Analysis of Vibration Characteristics of Tractor–Rotary Cultivator Combination Based on Time Domain and Frequency Domain

Abstract

A good planting bed is a prerequisite for improving planting quality, while complex ground excitation often leads to machine bouncing and operation vibration, which then affects the operation effect. In order to improve the quality of rotary tillage operations, it is necessary to study the effects of various vibration excitations on the unit during tractor rotary tillage operations and analyze the vibration interaction relationship among the tractor, the three-point suspension mechanism, and the rotary tiller. For this purpose, multiple three-way acceleration sensors were installed at different positions on the rotary tiller unit of a Lexing LS1004 tractor(Lexing Agricultural Equipment Co. Ltd., Qingdao, China) to collect vibration data at different operating speeds and conduct vibration characteristic analysis between different components. The test results showed that when the unit moved forward at 2.1 km/h, 3.6 km/h, and 4.5 km/h, respectively, the vibration acceleration of the tractor, the three-point suspension mechanism, and the rotary tiller increased with the increase in speed, and there was indeed interaction between them. The vertical acceleration change during the test in the three-point suspension mechanism was the most significant (5.914 m/s²) and was related to the increase in the speed of the vehicle and the vibration transfer of the rotary tiller. Meanwhile, the vertical vibration acceleration of the tractor’s symmetrical structure was not similar, suggesting the existence of structural assembly problems. From the perspective of frequency domain analysis, the resonant frequency at the cab of the tractor was reduced in a vertical vibration environment, with relatively low frequencies (0~80 Hz) and small magnitudes, which might be beneficial to the driver’s health. The rotary tillage group resonated around 350 Hz, and this characteristic can be used to appropriately increase the vibration of the rotary tiller to reduce resistance. The tractor cab resonated around 280 Hz, which must be avoided during field operations to ensure driver health and reduce machine wear. The research results can provide a reference for reducing vibration and resistance during tractor rotary tillage operations, as well as optimizing and improving the structure of rotary tillers and tractors.

1. Introduction

In agricultural production, land preparation is a key point. Through land preparation operations, the soil in the field can be made more suitable for the growth of crops. Traditional farming machinery, such as disc harrows and share plows, require greater tractor traction. In contrast, tractor rotary tillage units have become the main method for land preparation due to their wide range of applicable operations and lower power load requirements. Therefore, the research on the operation performance of a rotary tiller will help to improve the final operation quality and crop yield [1,2,3].

Due to the complex field operating environment, agricultural machinery often faces severe vibrations caused by multisource excitations during operation, which reduces the reliability of the machinery and leads to a decline in work quality [4,5]. However, the appropriate vibration can help reduce the resistance of rotary tillage operations and tractor power consumption. For this reason, it is necessary to understand the vibration characteristics of the tractor during rotary tillage operations. At present, there have been a large number of studies on the working quality of tractors and rotary tillers at home and abroad. In terms of tractors, Han et al. designed a coordinated control system between engine load characteristics and plowing depth to stabilize the engine load by adjusting the plowing depth, allowing the tractor to work within the range of high power and low fuel consumption [6]. An approach that combines multi-objective particle swarm optimization (MOPSO) and wavelet decomposition algorithms has been used to collect input vibration signals efficiently, making it extremely convenient for tractor bumping tests [7]. Watanabe et al. established a three-degree-of-freedom nonlinear tractor dynamics model and used a delayed feedback (DF) control algorithm to eliminate complex vibrations in tractor motion [8]. Singh et al. implemented the online transmission of raw acceleration data in all directions of the tractor cab seat and driver’s head based on the Internet of Things module and obtained its power spectral density (PSD) [9]. In addition to tractors, the mounted machine directly affects the quality of operation. Therefore, some scholars have studied the vibration characteristics of land preparation machinery [10,11]. For example, Lai et al. used EDEM 2017, ADAMS 2013, and other simulation software to derive the load model of the rotary tiller gearbox and then carried out stress–strain analysis to find out the design defects of the gearbox [12]. Guo et al. studied the vibration acceleration signals of the hood and handrails of the micro-tiller under four conditions and found that the anisotropic vibration of the hood and handrails was less than that of the static conditions when the engine was running at high speed, because the blades cutting the soil increased the damping of the whole machine [13]. Then, the soil’s absorption of certain frequency energies caused the tiller to experience violent vibrations in the handle due to unbalanced inertial force, providing a reference for reducing resistance and energy consumption during rotary tillage operations. Du et al. considered the influence of tractor wheel subsidence and structural deformation of rotary tiller unit on tillage depth and designed a system that could realize the automatic monitoring of the tillage depth of a suspended rotary tiller, which would allow for a comprehensive evaluation of the quality of tillage depth [14]. Chen took the micro-tiller as their research object, tested the vibration of each structure of the micro-tiller under eight working conditions, and analyzed the time domain and frequency domain, thereby reducing the work resistance of the micro-tiller [15]. She then verified the established dynamic model of the whole machine through modal analysis and other means and proposed optimization measures. In the field of the effectiveness of land leveling technology, laser-controlled leveling and GNSS-controlled leveling technologies have been used to enhance the practical benefits of land leveling, contributing valuable research ideas for the future direction of reducing mechanical energy loss during leveling technology [16].

