CENTROID SWINGING PROPERTY OF A MACHINE BODY UNDERGOING LONGITUDINAL EXCITATION IN A STRAW COMPRESSION BALER

Tang, Zhong; Wang, Haoyang; Jing, Tiantian; Liu, Sifan; Shen, Cheng

doi:10.1590/1809-4430-Eng.Agric.v44e20230109/2024

Zhong Tang ^** Corresponding author. School of Agricultural Engineering, Jiangsu University, Zhenjiang 212013, China. E-mail: tangzhong2012@126.com |

School of Agricultural Engineering, Jiangsu University, Zhenjiang 212013, China.

https://orcid.org/0000-0002-2724-115X

Haoyang Wang

School of Agricultural Engineering, Jiangsu University, Zhenjiang 212013, China.

Tiantian Jing

School of Agricultural Engineering, Jiangsu University, Zhenjiang 212013, China.

Sifan Liu

School of Agricultural Engineering, Jiangsu University, Zhenjiang 212013, China.

Cheng Shen

Nanjing Institute of Agricultural Mechanization, Ministry of Agriculture and Rural Affairs, Nanjing 210014, China.

* Corresponding author. School of Agricultural Engineering, Jiangsu University, Zhenjiang 212013, China. E-mail: tangzhong2012@126.com |

Area Editor: Fábio Lúcio Santos

Parameter	Value	Parameter	Value
Mass of the baling frame m₁	360 kg	Mass of the chassis frame m₂	416 kg
Mass of the rear roller m₃	52 kg	Mass of the engine m₄	150 kg
Mass of the conveying fork m₅	138 kg	Mass of the compression device m₆	125 kg
Mass of the header and conveyor trough m₇	340 kg	Mass of the front roller m₈	52 kg
Vertical stiffness of the baling frame k_m, k_n	5.91×10⁷ N/m	Vertical damping of the baling frame c_m, c_n	250 N·s/m
Vertical stiffness of the chassis frame k₂	5.91×10⁷ N/m	Vertical damping of the chassis frame c₂	0 N·s/m
Vertical stiffness of the engine k₄	6×10³ N/m	Vertical damping of the engine c₄	225 N·s/m
Vertical stiffness of the header and trough k₇	5.5×10³ N/m	Vertical damping of the header and trough c₇	300 N·s/m
Vertical stiffness of the front roller k₈	3.35×10³ N/m	Vertical damping of the front roller c₈	175 N·s/m
Vertical stiffness of the rear roller k₃	3.35×10³ N/m	Vertical damping of the rear roller c₃	175 N·s/m
Vertical stiffness of the conveying fork k₅	7.27×10⁴ N/m	Vertical damping of the conveying fork c₅	350 N·s/m
Vertical stiffness of the compression device k₆	8.05×10⁵ N/m	Vertical damping of the compression device c₆	400 N·s/m
Distance from the engine to the centre of mass l₄	0.4 m	Distance from the drive shaft of the trough to the centre of mass l₇	0.55 m
Distance from the drive shaft of the front roller to the centre of mass l₈	0.75 m	Distance from the drive shaft of the rear roller to the centre of mass l₃	0.5 m
Distance from the drive shaft of the conveying fork to the centre of mass l₅	0.15 m	Distance from the drive shaft of the compression mechanism to the centre of mass l₆	0.2 m
Distance between the front of the baling frame and the centre of mass l_m	0.6 m	Distance between the rear side of the baling frame and the centre of mass l_n	0.4 m

Equipment	Performance index	Parameter value
Three-direction acceleration sensor 1A312E	Range	±500g
	Frequency response	0.5~10 kHz
	Sensitivity	100 mV*g^-1
	Lateral sensitivity	<5%
Dynamic signal acquisition instrument DH5902N	Channel	32
	Sampling frequency	256 kHz
	Distortion factor	<0.5%
	Signal input method	IEPE

Test scenario	Status of the straw compression baler	Test environment	Driving speed, km·h^-1
1	Static, no load (engine only)	Indoor	0
2	Static, no load (all parts working)	Indoor	0
3	Moving state (engine only)	Outdoor	10
4	Moving state (all parts working)	Outdoor	10

