Evaluation of Radial Pressure Generated at Cylindrical ...

Journal of the Institute of Industrial Applications Engineers Vol.5, No.3, pp.141–149, (2017.7.25)DOI: 10.12792/JIIAE.5.141 Online edition: ISSN 2187-8811 Print edition: ISSN 2188-1758

Paper

Evaluation of Radial Pressure Generated at Cylindrical Pressure VesselWall during High Speed Compression Formation of Ice Pieces

Minoru Ishiguro∗† Non-member, Hiroki Hayashi† Non-memberShin-ichiro Kaneko† Non-member, Yotsumi Yoshii† Non-memberTomoki Tajiri† Non-member, Sotomi Ishihara† Non-memberKei-ichi Masuyama† Non-member, Naoki Sase† Non-member

(Received April 07, 2017, revised July 03, 2017)

Abstract: In snowy country, a compaction process of snow has been demanded for performing efficient snowremoval and disposal work. For achieving the work, a design of large pressure vessel is demanded in order toperform high speed compression of the snow and ice. This report aims to investigate the radial pressure generatedduring the high speed compression of ice pieces for obtaining a fundamental data to design a large pressure vessel.In the investigation, ice pieces were compressed by an axial formation pressure pz for pz = 0.0 to 5.0 MPa, andthe radial pressure pr during the compression test was evaluated. It was found that the ice column having D = 80mm diameter, H = 80 mm height and density of ρ = 0.84g · cm−3 was obtained at pz = 5.0 MPa. And, themaximum radial pressure pr max reached about 60 % of the axial formation pressure pz.

Keywords: Transportation of snow disposal, Compression of snow, Pressure vessel, Radial pressure

1. Introduction

In the snow country, there are some chronic snow removaland disposal problems. Especially, preservation of tempo-rary storage place of snow after plow snow removal has be-come the issue [1]∼[4]. There are huge amount of snow,and if it will over the capacity of the temporary storagespace, the snow has to be transported to another large stor-age place. But there is huge amount of snow overwhelm-ing the transportation capacity of it. As a result, there oc-curs chronic traffic delay. If the traffic delay occurs in mainroad in daytime, it gives huge amount damage for civil life[1]∼[4]. In other related issues that huge amount cost hasbeen allocated for the snow disposal transportation. Theplow-snow removal cost per 100 m is 3,000 Japan Yen, andsnow disposal cost per 100 m is 240,000 Japan Yen, respec-tively [1]. The disposal cost is very higher than plow ’sone, it is 80 times [3]. Recently, the way to pay the highdisposal cost has become a big problem of local govern-ment. And furthermore, recently, those processes have be-come difficult in marginal village by labor shortage causedby a declining birth rate, and an aging population [1]∼[3][5]. For solving the problem, the snow removal and dis-posal method [1] that can respond flexibly under depopu-lation has been studied by a request from local supporters.In the previous report [1], high speed compression processto decrease the snow and ice volume before carrying thesnow on truck was proposed, and its high speed compres-

∗ Corresponding author: [email protected]† National Institute of Technology, Toyama College

13, Hongo, Toyama-shi, Toyama, Japan 939-8045

sion process was investigated. There are another physicalresearch reports about snow and ice compression. For ex-ample about snow compression, Maeno et al. have somereports [6]∼[8]. The author performed artificial compres-sion test imitating ice sheet deformation of Antarctica. Inthose reports, they studied the low strain rate compressiontest of snow for ε ≤ 10−3s−1 by using close dies. Theyhave mainly investigated the relation between snow com-pact density and the axial formation pressure for the densityρ ≤ 0.84g · cm−3. And they clarified that the nonlinear rela-tion exists between them for the density ρ > 0.84g · cm−3