It can be seen from the studies above that research on the vibration characteristics of tillage and land preparation equipment has mostly focused on the tractor, and there is a lack of research on the analysis of the vibration characteristics of the tractor and rotary tiller combination during the operation [17,18,19]. Since rotary tillers and tractors are related to each other when working in the field, they are stimulated to vibrate and affect each other’s vibration [20]. To this end, this paper takes a rotary tiller, a tractor, and the three-point suspension mechanism used to fixedly connect the two as the research objects, collecting and analyzing the vibration conditions of the tractor, three-point suspension mechanism, and rotary tiller, exploring the possible interaction between the units at a stable speed and studying the impact of vibration on the normal operation of the unit, in order to provide a basis for improving the reliability of tractors and rotary tiller, as well as improving and optimizing the structure of the implements to reduce vibration and resistance from soil.

2. Materials and Methods

2.1. Tractor and Rotary Tiller Structure

In this test, a Lexing LS1004 tractor (Lexing Agricultural Equipment Co. Ltd., Qingdao, China) was used to pull the rotary tiller. Its main performance parameters are shown in

Table 1. Main performance parameters of tractor.

Rotating Speed/rpm	PTO/rpm	Overall Size/mm
2100	540/750/1000	4540 × 2000 × 2650

. The Dongfanghong 1GQN-250G rotary tiller (YTO GROUP CORPORATION, Luoyang, China) was selected for plowing operations, as shown in Figure 1, and it was connected to the tractor with a three-point suspension mechanism. Its main performance parameters are shown in

Table 2. Main performance parameters of rotary tiller.

Matching Horsepower/Hp	Cultivated Width/cm	Cultivation Depth/cm	PTO/rpm
90~105	250	2~16	720/540

[21].

The rotary tiller is mainly composed of a transmission system, a gear box, a linkage frame, a cover, a flat soil support plate, a rotary tiller shaft, and a rotary tiller blade. The tractor power was inputted into the gear box through the universal joint of the transmission system, driving the cutter shaft to rotate and the rotary tillage blade to perform soil plowing and soil crushing operations. The soil leveling board was used to prevent soil from splashing and further breaking up the soil during the operations.

2.2. Analysis of the Main Vibration Sources of the Unit

The Dongfanghong 1GQN-250G rotary tiller adopts an intermediate bevel gear transmission. The power of the tractor’s power output shaft was transmitted to the intermediate gearbox through the universal joint transmission shaft. The specific transmission path is shown in Figure 2, and the direction of power transmission has been marked with red arrows in the figure. It can be seen from the figure that when a tractor-mounted rotary tiller was operating, in addition to the tractor engine and the possible uneven field surface, its main vibration sources included the rotary tiller gear box, the rotary tiller blade shaft, and the impact load generated by the rotary tiller blade cutting the soil [22].

