Sensitivity analysis of leaf blower vibration isolator based on ISIGHT

2.1. The dynamic model of leaf blower power system

The power system of the leaf blower is shown in Fig. 2. The power system can be generally divided into five parts: fan, shaft, motor rotor, motor stator and collector. The rotor and the shaft of the motor are installed by interference fit. The fan and the shaft are fixed by bolts. The stator and the shaft are supported by two deep groove ball bearings. The stator and collectors are fixed by bolts. The collector and the housing are fixed through three bolts without any vibration isolation measures. Since the transmission force of the power system to the housing is studied in this paper and the mass of the blower housing is much greater than the power system, the housing can be regarded as a rigid foundation. It is known that the rotational speed of the blower is 17000 rpm. The stiffness of the shaft has a great influence on the dynamic response under high-speed rotation so that the shaft is built as a flexible body to establish a rigid-flexible coupling model of the power system. In this paper, the rigid-flexible coupling model of the power system was built by ADAMS and Hypermesh. The material properties of each component of the power system are shown in Table 1.

Fig. 2Structure and dynamic model of leaf blower power system where: 1 – bolt hole, 2 – motor, 3 – collector, 4 – shaft, 5 – fan

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b)

2.2. Parametric modeling of rubber isolator

The original blower power system is fixed to the casing by bolts and the vibration is not effectively isolated. Because the rubber isolator can be designed into various shapes and different hardness, it is widely used in mechanical products. The basic shape of the isolator used in this paper is shown in Fig. 3. The rubber isolator structure is modeled by the Solidworks parametric modeling method. The characteristic sizes of the control shape are inner diameter $d$, outer diameter $D$ and length $L$.

Fig. 3Size parameters and finite element model of rubber vibration isolator

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b)

The rubber material has a nonlinear characteristic in the case of large deformation but can be considered to be linear in the case of small deformation. Because there is little pressure on the rubber isolator of the blade power system, it can be assumed that the stiffness of the isolator is linear. In this paper, the Command file is used to record the steps in Hypermesh, the steps including importing 3D geometry files, meshing, creating rubber isolator materials and assigning properties, creating attachment points and creating load steps. The complex process of manual modeling can be introduced into parametric modeling by transforming the code in the Command file. In this paper, Optistruct is used to solve the first ten order CB modes of rubber isolators. The parametric modeling method in Optistruct is the same as the method in Hypermesh.

The ADAMS macro command is a set of command sets that can execute a series of ADAMS/View commands. When creating a macro command, the list of executed ADAMS/View commands need to be listed firstly and then write them as macro commands. There are three ways to create macro commands in ADAMS: recording mode, editing and creating macro commands with the macro editor and creating macro commands by importing files. In this paper, the first method is used to create an ADAMS macro command. The specific implementation process is as follows:

Step 1: Enable the macro command recording function in ADAMS;

Step 2: Complete the tasks required in ADAMS: open the dynamics model of the blower power system, introduce the MNF file of the isolator, create fixed pairs between the isolator and the ground, create fixed pairs between the isolator and the power system, create simulation script, set result output;

Step 3: Terminate the recording of macro commands in ADAMS, open the macro command file, and extract the various command segments for executing the task.

3.1. Optimized mathematical model

(1) Optimization.

In order to minimize the force transmitted by the power system to the blower housing. In this paper, the minimum total transmission force is used as the optimization in sensitivity analysis. The total transmission force can be expressed by Eq. (1):

Here $f_{xi}$, $f_{yi}$, $f_{zi}$ represent the reaction force of the $i$th ($i=$ 1, 2, 3) rubber isolator in $x$, $y$ and $z$ directions.

(2) Design variable.

Since the stiffness of the isolator is mainly related to the material and size parameters of the isolator, the inner diameter $d$, the outer diameter $D$, the length $L$ and the elastic modulus $E$ of the three ring-shaped rubbers are taken as design variables. The value range of the design variables is shown in Table 2.

(3) Constraint.

Since the vibration isolation rubber of blower power system is installed on the same plane, it is necessary to ensure that the length of the three rubber isolators is consistent. Considering the principle of vibration isolation, the smaller the stiffness of the brace, the better the vibration isolation effect is. However, the smaller the stiffness, the larger the amplitude of the power system will be. On the other hand, the greater the support stiffness, the smaller the amplitude, but the vibration isolation effect is poor. Taking into account the above constraints, the constraint expression is as follows:

Here $e$ is the amplitude of the centroid of the power system.

3.2. Sensitivity analysis

In order to analyze the influence of the structural design variables of the rubber isolator on the transmission force, the DOE was carried out in this section. In this paper, the Latin hypercube method was used to sampling based on the ISIGHT integration program built in the last section (Fig. 4).

The Pareto diagram is the histogram of the normalization coefficient of the factor, which indicates the influence on the result. Due to the large number of isolator parameters, the contribution of isolator parameters to the target value can be obtained by Pareto diagram (Fig. 5). The largest contribution is the length $L$ of the isolator, the contribution rate is about 42 %. The contribution rates of d1, d3, D3 and E3 are the smallest.

Fig. 4Sampling work flow chart

Fig. 5The contribution of the vibration isolator parameters to the optimization