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Foot design requirements.
Preface Dynamic design solves the dynamic parameters by modeling the transmission system: calculating the modal parameters of the system. Then, according to the actual situation of the project, these parameters are compared with the given dynamic characteristics requirements, and the structural modification design and the modified dynamic characteristic prediction are performed. The structure modification and prediction process need to be repeated several times until the design requirements are met.
This paper introduces a practical dynamic design method for gear transmission systems. The method uses sensitivity analysis to find out the design variables that affect the dynamic characteristics, and then modify them. Then, the first-order matrix perturbation method is used to predict the modified dynamic characteristics.
In order to avoid the cumbersome calculation, the implementation of the method is illustrated by taking the first stage cylindrical gear reducer as an example. According to the actual requirements, the first-order natural frequency of the reducer is not lower than 330 Hz. Table 1, Table 2 and Table 3 are the main parameters of the system.
Table 1 Motor parameters Tab.1 Numerical rated power / kW rated speed / rmin1 Moment of inertia Ji / kg - m2 Table 2 Gear original parameters Gear module / mm number of teeth Helix angle / (°) Tooth width / mm Table 3 axis of the main Original parameter Tab.3 Axis 1 Reducer Modeling 1.1 The model assumes that the radial and axial vibrations of the gear drive are not considered and only the torsional vibration is taken into account.
The coupling of the coupling between the motor and the gear is considered to be a rigid coupling.
The support bearing of the transmission system and the support of the case are relatively rigid and are considered rigid. The shaft is considered to be an elastic shaft with torsional stiffness and torsional damping, all calculated from the equivalent diameter and length of the shaft.
A pair of meshing gear teeth is considered an elastomer, and its meshing condition is equivalent to a parallel spring and damper.
More, its rotation can be regarded as a constant speed. If the coordinates are fixed on the mass it carries, it will not change the dynamic characteristics of the research object.
The moment of inertia of the shaft is equivalent to the inertia element at both ends of the shaft (generally halved). After the above assumptions, the corresponding kinetic model is.
According to the knowledge of mechanical vibration, directly write the system dynamics equation - left 1 J \ - the moment of inertia of the gear, kg * m2; /, - the equivalent of the axis of the mass element of the rotation of the inertia according to the system flexibility before and after conversion The principle of constant potential energy, the torsional stiffness is transformed into the axis I to k\-the torsional stiffness of the i-th elastic element.
(3) The calculation of the meshing stiffness of the gear is calculated according to the empirical formula. A2=(4) is substituted into the specific parameters. The 2 modal parameters are solved. The above parameters are substituted (3), and the model of the third-order natural frequency transmission system is obtained. The main reason is to analyze the natural frequency and vibration mode of the transmission system. The damping has no effect on this, and the external excitation has no effect on it. Therefore, it can be =0, the generation type (1), and ((4)-(1)2 is the characteristic matrix of the system. The frequency equation of the system is any one of the formulas (4), and the other two equations are combined. The system vibration mode is E, and the IWh is used to obtain the sensitivity analysis method. The sensitivity of the natural frequency to the design variable is obtained. - System first / design variables; 1J. - System i-group regular vibration mode.
Let o/j, ii i be the first-order approximation natural frequency and mode shape prediction value after perturbation of structural parameters, then there are = system parameters from a large aspect: gear meshing stiffness a2, shaft torsional stiffness and etc. The effect of the moment of inertia, 厶 and 厶. Then there is the natural frequency sensitivity to the stiffness of the natural frequency sensitivity to the moment of inertia = gentry) back) 丨丨 1; calculate the available sensitivity values ​​as shown in Table 4. Table 4 natural frequency pairs, the sensitivity of Tab.4 in the motor selected In the case of focusing on modifying the parameters of the reducer itself, A3 and /3 have the greatest influence on Wl. Further analysis shows that the order of magnitude is much larger than that of J3. Therefore, the main parameter that affects ik3 is the diameter of the axis between the large gear and the load. 4 First-order matrix perturbation method predicts the modified system dynamic characteristics first-order matrix perturbation method For small modification, it is programmed to calculate after 74 cycles, / 336, at this time people = 18033.1. From the changed stiffness, the straight axis after the axis change can be calculated. The process of dynamic redesign of the reducer introduces the design method based on sensitivity analysis. The method is simple and practical. Through the sensitivity analysis of the dynamic parameters to the design variables, the design variables with great influence on the dynamic characteristics are found. The first-order matrix perturbation method is used to predict the modified dynamic characteristics. This is repeated, and finally the dynamic characteristics of the transmission system meet the given requirements.
December 26, 2023