When the unit was performing rotary tillage operations, we set the tractor’s power take off (PTO) speed to 540 r/min. At this time, the theoretical engine speed was about 1680 r/min. In the test, the first-stage bevel gear transmission ratio of the rotary tiller gearbox was 15:22, and the theoretical rotation speed of the rotary tiller’s cutter shaft was 252 r/min [23]. The theoretical vibration frequency of the engine can be obtained according to Equation (1), and the theoretical vibration frequency of PTO and rotary blade shaft can be obtained according to Equation (2) [24]. The theoretical vibration frequencies of each vibration source are shown in

Table 3. Theoretical vibration frequency of the main vibration source of the unit.

Vibration Source	Theoretical Vibration Frequency/Hz
PTO	8~10
Tractor engine	54~58
Rotary tiller shaft	4~5

.

$$f_1=\frac{2}{60c}{n}_{i}i$$

(1)

where f₁ is the theoretical vibration frequency of the engine, Hz; c is the number of engine strokes; n_i is the theoretical engine speed, r/min; i represents the number of cylinders.

$$f=\frac{n}{60}$$

(2)

where f is the theoretical vibration frequency of PTO and rotary blade shaft, Hz; n is the theoretical speed of the kinematic mechanism, r/min.

2.3. Laboratory Equipment

The vibration acceleration acquisition and analysis system of the tractor rotary tillage unit mainly consists of a dynamic signal analyzer, three-way acceleration sensors, post-processing software, a voltage inverter, a 12 V DC power supply and a laptop, as shown in Figure 3. Among them, the Spider-80Xi analyzer (Crystal Instruments Company, Santa Clara, CA, USA) has 32 input channels and is powered by a DC power supply with a voltage of 10 V to 22 V; the three-way acceleration sensor model is BWJ13533, and the sensitivity of each sensor is shown in

Table 4. Sensor sensitivity in all directions.

Sensor Number	Sensitivity in All Directions/mV·g−1
	X	Y	Z
1	50.24	50.39	50.53
2	49.64	50.27	50.16
3	49.10	49.88	49.60
4	49.35	50.41	51.05
5	49.21	50.33	49.62
6	49.86	50.05	49.28
7	48.82	50.14	50.26
8	49.40	48.66	49.01

. The inverter model is BOKAI 3000 WDC/AC (Zhongshan Xinyihao E-commerce Co. Ltd, Zhongshan, China) inverter, which was used to convert 12 V DC power into 220 V AC power to power the dynamic signal analyzer.

In order to facilitate subsequent test data processing, during the test process, the unit’s traveling direction was set as the X direction, the vertical forward direction as the Y direction, and the vertical direction to the ground as the Z direction. In this way, the vibration test data at different positions of the unit were uniformly divided into three directions, X, Y, and Z.

2.4. Experimental Program

During the tractor rotary tillage operations, the vibration signals of the rotary tiller, tractor, and linkage were collected by the three-way acceleration sensors and transmitted to the road spectrum test and analysis system through the Spider-80Xi dynamic signal analyzer. Then, the characteristic values (RMS) of the acceleration signal were extracted, and the time domain analysis and PSD analysis were carried out to obtain the sequence of effects of the main excitation sources on the vibration magnitude of the unit components [25].

The experiment was conducted in a rice stubble field. Since the ground of the paddy field was relatively flat after beating and drying, the influence of uneven ground on the vibration of the machine was considered as a minor factor in this experiment. In order to reduce the impact of the tractor engine on the collected signals, sensors were arranged at different positions of the unit as a blank control in the experiment. As shown in Figure 4, three-way acceleration sensors were installed on the rotary tiller, tractor, and three-point suspension mechanism to obtain vibration data. The installation position should be as close as possible to the excitation source to obtain accurate measurement data [26]. For this purpose, the position of each measuring point was set as follows: measuring point 1 (center of the rotary cultivator), measuring point 2 (suspended lower left pull rod), measuring point 3 (suspended right lower pull rod), measuring point 4 (tractor left rear wheel), measuring point 5 (tractor right rear wheel), measurement point 6 (tractor cab), measurement point 7 (tractor left front wheel), and measurement point 8 (tractor right front wheel). Finally, a total of 8 measurement points and 3 working conditions were used to conduct vibration characteristics test experiments. Among them, measuring points 4, 5, 7, and 8 were all arranged on the front and rear axles of the tractor chassis. The three working conditions were, respectively, the operating status of the rotary tiller unit when traveling at speeds of 2.1 km/h, 3.6 km/h, and 4.5 km/h. In addition, in order to reduce the influence of external factors on the test results [27], the vibration characteristic parameters of the rotary tiller and tractor cab with zero speed were collected. Meanwhile, the operating parameters of the rotary tiller were kept unchanged during the experiment to test the effect of working speed and soil excitation on the vibration characteristics of the machine.

