Effects of tyre inflation pressure and forward speed on vibration of an unsuspended tractor

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Journal of Terramechanics Journal of Terramechanics 50 (2013) 185–198 www.elsevier.com/locate/jterra

Effects of tyre inflation pressure and forward speed on vibration of an unsuspended tractor Do Minh Cuong a,b, Sihong Zhu a,⇑, Yue Zhu a b

a College of Engineering, Nanjing Agricultural University, Nanjing 210031, PR China Faculty of Engineering and Post harvesting, Hue University of Agriculture and Forestry, Viet Nam

Received 10 October 2012; received in revised form 17 May 2013; accepted 21 May 2013 Available online 20 June 2013

Abstract Relationships among intensity of vibrations, tractor speed, soil moisture content and tyre inflation pressure are important for the design of tractor suspension systems. This study was designed to evaluate the effect of tyre inflation pressure and forward speed on tractor vibration in the paddy fields of Southern China by using a two-wheel-drive unsuspended tractor with different combinations of forward speed, tyre inflation pressure and soil moisture content. During experiments, the vertical vibration accelerations in front and rear axles and triaxial vibration accelerations of the tractor body were measured using three accelerometers. Fourier analysis was applied to determine root mean square acceleration values in the low frequency range from 0.1 to 10 Hz. The results of the study indicate that tractor vibration is strongly affected by changing forward speed and tyre inflation pressure, and especially by changing forward speed and rear tyre inflation pressure. The research also shows the variation in the pattern of vibration intensity especially at the tractor’s front axle when field soil moisture content is changed. Ó 2013 ISTVS. Published by Elsevier Ltd. All rights reserved. Keywords: Vibration; Paddy field; Fourier analysis; Tyre inflation pressure; Forward speed

1. Introduction Low-frequency vibration in an agricultural tractor is produced by the interaction between the tractor and the terrain, depending upon the terrain that the tractor is crossing and the speed of travel [1–3]. It is particularly severe in primary conventional tractors, which rely on tyres as the elastic component between road and tractor but tyres are unable to provide the proper suspension characteristics required to absorb vibrations. Tractor drivers experience discomfort when exposed to the excessive low-frequency vibration during many farm works, thus causing impaired performance of tractor drivers and leading to under-utilization of tractor power [4,5].

⇑ Corresponding author. Fax: +86 2558606699.

E-mail address: [email protected] (S. Zhu).

Most researchers have focused on the low frequency range from 0.1 to 20 Hz while studying tractor vibration in association with various operating conditions and working parameters. Fairley [3] predicted the discomfort in operators which was caused by the vibration of agricultural tractors in the frequency range between 0.5 and 20 Hz and he confirmed that there was no significant vibration in any of the tractors at a frequency higher than 10 Hz. Thuong and Griffin [6], meanwhile, studied the frequency range that causes discomfort to standing people who are exposed to horizontal and vertical vibrations in the range from 0.5 to 16 Hz. At frequencies less than 3.15 Hz, subjects experienced problems with their stability, whereas at higher frequencies they experienced sensations in their legs and feet. In vertical vibration, the discomfort was felt in the lower-body and upper-body at all frequencies. The significantly higher levels of low-frequency vibrations were found in the cabin of a combine, driven at 20 km/h on a concrete surface than when driven at lower

0022-4898/$36.00 Ó 2013 ISTVS. Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jterra.2013.05.001

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speeds on field roads [7]. They suggested that low-frequency vibration (0.5–5 Hz) need to be given more weight in seat or cabin suspension design and comfort assessment. Kumar et al. [8] indicate that the problem of tractor ride becomes a more critical factor when the dominant frequencies of the tractor (1–7 Hz) lie within the most critical natural frequency range of the human body. The results of all studies suggest that the human body possesses a major natural vertical resonance in the region of 5 Hz. In some cases a second mode of vibration has been evident in the region of 10 Hz, although there was not usually a resonance [9]. Also observed was that human operators experienced the greatest harm when exposed to vibrations in the frequency range of 2–6 Hz because the human body’s natural resonance is within this frequency range [1,10]. Marsili et al. [11] carried out a study under different field conditions both connecting and disconnecting the suspension for the front axle and/or shock absorber for the implement. Their research shows that vehicle suspension could cause a substantial reduction in acceleration (up to 36%), and that the vehicle suspension could compromise the driver’s health through an increase in daily exposure time of about 50% during ploughing and of more than 100% during harrowing. Muzammil et al. [4] evaluated the effects of vibration on tractor drivers and the results show that the effects of farm equipment and vibration level are statistically significant but that the effects of field type are statistically insignificant. The influence of tyre inflation pressure on whole-body vibrations transmitted to the operator during the movement of a cut-to-length timber harvester was evaluated by Sherwina et al. [12]. Vibration was predominant in the vertical (Z) direction while the peak root mean square (RMS) acceleration value for the operator seat occurred at approximately 3.2 Hz. The vibration total values recorded for the operator seat at the maximum tyre inflation pressure setting were classed as vertical seat vibration transmissibility and this was found to be highest between 4 and 8 Hz at the 345 kPa tyre pressure setting. In several studies, it was observed that acceleration levels increase as forward speed of travel increases under most of operating conditions [13–15]. However, the trends in the predicted RMS acceleration levels with changing vehicle speed were quite different from those that occur in practice [16]. Since tyres are the only primary suspension on most agricultural vehicles, reducing the inflation pressure seems to be a reasonable choice of technologies to improve the ride comfort of the vehicle without a substantial redesign or increase in cost pressure [17,18]. Factors that have been found to affect the stiffness and damping of tyres the most are inflation pressure and rolling speed. Tyre stiffness increases with tyre inflation pressure and decreases significantly at low rolling speeds, but at speeds above 10 km/h, it remains effectively constant [17]. In their study, Lines and Young [19] concluded that tyre stiffness has a linear relationship with inflation pressure. Tyre damping has been found to increase significantly with

