the throttle fully open	0.13	0.01	0.15	0.01	0.12	0.02

Time and frequency domain analysis of test data

The time domain curves of the collected vibration signals are band-pass filtered from 1 to 80 Hz. The seat surface measurement point vertical vibration time domain curves for each test condition was shown in Figure 6.

Figure 6.

Time domain curves of vertical vibration at the seat surface measurement points. (a) Field operations; (b) Field driving; (c) Driving on concrete; (d) Parking in place with the throttle fully open.

a_x, a_y and a_z are the acceleration at the seat surface in the X, Y and Z directions respectively. The units are m/s².

From the vibration values, the seat surface vibration are the largest with the condition of the driving on concrete, and the Z-directional vibration is larger than that of the other two directions. A larger is generated at higher vehicle speed due to the greater stiffness of the road surface. Comparing the field operation and field driving data, the interaction between the implement and the soil makes a greater impact on vibration. The vibration of the field driving condition is lower than that of the field operation condition. Engine excitation made little effect on seat surface vibration (Figure 7).

Figure 7.

1/3 octave curve of seat and seat rail measurement points for vertical vibration. (a) Field operations; (b) Field driving; (c) Driving on concrete road; (d) Parking in place with the throttle fully open.

As the one-third octave curves of the seat and seat rail pendulum from 1 to 80 Hz were analyzed, the vibration isolation of the seat from the seat rail position varies in different scenarios and condition. The best isolation was found in field operation conditions. Except for the in-place parking condition, the seat does not provide any vibration isolation in the 2–4 Hz band. This phenomenon should be related to the inherent frequency of the seat-driver system. The source of vibration in the in-place parking condition is mainly from the mid to high frequency excitation such as the engine ignition frequency. The vibration amplitude at the lower frequencies is very small and significantly different from the other conditions.

A similar conclusion exists for the analysis of the vibration data for the cab mounts. The left front suspension was taken as an example for analysis. The vibration isolation effect is best under field operation conditions. The rubber suspension makes essentially no vibration isolation effect at low frequencies within 20 Hz, as shown in Figure 8. According to the stiffness of the rubber mounts and the mass distribution of the cab, the sixth-order inherent frequency of the cab mounts system was between 3.8 and 15.7 Hz, which is precisely the reason for the failure of the vibration isolation of the cab mounts system in the low frequency band within 20 Hz.

Figure 8.

The 1/3 octave curves of vertical vibration at the left front suspension measurement point of the cab (a) Field operations; (b) Field driving; (c) Driving on concrete road; (d) Parking in place with the throttle fully open.

Smoothness analysis under four operating conditions

A 1/3 octave analysis was performed with an analysis bandwidth of 1 to 80 Hz. Each 1/3 octave component was multiplied by a weighting factor. The joint weighted acceleration at the seat surface was calculated according to the smoothness evaluation method described above. The results are shown in Table 5.

Table 5.

Driver whole body vibration results under different test conditions (m/s²).

Weighted acceleration test condition	a_wx	a_wy	a_wz	a_w
Field operations	0.52	0.72	0.61	1.39
Field driving	0.27	0.31	0.38	0.68
Driving on concrete	0.34	0.27	0.85	1.05
Park in place with the throttle fully open	0.01	0.01	0.05	0.05

The maximum value is 1.39 for field operation in terms of the smoothness evaluation index, leading to a subjective feeling of extreme discomfort. In terms of the different directions of vibration, the X and Y directions of vibration are significantly greater in field operations than in other test conditions. The X and Y components were multiplied by a factor of 1.4, as specified in ISO 2631-1. According to the European Directive 2002/44/EC, The typical whole-body vibration exposure on agricultural tractor operators is less than 1.15 m/s² for an 8-hour working day.¹⁵ According to this assessment, driving this tractor for long periods of time in the field can be detrimental to the physical and mental health of the operator (Figure 9).

Figure 9.

Manual test track measurements.

Test on artificial track

In accordance with GB/T 10910-2020 “Measurement of whole body vibration of drivers of agricultural wheeled tractors and field machines” (equivalent to ISO 5008), manual test track measurements were carried out on the measurement site and test conditions specified. The test was carried out on a 100 m long smoother runway, with the tractor without optional front and rear counterweights and tyre counterweights, without suspension of implements, using the same tyres as for the field measurements and with a tyre pressure of 170 kPa (Table 6).

Table 6.