2.5. Signal Acquisition and Analysis

According to the above-mentioned measurement requirements, the sensors were first installed in a specific position and their three-axis orientations were recorded. They were then connected to the dynamic signal analyzer via a wire harness to check whether the individual channel data were normal. Meanwhile, in order to ensure the accuracy of the experimental waveform, the sampling frequency should be at least twice the frequency of the analyzed signal [28]. Before the experiment, the Spider-80Xi dynamic signal analyzer sampling rate was set to 2560 Hz, continuous sampling mode was performed, and 24 input channels were turned on. After the settings were completed, the vibration signal collection test was performed. While the three working speeds were stable, the vibration acceleration data was collected. Under stable working conditions, the sampling time of each group was 40 s. Based on the acceleration data obtained under stable sampling time, the vibration characteristics of the tractor rotary tillage operation were analyzed.

2.5.1. Time Domain Analysis

The root mean square (RMS) is often used to measure the fluctuation of random signal near the mean value, which can directly reflect the strength of the signal [29]. Therefore, the vibration signal data were processed, and the RMS was calculated to provide a basis for subsequent vibration analysis. The calculation formula of the RMS is shown in Equation (3).

$$RMS=\sqrt{\frac{1}{N} {\displaystyle \sum _{k=1}^N{x}_k^2}}=\sqrt{\frac{x_1^2+x_2^2+x_3^2+\cdots +x_k^2}{N}}$$

(3)

where x_k is the vibration acceleration value, m/s²; N is the number of signals collected.

With a view to reduce the impact of the location distribution of measuring points on the measurement results and obtain more accurate measurement data, the sensors fixed on the unit components were arranged symmetrically along the center line of the unit. Among the 8 measuring points, measuring points 2 and 3 were symmetrical about the center line of the unit; measuring points 4 and 5 on the tractor’s rear axle were symmetrical about the tractor’s center line; and measuring points 7 and 8 on the tractor’s front axle were symmetrical about the tractor’s center line. The measurement data of measuring point 1 and measuring point 6 were not additionally processed.

2.5.2. Frequency Domain Analysis

In order to further analyze the vibration signal, the time domain signal is generally converted into the frequency domain signal through Fast Fourier Transformation (FFT) [30]. This method is often used to analyze the signal spectrum in digital signal processing. The PSD of the rotary tiller and the tractor can be obtained by analyzing their frequency domain data [31]. PSD is a measure of the mean square value of random variables. It eliminates the impact of frequency resolution on the amplitude of the spectral function and represents the distribution of signal power at each frequency point. For any random signal, the PSD expression can be determined through Equation (4) [32].

$$\underset{T\to \infty }{\lim }\frac{1}{T}{{\displaystyle {\int }_0^T\left|\sigma \left(t\right)\right|}}^{2}dt=\underset{T\to \infty }{\lim }\frac{1}{T}{{\displaystyle {\int }_{-\infty }^{+\infty }\left|F_{\sigma }\left(\omega \right)\right|}}^{2}df={\displaystyle {\int }_{-\infty }^{+\infty }{S}_{\sigma }}\left(f\right)df$$

(4)

where $\sigma \left(t\right)$ is a random signal; $F_{\sigma }\left(\omega \right)$ is $\sigma \left(t\right)$ after Fourier transform; $S_{\sigma }\left(f\right)$ represents the distribution of signal average power spectrum in frequency domain.

For the purpose of studying the influence of vehicle speed on the vibration characteristics of the rotary tillers and tractors, the vibration acceleration data of measuring point 1 on the rotary tiller and measuring point 6 on the tractor under three working conditions were processed. We then obtained the power spectrum peak value and corresponding peak frequency of each working condition of the two points.