decreasing inflation pressure and low speed and it depends on rolling speed at all speeds [20]. In a study that included predictions of the suspension characteristics of tractor tyres, Lines and Peachey [16] indicated that those made of suspension characteristics of rolling tyres were more accurate than those made of stationary tyre characteristics. For longitudinal characteristics of driving tyres, the damping coefficient is light and it reduced progressively as rolling speed is increased, it would result in a greater increase of the vibration [21]. Decreasing inflation pressures to as low as 41 kPa to minimize an oscillatory vibration problem has been recommended by agricultural tyre manufacturers [22]. Other benefits of lowering inflation pressures might include improved traction, flotation, ride, stability and less soil compaction, as well as decreased soil–tyre interface pressures and increased tyre performance [23–28]. The vibration of a vehicle traversing soft terrain is produced by surface roughness. Vehicle vibration then excites the soil resulting in a loss of energy through soil compaction and elastic wave production [29]. Part of the vibration energy is also dissipated by the damping material in the topsoil layer. The importance of soil material damping in response to displacement is significant in bringing down the peak of the displacements as well as in rapidly weakening free vibrations as an important source of energy dissipation [30]. Material damping in soil is a function of many parameters including soil type, moisture content and temperature. Clay soil tends to exhibit higher damping than does sandy soil. Wet sand attenuates less than dry sand because pore water between sand particles carries a significant portion of compressional energy and thus does not subject compressional waves as much as attenuate friction damping [31]. Much research has been carried out to improve the riding comfort of agricultural tractors but so far the focus has only been on driver seat and cabin vibration [4,11,13]. Some of the research has focused on the suspension systems of the front and rear axles [32] used by large sized tractors; most middle and small sized tractors do not have suspension systems because of the decreasing cost and practical complexity when used to work on soft plastic soils [15]. There are few studies on axle and body vibration of an unsuspended tractor. Therefore, in an investigation that has useful ramifications for the design of suspension systems for paddy field tractors, the authors of this paper have characterized and evaluated the vibration magnitudes of an unsuspended tractor working in a paddy field by changing tractor operating conditions (such as soil moisture content of the field), and tractor inherent parameters (such as tyre inflation pressure and tractor speed). 2. Materials and methods 2.1. Test tractor A two-wheel-drive farm tractor was used as a tested tractor (see Fig. 1). It had neither suspension system nor

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any attached implement. Some main specifications of the test tractor are presented in Table 1. The driver’s seat pan consists of eight horizontal coil springs covered with padding while the frame is rigidly mounted with the tractor body (spring constant 9.8 N/mm).

Table 1 Main specifications of the test tractor.

2.2. Instrumentation

Engine model Number of engine cylinders Engine power (kW) Rated engine speed (rpm) Travelling speed (km/h) Mass without driver (kg) Front tyre Rear tyre Wheelbase (mm) Distance from centroid to the front axle (mm) Distance from centroid to the rear axle (mm) Overall dimensions (L  W  H mm)

To determine vibration level on axles and tractor body, two single-direction accelerometers (CA-YD 185TNC with frequency bandwidths of 0.5–5000 Hz and maximum acceleration of 1000 m/s2) were attached at the mid-point of the front and rear axle of the tractor to measure the vertical acceleration of each axle. One triaxial accelerometer (CAYD 152A with frequency bandwidth of 0.5–5000 Hz and maximum acceleration value of 2500 m/s2) was attached at the tractor centroid to measure three orthogonal axes accelerations of the tractor body. At the same time, an air pressure sensor (NS-F 21121268) was used to measure tyre inflation pressure and an air compressor was used to change tyre inflation pressure. An LMS Test.Xpress data acquisition and analysis system was used to collect data signals during the measurement process, with a sample rate of acquisition of 200 Hz. The signals were recorded by computer. The LMS Test.Xpress data acquisition system and the computer and electric systems were affixed to the rear side of the driver’s seat. Two batteries and two transformers were used to apply electric power for the measurement systems. Test tractor and instruments are shown in Fig. 1, schematic of measurement and data acquisition systems are shown in Fig. 2. 2.3. Test conditions and treatments A paddy field on Jiangpu Farm, Nanjing, China was selected as the location for testing the various combinations of tyre inflation pressure and tractor speed. The soil 4

2

Characteristics Tractor model Type

Changfa – CF200 Four-wheel, rear-wheel drive ZS1115GM 1 14.7 2200 2.62–32.74 915 5.00–R16 7.50–R20 1440 823 619 2600  1230  1320

texture of the paddy field was sandy clay loam soil (particle size and soil composition: sand 56%, silt 28% and clay 16%; soil texture was determined by hydrometer method). For 48.3% field soil moisture content, the soil penetration resistance was 17, 19 and 31 kPa at depths of 0–5, 5–10 and 10– 15 cm, respectively, while for 62.4% field soil moisture content, the soil penetration resistance was 13, 17 and 24 kPa at depths of 0–5, 5–10, and 10–15 cm, respectively (soil penetration resistance was determined using a digital soil compaction meter). A lane 70 m long in the paddy field was prepared after harvesting and it contained no straw. Each field test was conducted on a separate track with topsoil of 15 cm depth (approximately) at 48.3% and 62.4% field soil moisture contents (soil moisture content of the field was measured by oven dry method). Vertical accelerations of the front and rear axle, and three orthogonal axes accelerations of the tractor body were measured during self–propels in a straight line for a total of 90 5

6 7

8

9

10

6

7 3 2 1

Fig. 1. Test tractor and instruments: (1) air compressor; (2), (6), (7) accelerometers; (3) air pressure sensor; (4) test tractor; (5) computer; (8) LMS data acquisition and analysis system device; (9) transformers; (10) batteries.

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Batteries DC12 V

Computer

Transformer

Transformer

Output: AC220V

Output: DC24V

LMS system Acquisition

Signal cable

8

Signal cable

Signal cable

Z

X Y

6

1. Front axle 2, 6, 7. Accelerometer sensor Z

2 1

4

5 7 3

Z

3. Rear axle 4. Air compress sensor 5. Tractor body 8. Signal cable

To tyre valve

From air compressor

Fig. 2. Schematic of measurement and acquisition systems.

treatments: seventy-five (75) treatments at three constant forward speeds of 1.16, 1.49 and 1.79 m/s during which tyre inflation pressure was changed from 90 to 210 kPa in the front tyre and from 60 to 180 kPa in the rear tyre (fixing front tyre inflation pressure, increase rear tyre inflation pressure and reverse, increment of 30 kPa) at 48.3% field soil moisture content; 15 treatments at speed of 1.43 m/s during which tyre inflation pressure was changed from 90 to 210 kPa in the front tyre and from 60 to 180 kPa in the rear tyre (in each treatment, the inflation pressure of front and rear tyre was increased by an increment of 30 kPa) at 62.4% field soil moisture content. The tyre inflation pressure was determined by air pressure sensor, which was affixed to the tractor front frame. The ambient Table 2 The abbreviated notations of the distribution of the inflation pressure of front and rear tyre. Front tyre F1: front tyre 90 kPa F2: front tyre 120 kPa F3: front tyre 150 kPa F4: front tyre 180 kPa F5: front tyre 210 kPa

Rear tyre inflation pressure is inflation pressure is inflation pressure is inflation pressure is inflation pressure is

