CN114707263A - Nonlinear super-harmonic resonance aging system and design method of nonlinear spring thereof - Google Patents
Nonlinear super-harmonic resonance aging system and design method of nonlinear spring thereof Download PDFInfo
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Abstract
The invention relates to the technical field of vibration aging. A nonlinear super-harmonic resonance aging system and a design method of a nonlinear spring thereof are disclosed, wherein the method comprises the following steps: step 1: selecting the type and the material of the nonlinear spring; step 2: determining the diameter D of a spring wire, the intermediate diameter D and the load bearing range of the nonlinear spring; and step 3: calculating the geometric structure parameters of the nonlinear spring; and 4, step 4: carrying out simulation analysis, and respectively analyzing the influence of the diameter d and the pitch t of the spring wire on the stiffness characteristic of the nonlinear spring by using a control variable method; and 5: fitting the assumed spring mechanical property equation and data obtained by spring compression simulation analysis; step 6: and (4) calculating the obtained spring data, and processing to obtain the nonlinear spring suitable for the nonlinear super-harmonic resonance aging system. The design method can accurately and quickly design the nonlinear spring of the nonlinear super-harmonic resonance aging system, and can improve the development efficiency of the nonlinear super-harmonic resonance aging system.
Description
Technical Field
The invention relates to the technical field of vibration aging, in particular to a nonlinear super-harmonic resonance aging system and a design method of a nonlinear spring thereof.
Background
The Vibratory Stress Relief (VSR) technique is considered to be a very effective method in eliminating residual stress of a workpiece, thermal stress relief is not easy to implement and has high cost, natural stress relief time is long, and efficiency is low, while the vibratory stress relief method has the advantages of low pollution, low price, high efficiency and the like. The principle of the vibration aging process is that a workpiece is excited by an excitation device, so that the generated dynamic stress and the residual stress in the workpiece meet the 'Wozney & Crawmer' criterion to reduce the residual stress of the workpiece. This requires that the exciter produce excitation frequencies that reach the resonant frequency of the workpiece. However, when the process object is a workpiece with a high natural frequency, the natural frequency of the high-rigidity press roll cannot be achieved due to the frequency generated by the traditional vibration exciter, and the purpose of reducing the residual stress of the press roll by generating a large dynamic stress is difficult to achieve. Aiming at the problem that the aging of the high-rigidity press roll cannot be realized by the common vibration aging, the applicant provides a scheme for forming a nonlinear super-harmonic resonance aging system by applying a nonlinear element to a traditional vibration aging system on the basis of a nonlinear vibration theory. In the nonlinear super-harmonic resonance aging system, the main nonlinear component is a nonlinear spring, namely the parameters of the nonlinear spring determine the nonlinear parameters of the whole system to a large extent, namely the vibration aging effect depends on the nonlinear spring as the core element. However, the design of the non-linear springs is little and few, and some cases are tested when selecting the non-linear springs, and the design methods of the non-linear springs for the non-linear vibration system are few. The existing method is only based on theoretical conception to obtain a stiffness curve required by the system, then a nonlinear spring which is as close to the stiffness curve as possible is found, and the attempt is made by adjusting other process parameters on site. The application of the nonlinear vibration aging method in engineering practice is influenced due to the absence of the nonlinear spring design method.
In order to solve the problem, the invention provides a nonlinear super-harmonic resonance aging system which is used for solving the problem of high-frequency workpiece resonance, and provides a design method for using the structural parameters of cylindrical springs (nonlinear springs) with unequal pitches aiming at the requirement of the nonlinear vibration aging system according to the design method of the nonlinear vibration aging system under the condition that the nonlinear vibration excitation frequency required by a vibration aging object (high-rigidity workpiece) is known.
Disclosure of Invention
Aiming at the technical problems, the nonlinear spring is optimally designed, the method is high in operability and reliability, overcomes the defect that the existing nonlinear spring design is optimized by depending on experience, can ensure that the design parameter value of the nonlinear spring in the design scheme is optimal, has the advantages of short design period and high efficiency, can enhance the adjustment capacity of the nonlinear spring on the resonance frequency, and is beneficial to improving the use strength and the stability precision of a workpiece and reducing deformation when the system carries out nonlinear vibration aging to eliminate residual stress.