Driver whole body vibration results measured on artificial track (m/s²).

Weighted acceleration test condition	a_wx	a_wy	a_wz	a_w
Artificial track 12km/h driving	1.03	1.45	1.39	2.85

The artificial test track consisted of 626 rigid concrete strips with undulating height, so the vibration tested on this track was mainly from road excitation. After the analysis of the test data, the whole-body vibration evaluation index aw for the driver was calculated to be 2.73, which is much higher than the field operating conditions. However, it still meets the requirements of aw ≤3.0 as stipulated in China agricultural machinery promotion and appraisal outline DG/T 001-2019 “Agricultural wheeled and crawler tractors.” The test value is more reasonable when compared with other domestic artificial test track test data.

Modeling and simulation

Multi-rigid body dynamics model for tractors

In this paper, the multi-body dynamics software, Adams is used for tractor multi-cylinder dynamics modeling. Adams uses the first class Lagrangian equations with multipliers to establish the dynamical equations of the system, and automatically establishes the Lagrangian equations of motion for the system based on the mechanical system model.

The cab is modeled to actual dimensions and its material and other properties are defined to match the solid. Components such as the engine and transmission system are modeled in an approximate manner, simplified into mass blocks and ensure that the spatial positioning relationship between the components is consistent with the actual tractor, the total mass is consistent with the actual tractor and the model center of mass position is the same as the actual tractor. Table 7 summarize model assembly masses, total masses of tractor parts are equally distributed on the housings.

Table 7.

Mass values of tractor parts.

Parts	Mass (kg)
Seat	30
Cab	974
Front wheel	215
Rear wheel	372
Front axle	374
Rear avle	527
Engine assembly	1500
Power train	3000
Front bracket	350
Suspension mechanism assembly	300
Fuel tank and oil	500
Front balance	800
Rear balance	400

The tractor does not have a frame, so the engine oil pan is strengthened, and the driveline, front and rear axles together constitute the tractor chassis system, which plays a load-bearing role. Rubber suspension is installed between the cab and chassis to form a four-point suspension cab system.

The simplified model of the whole tractor 1/2 is shown in Figure 10. Only the stiffness and damping of the seat mounts, cab mounts and tyre drops are shown in the figure, which are modeled in Adams considering stiffness and damping in all three directions. The engine, driveline, front and rear axles and front and rear mating points are rigidly connected, the cab is simplified to a rigid body without consideration of local vibrations, and the driver and seat suspension are considered as one part.¹⁶ The seat suspension and cab suspension stiffness and damping parameters were measured by the test, and the relevant parameters are shown in Tables 8 and 9.

Figure 10.

Simplified 1/2 model of the complete tractor.

Table 8.

Seat suspension parameters.

	x	y	z
Stiffness (N/mm)	500	500	10
Damping coefficient (Ns/mm)	1.0	1.0	1.0

Table 9.

Cab suspension parameters.

	Stiffness (N/mm)		Damping coefficient (Ns/mm)
	Radial-direction	Axial-direction	Radial-direction	Axial-direction
Front suspension	469	855	1.0	1.0
Rear suspension	469	1297	1.0	1.0

Tyre-road model

According to GB/T 10910-2020 (equivalent to ISO 5008-2002),¹⁷ the driver whole body vibration test was conducted on a 100 m smoother runway. The artificial test runway consisted of 626 rigid concrete strips with undulating height, with accurate numerical descriptions of the pavement unevenness to facilitate pavement model. The artificial test runway pavement file for simulation was prepared according to the data in Table 3 in the appendix of the standard, imported into Adams software and the artificial runway model was established (Table 10).

Table 10.

Tyre property parameters.

Property name	Unit	Front wheel	Rear wheel
Free radius	mm	742.5	972.5
Section width	mm	430	528
Height to width ratio	—	0.75	0.75
Vertical stiffness	N/mm	469.3	697.3
Longitudinal slip stiffness	N/mm	6000	8000
Lateral deflection stiffness	N/deg	36,000	47,000
Camber stiffness	N/deg	3000	4000
Radial damping ratio	—	3.0	3.0
Rolling resistance factor	—	0.05	0.05
Factor of static friction	—	0.94	0.94
Factor of dynamic friction	—	0.75	0.75

The tyre model is established in Adams software,¹⁸ and the tyre stiffness and damping parameters are calculated from the tyre pressure and size.^19,20 Constraints are established according to the motion relationship between the components, and the whole vehicle dynamics simulation model is shown in Figure 11.

