CN109580777A - A kind of the damping energy dissipation appraisal procedure and its application of honeycomb cardboard quality system - Google Patents
A kind of the damping energy dissipation appraisal procedure and its application of honeycomb cardboard quality system Download PDFInfo
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- CN109580777A CN109580777A CN201811433949.5A CN201811433949A CN109580777A CN 109580777 A CN109580777 A CN 109580777A CN 201811433949 A CN201811433949 A CN 201811433949A CN 109580777 A CN109580777 A CN 109580777A
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N29/00—Investigating or analysing materials by the use of ultrasonic, sonic or infrasonic waves; Visualisation of the interior of objects by transmitting ultrasonic or sonic waves through the object
- G01N29/04—Analysing solids
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N29/00—Investigating or analysing materials by the use of ultrasonic, sonic or infrasonic waves; Visualisation of the interior of objects by transmitting ultrasonic or sonic waves through the object
- G01N29/44—Processing the detected response signal, e.g. electronic circuits specially adapted therefor
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N2291/00—Indexing codes associated with group G01N29/00
- G01N2291/02—Indexing codes associated with the analysed material
- G01N2291/023—Solids
- G01N2291/0237—Thin materials, e.g. paper, membranes, thin films
Abstract
The present invention provides a kind of damping energy dissipation appraisal procedure of honeycomb cardboard quality system and its applications, the damping energy dissipation appraisal procedure is the following steps are included: obtain Typical Vibration transmission characteristic vibration transmissibility-frequency curve of honeycomb cardboard, curve includes platform area, amplification region and decay area, and the function that honeycomb cardboard vibration transmissibility curve is expressed as frequency is as the formula (1)；Obtaining honeycomb cardboard-quality system at any frequency according to damping energy dissipation basic theories, the energy of Damping work is as the formula (2) in a cycle；According to formula (2), damping energy dissipation when honeycomb cardboard quality system amplification Q region resonance Q is obtained.Technical solution of the present invention is based on vibration mechanics basic principle, provide the calculation method of honeycomb cardboard-quality system damping energy dissipation in vibration processes, damping energy dissipation for packaging system calculates and vibrationproof Performance Evaluation provides basic skills, and also the selection for packaging material honeycomb cardboard provides foundation.
Description
Technical field
The invention belongs to mechanical technology field more particularly to a kind of damping energy dissipation appraisal procedures of honeycomb cardboard quality system
And its application.
Background technique
In logistics progress, the breakage of product is mainly derived from the shock and vibration in logistics environment.Therefore, research packaging
The buffering and vibrationproof performance of material, are of great significance to package design.Honeycomb cardboard is a kind of environment friendly-type amortizing packaging
Material, cellular porous structure make it have the advantages that light weight, specific stiffness and specific strength are high, energy absorption characteristics are stablized, and are a kind of
Substitute the effective way of foamed plastics class padded coaming.The superiority and inferiority of packaging material cushion performance vibrationproof performance depends primarily on vibration
When Damping work energy size, at present people to the research of honeycomb cardboard-quality system vibration transmissibility and resonant frequency with
Based on qualitative analysis, lack the qualitative assessment of system damping energy consumption.Only energy consumption is vibrated to honeycomb cardboard to be quantitatively evaluated, it could be pre-
Honeycomb cardboard vibrationproof performance is surveyed, provides theoretical foundation for honeycomb cardboard Packaged Cushioning Design.Therefore honeycomb cardboard-quality system is probed into
The appraisal procedure of system damping energy dissipation is necessary.
Summary of the invention
Against the above technical problems, the invention discloses a kind of damping energy dissipation appraisal procedure of honeycomb cardboard quality system and
It is applied, and the damping energy dissipation for packaging system calculates and vibrationproof Performance Evaluation provides basic skills.