In order to achieve the purpose, the invention adopts the following technical scheme:
a design method of a nonlinear spring of a nonlinear super-harmonic resonance aging system comprises the following steps of material selection and parameter determination of the nonlinear spring material:
step 1: according to the using conditions of the nonlinear super-harmonic resonance aging system, carrying out model selection and material selection on the nonlinear spring;
and 2, step: selecting a spring characteristic curve p which is common in vibration as (ay + b) according to the structural characteristics of the nonlinear super-harmonic resonance aging system2Taking the form of a starting point, determining the wire diameter d and the pitch diameter of the nonlinear springD. Carrying load range, verifying strength condition;
the calculation formula is as follows:
δmin≤d≤δmax (1)
in the formula: deltamin、δmaxRefers to the maximum and minimum values of the spring spacing;
the convolution ratio is constrained by an empirical range:
the winding ratio is generally 8-12, i.e. Cmin＝8，Cmax＝12；
In the formula: tau is the maximum working shear stress of the spring; k is the curvature coefficient of the spring; [ tau ] is the allowable shearing force of the spring material; p is the working load of the spring;
and step 3: calculating the geometric structure parameters of the nonlinear spring:
the design method is equivalent to the straight combination of a plurality of spiral springs with different pitches, and the equivalent stiffness can be expressed as:
the stiffness of the coils making up the spring, given by k-dF/dF, is:
in the formula, F is the external force applied to the spring; f is the deformation of the spring; g is the shear modulus of the spring material;
assuming that the number of active turns of the spring isnThe stiffness K of the spring when not subjected to an external load:
assuming that the spring turns are arranged in a sequence of spring turns from small to large in the distance between the springs, when the spring turn i is at the force piAfter being pressed down, the remaining rigidity of the spring is Ki：
The effective number of working turns of the spring can be further obtained as follows:
the pitch of the ith turn of the spring, i.e. at the force piThe i-th coil of the spring is deformed under the action of the force, and when the deformation of the coil reaches deltaiWhen the springs are tightly combined, the spring rings are gradually contacted and tightly combined in the process that the deformation amount of the ith coil of the spring is
When the ith turn of the spring is pressed, the total deformation is as follows:
further obtaining:
Pi＝2kδi-Pi-1 (11)
and the pitch of the spring ring i is:
ti＝d+δi (12)
the free height of the spring is obtained according to the formula:
and 4, step 4: based on the step 3, performing simulation analysis by using ANSYS finite element software, keeping other parameters unchanged during analysis by using a control variable method, and respectively analyzing the influence of the diameter d and the pitch t of the spring wire on the stiffness characteristic of the nonlinear spring as long as the variable to be researched is changed;
and 5: according to the condition that the nonlinear super-harmonic resonance aging system generates super-harmonic vibration, the mechanical property equation of a spring is assumed as follows: y ═ a + bx + cx2The assumed spring mechanical property equation and the data obtained by spring compression simulation analysis are brought into data analysis software origin for fitting;
step 6: and processing the spring data obtained by calculation based on the steps to obtain the nonlinear spring suitable for the nonlinear super-harmonic resonance aging system.
The vibration damping device comprises a supporting seat, a vibration platform, a clamp, a vibration exciter, a vibration exciting block, an adjustable damper and a nonlinear spring designed by the design method; 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 a 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 exciting block is arranged between the vibration platform and the clamp.
Compared with the prior art, the invention has the following beneficial effects:
1. the design method combines the nonlinear spring design into the nonlinear super-harmonic resonance aging system, and provides a design idea for the application of the nonlinear unequal-pitch cylindrical helical spring in the aspect of nonlinear vibration aging.
2. Based on the requirements of a nonlinear super-harmonic resonance aging system, the invention takes a spring characteristic curve as a starting point and is assisted by mature finite element analysis software for research, thereby avoiding the phenomenon that the structural parameters of the spring are wrong and the work is repeated.
3. The design difficulty of the nonlinear spring is reduced, the nonlinear parameters are easy to adjust and control, according to the influence rule of various parameters of the nonlinear spring on the performance of the nonlinear super-harmonic resonance aging system, the method determines how to design various parameters under the existing conditions to improve the rigidity performance of the nonlinear spring so as to improve the performance of the nonlinear super-harmonic resonance aging system, and knows how to reduce the cost of the system under the condition that the performance of the nonlinear super-harmonic resonance aging system meets the requirements, so that the nonlinear super-harmonic resonance aging system with high performance and high cost performance is designed.