3. Results and Discussion

3.1. Time Domain Analysis of Rotary Tillage Unit

The vertical RMS values of the rotary tiller and tractor with zero speed are listed in

Table 5. Vertical vibration acceleration of the cab of rotary tiller and tractor under no-load condition.

The Location of the Measurement Point	RMS/m·s−2
Rotary tiller	20.865
Cab	1.201

. The RMS values of the vertical vibration acceleration at different positions of the unit under the three working conditions are shown in

Table 6. RMS of vertical vibration acceleration at different positions of the rotary tillage unit under three working conditions.

Speed/ km·h−1	RMS of Vertical Vibration Acceleration at Different Positions of the Unit/m·s−2
	Rotary Tiller	Three-Point Suspension Mechanism	Tractor Rear Wheels	Cab	Tractor Front Wheels
2.1	21.532	12.507	2.104	1.218	6.500
3.6	24.950	20.594	4.820	1.333	4.884
4.5	26.399	24.026	5.306	1.346	7.726
Average value	24.294	19.042	4.077	1.299	6.370
Standard deviation	2.499	5.914	1.726	0.070	1.425

, and the RMS values of the vertical acceleration on both sides of the rotary tillage unit are shown in

Table 7. RMS of vertical acceleration on both sides of the rotary tillage unit under three working conditions.

Speed/ km·h−1	RMS of Vertical Acceleration on Both Sides of the Rotary Tillage Unit/m·s−2
	Linkage Left Lower Tie Rod	Linkage Right Lower Tie Rod	Tractor Left Rear Wheel	Tractor Right Rear Wheel	Tractor Left Front Wheel	Tractor Right Front Wheel
2.1	20.382	4.632	4.129	0.078	10.973	2.018
3.6	24.463	16.725	9.566	0.074	7.192	2.575
4.5	27.509	20.543	10.529	0.082	12.848	2.603
Average value	24.118	13.967	8.075	0.078	10.338	2.399
Standard deviation	3.576	8.306	3.451	0.004	2.881	0.330

.

The following can be seen from the data in Table 5, Table 6 and Table 7:

(1)

The vertical amplitude of the rotary tiller and tractor cab in the working state was higher than in the no-load state, and the amplitude increased with the speed, indicating that the unit had other excitation sources besides the rotary tiller. However, this change would be obvious at a higher speed. When the vehicle speed was 2.1 km/h, the amplitude increased by only 0.667 m/s² and 0.017 m/s², respectively, compared with zero speed, while the amplitude increase was 5.534 m/s² and 0.145 m/s², respectively, at the speed of 4.5 km/h. During the tractor rotary tillage operations, the average vertical acceleration generated by the rotary tiller at different vehicle speeds was 24.294 m/s², and the average vertical acceleration generated by the three-point suspension mechanism was 19.042 m/s², which was much larger than the vertical acceleration everywhere of the tractor. This showed that the rotary tiller was the most important excitation source in the unit. In addition, an analysis of the vibration conditions at different positions of the tractor showed that the vertical vibration of the front wheel (6.370 m/s²) was greater than the tractor’s rear wheel (4.077 m/s²) and the cab (1.299 m/s²). In addition to the different distances from the rotary tiller, the reason might also be related to the front and rear wheel load, stubble thickness, front and rear wheel vibration amplitude, and other factors.

(2)

Investigating the changes in the vertical vibration acceleration of the different parts, it could be seen that the influence of working speed on each measurement part from large to small was as follows: three-point suspension mechanism > rotary tiller > tractor rear wheels > tractor front wheels > cab. Among them, the standard deviation of the three-point suspension mechanism (5.914 m/s²) was much larger than that of other parts, indicating that speed changes had the greatest impact on the three-point suspension mechanism. The reason may be that the three-point suspension mechanism, the tractor, and the rotary tiller used pins and other movable connections, so it was greatly affected by inertia. The vertical vibration change in the rotary tiller (2.499 m/s²) was second only to the three-point suspension mechanism, indicating that the vehicle speed was an important factor in the vibration changes in the rotary tiller operation, which, in turn, affected the quality of the rotary tillage operation. While the cab’s vertical vibration acceleration changed the least (0.070 m/s²), presumably because the tractor’s vibration damping device had good vibration damping performance near the cab.