In this regard, the technical solution adopted by the present invention are as follows:
A kind of honeycomb cardboard quality system damping energy dissipation appraisal procedure comprising following steps:
Step S1 obtains Typical Vibration transmission characteristic vibration transmissibility-frequency curve of honeycomb cardboard, and curve includes platform
Area, amplification region and decay area, it is f that dot frequency is played in platform area0, the resonant frequency in amplification region is fn, amplification region rise a dot frequency be
f1, the terminal frequency of amplification region is f2, wherein f1=fn- 50, f2=fn+50；The terminal frequency of decay area is f3；Honeycomb cardboard
Vibration transmissibility curve is expressed as the function of frequency are as follows:
Wherein, TrnIt is f for resonant frequencynWhen vibration transmissibility；
Step S2 obtains honeycomb cardboard-quality system a cycle at any frequency according to damping energy dissipation basic theories
The energy of interior Damping work are as follows:
Wherein, A is excitation acceleration amplitude, i.e. dynamic excitation, is given by user；C is the damping characteristic of padded coaming,Wherein m is the quality of product to be packaged；
Step S3, according to formula (2), damping energy dissipation when obtaining honeycomb cardboard quality system amplification Q region resonance Q is
Further, in step S1, the vibration transmissibility curve for obtaining honeycomb cardboard is tested by sine sweep.
The invention also discloses the application of honeycomb cardboard quality system damping energy dissipation appraisal procedure as described above, use with
Can lower step assessment honeycomb cardboard provide vibration protection when resonance:
Step S11 considers Fatigue Vibration, the vibration of product crisp value [G] vibration allowable and the crisp value [G] of vibratory impulsePunchingRelationship
Are as follows:
Step S12 considers that maximum conditions, the vibration transmissibility of product meetWherein A is means of transport excitation
Peak accelerator A；Resonant frequency fnExcept the frequency range of means of transport, i.e. fn≥200Hz；
Step S13 calculates the damping characteristic of padded coaming:Wherein, fnAnd TrBy vibration transmissibility
Curve determination obtains.
Step S14 calculates the damping energy dissipation when system resonance are as follows:
Step S15 calculates the static stress of padded coaming:Wherein m is the quality of product, and g is acceleration of gravity
9.8 meter per seconds, S are the bed-plate dimension of product；
Step S16 measures resonance frequency of the honeycomb cardboard sample under the static stress of step S15 by sine sweep experiment
Rate and maximum vibration transport；The resonant frequency and maximum vibration transport that experiment is obtained substitute into formula (3), and it is total to obtain the system
Theoretical damping energy consumption W when vibrationN reason；If Wn1≤WN reason, then the honeycomb cardboard can provide vibration protection as liner.
The invention also discloses the applications of honeycomb cardboard quality system damping energy dissipation appraisal procedure as described above, specifically push away
Reason process are as follows:
In amplification region left-half, f1<f<fn, the vibration transmissibility (T of the frequency bandr2) may be expressed as:
f1<f<fnIf Tr2≈k1f+b1
In amplification region right half part, fn<f<f2, the vibration transmissibility (T of the frequency bandr3) may be expressed as:
fn<f<f2If Tr3≈k2f+b2
In decay area, f2<f<f3, the vibration transmissibility (T of the frequency bandr4) may be expressed as:
Honeycomb cardboard Vibration transfer experiment the result shows that, the frequency range of amplification region is nearly all resonant frequency or so
Each 50Hz, and with axis bilateral symmetry, i.e. f where resonant frequency1=fn- 50, f2=fn+50.Therefore amplification region or so two parts shake
The slope of dynamic transport can respectively indicate are as follows:
Due to vibration transmissibility curve negotiating point (fn, Trn), it is calculated:
Subsection integral is carried out to formula (2), obtains the gross energy of Damping work in honeycomb cardboard-quality system vibration processes
Are as follows:
Wherein, b1, b2 are the intercept of the left and right two parts vibration transmissibility curve in amplification region,
According to honeycomb cardboard-quality system characteristic, the total energy for the Damping work that honeycomb cardboard is born in transit is calculated
Amount, and and WallIt is compared whether determining honeycomb cardboard can provide vibration protection.
Compared with prior art, the invention has the benefit that
Using technical solution of the present invention, it is based on vibration mechanics basic principle, honeycomb cardboard-quality system is provided and is shaking
The calculation method of damping energy dissipation during dynamic, the damping energy dissipation for packaging system calculates and vibrationproof Performance Evaluation provides substantially just
Method, also the selection for packaging material honeycomb cardboard provides foundation.
Detailed description of the invention
Fig. 1 is honeycomb cardboard Typical Vibration transmission characteristic curve of the invention.
Fig. 2 is honeycomb cardboard vibration transmissibility curve simplification figure of the invention.
Specific embodiment
Preferably embodiment of the invention is described in further detail below.