4. The nonlinear super-harmonic resonance aging system is reasonable in structure and strong in operability, the whole structure is more compact to reduce unnecessary vibration, the excitation block can generate vibration frequency far higher than the original excitation frequency of the vibration exciter by adopting a super-harmonic resonance type vibration aging mode, sufficient stress strain generated in the workpiece is ensured, the residual stress of the workpiece is effectively eliminated, and the vibration aging effect is obviously improved.
Drawings
FIG. 1 is a schematic view of the geometry of a cylindrical coil spring in an embodiment of the present invention;
FIG. 2 is a schematic diagram of the spiral of a cylindrical coil spring in an embodiment of the present invention;
FIG. 3 is a graph illustrating the effect of different pitches on a spring rate characteristic line according to an embodiment of the present invention;
FIG. 4 is a graph illustrating the effect of different wire diameters on the spring rate characteristic of an embodiment of the present invention;
FIG. 5 is a schematic structural diagram of a nonlinear super-harmonic resonance aging system according to the present invention;
wherein, labeled in the figures: 1. a supporting seat; 2. a vibration platform; 3. a clamp; 4. a vibration exciter; 5. an excitation block; 6. an adjustable damper; 7. a non-linear spring; 8, workpiece;
Detailed Description
The invention is further described with reference to the following figures and examples. It should be noted that the specific embodiments of the present invention are only for clearly describing the technical solutions, and should not be taken as a limitation to the scope of the present invention.
Referring to fig. 1-4, the method for designing a nonlinear spring of a nonlinear ultraharmonic resonance aging system according to the present invention includes material selection and parameter determination of the nonlinear spring, and the method includes the following steps:
step 1: according to the using conditions of the nonlinear super-harmonic resonance aging system, cylindrical coil springs with unequal pitches are selected as research objects, and are shown in figures 1-2. According to a mechanical design manual and GB/T18983-2003, the oil quenching tempered carbon spring steel wire has good straightness, no residual stress, uniform and consistent performance and tensile strength sigmab235kgf/mm, 8000kgf/mm, and allowable stress [ tau ] thereof]＝0.4σb0.4 × 235 ═ 94 kgf/mm; the hardness is 48 HRC-55 HRC, and the surface is subjected to black oxidation treatment.
Step 2: the characteristic curve p of the spring commonly used in vibration research is selected from the structural characteristics of the nonlinear super-harmonic resonance aging system (ay + b)2The form of (1) is taken as a starting point, the wire diameter D, the middle diameter D and the load bearing range of the nonlinear spring are determined, the strength condition is verified, and the characteristic curve equation P is (0.1X +2.62)2The mass according to the nonlinear vibration table is 25Kg, so the linear segment p of the characteristic line0＝25kgf。
From the coil spring characteristic curve equation, in combination with equation (1):
δmin＝3≤d≤δmax＝16.7
obtaining:
according to the formula (2), the spring pitch diameter can be calculated
D＝90
According to the material performance and system requirement, the load range capable of being carried by the material is assumed to be 0-400 kgf. The strength conditions are as follows:
and step 3: according to the spring characteristic curve equation P ═ (0.1y +2.62)2Can be obtained byiAnd a stiffness KiThe relationship of (1) is:
Pi＝25Ki 2
the stiffness of the coils making up the spring can be calculated according to the formula:
in the formula, F is the external force applied to the spring; f is the deformation of the spring; g is the shear modulus of the spring material;
according to P0Can find y from the initial value of0And further obtaining the intersection point of the equation curve and the initial line segment of the spring. The overall spring rate before the spring is not looped is:
the effective number of turns of the spring can be obtained according to the formula:
obtaining the rigidity K after the first circle is combined according to a formula1:
Further, the following are obtained: k1＝1.137kgf/mm
So as to obtain the force required for the first lap to lap:
P1＝25K1 2＝32kgf
the deformation of the first ring, i.e. the pitch of the first ring, is given by the formula:
the pitch of the first turn, is given by:
t1＝d+δ1＝12.6mm
repeating the above process can calculate delta1、δ2、δ3、δ4The.................. the calculation results are shown in table 1 below.
TABLE 1 parameter calculation table for unequal pitch springs
Table 1.Parameter calculation table of unequal pitch spring
And 4, step 4: spring modeling is carried out by utilizing three-dimensional software, the three-dimensional model is introduced into ANSYS finite element analysis software for analysis, the influence of the diameter d and the pitch t of the spring wire on the stiffness characteristic of the nonlinear spring is researched, and the influence curve graph is shown in figures 3-4.