[6]∼[8]. And Wilkinson [9] did theoretical investigationabout the relation between ice compact density and meannormal stress on consolidation of Antarctica’s snow firn.He showed that the theoretical and observation results havea good agreement with each other. At that time the strainrate ε was ranged for ε ≤ 10−9s−1. Above theoretical in-vestigation result focused about actual snow having densityρ ≤ 0.84g · cm−3 and strain rate ε ≤ 10−9s−1. Sakai etal. [10] reported the products case of the Snow to Ice Con-verter: SIC manufactured by Mitsubishi Heavy Industries,LTD. And Adachi et al. [11] reported the characteristic ofthe SIC equipment made by Japan Steel Works, Ltd. Thosemachines could produce high density snow compact hav-ing ρ > 0.84g · cm−3 by their fast compression speed withε ≈ 10−1s−1. But, it need 8.0 MPa axial formation pres-sure and about 100 ton compression load for manufacturinglarge snow compact having cube edges L = 300 mm. There-fore, these equipment need large and tough pressure vesselhaving 7.0 ton weight and 4.0m length. Ishiguro [1] hasinvestigated about manufacture procedure of snow compact

Published by IIAE. 2017 141

142 M. Ishiguro, H. Hayashi, S. Kaneko, Y. Yoshii, T. Tajiri, S. Ishihara, K. Masuyama and N. Sase

having ρ > 0.84g · cm−3 by high speed compression withε ≈ 10−1s−1 by using simulative small cylinder apparatus.The machine needed 2.0 MPa axial formation pressure forobtaining ρ = 0.84g · cm−3 ice compact. For the present,Ishiguro et al. have designed and developed actual size ma-chine. It is very lightweight and can be pulled by automo-bile and move easily among residence area. In this report,the relation between the radial pressure generated at thesteel pressure vessel wall and axial formation pressure dur-ing ice compression test with strain rate ε ≈ 5.0 × 10−2s−1

was studied for designing and developing durable compres-sion machine. And moreover, the relation between ice com-pact density and the mean normal stress was also investi-gated.

2. Proposed snow disposal process2.1 Outline of snow compression machine In exist-ing human intensive snow removal and disposal process,there are huge amount of truck transportation of snow. Thisis a serious problem, and it becomes bottleneck of wholesnow removal schedule. In the proposed process [1], thesnow is completely compressed into ice column for decreas-ing its volume before carrying it onto the truck. So, pro-posed process can get high efficiency in the snow removalwork. Results from imitating experiment of proposed pro-cess shows that the density of snow disposal increases andthe carry efficiency would be improved by 200 % in thecase of wet snow, and 400 % in the case of dry snow, re-spectively [1]. The proposed snow disposal process can beadopted to human intensive snow removal at rural area andto snow removal by heavy equipment at urban area havingsnow storage place problem.

Schematic illustration of proposed compression and ex-trusion process machine is shown in Fig. 1. The machineconsist of compaction pressure vessel, movable push dies,movable shutter, extrusion dies, hinge door platen, snowremoval collecting box and motive energy. The rough di-mensions are 1,000 mm height, 600 mm width and 500mm length. The extruded ice column has 250 mm height× 250 mm width, and range of 170 to 250 mm length. Indesign the compression maximum formation speed of mov-able push dies is 500 mm·s−1, and the assumed minimumlongitudinal length of dies is 250 mm. The strain rate wasassumed at least almost ε = 2.0s−1. Here, the strain rate wasdefined by the following equation (1). In this report, the re-lation between the radial pressure generated at the pressurevessel and the axial formation pressure was investigated forthe compression test with strain rate ε ≈ 0.05s−1 by the rea-son of experimental equipment setup.

ε =Assumed minimum longitudiral lenghto f dies

Maximum f ormation speed o f movable push dies(1)

Schematic illustration of operation of the proposed com-pression and extrusion processes is shown in Fig. 2. Somesnow is collected by using agriculture small dozer or hu-man. Then snow is thrown into collecting box. And then itis compressed in the pressure vessel as shown in Fig. 2 (a) -(c). And then, the hinge door platen is opened as shown in

Figure 1: Schematic illustration of the proposed compres-sion and extrusion process machine.

