CN114707263B - Nonlinear super-harmonic resonance aging system and nonlinear spring design method thereof - Google Patents

Abstract

The present invention relates to the field of vibration aging technology. A design method for a nonlinear superharmonic resonance aging system and a nonlinear spring thereof, the method comprising the following steps: Step 1: selecting the type and material of the nonlinear spring; Step 2: determining the spring wire diameter d, the middle diameter D, and the load-bearing range of the nonlinear spring; Step 3: calculating the geometric structure parameters of the nonlinear spring; Step 4: performing simulation analysis, using the control variable method to analyze the influence of the spring wire diameter d and the pitch t on the nonlinear spring stiffness characteristics; Step 5: fitting the assumed spring mechanical characteristic equation and the data obtained by the spring compression simulation analysis; Step 6: processing the calculated spring data to obtain a nonlinear spring suitable for a nonlinear superharmonic resonance aging system. The design method of the present invention can accurately and quickly design a nonlinear spring of a nonlinear superharmonic resonance aging system, and can improve the development efficiency of a nonlinear superharmonic resonance aging system.

Description

A nonlinear superharmonic resonance time-effect system and a design method of its nonlinear spring

Technical Field

The invention relates to the technical field of vibration aging technology, and in particular to a nonlinear superharmonic resonance aging system and a design method of a nonlinear spring thereof.

Background technique

Vibration aging technology (VSR) is considered to be a very effective method for eliminating residual stress in workpieces. Thermal aging is not easy to achieve and has high cost, and natural aging is long and inefficient. The vibration aging method has the advantages of low pollution, low price and high efficiency. The principle of the vibration aging process is to excite the workpiece through an excitation device so that the generated dynamic stress and the residual stress inside the workpiece meet the "Wozney & Crawmer" criterion to reduce the residual stress of the workpiece. This requires that the excitation frequency generated by the exciter must reach the resonant frequency of the workpiece. However, when the process object is a workpiece with a higher natural frequency, since the frequency generated by the traditional exciter cannot reach the natural frequency of the high-rigidity press roll, it is difficult to generate a large dynamic stress to achieve the purpose of reducing the residual stress of the press roll. In view of the problem that ordinary vibration aging cannot achieve high-rigidity press roll aging, the applicant proposed a solution based on nonlinear vibration theory to use nonlinear elements in the traditional vibration aging system to form a nonlinear superharmonic resonance aging system. In the nonlinear superharmonic resonance aging system, the main nonlinear component is the nonlinear spring, that is, the parameters of the nonlinear spring largely determine the nonlinear parameters of the entire system, that is, the effect of its vibration aging depends on its core component-the nonlinear spring. However, there is very little information on the design of nonlinear springs. Some cases use experimental methods when selecting nonlinear springs, and there are even fewer design methods for nonlinear springs for nonlinear vibration systems. The existing method is only based on theoretical conception to obtain the stiffness curve required by the system, and then find a nonlinear spring that is as close to the stiffness curve as possible, and then try it by adjusting other process parameters on site. This method is suitable for the design of large-scale production lines. For the vibration aging of a single workpiece, this method is difficult to obtain enough nonlinear springs to meet production needs. The lack of nonlinear spring design methods has affected the application of nonlinear vibration aging methods in engineering practice.

In order to solve this problem, the present invention proposes to design a nonlinear superharmonic resonance aging system to solve the high-frequency workpiece resonance problem, and based on the design method of the nonlinear vibration aging system when the nonlinear vibration excitation frequency required by the vibration aging object (high stiffness workpiece) is known, a design method for the structural parameters of unequal pitch cylindrical springs (nonlinear springs) for the requirements of the nonlinear vibration aging system is proposed.

Summary of the invention

In view of the above technical problems, the present invention optimizes the design of the nonlinear spring. The method has strong operability and reliability, makes up for the shortcomings of the existing nonlinear spring design optimization method relying on experience, can ensure that the design parameter values of the nonlinear spring in the design scheme are optimal, has the advantages of short design cycle and high efficiency, can enhance the nonlinear spring's ability to adjust the resonance frequency, and at the same time, when the system performs nonlinear vibration aging to eliminate residual stress, it can be beneficial to improve the use strength and stability accuracy of the workpiece and reduce deformation.