R1: rear 60 kPa R2: rear 90 kPa R3: rear 120 kPa R4: rear 150 kPa R5: rear 180 kPa

tyre inflation pressure is tyre inflation pressure is tyre inflation pressure is tyre inflation pressure is tyre inflation pressure is

temperature was 11 °C. Each treatment was conducted three times with a measurement time of 30 s. Tractor speed was calculated by following eq. s m¼ ðm=sÞ ð1Þ t where v is speed of tractor (m/s), S is the distance travelled by tractor (m) and t is time (s). The abbreviated notations of the distribution of the inflation pressure of front and rear tyre are represented in Table 2. 2.4. Analytical method Through LMS Test.Xpress data acquisition and analysis system, a fast Fourier transform was done to convert acceleration signals from time domain to frequency domain. For this paper, the RMS data in a frequency range of 0.1–10 Hz are used [21,33]. The RMS acceleration values of front and rear axle were measured in the vertical (Z) direction only when the RMS acceleration levels of the tractor body were measured in all three directions i.e., longitudinal (X), lateral (Y) and vertical (Z), and were calculated by using each frequency component following equation [33], " #1=2 X 2 Arms ¼ armsi ðm=s2 Þ ð2Þ i

D.M. Cuong et al. / Journal of Terramechanics 50 (2013) 185–198

The results were statistically analyzed using the analysis of variance (ANOVA) technique (by using SPSS version 16 software) to evaluate the effects of tyre inflation pressure and tractor speed on tractor vibration. In accordance with ISO 2631-1 [34], the value of acceleration vector sum av in m/s2 is obtained by combining three accelerations awx, awy, awz on each axis of the tractor body by the following equation: av ¼ ½ðawx Þ2 þ ðawy Þ2 þ ðawz Þ2 

1=2

ðm=s2 Þ

ð3Þ

Fig. 3a shows a sample signal of acceleration of tractor rear axle that was recorded by the measurement system. The acceleration signals were converted from time domain to frequency domain (Fig. 3b) by fast Fourier transform (FFT) algorithm through the LMS Test.Xpress data acquisition and analysis system and computer.

189

3. Results and discussion 3.1. Variation of the RMS value of acceleration at 48.3% field soil moisture content The RMS values of accelerations of the front, rear axle and tractor body always increased with the forward speed but they did not always increase with tyre inflation pressure (Figs. 4–9). The analytical results showed that there were significant differences in the RMS accelerations at P < 0.01 between three forward speeds of the tractor by keeping the same tyre inflation pressure, while there were also significant differences in the RMS accelerations at P < 0.05 at five levels of tyre inflation pressure for the same tractor speed when the front tyre pressure was kept constant and rear inflation pressure changed or the rear tyre

2

D29: Tractor vibration on paddy field C3: Acceleration of rear axle [m/s ]

(a) 2

[m/s²]

1

0 -1

-2

0.0

0.5

1.0

1.5

2.0

2.5

3.0

Time [s]

Time Traces: 1/1 Uncompressed

2

(b)

D29: Tractor vibration on paddy field M1: FFT of rear axle acceleration : FFT(C3) [m/s ] 0 [s]

0.12 0.10

[m/s²]

0.08 0.06 0.04 0.02 0.00 2 Frequency Traces: 1/1 Uncompressed

4

6

8

Frequency [Hz]

Fig. 3. Sample signal of acceleration of rear axle and FFT of rear axle acceleration.

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F5-R5

F5-R4

F5-R2

F5-R3

F4-R5

F5-R1

F4-R4

F4-R2

F4-R3

v = 1.79 (m/s)

F4-R1

F3-R5

F3-R4

F3-R3

F3-R2

F3-R1

v = 1.49 (m/s)

F2-R5

F2-R4

F2-R3

F2-R1

F1-R5

F1-R3

F1-R4

F1-R2

F2-R2

v = 1.16 (m/s)

2.4 2.2 2.0 1.8 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 F1-R1

RMS acceleration (m/s2 )

190

Distribution of tyre pressure (kPa)

v = 1.16 (m/s)

v = 1.49 (m/s)

v = 1.79 (m/s)

F5-R5

F5-R4

F5-R3

F5-R2

F5-R1

F4-R5

F4-R4

F4-R3

F4-R2

F4-R1

F3-R5

F3-R4

F3-R3

F3-R2

F3-R1

F2-R5

F2-R4

F2-R3

F2-R2

F2-R1

F1-R4

F1-R5

F1-R3

F1-R1

0.75 0.70 0.65 0.60 0.55 0.50 0.45 0.40 0.35 0.30 0.25 0.20 F1-R2

RMS acceleration (m/s2 )

Fig. 4. Variation in the RMS vertical acceleration at the mid-point of the tractor front axle.

Distribution of tyre pressure (kPa)

0.50

v = 1.16 (m/s)

v = 1.49 (m/s)

v = 1.79 (m/s)

0.45 0.40 0.35 0.30 0.25 0.20 F5-R5

F5-R3

F5-R4

F5-R2

F5-R1

F4-R5

F4-R4

F4-R3

F4-R2

F4-R1

F3-R5

F3-R4

F3-R3

F3-R2

F3-R1

F2-R5

F2-R4

F2-R3

F2-R2

F2-R1

F1-R4

F1-R5

F1-R3

F1-R2

0.15 F1-R1

RMS acceleration (m/s2 )

Fig. 5. Variation in the RMS vertical acceleration values at the mid-point of the tractor rear axle.

Distribution of tyre pressure (kPa)

F5-R5

F5-R4

F5-R3

F5-R2

F5-R1

F4-R5

F4-R4

F4-R3

F4-R2

v = 1.79 (m/s)

F4-R1

F3-R5

F3-R4

F3-R3

F3-R2

F2-R5

v = 1.49 (m/s)

F3-R1

F2-R4

F2-R3

F2-R2

F1-R5

F1-R4

F1-R3

F1-R1

F2-R1

v = 1.16 (m/s)

0.65 0.60 0.55 0.50 0.45 0.40 0.35 0.30 0.25 0.20 F1-R2

RMS acceleration (m/s2 )

Fig. 6. Variation in the RMS acceleration values in a longitudinal direction (X axis) of the tractor body.

Distribution of tyre pressure (kPa)

Fig. 7. Variation in the RMS acceleration values in a lateral direction (Y axis) of the tractor body.