Measuring point	Location	Measuring point	Location
1	Transition frame for engine output shaft	2	Bearing housing for pickup drive shaft
3	Upper end of front roller shaft	4	Upper end of rear roller shaft
5	Bearing housing for the drive shaft of the conveying fork	6	Bearing housing for drive shaft of compression mechanism
7	Left front of chassis frame	8	Left rear of chassis frame
9	Right front of hay box	10	Rear right of hay box
11	Support for driver's seat	12	Bottom plate of the driver's platform

Vibration source	Rotating speed /rpm	Frequency /Hz	Vibration source	Rotating speed /rpm	Frequency /Hz
Engine	2400	40	Gear transmission	391.7	6.53
Engine drive shaft	1354	22.57	Rear roller	569.8	9.50
Knotted shaft	96.5	1.61	Front roller	341.8	5.70
Compression mechanism shaft	96.5	1.61	Picking up device	141	2.35
Transport bale shaft	193	3.22	Feeding auger	226	3.77

Number	Effective value of vibration acceleration (a_rms, m·s^-2) and peak-to-peak displacement (x_pp, mm)
	Test condition 1						Test condition 2
	X		Y		Z		X		Y		Z
	a_rms	x_pp	a_rms	x_pp	a_rms	x_pp	a_rms	x_pp	a_rms	x_pp	a_rms	x_pp
1	3.135	0.633	2.827	0.826	2.261	0.432	7.682	16.951	8.319	9.071	4.455	3.816
2	0.538	0.102	0.429	0.285	0.491	0.292	8.768	31.510	13.700	44.104	9.833	51.074
3	0.611	0.193	1.162	0.278	0.970	0.400	5.508	24.563	2.209	6.987	5.718	13.209
4	0.759	0.117	3.906	0.256	0.604	0.085	8.203	19.314	6.745	14.396	10.107	26.858
5	0.782	0.182	1.193	0.555	1.458	0.166	7.940	34.173	11.730	13.155	9.347	21.449
6	0.266	0.087	1.188	0.165	0.429	0.146	5.181	34.826	3.985	17.537	5.375	2.900
7	0.703	0.103	1.434	0.135	2.085	0.134	3.850	24.068	4.664	3.064	10.469	13.776
8	0.842	0.085	1.162	0.659	1.995	0.744	5.736	24.771	3.187	12.515	7.287	27.886
9	1.031	0.594	0.683	0.320	1.064	0.490	1.586	14.313	1.386	6.085	2.977	17.941
10	0.974	0.513	0.798	0.409	1.112	0.478	1.759	12.444	1.539	15.970	3.030	46.002
11	2.464	0.190	3.372	0.384	7.104	1.191	2.888	15.037	3.655	3.107	8.296	3.483
12	2.341	0.247	3.942	0.337	7.981	0.744	4.702	19.595	5.269	5.031	14.044	15.028

