Dynamic analysis of rotary tiller gearbox based on EDEM,ADAMS and ANSYS

Abstract

Rotary tiller gearbox bears alternate and complex dynamic load. To provide accurate load for its design, use UG software to establish 3D parametric modeling of main parts. Import 3D parametric modeling of blade and shaft into EDEM software. Use Bonding model to establish simulation model of soil particles. Through numerical simulation of the impact load from blade and soil, the dynamic load parameters of blade and shaft are derived. Obtain the model of gearbox housing in ANSYS software and import it into ADAMS software as flexible body. Based on the dynamic load parameters of blade and the model of gearbox housing, multi-body dynamical rigid-flexible coupling simulation analysis for rotary tiller is done with ADAMS software. ADAMS software solves the model by adopting Lagrange dynamics equation, rigidity integral algorithm and sparse matrix technology, through which the load model of gearbox is derived. Finally, import the load model into ANSYS software, and make stress and strain analysis on the rotary tiller gearbox, by applying the load same as recorded in load file, to find out design defects and weakness of rotary tiller gearbox, which provide references for the design of rotary tiller gearbox, and help to optimize the design.

Keywords

Rotary tiller gearbox EDEM ADAMS ANSYS rigid-flexible coupling

1 Introduction

Rotary tillers are among the most commonly used machines for land cultivation and soil preparation. As the gearbox is a key component for power transmission in these machines, the stability of the gearbox has a significant impact on the reliability of rotary tillage [19]. A rotary tiller operates under highly adverse conditions, and with the continuous development of agronomic techniques, the performance requirements for rotary tillers are becoming increasingly stringent [13]. Therefore, the stiffness and strength of rotary tiller gearboxes must meet operational requirements. The design of gearboxes and the calculations involved in these designs traditionally employ empirical and analytical methods. However, with these methods, it is difficult to produce rational structural designs that guarantee the stiffness and strength of the resultant gearbox [17]. At present, there is a large amount of research on the use of finite element analysis techniques in engineering applications [3 , 18]. For example, foreign scholars such as P Weis [14] used the ANSYS program to perform modal analyses on loaded gear housings, from which the natural frequency and vibrational modes of these housings were obtained. AT Pfeiffer [1] used ANSYS and ADAMS software to analyze the flexible multibody dynamics of an ornithopter. DR Curry [4] used EDEM and ADAMS for coupled simulations and analyses of heavy-duty loaders. Several studies have also been conducted by Chinese scholars in this field. For example, Mao [11] used ANSYS to analyze the static mechanics of a rotary tiller’s transmission gearbox, and verify the strength and stiffness of the gearbox. Niu et al. [12] used ADAMS to study the dynamics of a gearbox’s transmission system. Guo et al. [7] used ANSYS and ADAMS to perform dynamic analysis on the housing of a thin seam shearer’s rocker arm. Wang et al. [16] used ANSYS and ADAMS to perform simulation analysis on an excavator boom. Liu [10] used EDEM and ADAMS to perform coupled simulation analyses on the impact crushing mined ores. Chen et al. [2] used EDEM and ADAMS to perform discrete element analyses on the excavation resistance of an excavator boom, and exported the excavation resistances obtained using EDEM to ADAMS, which was then used in the dynamic analysis of a dynamic model of the excavator. Fang et al. [6] used EDEM to analyze the forces on a rotary tiller’s blades during their operation on soils. Based on the above research, a novel dynamic analysis scheme for rotary tiller gearboxes based on EDEM, ADAMS, and ANSYS is presented in this paper. This scheme will allow the more precise simulation of a rotary tiller’s operational conditions on soils, and accurately reproduce the force curves of a rotary tiller’s gearbox. The findings of this study will therefore provide a useful reference for gearbox design.

2 Simulation analysis process

The simulation analysis consists of six main steps:

Establish 3D solid model of the mechanism in UG according to the real object of rotary tiller, and the assembly is carried out.

Establish the simulation model of soil particle by using Bonding model.

Import 3D model of rotary tiller blade and blade shaft into EDEM system to complete discrete element simulation analysis. Through the numerical simulation of the impact load from blade and soil, generate load parameters of rotary tiller blade shaft.

Load the 3D model of rotary tiller gearbox into ANSYS software to generate the modal model.

Import the load parameters of rotary tiller blade shaft generated from EDEM into ADAMS, and replace the modal model of rotary tiller gearbox with the rigid body in ADAMS. Multibody dynamical rigid-flexible coupling simulation analysis for rotary tiller is done with ADAMS software, then the load model of rotary tiller gearbox is obtained.

After importing the load model into ANSYS, carry out the finite element analysis for the rotary tiller gearbox, then the stress cloud spectrum can be obtained.

The simulation process is shown in Fig. 1.

Fig.1

Setting for document template.