Figure 11.

Tractor road surface model.

Simulation results

The simulation studies the situation of a tractor running on the artificial test track. The simulated acceleration time domain signals in the three directions at the seat surface are shown in Figure 12. The simulated combined acceleration of the driver's whole body vibration is 2.66, which is 6.7% smaller than the test value of 2.85. The error in all three directions is within 10%, indicating that the simulation model has a high degree of confidence.

Figure 12.

Seat position acceleration in three directions (a) X-axis; (b) Y-axis; (c) Z-axis with tractor running on the artificial test track.

Numerical model-based analysis of smoothness influencing factors

The factors affecting the smoothness of tractor driving are analyzed based on a numerical dynamic model of a tractor running on an artificial track. This model only changes the parameters, such as the stiffness and damping of the elastic elements, without considering the changes in speed and mass distribution (Figure 13).

Figure 13.

Comparison of simulation and test results with tractor running on the artificial test track.

Seat suspension parameters

Figure 14 shows the effect of changing the seat suspension stiffness. The horizontal coordinates are dimensionless values. Value 1 is the base value and the stiffness value in the initial simulation model. Value 2 represents a 100% increase and value 0.5 represents a 50% decrease compared with the base value. The vertical coordinate is the joint acceleration of the driver’s whole-body vibration obtained from the numerical research. Figure 15 shows the effect of changing the seat suspension damping. The physical meaning of the horizontal and vertical coordinates is the same as above.

Figure 14.

Effect of seat suspension stiffness.

Figure 15.

Effect of seat suspension damping.

The z-directional stiffness of the seat suspension makes a greater effect on the joint acceleration of the driver’s whole-body vibration. The smaller the z-directional stiffness is, the more the seat suspension absorbs the impact from the road, resulting in less whole-body vibration for the driver. The change in damping has a definite effect on the smoothness of driving. In addition, the vehicle may have acceleration, deceleration, and non-linear driving behavior in actual driving, so the effect of x- directional and y-directional stiffness and damping is more related to the driver's operating behavior. Since the tractor in the model is driven along a straight line at a perfectly constant speed, the changes in lateral and longitudinal model parameters make little effect on the results.

Cab suspension parameters

Figures 16 and 17 show the effects of changing the cab mount stiffness and damping, respectively. The cab has four rubber mounts, and the analysis was carried out separately for the front and rear mounts. As can be seen from the figures, reducing the rigidity of the cab mounts in the current scenario instead makes the driver’s whole-body vibration intense, revealing the complexity of the multi-system dynamics. The effect of damping on the results is largely negligible.

Figure 16.

Effect of cab suspension stiffness.

Figure 17.

Effect of cab suspension damping factor.

Tyre parameters

Because the sizes of the front and rear tyres are different, and the seat is closer to the rear tyre in spatial location, the effects of the front and rear tyres need to be considered separately in the numerical model. As shown in Figures 18 and 19, both tyre vertical stiffness and damping make a great effect on the results, with the tyre stiffness making a particularly significant effect. As can be seen from the graphs, increasing tyre stiffness significantly increases driver’s whole-body vibration in the current scheme. And the driver’s whole-body vibration decreases when the tyre damping increases. The stiffness and damping of the rear tyre make a greater effect on the results than the stiffness and damping of the front tyre.

Figure 18.

Effect of tyre vertical stiffness.

Figure 19.

Effect of tyre damping.

Conclusions

The objective of the work was to establish a simulation model to evaluate the main factors affecting the magnitude of driver’s whole body vibration. The main conclusions are as follows:

(1) The results show that the seat surface vibration is highest and the subjective feeling is uncomfortable under the field working condition. The vibration isolation performance of the seat and cab suspension is significantly different under varying conditions. The result of spectrum analysis shows that the seat does not have any vibration isolation in 2–4 Hz and the cab mounts do not have any vibration isolation below 20 Hz. This phenomenon is related to the inherent frequency of the respective systems.

(2) The influence of the model parameters on the driver’s whole-body vibration was further analyzed by building a numerical dynamics model of the tractor being driven on an artificial track. The analysis showed that the factors with greater influence were the vertical stiffness of the seat suspension and the vertical stiffness and damping factor of the tyres.

Footnotes

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

This research was funded by Ministry of Science and Technology of the People’s Republic of China, grant number 2022YFD2001202.

ORCID iD

Liming Sun

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