In order to achieve the above object, the present invention adopts the following technical solution:

A design method for a nonlinear spring of a nonlinear superharmonic resonance aging system includes material selection and parameter determination of the nonlinear spring. The design method includes the following steps:

Step 1: According to the use conditions of the nonlinear superharmonic resonance aging system, select the nonlinear spring and the material;

Step 2: Based on the structural characteristics of the nonlinear superharmonic resonance aging system, the more common spring characteristic curve p = (ay + b) ² in vibration is selected as the starting point to determine the spring wire diameter d, the middle diameter D, and the load range of the nonlinear spring to verify its strength conditions;

The calculation formulas are as follows:

δ _min ≤d≤δ _max (1)

Where: δ _min and δ _max refer to the maximum and minimum values of the spring spacing;

Empirical range constraints for convolution ratio:

The convolution ratio is generally 8-12, that is, C _min = 8, C _max = 12;

Where: τ is the maximum working shear stress of the spring; K is the curvature coefficient of the spring; [τ] is the allowable shear force of the spring material; P is the working load of the spring;

Step 3: Calculation of nonlinear spring geometry parameters:

This design method is equivalent to a series combination of multiple unequal pitch helical springs, and its equivalent stiffness can be expressed as:

According to k = dF/df, the stiffness of each coil of the spring is:

In the formula, F is the external force on the spring; f is the deformation of the spring; G is the shear modulus of the spring material;

Assuming that the effective number of working turns of the spring is _n , the stiffness K of the spring when it is not subjected to external load is:

Assume that the spring coils are arranged in ascending order according to the spacing between the springs. When the spring coil i is compressed under the force _pi , the remaining stiffness of the spring is _Ki :

Then the effective working number of the spring can be obtained:

The spacing of the i-th coil of the spring is the deformation of the i-th coil of the spring under the action of force _pi , and when the deformation of the coil reaches _δi , the coils of the spring are tightened, and the tightening process is gradual contact and tightening. In this process, the deformation of the i-th coil of the spring is When the i-th coil of the spring is compressed, the total deformation is:

Further:

_Pi = 2kδi _{- Pi-1} (11)

The pitch of spring coil i is:

t _i = d + δ _i (12)

The free height of the spring is given by the formula:

Step 4: Based on step 3, ANSYS finite element software is used for simulation analysis. The control variable method is used. Other parameters are kept unchanged during the analysis, and only the variables to be studied are changed. The influence of spring wire diameter d and pitch t on the nonlinear spring stiffness characteristics is analyzed respectively;

Step 5: Based on the conditions for superharmonic vibration of the nonlinear superharmonic resonance aging system, assume that the mechanical characteristic equation of the spring is: y = a + bx + cx ² , and bring the assumed spring mechanical characteristic equation and the data obtained from the spring compression simulation analysis into the data analysis software origin for fitting;

Step 6: Based on the spring data calculated in the above steps, a nonlinear spring suitable for a nonlinear superharmonic resonance aging system is obtained by processing.

It includes a support seat, a vibration platform, a fixture, an exciter, an excitation block, an adjustable damper and a nonlinear spring designed by the above-mentioned design method; the vibration platform is arranged on the support seat, the support seat is used to support the vibration platform, the fixture is located below the vibration platform, and the workpiece is clamped between the fixture and the vibration platform; the exciter is arranged on the vibration platform and applies power to the vibration platform, the adjustable damper is connected to the output of the exciter, the nonlinear spring is arranged on the support seat for applying amplitude to the workpiece, and the excitation block is arranged between the vibration platform and the fixture.

Compared with the prior art, the present invention has the following beneficial effects:

1. The design method of the present invention combines the nonlinear spring design with the nonlinear superharmonic resonance aging system, providing a design idea for the application of nonlinear unequal pitch cylindrical helical springs in nonlinear vibration aging.

2. The present invention is based on the needs of nonlinear superharmonic resonance aging system, takes the spring characteristic curve as the starting point, and is supplemented by mature finite element analysis software to conduct research to avoid errors in spring structure parameters and cause duplication of work.