And 5: the mechanical property equation of the spring is as follows: p ═ 0.1y +2.62)2And substituting the assumed spring mechanical property equation and data obtained by spring compression simulation analysis into data analysis software origin for fitting.
Step 6: and processing the spring data obtained by calculation based on the steps to obtain the nonlinear spring suitable for the nonlinear super-harmonic resonance aging system.
The design method combines the nonlinear spring design into the nonlinear super-harmonic resonance aging system, and provides a design idea for the application of the nonlinear unequal-pitch cylindrical spiral spring in the aspect of nonlinear vibration aging. Based on the requirements of a nonlinear super-harmonic resonance aging system, the invention takes a spring characteristic curve as a starting point and is assisted by mature finite element analysis software for research, thereby avoiding the phenomenon that the structural parameters of the spring are wrong and the work is repeated.
Referring to fig. 5, the invention further provides a nonlinear super-harmonic resonance aging system, which comprises a supporting seat 1, a vibration platform 2, a clamp 3, a vibration exciter 4, a vibration exciting 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 supporting seat 1, the supporting seat 1 is used for supporting the vibration platform 2, the clamp 3 is positioned below the vibration platform 2, the clamp 3 is used for clamping a workpiece 8, and the workpiece 8 is clamped between the clamp 3 and the vibration platform 2; specifically, 3 bottoms of anchor clamps can directly set up and ground, and work piece 8 is fixed between vibration platform 2 and ground through anchor clamps 3, vibration exciter 4 sets up vibration platform 2 is last and to vibration platform 2 applys power, adjustable attenuator 6 with vibration exciter 4's output is connected, nonlinear spring 7 set up in on the supporting seat 1 be used for right work piece 8 applys the amplitude, vibration exciting block 5 sets up vibration platform 2 with between anchor clamps 3, applys the vibrational force of setting for amplitude and frequency to work piece 8 by vibration exciter 4 and vibration exciting block 5. The nonlinear spring 7 is arranged on the supporting seat 1, the nonlinear spring 7 can be designed according to working requirements to be connected with the side surface or the bottom surface of the workpiece 8 and used for applying amplitude in the horizontal direction or the vibration direction to the workpiece 8, the nonlinear spring 7 is arranged on the side surface of the supporting seat 1 and connected with the side surface of the workpiece 8 and used for applying amplitude in the horizontal direction to the workpiece 8, the vibration exciter 4 acts on the vibration exciter 5 to enable the vibration exciter to generate super-harmonic resonance higher than the original vibration excitation frequency of the vibration exciter 4, the workpiece 8 on the clamp 3 is excited by the vibration exciter 5, and the vibration exciter 5 acts on the workpiece 8 at the super-harmonic resonance frequency close to the natural frequency of the workpiece 8 to enable the workpiece 8 to generate main resonance and corresponding dynamic stress so as to reduce the residual stress of the workpiece 8.
The system adopts a super-harmonic resonance type vibration aging mode, the vibration excitation block 5 can generate vibration frequency far higher than the original vibration excitation frequency of the vibration exciter 4, sufficient stress strain generated inside the workpiece 8 is ensured, the residual stress of the workpiece 8 is effectively eliminated, and the effect of vibration aging is obviously improved.
The above description is for the purpose of illustrating the preferred embodiments of the present invention, but the present invention is not limited thereto, and all changes and modifications that can be made within the spirit of the present invention should be included in the scope of the present invention.