1, the simplification and characterization of honeycomb cardboard vibration transmissibility curve
Many experiments show the Typical Vibration transmission characteristic curve of honeycomb cardboard as shown in Figure 1, can according to the characteristics of curve
It can be divided into following region: platform area, amplification region and decay area.Due to wave zone peak value and frequency variation compared with
Machine is ignored herein, and honeycomb cardboard vibration transmissibility curve can simplify as shown in Fig. 2.F in figure0For frequency sweep starting point, f1
For amplification region starting point, f2For amplification region terminal, f3For frequency sweep terminal.
According to the feature of different phase vibration transmissibility curve, simplified vibration transmissibility-is expressed with piecewise function
Frequency curve.In platform area, f0<f<f1, the vibration transmissibility (T of the frequency bandr1) may be expressed as:
Tr1≈1 (11)
In amplification region left-half, f1<f<fn, the vibration transmissibility (T of the frequency bandr2) may be expressed as:
f1<f<fn, Given Tr2≈k1f+b1 (12)
In amplification region right half part, fn<f<f2, the vibration transmissibility (T of the frequency bandr3) may be expressed as:
fn<f<f2, Given Tr3≈k2f+b2 (13)
In decay area, f2<f<f3, the vibration transmissibility (T of the frequency bandr4) may be expressed as:
Honeycomb cardboard Vibration transfer experiment the result shows that, the frequency range of amplification region is nearly all resonant frequency or so
Each 50Hz, and with axis bilateral symmetry, i.e. f where resonant frequency1=fn- 50, f2=fn+50.Therefore amplification region or so two parts shake
Dynamic transmission characteristic slope of a curve can respectively indicate are as follows:
Due to vibration transmissibility curve negotiating point (fn, Trn), therefore amplification region is calculated or so two parts vibration transmitting is special
The intercept of linearity curve is respectively as follows:
To sum up, honeycomb cardboard vibration transmissibility curve can be expressed as to the function of frequency:
Wherein, TrnIt is f for resonant frequencynWhen vibration transmissibility.
2, damping energy dissipation basic theories and honeycomb cardboard damping energy dissipation derive
By vibration mechanics basic principle it is found that in a cycle Damping work energy (Wc) it is the machine that damping force consumes
Tool energy integrates the function that damping force is done in one cycle, obtains WcAre as follows:
By transportation and packing basic theories[14]It is found that single-degree-of-freedom linear system is in harmonic excitation accelerationUnder
Steady-state response accelerationAre as follows:It is carried out once to integrate and obtains speedExpression formula are as follows:
It brings formula (9) into formula (8) and carries out integral operation, single-degree-of-freedom linear system under harmonic excitation acceleration can be obtained and shaken
When dynamic, the energy of Damping work at any frequency are as follows:
C indicates the damping characteristic of padded coaming in formula, and has:
C=2m ξ ωn=4 π m ξ fn (24)
ξ indicates that damping ratio, damping ratio can be estimated by formula (24):
Formula (23) expresses the energy that single-degree-of-freedom linear system is dissipated in damping force a cycle at any frequency, formula
Middle TrThe vibration transmissibility and frequency of any point on padded coaming vibration transmissibility curve are respectively indicated with f.Formula (7) is brought into
Formula (10), the energy of available honeycomb cardboard-quality system Damping work in a cycle at any frequency, is frequency
Function of a single variable:
Wherein, A is excitation acceleration amplitude, and c is the damping characteristic of padded coaming,Wherein m is the matter of product
Amount；
According to formula (2), damping energy dissipation when obtaining honeycomb cardboard quality system amplification Q region resonance Q is
Subsection integral is carried out to formula (2), obtains the damping energy dissipation in each region.That is damping energy dissipation (the W of platform area1) are as follows:
Amplification region-left-half damping energy dissipation (W2) are as follows:
Amplification region-right half part damping energy dissipation (W3) are as follows:
Damping energy dissipation (the W of decay area4) are as follows:
To sum up, the gross energy (W that amplification region is dissipated23) are as follows:
W23=W2+W3 (29)
Gross energy (the W of Damping work in honeycomb cardboard-quality system vibration processesall) are as follows:
Wall=W1+W2+W3+W4 (30)
Obtain the gross energy of Damping work in honeycomb cardboard-quality system vibration processes are as follows:
Wherein, k1、k2For amplification region or so two parts vibration transmissibility slope of a curve, it is respectively as follows:
Due to vibration transmissibility curve negotiating point (fn, Trn), the left and right two parts vibration transmissibility in amplification region is calculated
The intercept of curve is respectively
The vibration transmissibility curve of honeycomb cardboard is obtained below by sine sweep experiment, and then assesses honeycomb paper
The damping capacity that plate-quality system is given dissipates.