3. The present invention reduces the design difficulty of nonlinear springs, and nonlinear parameters are easy to adjust and control. According to the influence of various parameters of nonlinear springs on the performance of nonlinear superharmonic resonance aging system, it is determined how to design various parameters under existing conditions to improve the stiffness performance of nonlinear springs, thereby improving the performance of nonlinear superharmonic resonance aging system. It is known how to reduce the cost of the system when the performance of the nonlinear superharmonic resonance aging system meets the requirements, thereby designing a nonlinear superharmonic resonance aging system with high performance and high cost performance.

4. The nonlinear superharmonic resonance aging system of the present invention has a reasonable structure and strong operability. Its overall structure is more compact to reduce unnecessary vibration. It adopts a superharmonic resonance vibration aging method. The excitation block can generate a vibration frequency far higher than the original excitation frequency of the exciter, ensuring that sufficient stress and strain are generated inside the workpiece, effectively eliminating the residual stress of the workpiece, and significantly improving the effect of vibration aging.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG1 is a schematic diagram of the geometric shape of a cylindrical helical spring in an embodiment of the present invention;

FIG2 is a schematic diagram of the helical line of a cylindrical helical spring in an embodiment of the present invention;

3 is a graph showing the influence of different pitches on the spring stiffness characteristic line according to an embodiment of the present invention;

FIG4 is a graph showing the influence of different spring wire diameters on the spring stiffness characteristic line according to an embodiment of the present invention;

FIG5 is a schematic diagram of the structure of a nonlinear superharmonic resonance aging system according to the present invention;

Among them, the following are marked in the attached drawings: 1, support seat; 2, vibration platform; 3, fixture; 4, exciter; 5, excitation block; 6, adjustable damper; 7, nonlinear spring; 8 workpiece;

Detailed ways

The present invention is further described below in conjunction with the accompanying drawings and embodiments. It should be noted that the specific embodiments of the present invention are only for the purpose of more clearly describing the technical solution and cannot be used as a limitation on the protection scope of the present invention.

Please refer to FIG. 1 to FIG. 4 , a design method of a nonlinear spring of a nonlinear superharmonic resonance aging system of the present invention includes material selection and parameter determination of the nonlinear spring, and the design method includes the following steps:

Step 1: According to the use conditions of the nonlinear superharmonic resonance aging system, select the unequal pitch cylindrical helical spring as the research object, as shown in Figure 1-Figure 2. According to the mechanical design manual and GB/T18983-2003, the oil quenched and tempered carbon spring steel wire has good straightness, no residual stress and uniform performance, tensile strength σ _b = 235kgf/mm, shear modulus G = 8000kgf/mm, and its allowable stress [τ] = 0.4σ _b = 0.4×235 = 94kgf/mm; its hardness is 48HRC---55HRC, and the surface is black oxidized.

Step 2: Based on the structural characteristics of the nonlinear superharmonic resonance aging system, the spring characteristic curve p = (ay + b) ² commonly used in vibration research is selected as the starting point to determine the spring wire diameter d, the middle diameter D, and the load range of the nonlinear spring, and verify its strength conditions. With the characteristic curve equation P = (0.1X + 2.62) ² , the mass of the nonlinear vibration table is 25Kg, so the linear segment of the characteristic line p ₀ = 25kgf.

Calculate from the spiral spring characteristic curve equation combined with equation (1):

δ _min =3≤d≤δ _max =16.7

have to:

According to formula (2), the spring diameter can be calculated, and

D＝90

According to the material properties and system requirements, it is assumed that the load range it can bear is 0 to 400 kgf. Its strength conditions are:

Step 3: According to the spring characteristic curve equation P = (0.1y + 2.62) ^2, the relationship between force _Pi and stiffness _Ki is:

P _i = 25K _i ²

The stiffness of each coil of the spring can be calculated according to the formula:

In the formula, F is the external force on the spring; f is the deformation of the spring; G is the shear modulus of the spring material;

According to the initial value of P _0, y ₀ can be obtained, and the intersection point of the equation curve and the spring initial line segment can be further obtained. Then the stiffness of the entire spring before the spring is coiled is:

According to the formula, the effective number of coils of the spring is:

According to the formula, the stiffness K ₁ after the first circle is combined is:

Then we get: K ₁ = 1.137 kgf/mm

Thus, the force required for the first circle is obtained:

P ₁ = 25K ₁ ² = 32kgf

The deformation of the first circle, that is, the spacing of the first circle, is obtained by the formula:

The pitch of the first circle is obtained by the formula:

t ₁ = d + δ ₁ = 12.6 mm

By analogy, by repeating the above process, δ ₁ , δ ₂ , δ ₃ , δ ₄ .................. can be calculated in turn. The calculation results are shown in Table 1 below.

Table 1 Parameter calculation table of unequal pitch springs

Table 1. Parameter calculation table of unequal pitch spring

Step 4: Use 3D software to model the spring, import the 3D model into ANSYS finite element analysis software for analysis, and study the influence of spring wire diameter d and pitch t on the nonlinear spring stiffness characteristics. The influence curves are shown in Figures 3 and 4.

Step 5: The mechanical characteristic equation of the spring is: P = (0.1y + 2.62) ² . The assumed mechanical characteristic equation of the spring and the data obtained from the spring compression simulation analysis are brought into the data analysis software origin for fitting.

Step 6: Based on the spring data calculated in the above steps, a nonlinear spring suitable for a nonlinear superharmonic resonance aging system is obtained by processing.

The design method of the present invention combines the nonlinear spring design with the nonlinear superharmonic resonance aging system, and provides a design idea for the application of nonlinear unequal pitch cylindrical helical springs in nonlinear vibration aging. The present invention is based on the needs of the nonlinear superharmonic resonance aging system, takes the spring characteristic curve as the starting point, and is supplemented by mature finite element analysis software for research to avoid errors in spring structure parameters and cause duplication of work.

Please refer to Figure 5. The present invention also provides a nonlinear superharmonic resonance aging system, including a support base 1, a vibration platform 2, a fixture 3, an exciter 4, an excitation block 5, an adjustable damper 6 and a nonlinear spring 7 designed by the above design method; the vibration platform 2 is arranged on the support base 1, and the support base 1 is used to support the vibration platform 2. The fixture 3 is located below the vibration platform 2, and the fixture 3 is used to clamp the workpiece 8, and the workpiece 8 is clamped between the fixture 3 and the vibration platform 2; specifically, the bottom of the fixture 3 can be directly set on the ground, and the workpiece 8 is fixed between the vibration platform 2 and the ground through the fixture 3. The exciter 4 is arranged on the vibration platform 2 and applies power to the vibration platform 2. The adjustable damper 6 is connected to the output of the exciter 4. The nonlinear spring 7 is arranged on the support base 1 for applying amplitude to the workpiece 8. The excitation block 5 is arranged between the vibration platform 2 and the fixture 3, and the exciter 4 and the excitation block 5 apply a vibration force of set amplitude and frequency to the workpiece 8. The nonlinear spring 7 is arranged on the support seat 1. The nonlinear spring 7 can be designed to be connected to the side or bottom of the workpiece 8 according to work needs, so as to apply an amplitude in the horizontal direction or vibration direction to the workpiece 8. In this embodiment, the nonlinear spring 7 is arranged on the side of the support seat 1 and connected to the side of the workpiece 8, so as to apply an amplitude in the horizontal direction to the workpiece 8. The exciter 4 acts on the excitation block 5 to generate a superharmonic resonance higher than the original excitation frequency of the exciter 4. The workpiece 8 on the fixture 3 is excited by the excitation block 5, and the excitation block 5 then acts on the workpiece 8 at a superharmonic resonance frequency close to the natural frequency of the workpiece 8, so that it generates a main resonance and corresponding dynamic stress to reduce the residual stress of the workpiece 8.

This system adopts a superharmonic resonance vibration aging method. The exciting block 5 can generate a vibration frequency that is much higher than the original exciting frequency of the exciter 4, ensuring that sufficient stress and strain are generated inside the workpiece 8, effectively eliminating the residual stress of the workpiece 8, and significantly improving the effect of vibration aging.