\begin{matrix} x = {[x_{1}, x_{2}, α, x_{3}, x_{4}, x_{5}, x_{6}, x_{7}, x_{8}]}^{T} \\ M = [\begin{matrix} m_{1} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & m_{2} & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & J & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & m_{3} & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & m_{4} & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & m_{5} & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & m_{6} & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & m_{7} & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & m_{8} \end{matrix}]; C = [\begin{matrix} c_{11} & - (c_{m} + c_{n}) & c_{13} & - c_{3} & 0 & - c_{5} & - c_{6} & - c_{7} & - c_{8} \\ - (c_{m} + c_{n}) & (c_{4} + c_{m} + c_{n}) & c_{m} l_{m} - c_{n} l_{n} & 0 & - c_{4} & 0 & 0 & 0 & 0 \\ C_{31} & c_{m} l_{m} - c_{n} l_{n} & c_{33} & c_{3} l_{3} & 0 & - c_{5} l_{5} & - c_{6} l_{6} & c_{7} l_{7} & c_{8} l_{8} \\ - c_{3} & 0 & c_{3} l_{3} & c_{3} & 0 & 0 & 0 & 0 & 0 \\ 0 & - c_{4} & 0 & 0 & c_{4} & 0 & 0 & 0 & 0 \\ - c_{5} & 0 & - c_{5} l_{5} & 0 & 0 & c_{5} & 0 & 0 & 0 \\ - c_{6} & 0 & - c_{6} l_{6} & 0 & 0 & 0 & c_{6} & 0 & 0 \\ - c_{7} & 0 & c_{l} l_{7} & 0 & 0 & 0 & 0 & c_{7} & 0 \\ - c_{8} & 0 & c_{8} l_{8} & 0 & 0 & 0 & 0 & 0 & c_{8} \end{matrix}] \\ C_{11} = c_{m} + c_{n} + c_{7} + c_{8} + c_{3} + c_{5} + c_{6}; \\ C_{13} = C_{31} = - (c_{m} l_{m} - c_{n} l_{n} + c_{7} l_{7} + c_{8} l_{8} + c_{3} l_{3} - c_{5} l_{5} - c_{6} l_{6}); \\ C_{33} = c_{m} l_{m}^{2} + c_{n} l_{n}^{2} + c_{7} l_{7}^{2} + c_{8} l_{8}^{2} + c_{3} l_{3}^{2} + c_{5} l_{5}^{2} + c_{6} l_{6}^{2} \\ K = [\begin{matrix} K_{11} & - (k_{m} + k_{n}) & K_{13} & - k_{3} & 0 & - k_{5} & - k_{6} & - k_{7} & - k_{8} \\ - (k_{m} + k_{n}) & (k_{4} + k_{m} + k_{n} + k_{2}) & k_{m} l_{m} - k_{n} l_{n} & 0 & - k_{4} & 0 & 0 & 0 & 0 \\ K_{31} & k_{m} l_{m} - k_{n} l_{n} & K_{33} & k_{3} l_{3} & 0 & - k_{5} l_{5} & - k_{6} l_{6} & k_{7} l_{7} & k_{8} l_{8} \\ - k_{3} & 0 & k_{3} l_{3} & k_{3} & 0 & 0 & 0 & 0 & 0 \\ 0 & - k_{4} & 0 & 0 & k_{4} & 0 & 0 & 0 & 0 \\ - k_{5} & 0 & - k_{5} l_{5} & 0 & 0 & k_{5} & 0 & 0 & 0 \\ - k_{6} & 0 & - k_{6} l_{6} & 0 & 0 & 0 & k_{6} & 0 & 0 \\ - k_{7} & 0 & k_{7} l_{7} & 0 & 0 & 0 & 0 & k_{7} & 0 \\ - k_{8} & 0 & k_{8} l_{8} & 0 & 0 & 0 & 0 & 0 & k_{8} \end{matrix}], \\ K_{11} = k_{m} + k_{n} + k_{7} + k_{8} + k_{3} + k_{5} + k_{6} \\ K_{13} = K_{31} = - (k_{m} l_{m} - k_{n} l_{n} + k_{7} l_{7} + k_{8} l_{8} + k_{3} l_{3} - k_{5} l_{5} - k_{6} l_{6}); \\ K_{33} = k_{m} l_{m}^{2} + k_{n} l_{n}^{2} + k_{7} l_{7}^{2} + k_{8} l_{8}^{2} + k_{3} l_{3}^{2} + k_{5} l_{5}^{2} + k_{6} l_{6}^{2}; \\ f (t) = {[\begin{matrix} 0 & 0 & 0 & f_{3} (t) & f_{4} (t) & f_{5} (t) & f_{6} (t) & f_{7} (t) & f_{8} (t) \end{matrix}]}^{T} \end{matrix}

{\begin{matrix} s = r \cos θ + l \cdot \cos φ \\ a_{c} = - ω^{2} r \cos θ + ω^{2} \frac{r^{2} [l^{2} (1 - 2 \cos^{2} θ) - r^{2} \sin^{4} θ]}{{[l^{2} - (r \sin θ)^{2}]}^{\frac{3}{2}}} \end{matrix}

[1] * Corresponding author. School of Agricultural Engineering, Jiangsu University, Zhenjiang 212013, China. E-mail: tangzhong2012@126.com |

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CENTROID SWINGING PROPERTY OF A MACHINE BODY UNDERGOING LONGITUDINAL EXCITATION IN A STRAW COMPRESSION BALER

ABSTRACT