(3)

The vertical vibration amplitude and vibration acceleration standard deviation of the rotary tiller and the three-point suspension mechanism were much larger than those of the tractor components, indicating that the biggest excitation source for the two came from their interaction, which meant their interaction led to a severe vibration. The vertical acceleration amplitude of the rear wheels of the tractor (4.077 m/s²) was generally smaller than that of the front wheels (6.370 m/s²), which was related to the fact that the mass of the rear wheel was greater than that of the front wheel. However, the acceleration changes in the rear wheels (1.726 m/s²) were greater than those in the front wheel (1.425 m/s²). It was speculated that the rear wheels were affected by the violent vibration of the three-point suspension device, which accelerated the change in its own vibration amplitude.

(4)

From working condition 1 to working condition 3, the overall vertical vibration acceleration of the rotary tiller and tractor increased, but the growth rate slowed down. The vibration acceleration of each part of the tractor increased as the vehicle sped up as a whole but the vibration acceleration of the tractor’s front wheel decreased by 1.616 m/s² from 2.1 km/h to 3.6 km/h, and then increased again when it reached 4.5 km/h. It was speculated that when the vehicle speed was 3.6 km/h, the load distribution of the tractor changed, and the load on the left front wheel became smaller.

(5)

The durability of agricultural machinery could be detected using vibration signals [33]. The vibration of the symmetrical structure of the wheeled tractor should be similar, but the vibration acceleration on the left side of each measured part in Table 5 was greater than that of the right side. This might have been caused by problems with the tractor parts and structural assembly, which, in turn, led to abnormal vibration transmission paths of the front and rear wheels and the three-point suspension mechanism symmetry point [34]. The vibration acceleration of the tractor’s front left wheel only decreased by 3.781 m/s² when the speed was 3.6 km/h, resulting in a decrease in the vibration acceleration of the tractor’s front wheel, as in Table 7. At this time, the tractor’s vibration damping mechanism could not achieve a more balanced vibration suppression effect on the left and right sides, and further inspection of the quality of the tractor’s assembly and parts was required.

(6)

During the experiment, the three-point suspension mechanism produced the maximum amplitude, influencing the rotary tiller and tractor connected to its axle pin to produce greater vibration, which, in turn, affected the operation of the unit. For the tractor, the vibration was transmitted from the rear axle to the cab, causing a higher vibration of the seat, resulting in reduced comfort of the tractor seat, which was not conducive to the driver’s long-term operation of the tractor. At the same time, appropriately increasing the amplitude of the rotary tiller could reduce the cutting resistance of the rotary tiller blade into the soil, which is conducive to improving the quality of rotary tillage operation [35], but excessive vibration may also aggravate blade fatigue damage. For this reason, the resonance frequency of the rotary tiller should be avoided as much as possible.

(7)

Judging from the results of time domain analysis alone, higher speed means larger amplitude for each component, but this inference still needs further verification.

3.2. Frequency Domain Analysis of Rotary Tillage Unit

In order to obtain the change in the energy occupied by the center of mass vibration signal of the rotary cultivator and tractor in the unit frequency band along with the frequency, the collected time domain data was processed. Since measuring point 6 was installed in the cab, the vibration it measured could also reflect the vibration characteristics to the operator to a certain extent. For this reason, FFT transformation was performed on the vertical vibration data of measuring point 6 at three speeds, and the frequency domain data in the range of 0~80 Hz were obtained, as shown in Figure 5. The power spectrum peaks and corresponding peak frequencies at the center of mass of the rotary tiller and tractor under different working conditions are shown in

Table 8. Peak power spectrum of center of mass of rotary tiller and tractor.