Claims (2)
1. A design method of a nonlinear spring of a nonlinear super-harmonic resonance aging system comprises the steps of material selection of the nonlinear spring and parameter determination, and is characterized in that: the design method comprises the following steps:
step 1: according to the using conditions of the nonlinear super-harmonic resonance aging system, carrying out model selection and material selection on the nonlinear spring;
and 2, step: selecting the characteristic curve p of the spring in vibration as (ay + b) according to the structural characteristics of the nonlinear super-harmonic resonance aging system2The form of the non-linear spring is taken as a starting point, the diameter D of a spring wire, the intermediate diameter D and the load bearing range of the non-linear spring are determined, and the strength condition of the non-linear spring is verified;
the calculation formula is as follows:
δmin≤d≤δmax (1)
in the formula: delta. for the preparation of a coatingmin、δmaxRefers to the maximum and minimum values of the spring spacing;
the convolution ratio is constrained by an empirical range:
the winding ratio is 8-12, i.e. Cmin＝8，Cmax＝12；
In the formula: tau is the maximum working shear stress of the spring; k is the curvature coefficient of the spring; [ tau ] is the allowable shearing force of the spring material; p is the working load of the spring;
and step 3: calculating the geometric structure parameters of the nonlinear spring:
the design method is equivalent to the straight combination of a plurality of helical springs with different pitches, and the equivalent stiffness of the helical springs can be expressed as follows:
the stiffness of the individual coils making up the spring can be found from k-dF/dF as:
in the formula, F is the external force applied to the spring; f is the deformation of the spring; g is the shear modulus of the spring material;
assuming that the number of active turns of the spring isnThe stiffness K of the spring when not subjected to an external load:
assuming that the spring turns are arranged in a sequence of spring turns from small to large in the distance between the springs, when the spring turn i is at the force piAfter being pressed down, the remaining rigidity of the spring is Ki：
The effective number of turns of the spring is then obtained:
the pitch of the ith turn of the spring, i.e. at the force piThe i-th coil of the spring is deformed under the action of the force, and when the deformation of the coil reaches deltaiWhen the springs are tightly combined, the spring rings are gradually contacted and tightly combined in the process that the deformation amount of the ith coil of the spring is
When the ith turn of the spring is pressed, the spring is alwaysThe deformation amounts of (a) are:
further obtaining:
Pi＝2kδi-Pi-1 (11)
and the pitch of the spring ring i is:
ti＝d+δi (12)
the free height of the spring is obtained according to the formula:
and 4, step 4: based on the step 3, performing simulation analysis by using ANSYS finite element software, keeping other parameters unchanged during analysis by using a control variable method, and respectively analyzing the influence of the diameter d and the pitch t of the spring wire on the stiffness characteristic of the nonlinear spring as long as the variable to be researched is changed;
and 5: according to the condition that the nonlinear super-harmonic resonance aging system generates super-harmonic vibration, the mechanical property equation of a spring is assumed as follows: y ═ a + bx + cx2The assumed spring mechanical property equation and the data obtained by spring compression simulation analysis are brought into data analysis software origin for fitting;
and 6: and processing the spring data obtained by calculation based on the steps to obtain the nonlinear spring suitable for the nonlinear super-harmonic resonance aging system.
2. A nonlinear super-harmonic resonance aging system is characterized in that: the vibration damping device comprises a supporting seat, a vibration 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 a 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 exciting block is arranged between the vibration platform and the clamp.
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Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| DE4410963A1 (en) * | 1993-03-29 | 1994-10-06 | Suncall Corp | Sinuous spring |
| WO2017074175A1 (en) * | 2015-10-29 | 2017-05-04 | Universiti Putra Malaysia | A nonlinear spring bracing device |
| CN111120557A (en) * | 2020-01-07 | 2020-05-08 | 长沙理工大学 | Ultralow frequency vibration isolator and design method thereof |
| CN112949111A (en) * | 2021-01-29 | 2021-06-11 | 东风银轮(十堰)非金属部件有限公司 | Design optimization method for leaf spring |
-
2022
- 2022-03-24 CN CN202210297351.8A patent/CN114707263A/en active Pending
Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| DE4410963A1 (en) * | 1993-03-29 | 1994-10-06 | Suncall Corp | Sinuous spring |
| WO2017074175A1 (en) * | 2015-10-29 | 2017-05-04 | Universiti Putra Malaysia | A nonlinear spring bracing device |
| CN111120557A (en) * | 2020-01-07 | 2020-05-08 | 长沙理工大学 | Ultralow frequency vibration isolator and design method thereof |
| CN112949111A (en) * | 2021-01-29 | 2021-06-11 | 东风银轮(十堰)非金属部件有限公司 | Design optimization method for leaf spring |
Non-Patent Citations (3)
| Title |
|---|
| ZHAO L: "Influence of the Nonlinear Stiffness Parameter of the Vibratory Stress Relief Device on Strong Nonlinear Superharmonic Resonance", IEEE ACCESS, 4 January 2021 (2021-01-04) * |
| 莫荣献: "非线性超谐共振时效系统弹簧设计方法的研究", 机械设计与制造, 10 May 2024 (2024-05-10) * |
| 郭晓东: "振动时效平台非线性弹簧的设计", 装备制造技术, no. 11, 30 November 2019 (2019-11-30) * |
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