191

F5-R5

F5-R4

F5-R3

F5-R2

F5-R1

F4-R5

F4-R4

F4-R3

F4-R2

F4-R1

v= 1.79 (m/s)

F3-R5

F3-R4

F3-R3

F3-R2

F3-R1

F2-R5

v= 1.49 (m/s)

F2-R4

F2-R3

F2-R2

F2-R1

F1-R4

F1-R3

F1-R2

F1-R5

v= 1.16 (m/s)

1.15 1.00 0.85 0.70 0.55 0.40 0.25 0.10 F1-R1

RMS acceleration (m/s2 )

D.M. Cuong et al. / Journal of Terramechanics 50 (2013) 185–198

Distribution of tyre pressure (kPa)

F5-R5

F5-R4

F5-R3

F5-R2

F5-R1

F4-R5

F4-R4

F4-R3

F4-R2

F4-R1

v = 1.79 (m/s)

F3-R5

F3-R4

F3-R3

F3-R2

F3-R1

v = 1.49 (m/s)

F2-R5

F2-R4

F2-R3

F2-R2

F1-R5

F1-R4

F1-R3

F1-R2

F2-R1

v = 1.16 (m/s)

1.40 1.30 1.20 1.10 1.00 0.90 0.80 0.70 0.60 0.50 0.40 0.30 F1-R1

RMS acceleration (m/s2 )

Fig. 8. Variation in the RMS acceleration values in a vertical direction (Z axis) of the tractor body.

Distribution of tyre pressure (kPa)

Fig. 9. Variation in the RMS acceleration vector sum av values of the tractor body.

pressure was kept constant and front tyre pressure changed (Appendices A–C). 3.1.1. Front and rear axle For the front axle, when the forward speed increased from 1.16 to 1.79 m/s, the RMS accelerations increased significantly from 0.337 to 0.987 m/s2 when the tyre pressure was F1–R1, from 0.565 to 1.237 m/s2 when the tyre pressure was F2–R2 and from 0.591 to 1.518 m/s2 when the tyre pressure was F3–R3 (the abbreviated notations of tyre pressure was presented in Table 2). A similar trend was observed when the tyre pressure was F4–R4 and F5–R5. By increasing tyre inflation pressure of the front tyre from 90 to 210 kPa and the rear tyre from 60 to 180 kPa, the RMS accelerations increased significantly from 0.337 to 1.270 m/s2, from 0.772 to 1.578 m/s2 and from 0.987 to 2.038 m/s2 at speeds of 1.16 m/s, 1.49 m/s and 1.79 m/ s, respectively (Fig. 4). The highest magnitude of vibration that was observed occurred at a maximum acceleration of 2.038 m/s2. It can be seen from the data that the RMS accelerations increased significantly when forward speed and rear tyre pressure were increased, but that there was not much impact on the acceleration observed at the front axle when the front tyre inflation pressure was changed. So a reduction in front tyre pressure was not found to be useful to reduce vibration of the front axle of the tractor while working in a paddy field. It is clear then that to improve riding performance and also handling, a suspension system for front axle should be installed. Fig. 4 also indicates that the vibration magnitudes of the front axle were greatly influenced by changing the rear

inflation pressure. Most peaks occurred when the rear tyre pressure attained a maximum value of 180 kPa, because the tractor body or frame was rigidly mounted to the rear axle while it was mounted to the front axle by a pivot. This revealed that the variation of the rear suspension characteristics related to the vibrations on the tractor’s front axle. For the rear axle, the RMS values of acceleration increased significantly with forward speed and tyre inflation pressure. By keeping a front tyre pressure of 90 kPa and changing the rear tyre pressure from 60 to 180 kPa, with an increment of 30 kPa for each treatment, the RMS acceleration increased significantly from 0.229 to 0.344 m/s2, from 0.287 to 0.444 m/s2 and from 0.423 to 0.602 m/s2 at forward speeds of 1.16, 1.49 and 1.79 m/s, respectively. Similar trend was observed in cases of keeping the front tyre pressure of 120, 150, 180 or 210 kPa and changing the rear tyre pressure from 60 to 180 kPa (Fig. 5). The RMS acceleration value increased significantly from 0.240 m/s2 to 0.331 m/s2 and then to 0.441 m/s2 as forward speed increased from 1.16 m/s to 1.49 m/s and then to 1.79 m/s by keeping the front and rear tyre pressure at 90 kPa. As another study, published by Nguyen and Inaba [15], indicates the RMS bounce acceleration at the rear axle increases significantly from 0.10 m/s2 to 0.19 m/s2 and then to 0.58 m/s2 when forward speed increases from approximately 0.6 m/s to 1.6 m/s and then to 2.6 m/s at a tyre inflation pressure of 80 kPa. Although the results of the current study and that of Nguyen and Inaba differ slightly due to different experimental conditions, both results show the same trend: that acceleration magnitude increases by increasing tractor speed. Most of

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the peaks that were occurred when the rear tyre pressure was 180 kPa. The results further reveal that the variation in acceleration of the rear axle is less varied when the front tyre inflation pressure is changed. By changing front tyre pressure from 90 to 210 kPa and then keeping rear tyre pressure at 180 kPa, the RMS acceleration increased slightly from 0.344 to 0.440 m/s2 at a speed of 1.16 m/s, from 0.444 to 0.540 m/s2 at a speed of 1.49 m/s and from 0.602 to 0.720 m/s2 at a speed of 1.79 m/s. This shows that the variation of the front suspension characteristics also related to the vibrations at the rear axle of the tractor but only slightly relative. At forward speeds of 1.16 m/s and 1.49 m/s, the RMS accelerations did not change much and did not always increase when the front tyre pressure was changed whereas they strongly increased at a forward speed of 1.79 m/s, thus indicating that the change of front tyre pressure greatly affects rear axle vibration when the tractor moved forward with the high speed (as observed at forward speed of 1.79 m/s). Typically tractor seats are mounted on top of the rear axle so they are greatly affected by rear axle vibration. Therefore reduction of rear tyre inflation pressure may be an appropriate method for reducing vibration of the tractor seat. As seen in Figs. 4 and 5 and Appendix A, when the vibration magnitudes of the rear and front axle obtained under the same conditions were compared, it became clear that the magnitude of the vibration of the front axle was much higher than that of the rear axle when the maximum RMS acceleration value of front axle was 2.038 m/s2 and the maximum RMS acceleration value of rear axle was 0.720 m/s2. Because of the soft soil, the crossing of front tyre could induced the deformation of the bump by front wheel loads and produced a tyre rut, subsequently the rear wheel crossed over it and the original soil profile was altered significantly by the vehicle [36]. In addition, the damping of the rear tyre was higher than that of the front tyre because of the differences in tyre load, tyre size and tyre inflation pressure. Most of the peaks of vibration of front and rear axle were observed when the rear tyre pressure was 180 kPa. The vibration of front and rear axle was only slightly affected by changing front tyre pressure whereas it was strongly affected by changing rear tyre pressure. The results indicate that reduction of tyre inflation pressure as low as possible may reduce the vibration of the tractor. As noted by Raper et al. [22], an inflation pressure of 41 kPa was recommended by agricultural tyre manufacturers for minimizing an oscillatory vibration problem. Of additional interest, the reduction of tractor tyre inflation pressure was also found to be useful in minimizing soil compaction [37]. 3.1.2. Tractor body The RMS acceleration values along the X, Y and Z axes increased proportionately when rear tyre pressure and forward speed increased, whereas they did not always increase when the front tyre pressure was increased. The variation