Measuring Point Location	Rotary Tiller Gearbox			Tractor Cab
Speed/km·h−1	2.1	3.6	4.5	2.1	3.6	4.5
Peak axial	X	Y	Y	X	X	X
Peak/(m·s−2)2	15.728	7.213	7.958	0.216	0.115	0.794
Frequency/Hz	351	466	548	270	275	274

, and the PSD is shown in Figure 6. For non-stationary random signals, the above processing could not reflect the characteristics of the signal frequency changing with time. In order to process non-stationary random signals, it was necessary to jointly represent the time domain and frequency domain of the signal in two dimensions, which means, time–frequency analysis. The signal analyzer in Matlab 2022a could be used to perform time–frequency analysis on the original time domain data collected. The local time–frequency analysis of the gearbox and cab under working condition 1 is shown in Figure 7.

Based on the data charts above, the relationship between vibration acceleration and frequency changes near the gearbox (rotary tiller) and tractor cab (tractor) was analyzed, and the following conclusions were drawn:

(1)

At the three working speeds, the amplitude of the tractor cab appeared as small peaks in the frequency range of 0~8 Hz, and with the increase in working speed, the peak frequency of the amplitude reduced from 6.8 Hz to 4.9 Hz. As the human body is more sensitive to vertical vibration frequencies in the range of 4–8 Hz, it would not be appropriate to work for a long time in that environment. The change in the peak frequency of the seat vibration in the low frequency range (1~16 Hz) was consistent with the content in the literature [36]. Therefore, maintaining high-speed operation of the unit in actual operation may avoid the sensitive frequency interval of the human body and maintain human health.

(2)

For the tractor, the peaks of vibration energy first occurred intensively in the low-frequency range of 0~100 Hz. Under the three working speeds, the power spectrum density in the X, Y, and Z directions all produced the first peak near 33 Hz. Regardless of the speed and direction, in the frequency range of 30~50 Hz, the energy occupied by the tractor’s vibration signal began to gather significantly, especially at the highest speed, indicating that the first-order natural frequency of the tractor may exist in the continuous range of 30~50 Hz. In the wide range of 100~500 Hz, the power spectrum density values of the tractor in each direction varied, and the overall vibration energy density was higher. Combined with the corresponding frequency of the power spectrum peak of the rotary tiller in Table 8, it could be seen that the tractor had a resonance band of a certain width in this range. Unlike the tractor, the vibration signal power distribution of the rotary tiller in the range of 0~100 Hz was not significant, and the vibration energy in all directions was less than in the range above 250 Hz. Considering that its design purpose was to loosen the topsoil, it is beneficial for the rotary tiller to have much greater vibration energy than the tractor cab when working.

(3)

For the movement of the rotary tiller in the X direction, the peak power spectrum of working condition 1 (15.728 (m/s²)²) was much larger than that of working conditions 2 and 3. Figure 7a is the time–frequency diagram of the X-direction vibration of the rotary tiller gearbox under working condition 1. After processing with the band stop filter, it could be seen that there was a relatively obvious vibration energy distribution at various frequencies, among which the energy distribution at a frequency of about 350 Hz was the most significant, and the energy concentration did not change over time. More concentrated energy distributions could also be seen when the frequencies were near 700 Hz, 1050 Hz, and 1400 Hz (that was, integer multiples of 350 Hz). In the short period, the other frequency components except 350 Hz were not significant, indicating that the energy of the rotary tiller under working condition 1 was the most concentrated at the frequency of 350 Hz. This was consistent with the frequency corresponding to the gearbox vibration peak in Table 8 (351 Hz). It was inferred that the center of mass of the rotary cultivator resonated near the frequency of 350 Hz.

(4)

Figure 7b is a time–frequency diagram of the vibration of the tractor cab in the X direction under working condition 1. The figure showed that the frequency corresponded to the maximum vibration at about 280 Hz, and the energy there remained unchanged during the sampling time. In Table 8, the tractor centroid power spectrum peak at a frequency of 274 Hz under working condition 3 increased significantly (0.794 (m/s²)²), and the peak frequencies under the three working conditions were all in the 270–280 Hz range. Therefore, it can be speculated that there was a resonance frequency in this interval.

(5)

The X-direction resonance frequency of the rotary tiller was around 350 Hz, which was higher than the X-direction resonance frequency of the tractor cab (280 Hz). For tractors, people would want to avoid resonance, but this is different for rotary tillers. For the entire unit, improving operating efficiency is to better perform the rotary tillage operations. Since increasing the vibration of the rotary tiller can reduce the adhesion of soil to the rotary tiller blades [37], the operating speed can be increased to increase the amplitude of the rotary tiller operation, thereby reducing the resistance of the soil to the rotary tiller operation and improving operating efficiency and quality.