Figure 2: Schematic illustration of operation of proposedcompression and extrusion processes.

Fig. 2 (d). And the movable dies go back, and new snow isfilled in the pressure vessel as shown in Fig. 2 (e). Then thenew snow is re-compressed between the movable dies andcompacted ice. And after, the compacted ice are sequen-tially extruded as shown in Fig. 2 (f). The compacted iceis extruded out when the compression formation pressurereaches over the extrusion formation pressure.

2.2 Cyclic compression test of ice pieces by usingacrylic pressure vessel Simulation experiment wasperformed with acrylic pressure vessel instead of steel onefor observing ice compaction behavior. Photographs ofbreakage of the acrylic compression pressure vessel in sim-ulation experiment are shown in Fig. 3. The rectangularcross section pressure vessel as shown Fig. 3 and a cir-cular cross section pressure vessel were used for the sim-ulative test. In the case of using rectangular cross sectionpressure vessel of Fig. 3, fatigue crack occurred at the lat-eral wall of the pressure vessel by applying repeated axial

IIAE Journal, Vol.5, No.3, 2017

Evaluation of Radial Pressure Generated at Cylindrical Pressure Vessel Wall during High Speed Compression Formation ... 143

(a) Rectangular cross section pressure vessel

(b) Fatigue cracked lateral bolting acrylic plate

Figure 3: Photographs of breakage of the acrylic compres-sion pressure vessel in the simulation experiment.

formation pressure pz = 4.0 MPa 10 times. And, thoughthe photograph was omitted, in the case of using the circu-lar cross section pressure vessel, the acrylic pressure vesselwas cracked by applying repeated axial formation pressurepz = 4.0 MPa about 100 times. It is assumed that numer-ous times of compression formation would be performed inthe proposed snow removal process. Therefore, a reliableand safety design criteria about fatigue fracture of the com-pression pressure vessel is needed. To that end, clarificationof the relation between the radial pressure generated at theinner wall of the compression pressure vessel and the axialformation pressure is needed.

2.3 Relation between the radial pressure pr at the in-ner wall of the compression pressure vessel and the ax-ial formation pressure pz during the compression for-mation of ice pieces Ebinuma et al. [6]∼[8] reportedthat the compression properties of snow shows stronglynonlinearity during snow compression formation for ρ ≤0.84g · cm−3. They also reported that especially, in com-pression of ρ ≤ 0.84g · cm−3 snow, air was trapped betweeninterface of each ice particles, and the axial formation pres-sure increases rapidly with trapping of air. Usually, the gen-erated stress and strain of the pressure vessel caused by fluidpressure is calculated based on the formula of strength ofmaterials. However, it is known [12] [13] that these stressand strain of the pressure vessel vary with the inner diam-eter, thickness and height of the pressure vessel. So, theFinite Element Analysis: FEA was performed especiallyfor obtaining detail information about the pressure vesseldeformation behavior [14] [15]. But unfortunately, the Pas-cal’s principle is not applicable to the compression of snowunlike in the case of water. Therefore, in the case of the

compression of snow, it is difficult to obtain the relationbetween the radial pressure generated at the compressionpressure vessel and the axial formation pressure by FEA[15]. In this report, the above relation was investigated byboth of FEA and experimental observation. First, the cal-ibration test was performed by using water instead of icepieces with reference of Xin et al. [15]. The relation be-tween the circumferential strain εθ and the axial pressure pz,i.e. εθ − pz relationship was obtained by the test using wa-ter. The strain εθ is able to measure experimentally by usingattached strain gauge on the pressure vessel. And then therelation of pz = pr from Pascal’s principle was adapted tothe calibration relation εθ vs. pz. So, it will be able to obtainthe relation between the radial pressure pr generated at thepressure vessel wall and the circumferential strain εθ, i.e.pr−εθ relation. Then the compressive material was changedfrom water to ice pieces for performing compression test ofice pieces. At that time, the circumferential strain εθ wasmeasured by using strain gauge. Then, the measured strainεθ was substituted into the pr − εθ relation, which was ob-tained from the calibration test using water, to evaluate theradial pressure pr generated at the pressure vessel wall dur-ing the ice compression.