in acceleration in this study follows the same trend as was seen in the research of Gao and Chen [38]. When the tyre inflation pressure increased from 90 to 210 kPa in the front tyre and from 60 to 180 kPa in the rear tyre, the acceleration values on the X-axis increased significantly at each change in tyre inflation pressure, from 0.180 to 0.310 m/s2 at a speed of 1.16 m/s, from 0.233 to 0.391 m/ s2 at a speed of 1.49 m/s and from 0.277 to 0.440 m/s2 at a speed of 1.79 m/s (Fig. 6). Similarly, the acceleration values on the Y-axis increased from 0.239 to 0.426 m/s2 at a speed of 1.16 m/s, from 0.290 to 0.490 m/s2 at a speed of 1.49 m/s and from 0.349 to 0.583 m/s2 at a speed of 1.79 m/s (Fig. 7), the accelerations seen on the Z-axis also increased from 0.210 to 0.670 m/s2 at a speed of 1.16 m/s, from 0.363 to 0.867 m/s2 at a speed of 1.49 m/s and from 0.590 to 1.091 m/s2 at a speed of 1.79 m/s (Fig. 8). It can be observed that the change in tyre inflation pressure and forward speed has a direct relation with acceleration. However, the change in the front tyre pressure only slightly affects the accelerations of the X, Y and Z-axes at forward speeds of 1.16 m/s and 1.49 m/s (Figs. 6–8). Therefore, there was not much impact on the reduction of vibration magnitude of the tractor body when the front inflation pressure was changed at low speed, which is how a tractor normally works in a paddy field. As Hansson’s study [35] concluded, front axle suspension characteristics have limited effect on the level of vibration in the cab while those of the rear axle have a larger effect. Thus, the current study confirms that the effects of rear axle inflation pressure change on the vibration of a tractor body are of great significance. In addition, the results of this study show that accelerations in the longitudinal, lateral and vertical directions of tractor body are also a function of tractor forward speed, the same conclusion as was stated in the research of Crolla et al. [39]. For the acceleration vector sum av for the three X, Y and Z directions of the tractor body (Fig. 9), a strong change in acceleration occurred when forward speed and tyre inflation pressure were changed. The RMS accelerations were always seen to increase when the forward speed and tyre inflation pressure were increased. When tyre inflation pressure increased from 90 to 210 kPa in the front tyre and from 60 to 180 kPa in the rear tyre, the RMS acceleration vector sum av increased significantly from 0.366 to 0.852 m/ s2 at a forward speed of 1.16 m/s, from 0.519 to 1.070 m/s2 at a forward speed of 1.49 m/s and from 0.739 to 1.313 m/ s2 at a forward speed of 1.79 m/s. Although a part of the tractor’s vibration energy dissipated due to wheel–soil interaction [30,31], the magnitude of the vibration of the tractor body was very high (the maximum acceleration value was 0.852 m/s2 at a forward speed of 1.16 m/s, 1.070 m/s2 at a forward speed of 1.49 m/s and 1.313 m/s2 at a forward speed of 1.79 m/s). These vibrations are transmitted to driver’s seat directly affect the driver’s health, decreasing daily exposure time. Furthermore, in an unsuspended tractor, the vibration of the tractor body is also transmitted directly to the driver’s feet. There-

D.M. Cuong et al. / Journal of Terramechanics 50 (2013) 185–198

F5-R5

F5-R4

F5-R3

F5-R2

F5-R1

F4-R4

F4-R5

F4-R3

F4-R2

Along Z axis

F4-R1

F3-R5

F3-R4

F3-R3

F3-R2

F3-R1

F2-R4

Along Y axis

F2-R5

F2-R3

F2-R1

F2-R2

F1-R4

F1-R5

F1-R3

F1-R2

Along X axis

F1-R1

RMS acceleration (m/s2 )

1.15 1.05 0.95 0.85 0.75 0.65 0.55 0.45 0.35 0.25 0.15

193

Distribution of tyre pressure (kPa)

RMS acceleration (m/s2 )

Fig. 10. Comparison of the RMS acceleration values in longitudinal (X axis), lateral (Y axis) and vertical (Z axis) directions of the tractor body at a speed of 1.79 m/s.

0.75

For front axle

For rear axle

0.65 0.55 0.45 0.35 0.25 0.15 F1-R1

F2-R2

F3-R3

F4-R4

F5-R5

Distribution of tyre pressure (kPa)

Fig. 11. Variation in the RMS vertical acceleration values at the front and rear axle.

0.90

RMS acceleration (m/s 2 )

0.80

Along X-Axis Along Y-Axis

0.70

Along Z-Axis

0.60

Combine three Axis

0.50 0.40 0.30 0.20 0.10 0.00 F1-R1

F2-R2

F3-R3

F4-R4

F5-R5

Distribution of tyre pressure (kPa)

Fig. 12. Variation in the RMS acceleration values in X, Y and Z axis of tractor body.

fore, a suspension system is mounted on the tractor that is necessary to increase working time, this has also been confirmed by Marsili et al. [11]. When comparing the RMS acceleration values for all three (X, Y and Z) directions at the same forward speed, significant differences were noted between the acceleration values for each direction (Fig. 10). It was observed that vertical acceleration (Z axis) was strongly affected, while acceleration in the longitudinal (X axis) and lateral (Y axis) direction were only slightly affected due to the change in tyre inflation pressure. The results also indicate that a decrease in tyre inflation

pressure could minimize an oscillatory vibration problem, especially in the vertical direction (Z axis). This acceleration trend was also seen in the results of other studies [12,15,23]. 3.2. Variation in the RMS acceleration values at 62.4% field soil moisture content The experiment was repeated at 62.4% soil moisture content in the field with five levels of tyre inflation pressure and at a constant speed of 1.43 m/s. The acceleration trends for front axle, rear axle and tractor body were the

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Table 3 Comparison of a tractor’s vibration RMS acceleration values between two field soil moisture contents. Tyre pressure (kPa)

Field moist content (%)

RMS a of front axle (m/s2)

RMS a of rear axle (m/s2)

RMS a of X axis of tr. body (m/s2)

RMS a of Y axis of tr. body (m/s2)

RMS a of Z axis of tr. body (m/s2)

Combine three axis of tr.body (m/s2)