The above description is a detailed description of the preferred feasible embodiments of the present invention, but the embodiments are not intended to limit the scope of the patent application of the present invention. All equivalent changes or modified changes completed under the technical spirit suggested by the present invention should fall within the patent scope covered by the present invention.

Claims (2)

1. A design method of a nonlinear spring of a nonlinear super-resonance aging system comprises material selection and parameter determination of nonlinear spring materials, and is characterized in that: the design method comprises the following steps:

step 1: according to the service conditions of the nonlinear super-harmonic resonance aging system, selecting nonlinear springs and selecting materials;

Step 2: the method comprises the steps of selecting a form of a characteristic curve p= (ay+b) ² of a spring in vibration as a starting point according to the structural characteristics of a nonlinear super-harmonic resonance aging system, determining the spring wire diameter D, the intermediate diameter D and the load bearing range of the nonlinear spring, and verifying the strength condition of the nonlinear spring;

The respective formulas are as follows:

δ_min≤d≤δ_max (1)

Wherein: δ _min、δ_max refers to the maximum and minimum values of the spring spacing;

The specific rotation empirical range constraint:

the swirl ratio is 8-12, i.e. C _min＝8,C_max =12;

Wherein: τ is the maximum working shear stress of the spring; k is the curvature coefficient of the spring; [ tau ] is the allowable shear force of the spring material; p is the working load of the spring;

Step 3: calculating the nonlinear spring geometric structure parameters:

this design approach corresponds to an in-line combination of a plurality of unequal pitch coil springs, whose equivalent stiffness can be expressed as:

the stiffness of each turn of the constituent spring is obtained from k=df/dF:

Wherein F is the external force applied by the spring; f is the spring deflection; g is the shear modulus of the spring material;

Assuming that the effective number of turns of the spring is _n, the spring's stiffness, K, when not under external load:

Assuming that the spring coils are arranged with a small to large spacing between the springs, when spring coil i is pressed under force p _i and then the spring has a remaining stiffness of K _i:

the effective working turns of the spring can be obtained by the method:

the spacing of the i-th coils of the spring, i.e. the deformation of the i-th coils of the spring under the action of the force p _i, and when the deformation of the coils reaches delta _i, the coils of the spring are tightly combined, and the tight combination process is gradually contacted and tightly combined, in which the deformation of the i-th coils of the spring is that When the spring is pressed together in the ith turn, the total deformation is:

further obtain:

P_i＝2kδ_i-P_i-1 (11)

while the pitch of the coils i is:

t_i＝d+δ_i (12)

The free height of the spring is given by the formula:

Step 4: based on the step 3, performing simulation analysis by utilizing ANSYS finite element software, and using a control variable method, keeping other parameters unchanged during analysis, and respectively analyzing the influence of the spring wire diameter d and the pitch t on the non-linear spring stiffness characteristic only by changing the variables to be researched;

Step 5: according to the condition that the nonlinear super-harmonic resonance aging system generates super-harmonic vibration, the mechanical characteristic equation of the spring is assumed to be: y=a+bx+cx ², and carrying the assumed spring mechanical characteristic equation and the data obtained by the spring compression simulation analysis into a data analysis software origin for fitting;

Step 6: and processing the nonlinear spring based on the spring data calculated in the steps to obtain the nonlinear spring suitable for the nonlinear super-harmonic resonance aging system.

2. A nonlinear super-harmonic resonance aging system, characterized by: the device comprises a supporting seat, a vibrating platform, a clamp, a vibration exciter, a vibration exciting block, an adjustable damper and a nonlinear spring designed by the design method of claim 1; the vibration platform is arranged on the supporting seat, the supporting seat is used for supporting the vibration platform, the clamp is positioned below the vibration platform, and the workpiece is clamped between the clamp and the vibration platform; the vibration exciter is arranged on the vibration platform and applies power to the vibration platform, the adjustable damper is connected with the output of the vibration exciter, the nonlinear spring is arranged on the supporting seat and used for applying amplitude to the workpiece, and the vibration excitation block is arranged between the vibration platform and the clamp.