Referring to GB/T 8169-2008 (ASTM D3580-95 (2015)), sine is carried out to honeycomb cardboard-quality system and is swept
Frequency is tested.Laboratory apparatus is DC-300-3 electric vibrating experimental system (Suzhou Sushi Testing Instrument Co., Ltd.'s manufacture).
Using logarithm sweep method, sweep rate 1oct/min, swept frequency range 5-500Hz, target spectral acceleration peak value 0.5g.
Five kinds of honeycomb cardboard samples are selected, core paper is fluting medium, and facial tissue is brown paper.Specimen size 200 ×
200mm2, experimental sample material parameter and structural parameters are shown in Table 1.Specimen coding mode is Sl/T, and wherein l is honeycomb cell element side
Long, T is honeycomb cardboard thickness.Such as: S10/20 indicates that cell element side length is 10mm, and the honeycomb cardboard that calliper is 20mm tries
Sample.Vibration transfer experiment is carried out at four kinds of quality (12.85kg, 16kg, 20.85kg and 24kg) to five kinds of samples, is obtained
Obtain its resonant frequency (fn) and maximum vibration transport (Trn).200 × 200mm of mass block area2, the change of quality pass through height
It adjusts.Experiment condition number is Sl/T-Mm, and wherein m indicates the quality of mass block.Such as: S10/20-16 indicates that cell element side length is
The Vibration transfer experiment of 10mm, the honeycomb cardboard sample that calliper is 20mm under 16kg mass block.
The material parameter and structural parameters of 1 experimental sample of table
Resonant frequency shows that near the Frequency point, the acceleration responsive of product will be amplified at double, each cycle interior suction
The energy for receiving the external world is most, therefore formula (23) is utilized to calculate damping energy dissipation (W when resonatingn), A is excitation acceleration width in formula (3)
It is worth, A is 4.9m/s in this experiment2.Calculated result is shown in Table 2.
2 experimental result of table and damping ratio, damping and the damping energy dissipation thus calculated
As it can be seen that the damping energy dissipation of packaging system depends on the vibration transmissibility of packaging material.If obtaining the vibration of material
Transport-frequency curve, can computing system resonance damping energy dissipation, and the damping that honeycomb cardboard is born in transit can be calculated
The gross energy of dissipation.According to honeycomb cardboard-quality system characteristic, the Damping work that honeycomb cardboard is born in transit is calculated
Gross energy, and and WallIt is compared whether determining honeycomb cardboard can provide vibration protection；Or honeycomb cardboard is calculated in resonance
The energy of the Damping work of receiving, and the value calculated with formula (4) is compared, and it is anti-to determine whether honeycomb cardboard can provide resonance
Shield.Specific embodiment is set forth below to be illustrated.
Embodiment 1
The quality of product is 16kg, and bed-plate dimension is 200 × 200mm2, Shock fragility allowable is 10g.Known means of transport
The peak accelerator of the vertical direction of generation is 0.3g, frequency range 10-200Hz.Surge guard design uses comprehensive
Way to play for time, having selected cell element side length is 10mm, and calliper is the Honeycomb paperboard cushion of 30mm, and core paper is quantitative 110g/
m2Fluting medium, thickness is 0.17mm；Facial tissue is quantitative 230g/m2Brown paper, thickness is 0.3mm.Consider Fatigue Vibration,
Determine that can such liner provide enough vibration protections.