F1–R1

62.4I 48.3II

0.374a,A 0.772b

0.273a,A 0.287b

0.266a,A 0.233b

0.242a,A 0.290a

0.315a,A 0.363b

0.502a,A 0.519b

F2–R2

62.4I 48.3II

0.392a,B 0.920b

0.322a,B 0.391b

0.285a,B 0.294a

0.273a,B 0.365b

0.373a,B 0.547b

0.541a,A 0.720b

F3–R3

62.4I 48.3II

0.478a,C 1.115b

0.367a,C 0.480b

0.332a,C 0.307b

0.402a,C 0.430a

0.444a,C 0.640b

0.685a,B 0.830b

F4–R4

62.4I 48.3II

0.635a,D 1.200b

0.460a,D 0.470a

0.364a,D 0.347b

0.412a,C 0.437b

0.548a,D 0.680b

0.770a,C 0.878b

F5–R5

62.4I 48.3II

0.663a,E 1.578b

0.477a,E 0.540b

0.426a,E 0.391b

0.415a,C 0.490b

0.574a,E 0.867b

0.804a,D 1.070b

Different superscript letters a, b indicate significant differences at P < 0.05 between two soil moisture content levels for the same tyre inflation pressure. Different superscript letters A, B, C, D, E indicate significant difference at P < 0.05 between five levels of tyre inflation pressure for a soil moisture content of 62.4%. Same superscript letters indicate no significant differences. I Measured at a speed of 1.43 (m/s). II Measured at a speed of 1.49 (m/s).

same as in case of 48.3% soil moist content (Figs. 11 and 12). Significant differences were found between acceleration magnitudes at the front and rear axles (Table 3). When the front tyre inflation pressure increased from 90 to 210 kPa and the rear tyre pressure increased from 60 to 180 kPa, the RMS acceleration values increased significantly from 0.374 to 0.663 m/s2 at the front axle and from 0.273 to 0.477 m/s2 at the rear axle. Therefore, on a field with 62.4% soil moisture content, a reduction of tyre inflation pressure may also be an appropriate method to reduce tractor vibration. Fig. 12 shows that there is no difference between vibration magnitudes in X and Y axis at each tyre inflation pressure but that tyre inflation pressure increases proportionately by increasing tyre pressure and that the acceleration value in Z-axis increased predominantly. The acceleration values when all three axes are combined also increase significantly when the tyre inflation pressure increases. 3.3. Comparison of the RMS acceleration values between 48.3% and 62.4% field soil moisture content By comparing the vibration of the tractor at the same tyre inflation pressure first with a forward speed of 1.43 m/s and a 62.4% soil moisture content and then with a forward speed of 1.49 m/s and a 48.3% soil moisture content (Table 3), it was found that for front and rear axles, the RMS acceleration values increased significantly when field soil moisture content decreased from 62.4% to 48.3%. This was true especially when acceleration at the front axle increased 206% at F1–R1 tyre pressure, 233% at F3–R3 tyre pressure and 238% at F5–R5 tyre pressure, while the acceleration of rear axle increased 107% at F1R1 tyre pressure, 131% at F3–R3 tyre pressure and 113% at F5–R5 tyre pressure.

For the tractor body, the RMS acceleration values along the X axis decreased significantly when soil moisture content decreased, whereas the acceleration along the Y and Z axes proportionately increased by decreasing soil moisture content. The overall acceleration av was evident when increased 121% at F3–R3 tyre pressure or 133% at F5–R5 tyre pressure, etc. These results indicate that change in soil moisture content changes soil damping characteristics [30,31], and tractor vibration magnitude can be reduced by dissipating the vibration energy of the soil. 4. Conclusions

(1) The values of RMS acceleration on front, rear axle and tractor body were significantly decreased by decreasing forward speed and tyre inflation pressure when working with two different of field soil moisture contents. Most of the acceleration peaks were observed at the front, rear axle and tractor body when the rear tyre inflation pressure was 180 kPa. The values of RMS accelerations always increased proportionately as the tractor forward speed increased but did not always increase by increasing tyre inflation pressure. Vibration magnitudes of the front, rear axle and tractor body depended greatly on tractor speed as well as tyre inflation pressure, especially rear tyre pressure. In addition, the results revealed that the variation of the front or rear suspension characteristics related to the vibrations at the rear or front axle of the tractor. (2) The impact of the reduction of front tyre inflation pressure was significant with respect to the reduction of the vibration magnitude of tractor, but the reduction had less impact when the tractor was worked on

D.M. Cuong et al. / Journal of Terramechanics 50 (2013) 185–198

a field with high moisture content. So, the reduction of front tyre inflation pressure in order to reduce tractor vibration was not found to be feasible. (3) The RMS acceleration values at the front axle were higher than at the rear axle. Vibration in the vertical direction (Z axis) was also predominant; the RMS acceleration values in the vertical direction (Z axis) were higher than they were in the longitudinal (X axis) and lateral (Y axis) direction. (4) The value of RMS acceleration was significantly changed by changing soil moisture content in the field. Tractor vibration could be significantly decreased by conducting suitable soil moisture content in the field. (5) Although a part of the vibration energy of tractor was dissipated by the wheel–soil interaction, the vibration level of the tractor body was still very high, because of the high vibration at the front and rear

195

axles. Therefore, in order to reduce tractor vibration, besides controlling tractor speed, it would be necessary to mount a suspension system for the front axle. While a reduction of rear tyre inflation pressure has a significant impact on reducing tractor vibration. From these results, it is concluded that, for tractors without suspension system, a reduction in tractor forward speed and tyre inflation pressure may be an appropriate method to reduce tractor vibration. Furthermore, the results from this experimental research can be used as a basis for designing tractor suspension systems. Acknowledgement The author is very grateful to Agronomics lab of Nanjing Agricultural University, Nanjing 210031, PR China for their considerable assistance in the doing experiments.