3. Experimental procedure and Finite element analy-sis

3.1 Compression test of water The compression testof water column was performed to obtain the calibration re-lation between the circumferential strain εθ and the axialformation pressure pz. The water column was compressedvia the upper tool made of steel by using the Autograph:Shimadzu Corporation AG-50k, which was equipped withTrapezium X software for precision testing. The water col-umn was kept in the cylinder by using O-ring for preventingleak of the liquid during the compression test. A photographof the cylindrical compression pressure vessel is shown inFig. 4. The circumferential strain was measured by us-ing strain gauge as shown in Fig. 4. The strain gauge:Tokyo Sokki Kenkyujo, UFLA-5-17 having gauge factorKs = 2.12, electric resistance R = 120Ω, was used. Thestrain was measured by using dynamic strain meter: TokyoSokki Kenkyujo, DA-16A, which has a bridge voltage of2.0 V, gauge factor of 2.0. The relation between the circum-ferential strain εθ of the pressure vessel and the axial for-mation pressure pz was obtained from the above calibrationtest. By adopting the Pascal’s principal of pz = pr to the εθvs. pz relation, the relation between the radial pressure pr

and the circumferential strain εθ was obtained.

3.2 Compression test of ice pieces Compressive ma-terial was changed from water to ice pieces. And the com-pression of ice pieces was performed to obtain the relationbetween the circumferential strain εθ and axial formationpressure pz. In the compression test of ice pieces, the O-ringthat was used for the case of water was detached. Duringthe test, the temperature of some ice pieces was maintainedfrom -11 to 0. And all dies tools were kept at the tem-perature from 2 to 7 before and during the test. Someice pieces were melted but the melting was negligible. The



Figure 4: Photograph of the cylindrical compression pres-sure vessel.

radial pressure pr at the pressure vessel wall can be evalu-ated by substituting the measured circumferential strain εθinto the calibration relation, pr − εθ. The ice compressiondensity was measured after the compression test performedat each of the axial formation pressure pz. Averages of 5measurements of the mass, height and diameter were eval-uated.

3.3 Elastic deformation analysis of pressure vesselduring the compression test of water It is known[12]∼[16] that some cylindrical steel pressure vessel showscomplex elastic deformation when applying internal pres-sure. Therefore, in this report, the elastic deformation be-havior of the pressure vessel was analyzed by using fi-nite element method: FEM and experimental observation.Schematic illustrations and dimensions of biased and cen-ter configurations of pressure vessel for FEA are shown inFig. 5. It shows schematic illustrations and dimensions ofconfigurations of the two types of pressure vessel calledas biased and center configurations, which were analyzedby the FEM. The pressure vessel consists of steel cylinder,push dies, O-ring and compressive material of water or icepieces. The word “biased configuration” of Fig. 5(a) meansthat the centroid of water and the one of the pressure vesselare different, not the same. The word “center configuration”of Fig. 5(b) means that the centroid of water and the one ofthe pressure vessel are the same. In the proposed processes,usually the ice would be compressed to horizontal direction,but in the imitating experiment at the laboratory the ice wascompressed to vertical direction from the reason of experi-mental equipment setup. As a compressive material, water,which is applicable material of the Pascal’s principal, wasused for the calibration test and FEA.