(1) consider Fatigue Vibration, vibrate 0.25 times that crisp value allowable is represented by Shock fragility, it may be assumed that
(2) consider maximum conditions, the vibration transmissibility of product should be no more than vibration crisp value [G] allowableVibrationSwash with means of transport
Encourage the ratio between peak accelerator A；Resonant frequency fnIt should be except the frequency range of means of transport.That is:
fn≥200Hz
(3) damping characteristic of padded coaming is calculated:
(4) damping energy dissipation when system resonance is calculated:
(5) static stress of padded coaming is calculated:
(6) it is 252.3Hz that experiment, which measures resonant frequency of the honeycomb cardboard sample for changing size under 3.92kPa static stress,
Maximum vibration transport is 6.035.Experiment condition are as follows: logarithm sweep method, sweep rate 1oct/min, swept frequency range 5-
500Hz, target spectral acceleration peak A are 0.5g.The resonant frequency and maximum vibration transport that experiment is obtained substitute into formula (4),
Obtain the damping energy dissipation when system resonance are as follows:
So the liner selected by surge guard can provide enough vibration protections.
The above content is a further detailed description of the present invention in conjunction with specific preferred embodiments, and it cannot be said that
Specific implementation of the invention is only limited to these instructions.For those of ordinary skill in the art to which the present invention belongs, exist
Under the premise of not departing from present inventive concept, a number of simple deductions or replacements can also be made, all shall be regarded as belonging to of the invention
Protection scope.
Claims (4)
1. a kind of damping energy dissipation appraisal procedure of honeycomb cardboard quality system, it is characterised in that: itself the following steps are included:
Step S1, obtains Typical Vibration transmission characteristic vibration transmissibility-frequency curve of honeycomb cardboard, curve include platform area,
Amplification region and decay area, it is f that dot frequency is played in platform area0, the resonant frequency in amplification region is fn, the dot frequency that rises of amplification region is f1,
The terminal frequency of amplification region is f2, wherein f1=fn- 50, f2=fn+50；The terminal frequency of decay area is f3；Honeycomb cardboard vibration
Transmission characteristic curve is expressed as the function of frequency are as follows:
Wherein, TrnIt is f for resonant frequencynWhen vibration transmissibility；
Step S2 obtains a cycle internal resistance at any frequency of honeycomb cardboard-quality system according to damping energy dissipation basic theories
The energy that Buddhist nun dissipates are as follows:
Wherein, A is excitation acceleration amplitude, and c is the damping characteristic of padded coaming,Wherein m is the quality of product；
Step S3, according to formula (2), damping energy dissipation when obtaining honeycomb cardboard quality system amplification Q region resonance Q is
2. honeycomb cardboard quality system damping energy dissipation appraisal procedure according to claim 1, it is characterised in that: step S1
In, the vibration transmissibility curve for obtaining honeycomb cardboard is tested by sine sweep.
3. the application of honeycomb cardboard quality system damping energy dissipation appraisal procedure according to claim 1, it is characterised in that: adopt
Vibration protection when resonance can be provided with following steps assessment honeycomb cardboard:
Step S11 considers Fatigue Vibration, the vibration of product crisp value [G] vibration allowable and the crisp value [G] of vibratory impulsePunchingRelationship are as follows:
Step S12 considers that maximum conditions, the vibration transmissibility of product meetWherein A is means of transport excitation peak
Acceleration A；Resonant frequency fnExcept the frequency range of means of transport, i.e. fn≥200Hz；
Step S13 calculates the damping characteristic of padded coaming:
Step S14 calculates the damping energy dissipation when system resonance are as follows:
Step S15 calculates the static stress of padded coaming:Wherein m be product quality, g be 9.8 meters of acceleration of gravity/
Second, S is the bed-plate dimension of product；
Step S16, by sine sweep experiment measure the resonant frequency of the honeycomb cardboard sample under the static stress of step S15 and
Maximum vibration transport；The resonant frequency and maximum vibration transport that experiment is obtained substitute into formula (3), when obtaining the system resonance
Theoretical damping consume energy WN reason；If Wn1≤WN reason, then the honeycomb cardboard can provide vibration protection as liner.
4. the application of honeycomb cardboard quality system damping energy dissipation appraisal procedure according to claim 1, it is characterised in that: right
Formula (2) carries out subsection integral, obtains the gross energy of Damping work in honeycomb cardboard-quality system vibration processes are as follows:
Wherein, k1、k2For the slope of amplification region or so two parts vibration transmissibility, the left and right two parts vibration transmissibility in amplification region
The intercept of curve is respectively
According to honeycomb cardboard-quality system characteristic, the gross energy for the Damping work that honeycomb cardboard is born in transit is calculated, and
With WallIt is compared whether determining honeycomb cardboard can provide vibration protection.
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