Appendix A The vertical RMS values of acceleration in front, rear axle and the results of ANOVA test. Test code

F1–R1 F1–R2 F1–R3 F1–R4 F1–R5 F2–R1 F2–R2 F2–R3 F2–R4 F2–R5 F3–R1 F3–R2 F3–R3 F3–R4 F3–R5 F4–R1 F4–R2 F4–R3 F4–R4 F4–R5 F5–R1 F5–R2 F5–R3 F5–R4 F5–R5

The RMS acceleration value in front axle for each velocity (m/s2)

The RMS acceleration value in rear axle for each velocity (m/s2)

1.16

1.16

1.49 A,a,I

0.337 0.416A,b,I 0.502A,c,I 0.733A,d,I 0.792A,e,I 0.390A,a,K 0.565A,b,K 0.591A,c,K 0.740A,d,I 0.880A,e,K 0.586A,a,M 0.688A,b,M 0.591A,a,K 0.838A,c,K 1.110A,d,L 0.408A,a,K 0.662A,b,L 0.899A,d,L 0.860A,c,K 1.130A,e,L 0.466A,a,L 0.585A,b,K 0.885A,c,L 0.860A,c,K 1.270A,d,M

1.79 B,a,K

0.772 0.769B,a,I 1.015B,b,I 1.108B,b,IK 1.340B,c,I 0.890B,a,M 0.920B,a,K 1.115B,b,I 1.080B,b,I 1.310B,c,I 0.831B,a,L 0.930B,b,K 1.115B,c,I 1.100B,c,IK 1.600B,d,KL 0.750B,a,I 0.800B,a,I 1.134B,b,I 1.200B,b,K 1.660B,c,L 0.838B,a,L 1.070B,b,L 1.237B,c,I 1.170B,bc,IK 1.578B,d,K

C,a,I

0.987 1.318C,b,IK 1.402C,bc,I 1.570C,cd,IK 1.630B,d,I 1.148C,a,I 1.237C,ab,I 1.590C,bc,K 1.700C,c,KL 1.845C,c,IK 1.098C,a,I 1.403C,b,KL 1.518C,b,IK 1.455C,b,I 1.970C,c,KL 1.206C,a,I 1.570C,b,M 1.540C,b,K 1.832C,c,L 2.152C,d,L 1.219C,a,I 1.440C,b,L 1.607C,c,K 1.660C,c,K 2.038C,d,KL

1.49 A,a,I

0.229 0.240A,a,I 0.290A,b,I 0.260A,ab,I 0.344A,c,I 0.229A,a,I 0.298A,b,K 0.288A,b,I 0.296A,b,K 0.330A,c,I 0.274A,a,IK 0.313A,b,K 0.330A,b,K 0.389A,c,L 0.395A,c,K 0.289A,a,K 0.344A,b,L 0.382A,c,L 0.379A,c,L 0.394A,c,K 0.277A,a,IK 0.313A,b,K 0.369A,c,L 0.433A,d,M 0.440A,d,L

1.79 A,a,I

0.287 0.331B,ab,I 0.397B,c,I 0.371B,bc,I 0.444B,d,I 0.330B,a,K 0.391B,b,K 0.376B,b,I 0.440B,cK 0.452B,c,I 0.376B,a,LM 0.429B,b,L 0.480B,c,K 0.486B,c,L 0.502B,c,K 0.350B,a,KL 0.389A,b,K 0.464B,c,K 0.470B,c,L 0.493B,c,K 0.400B,a,M 0.460B,b,L 0.465B,b,K 0.516B,c,M 0.540B,c,L

0.423B,a,I 0.441C,a,I 0.486C,b,I 0.587C,c,I 0.602C,c,I 0.465C,a,K 0.563C,bc,K 0.560C,b,K 0.596C,c,I 0.652C,d,K 0.532C,a,L 0.571C,b,K 0.606C,c,L 0.672C,d,K 0.694C,d,L 0.552C,a,M 0.580B,b,K 0.670C,c,M 0.694C,cd,K 0.700C,d,LM 0.619C,a,N 0.664C,b,L 0.650C,b,N 0.700C,c,K 0.720C,d,M

Different superscript letters A, B, C indicate significant differences at P < 0.01 between three tractor forward speeds for the same tyre inflation pressure. Different superscript letters a, b, c, d, e indicate significant differences at P < 0.05 between five levels of tyre inflation pressure for the same tractor speed, in case of the front tyre pressure is kept constant and changing rear inflation pressure. Different superscript letters I, K, L, M, N indicate significant differences at P < 0.05 between five levels of tyre inflation pressure for the same tractor speed, in case of the rear tyre pressure is kept constant and changing front tyre pressure. Same superscript letters indicate no significant differences.

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D.M. Cuong et al. / Journal of Terramechanics 50 (2013) 185–198

Appendix B The RMS values of acceleration in X-axis, Y-axis of the tractor body and the results of ANOVA test. Test code

F1–R1 F1–R2 F1–R3 F1–R4 F1–R5 F2–R1 F2–R2 F2–R3 F2–R4 F2–R5 F3–R1 F3–R2 F3–R3 F3–R4 F3–R5 F4–R1 F4–R2 F4–R3 F4–R4 F4–R5 F5–R1 F5–R2 F5–R3 F5–R4 F5–R5

The RMS value of acceleration in the X axis of tractor body for each velocity (m/s2)

The RMS value of acceleration in the Y axis of tractor body for each velocity (m/s2)

1.16

1.16

1.49 A,a,I

0.180 0.210A,b,I 0.230A,c,I 0.240A,c,I 0.260A,d,I 0.203A,a,K 0.237A,b,K 0.257A,b,K 0.254A,b,I 0.280A,c,K 0.233A,a,L 0.245A,ab,K 0.258A,bc,K 0.280A,d,K 0.273A,cd,IK 0.230A,a,L 0.250A,b,K 0.291A,c,L 0.294A,cd,KL 0.309A,d,L 0.260A,a,M 0.284A,b,L 0.304A,bc,L 0.300A,bc,L 0.310A,c,L

1.79 B,a,I

0.233 0.238AB,a,I 0.266B,b,I 0.273B,b,I 0.287B,b,I 0.260B,a,K 0.294B,b,KL 0.311B,bc,K 0.304B,bc,K 0.320B,c,K 0.272B,a,K 0.280B,b,K 0.307B,bc,K 0.304A,b,K 0.329B,c,K 0.273B,a,K 0.303B,b,L 0.324B,c,K 0.347B,d,L 0.369B,e,L 0.305B,a,L 0.333B,b,M 0.358B,c,L 0.384B,d,M 0.391B,d,L

C,a,I

0.277 0.280B,a,I 0.303C,ab,I 0.318C,b,I 0.334C,b,I 0.285B,a,I 0.334B,b,K 0.344C,bc,K 0.355C,bc,I 0.369C,c,K 0.315C,a,K 0.350C,a,KL 0.366C,a,L 0.365A,a,I 0.394C,a,KL 0.330C,a,KL 0.344C,a,K 0.348B,a,KL 0.387C,b,I 0.400C,b,L 0.336B,a,L 0.387C,b,L 0.403C,b,M 0.411B,bc,I 0.440B,c,M

1.49 A,a,I

0.239 0.263A,a,I 0.307A,b,I 0.334A,bc,I 0.348A,c,I 0.269A,a,I 0.294A,a,K 0.342A,b,K 0.345A,bc,I 0.372A,c,K 0.334A,a,K 0.357A,b,L 0.360A,b,KL 0.391A,c,K 0.406A,c,L 0.351A,a,K 0.360A,bc,L 0.378A,b,LM 0.380A,b,K 0.413A,c,LM 0.337A,a,K 0.358A,b,L 0.394A,c,M 0.394A,c,K 0.426A,d,M