(6)

For the movement of the gearbox in the Y direction, the PSD diagram showed that its vibration energy was concentrated in the high-frequency range of 750~1000 Hz, which was much higher than the resonance frequencies in the X and Z directions. Therefore, when considering avoiding resonance of the rotary cultivator, only the vibration in the X and Z directions need to be considered. The tractor cab in the Y direction generated a large vibration acceleration near 78 Hz. The vibration energy was concentrated in the lower frequency range of 75~135 Hz under various working conditions, but the overall vibration acceleration of the Y-axis was low, causing little impact.

(7)

The Z-direction rotary tiller gearbox had a wide frequency range of violent vibrations, and large vibrations occurred between 430 and 1200 Hz under three working conditions. It was speculated that this was related to the fact that the rotary tiller would jump up and down in the vertical direction due to the rotary tiller blade encountering resistance when entering the soil and the vibration acceleration of the blade axis changing more obviously in the Z direction. The maximum vibration acceleration frequencies generated by the tractor in the Z direction were 66 Hz, 78 Hz, and 272 Hz, respectively, which were more concentrated than those in the X and Y directions.

(8)

The results of the frequency domain analysis showed that high speed did not always lead to high amplitude. Sometimes, the PSD values of the rotary tiller in each direction at low speed were higher than those at high speed. In the low-frequency range relevant to human health, the low-speed amplitude was also greater than the high-speed amplitude.

(9)

When using the signal analyzer in Matlab 2022a for the time–frequency analysis shown in Figure 7, a band-stop filter was also used to preprocess the original signal data, and the frequency components of the resulting time–frequency diagram were still relatively complex. In order to obtain a time–frequency diagram with clearer vibration energy distribution and better time–frequency aggregation, the next step could be to use continuous wavelet transform and other analysis methods with good time–frequency resolution to extract the characteristics of the vibration signal.

4. Conclusions

This paper took the rotary tiller, tractor, and three-point suspension mechanism as research objects and explored the interaction between the units at different speeds through vibration characteristic analysis. Based on the results of the vibration test experiments of the rotary tillage unit under three working speed conditions, combined with time domain and frequency domain analysis, the following conclusions can be drawn:

(1)

The vibration amplitude of the rotary tiller needs to be appropriately increased to reduce the resistance to soil penetration, but the interaction between the tractor and the rotary tiller causes the vibration to be transmitted to the tractor synchronously, which is harmful to the tractor. Therefore, while the tractor is mounted with a rotary tiller and operates at high speed and efficiency, the vibration reduction capacity of the tractor also needs to be optimized to achieve higher quality of work and more stable operation.

(2)

Generally speaking, the vibration acceleration at each measurement point increased with the increase in working speed, but this was not necessarily the case in certain frequency domain intervals. In some frequency domain intervals, the amplitude did not always increase with increasing speed. It might be that the low-frequency range is less affected at low speed, while the amplitude change in the high-frequency range at higher speeds still needs to be tested.

(3)

The reason for why the vibration amplitude of the unit increased with the tractor speed might be related to the more violent collision between the unit and the stubble surface caused by the increase in speed. However, in the low-frequency and low-amplitude range, which has an important impact on human health, the vertical resonance frequency of the cab seat decreased with the increase in amplitude (from 6.8 Hz to 4.9 Hz). In the future, the change law of the vertical amplitude of the seat under high-speed operation of the unit can be studied to help the driver operate the tractor more healthily.

This paper obtained the interaction relationship among the components of the unit by collecting and analyzing the vibration data of the tractor, three-point suspension mechanism, and rotary tiller under different working conditions, and it also speculated on the possible structural assembly problems of the tractor within the experiment. The vibration data analysis method used in this paper can be further used to explore the interaction relationship and vibration characteristics between the tractor and the suspension agricultural implement system. In the future, the vibration analysis method can be further used to study the influence of factors such as field surface flatness and of PTO speed on the combined operation effect of the tractor and rotary tiller.