3 Rotary tiller model

The main components of rotary tiller are gearbox housing, driving shaft, driven shaft, driven bevel gear, rotary blade shaft, rotary blade and bearing. The rotary tiller blade shaft and the rotary tillage blade are fastened with bolts. The blade shaft and the driven shaft are meshed with the rectangular spline, and the driven bevel gear and the driven shaft are meshed through the involute spline. Use UG software to establish 3D model of the main components of rotary tiller. The assembly drawing of rotary tiller is shown in Fig. 2.

Fig.2

3D model of the main parts of rotary tiller.

4 The discrete element simulation

4.1 Establish soil particle simulation model

In this paper, the Hertz-Mindlin with Bonding model is used to set up 300000 soil particles with diameter of 5 mm to simulate soil particle environment. Discrete element simulation parameters mainly consists of material parameter and contact parameter. Material parameters include density of soil and rotary tillage blade, Poisson ratio and shear modulus, etc. Contact parameters include soil-soil, static and rolling friction factor and coefficient of restitution between soil-rotary tillage blade [5], etc. The test parameters in this paper are shown in Table 1. Import the 3D model of rotary tiller into EDEM software. The simulation of rotary tiller operating in soil is shown in Fig. 3.

Table 1
Parameters used in simulation

Parameters value

soil density ρ₁/(kg · m^-1) 1850

Soil Poisson ratio ν₁ 0.38

Shear modulus of soil G₁/Pa 1 × 10⁶

density of iron ρ₂/(kg · m^-1) 7865

Poisson’s ratio of iron ν₂ 0.3

Iron shear modulus G₂/Pa 7.9 × 10¹⁰

Soil - soil recovery coefficient e₁ 0.6

Soil - iron recovery coefficient e₂ 0.6

Soil - soil static friction factor f_s1 0.6

Soil - iron static friction factor f_s2₁ 0.6

Soil - soil rolling friction factor f_d1 0.4

Soil - iron rolling friction factor f_d2 0.05

Parameters	value
soil density ρ₁/(kg · m^-1)	1850
Soil Poisson ratio ν₁	0.38
Shear modulus of soil G₁/Pa	1 × 10⁶
density of iron ρ₂/(kg · m^-1)	7865
Poisson’s ratio of iron ν₂	0.3
Iron shear modulus G₂/Pa	7.9 × 10¹⁰
Soil - soil recovery coefficient e₁	0.6
Soil - iron recovery coefficient e₂	0.6
Soil - soil static friction factor f_s1	0.6
Soil - iron static friction factor f_s2₁	0.6
Soil - soil rolling friction factor f_d1	0.4
Soil - iron rolling friction factor f_d2	0.05

Fig.3

Simulation of interaction from rotary tiller and soil.

4.2 Discrete element simulation of rotary tiller

Set the working parameters in EDEM. The rotation speed of rotary tiller blade shaft is 10.5 rad/s. Advance speed is 0.2 m/s. Contact depth in soil is 0.1 m. Simulation time step is set to 20% of Rayleigh time step. Data storage frequency is set to 0.05 s. The load situation of rotary tiller blade shaft is shown in Fig. 4. The load parameters of rotary tiller blade shaft are finally saved in text form.

Fig.4

Force curve of rotary tiller shaft in the X, Y and Z axial direction.

5 Generate modal model

Import the 3D model of rotary tiller gearbox into ANSYS software. Define the unit type, select SOLID185, BEAM188. Define material properties: select HT250 materials with elastic modulus of 1.26E+11 Pa, Poisson ratio of 0.3 and density of 7305 kg/m cubed. Secondly, the flexible body is divided into grid. Define the external node and establish the rigid area, as shown in Fig. 5. This paper establishes four nodes for the rotary tiller gearbox to ensure that the flexible body can be correctly located in ADAMS software, and avoid the stress concentration in later stress and strain analysis. Derive the model from the ANSYS-ADAMS interface module, and generate the modal model, which contains information such as the weight, center of mass, frequency, vibration type and participation factor of the load of the flexible body.

In order to verify the precision of the modal model generated from the ANSYS software, the vibration mode and frequency of the original and current modal model should be compared. Considering the more advanced of the modal model, the less influence in calculation results, this paper selects 6-scale to compare the vibration mode and frequency of rotary tiller gearbox modality. The comparison of 6-scale modal vibration mode of the original and the current modal model is shown in Figs. 6 and 7. The frequency comparison of 1– 6 scales is shown in Table 2.

Fig.5

Finite element model of rotary tiller gearbox.

Fig.6

The 6th scale model vibration mode of original modality.

Fig.7

The 6th scale modal vibration mode of current modality.