1.79 AB,a,I

0.290 0.323B,b,I 0.342A,b,I 0.373A,c,I 0.390B,c,I 0.324B,a,K 0.365B,b,K 0.403B,c,K 0.399A,c,IK 0.417B,c,K 0.370B,a,L 0.402A,b,L 0.430B,bc,L 0.433B,c,K 0.460B,c,L 0.374A,a,L 0.405B,b,L 0.405B,b,K 0.433B,c,K 0.460B,d,L 0.374Ba,L 0.420B,b,L 0.450B,c,L 0.470B,cd,L 0.490B,d,M

0.349B,a,I 0.380C,b,I 0.420B,c,I 0.430C,c,I 0.466C,d,I 0.366B,a,I 0.398C,b,I 0.450C,c,K 0.468C,c,K 0.509C,d,K 0.436C,a,K 0.477B,b,K 0.482C,b,L 0.491C,b,K 0.518C,c,K 0.435B,a,K 0.458C,a,K 0.460C,a,KL 0.523C,b,L 0.550C,c,L 0.480C,a,L 0.516C,b,L 0.570C,c,M 0.560C,c,M 0.583C,c,M

Different superscript letters A, B, C indicate significant differences at P < 0.01 between three tractor forward speeds for the same tyre inflation pressure. Different superscript letters a, b, c, d, e indicate significant differences at P < 0.05 between five levels of tyre inflation pressure for the same tractor speed, in case of the front tyre pressure is kept constant and changing rear inflation pressure. Different superscript letters I, K, L, M, N indicate significant differences at P < 0.05 between five levels of tyre inflation pressure for the same tractor speed, in case of the rear tyre pressure is kept constant and changing front tyre pressure. Same superscript letters indicate no significant differences.

D.M. Cuong et al. / Journal of Terramechanics 50 (2013) 185–198

197

Appendix C The RMS values of acceleration in Z-axis, the combination of three X–Y–Z axis of tractor body and the results of ANOVA test. Test code

F1–R1 F1–R2 F1–R3 F1–R4 F1–R5 F2–R1 F2–R2 F2–R3 F2–R4 F2–R5 F3–R1 F3–R2 F3–R3 F3–R4 F3–R5 F4–R1 F4–R2 F4–R3 F4–R4 F4–R5 F5–R1 F5–R2 F5–R3 F5–R4 F5–R5

RMS of acceleration in Z axis of tractor body for each of velocity (m/s2)

Total acceleration of body for each of velocity (m/s2)

1.16

1.16

1.49 A,a,I

0.210 0.270A,b,I 0.350A,c,I 0.360A,c,I 0.440A,d,I 0.297A,a,K 0.374A,b,K 0.390A,b,K 0.420A,c,K 0.480A,d,K 0.330A,a,L 0.390A,b,K 0.390A,b,K 0.480A,c,L 0.520A,d,L 0.362A,a,M 0.421A,b,L 0.480A,c,L 0.452A,bc,KL 0.530A,d,L 0.329A,a,L 0.410A,b,L 0.455A,c,L 0.560A,d,M 0.670A,e,M

1.79 B,a,I

0.363 0.421B,b,I 0.520B,c,I 0.540B,c,I 0.660B,d,I 0.455B,a,K 0.547B,b,K 0.550B,b,K 0.650B,c,K 0.662B,c,I 0.544B,a,L 0.590B,b,L 0.640B,c,L 0.670B,d,KL 0.737B,e,K 0.541B,a,L 0.627B,b,M 0.615B,b,L 0.680B,c,L 0.750B,d,K 0.554B,a,L 0.636B,b,M 0.640B,b,L 0.813B,c,M 0.867B,d,L

C,a,I

0.590 0.660C,b,I 0.720C,c,I 0.751C,d,I 0.860C,e,I 0.730C,a,K 0.799C,b,K 0.912C,c,K 0.928C,c,K 0.936C,c,K 0.779C,a,L 0.840C,b,L 0.915C,c,K 0.953C,d,K 0.971C,e,K 0.787C,a,L 0.807C,a,K 0.953C,b,L 1.005C,bc,L 1.040C,c,L 0.823C,a,M 0.930C,b,M 0.960C,b,L 1.030C,c,L 1.091C,d,L

1.49 A,a,I

0.366 0.431A,b,I 0.519A,c,I 0.546A,c,I 0.618A,d,I 0.449A,a,K 0.531A,b,K 0.579A,c,K 0.600A,c,K 0.669A,d,K 0.524A,a,L 0.583A,b,L 0.590A,b,K 0.680A,c,L 0.714A,d,L 0.554A,a,L 0.608A,b,M 0.677A,c,L 0.660A,c,L 0.740A,d,M 0.538A,a,L 0.614A,b,M 0.674A,c,L 0.748A,d,M 0.852A,e,N

1.79 B,a,I

0.519 0.582B,b,I 0.677B,c,I 0.711B,d,I 0.819B,e,I 0.616B,a,K 0.720B,b,K 0.749B,b,K 0.821B,c,K 0.845B,c,I 0.712B,a,L 0.767B,b,L 0.830B,c,L 0.854A,d,L 0.929B,e,K 0.712B,,a,L 0.806B,b,M 0.805B,b,L 0.878B,c,L 0.954B,d,K 0.735B,a,M 0.832B,b,M 0.860B,c,M 1.015B,d,M 1.070B,e,L

0.739C,a,I 0.811C,b,I 0.887C,c,I 0.922C,d,I 1.034C,e,I 0.865C,a,K 0.953C,b,K 1.074C,c,K 1.098C,c,K 1.128C,d,K 0.946C,a,L 1.027C,ab,M 1.097C,bc,L 1.132B,c,KL 1.169C,c,K 0.957C,a,L 0.990C,a,L 1.114C,b,L 1.197C,c,L 1.243C,c,L 1.011C,a,M 1.132C,b,N 1.187C,c,M 1.242C,d,L 1.313C,e,M

Different superscript letters A, B, C indicate significant differences at P < 0.01 between three tractor forward speeds for the same tyre inflation pressure. Different superscript letters a, b, c, d, e indicate significant differences at P < 0.05 between five levels of tyre inflation pressure for the same tractor speed, in case of the front tyre pressure is kept constant and changing rear inflation pressure. Different superscript letters I, K, L, M, N indicate significant differences at P < 0.05 between five levels of tyre inflation pressure for the same tractor speed, in case of the rear tyre pressure is kept constant and changing front tyre pressure. Same superscript letters indicate no significant differences.

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