The compression tests of water at the cases of the abovetwo- types were numerically analyzed using FEM. Thecommercial FEM software MSC Marc 2015 was used forthe purpose. Axisymmetric FEM analysis was conducted ofthe steel cylinder pressure vessel. The pressure vessel wallwas divided into the isoparametric quadrilateral elementswith size of 1 mm×1 mm by using MSC Mentat 2015. Thethree strain components, axial, radial and hoop strains at theouter pressure vessel wall were calculated. In the analysis,

(a) Biased configuration

(b) Center configuration

Figure 5: Photographs of breakage of the acrylic compres-sion pressure vessel in the simulation experiment.

the values of Young’s modulus E = 210 GPa, and Poisson’sratio ν = 0.25 were used. The radial pressure was applied tothe inner surface of the pressure vessel wall as the boundarycondition for imitating the radial pressure generated duringwater column compression test. From the Pascal ’s princi-ple, the radial pressures were given within the range from0.0 MPa to 5.0 MPa corresponding with the axial formationpressure. In addition, the radial direction pressure due tothe O-ring was also applied to the inner surface of the pres-sure vessel wall. In the preliminary test, the friction forcebetween the O-ring and inner surface of the pressure ves-sel wall was measured during the compression test. It wasalmost 600 N. So, the effect of the friction force was ne-glected in FEA. And the bottom of the cylindrical pressurevessel was only constrained in the axial direction z as shownin Fig. 5 (a-2) and (b-2). And the boundaries of radial andcircumferential directions were unconstrained.

4. FEA result about relation between circumferentialstrain εθ and axial formation pressure pz duringcompression test of water

Distributions of axial direction strain εz, circumferential di-rection strain εθ and radial direction strain εr were analyzed



Figure 6: Circumferential strain distribution along pres-sure vessel height at every water column length increment∆L = 10 mm from L = 30 mm to 150 mm obtained fromFEA.

along the height direction of the pressure vessel for deter-mining the measurement point of the circumferential strainεθ. The compression tests of water under the both condi-tions shown in Fig. 5 were numerically analyzed. From theresult, though the figure was omitted, it was clarified that itis difficult to obtain the relation between the circumferen-tial strain εθ and the axial formation pressure pz in the caseof the biased configuration of Fig. 5(a). Hence, in the fol-lowing, the calibration relation between the circumferentialstrain εθ and the axial formation pressure pz for the centerconfiguration of Fig. 5(b) will only be stated.

Circumferential strain distribution along pressure vesselheight at every water column length increment ∆L = 10 mmfrom L = 30 mm to 150 mm obtained from FEA are shownin Fig. 6, where the lengths of water column were variedfrom L = 30 mm to 150 mm with an increment of ∆L = 10mm, and the axial formation pressure pz was set to be 5.0MPa. As can be seen from the figure, the εθ distributionhas convex shape, and the maximum εθ value yields at themiddle point of the height. But, the strain values εθ at eachends have different values, this is because the boundary con-ditions at each ends differ from each other. Therefore, thestrain distribution curve is not symmetry along the heightdirection. As seen from Fig. 6, the maximum value of thecircumferential strain εθ max increases with an increase ofwater column length from L = 30 mm to 50 mm, and thenfollowed by saturation for the region L ≤ 50 mm. The satu-rated value was almost εθ = 85×10−6 strain. And the widthof the saturated region becomes longer with increasing wa-ter column length L from 50 mm to 150 mm. The shapes ofthe strain curves are almost the same regardless of the axialpressure pz.

Then, the distribution of the axial direction strain εz, andthe distribution of the radial strain ε r along the pressure

Figure 7: Relation between circumferential strain at the mid-dle of pressure vessel in height and water column length.

vessel height z were also analyzed by FEM. The lengths ofwater column were varied from L = 30 mm to 150 mmwith an increment of ∆L = 10 mm, and the axial forma-tion pressure pz was set to be 5.0 MPa. Though the resultswere omitted, the distribution of the axial direction strain εz

along z fluctuated intensely, and the shape of the εz distri-bution was complicated. The radial strain εr along the pres-sure vessel height z was almost zero and negligible. Theabove results are same at the biased and center configura-tions shown in Fig. 5. So, the distributions of εz and εr vs.pz are inappropriate to use for obtaining the calibration re-lations in the present study. However, only the relation, εθvs. pz for the case of center configurations of Fig. 5(b) isuseful for obtaining calibration equation.