Table 2

Factors and levels of test

Order number	Frequency mode frequency (HZ)	Mode frequency after generating MNF file (HZ)
1	0.0000	0.0000
2	0.0000	0.17727
3	0.05703	0.23022
4	0.12913	0.35740
5	0.16530	0.36436
6	0.19897	0.47953

6 Multi-body dynamic simulation analysis of the rigid-flexible coupling of rotary tiller and establishment of its equation

6.1 Carry out multi-body dynamical rigid-flexible coupling simulation analysis

Import the 3Dmodel of the entire rotary tiller into ADAMS software, as shown in Fig. 8. Import load parameters of rotary tiller blade shaft generated from EDEM software into ADAMS with the methods of Spline function, and set the transmission speed of driving shaft to 10.5 rad/s. First step is to check whether the simulation movement operates rightly and then import the modal model of the gearbox into ADAMS to replace original rigid model, as shown in Fig. 9. At this moment, gearbox of rigid body will be treated flexibly. Set up the remaining related parameters, carry out multi-body dynamical rigid-flexible coupling simulation analysis, through which the load and displacement spectrum, of rotary tiller gearbox is obtained, and finally generate the load model of rotary tiller gearbox.

Fig.8

3D model of rotary tiller import into ADAMS software.

Fig.9

Multi-body dynamical analysis on rigid-flexible coupling.

6.2 Equation establishment of rigid-flexible coupling multibody dynamics

ADAMS software solves model by adopting Lagrangian dynamics equation, supported with the rigid integral algorithm and the sparse matrix technique. Referring to the dynamics theory of multi-rigid-body and multi-flexible-body system, and combining the analysis results of flexible body and the research methods of rigid body, obtain the equation of rigid-flexible coupling multi-body dynamics. Establish the equation of ist flexible or rigid body by adopting Lagrange multiplier method as follows:

$\frac{d}{dt} + {(\frac{\partial T}{\partial {\dot{q}}^{i}})}^{T} + (\frac{\partial T}{\partial q^{i}}) + C_{q}^{iT} λ = Q^{i}$ (1)

In the formula:

T– the kinetic energy form of the system.

Qⁱ–force in broad sense, including the elastic deformation of the unit and the generalized force caused by the external load.

λ– Laplace’s multiplier.

The sum of the two items on the left of Equation (1) is further generated:

$M^{i} {\ddot{q}}^{i} + {\dot{M}}^{i} {\dot{q}}^{i} - {[\frac{\partial}{\partial q^{i}} (\frac{1}{2} q^{iT} {\dot{M}}^{i} {\dot{q}}^{i})]}^{T}$ (2)

Suppose: $Q_{ν}^{i} = - {\dot{M}}^{i} {\dot{q}}^{i} + \frac{1}{2} {[\frac{\partial}{\partial q^{i}} (q^{iT} {\dot{M}}^{i} {\dot{q}}^{i})]}^{T}$ $Q^{i} = Q_{e}^{i} + Q_{ν}^{i}$

In the formula:

Q_ν – velocity binomial.

Q_eⁱ– unit external load.

Substituting the above results into Equation (1): $M^{i} {\dot{q}}^{i} + ξ^{i} {\dot{q}}^{i} + C_{qi}^{iT} λ = Q_{e}^{i} + Q_{ν}^{i}$ (3)

The Equation (3) is coupled with the constraint equation C (q, t) =0 of the system (t means time), which establishes the dynamics equation of the rigid-flexible coupling system.

7 Finite element analysis of rotary tiller gearbox

Using the ANSYS-ADAMS interface module, import the load model of rotary tiller gearbox into ANSYS, and set the constraints and boundary conditions to carry out static analysis. In this paper, the stress and displacement in five corresponding time points are calculated. The nephogram of the gearbox in 5th time point is shown in Fig. 10.

Fig.10

The stress and displacement nephogram of rotary tiller gearbox.

8 Conclusion

As described in this paper, based on the discrete element method and Hertz-Mindlin with Bonding model, we simulate the operation process of the rotary blade contacting with the soil with the help of EDEM software, as a result we obtain the force curve of rotary tiller blade shaft in the X, Y and Z-axis direction. Then import the load parameters of blade shaft generated from EDEM software into ADAMS software by the method of Spline function, through which accurately simulate the force situation of the entire rotary tiller can be precisely simulated. Afterwards, carry out multi-body dynamical rigid-flexible coupling simulation analysis and obtain the load data of rotary tiller gearbox. Finally, start static analysis on gearbox in ANSYS software based on the load spectrum, and find out the design defects and weakness of the gearbox.

From stress nephogram of rotary tiller in Fig. 10, the maximum stress is in the connection point of rotary tiller gearbox and the tractor. Its stress value is 0.691E+08 Pa, and its allowable stress is 2.5E+08 Pa. Since its maximum stress is not beyond the material strength limit, we conclude rotary tiller gearbox is safe and reliable. Based on the software of EDEM, ADAMS and ANSYS, carry out the dynamics analysis on the rotary tiller gearbox, in order to find out the concentration position of the stress, which can offer references for the design of the gearbox.

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