The relation between the circumferential strain εθ at mid-dle of pressure vessel height and water column length L forpz = 1.0 − 5.0 MPa was calculated by FEA. The values ofstrain εθ at the middle of pressure vessel were measured tocompare with result value of FEM. The axial pressure wasset to be pz = 5.0 MPa. Relation between circumferentialstrain at the middle of pressure vessel in height and watercolumn length are shown in Fig. 7. It shows the relation be-tween circumferential strain εθ at the middle of the pressurevessel in height and water column length of L. The exper-imental results εθ as shown by open circles at pz = 5.0MPa, which were measured by strain gauge are also shownin this figure for a comparison purpose. As can be seen fromthe figure, the strain εθ increases monotonically as increasesof L up to 70 mm for all of the axial formation pressurepz. FEM results have good agreements with the experimen-tal results. It can see that the maximum strain εθ yields ataround L = 70 − 80 mm. So, the strain gauge for mea-suring the circumferential strain was attached on the outercylindrical pressure vessel at the height L = 75 mm.

The relation between circumferential strain εθ and axialformation pressure pz, which were obtained by both FEA



Figure 8: Relation between circumferential strain εθ and ax-ial formation pressure pz at L = 70 and 80 mm.

and experiment for the case of water column length L = 70and 80 mm, are shown in Fig. 8. The vertical axis of thefigure indicates the strain εθ at the middle point of the pres-sure vessel L = 75 mm. From the figure, good agreementbetween the FEA and the experimental result can be seen.And there is a linear relationship between εθ and pz as ex-pressed by equation (2).

εθ[10−6strain] = 18[strain ·MPa−1] × pz[MPa] (2)

The slope of the straight line is 18 × 10−6strain ·MPa−1.The error from the linear approximation is almost e = ±10%. Therefore, the strain εθ has one to one correspondencerelation with the axial formation pressure pz.

5. Compression test of ice pieces5.1 Relation between the radial pressure pr generatedat the pressure vessel wall and axial formation pressurepz during the compression test of ice pieces It is dif-ficult to obtain the natural snow for doing the snow com-pression test every time. It is known [1] that it is possible tosimulate snow compression behavior by using cubic shapedice pieces with dimensions, 8 × 8 × 8mm. So, in this study,some ice pieces were used for the compression test insteadof natural snow. The compression test of ice pieces wasperformed by using the steel cylindrical pressure vessel tostudy the relation between the circumferential strain εθ andaxial formation pressure pz. In the test, it is able to obtainthe relation between the radial pressure pr generated at thepressure vessel wall and the axial formation pressure pz, bycombining the pz − εθ relation obtained from this ice com-pression test, and the calibration relation pr − εθ obtainedfrom the water compression test.

Relation between the radial pressure pr generated at thepressure vessel wall in the ice compression and the axialformation pressure pz is shown in Fig. 9. It shows the rela-tion between the radial pressure pr generated at the pressure

Figure 9: Relation between the radial pressure pr generatedat the pressure vessel wall in the ice compression and theaxial formation pressure pz.

vessel wall and the axial formation pressure pz. The val-ues of pr plotted by the solid circles were conducted eighttimes at each of the pz. As can be seen from the figure, theradial pressure pr increases as increases of the axial forma-tion pressure pz. The dotted line expressing pr = 0.6 · pz

shows the upper limit of the radial pressure pr of the icepieces. So, in the case of the ice compression, the maxi-mum value of the radial pressure pr is less than 60 % of theaxial formation pressure pz. The straight line expressingpr = pz shows the Pascal’s principle applicable to the caseof the water compression is also shown by the solid line fora comparison purpose.

5.2 Effect of the axial formation pressure on ice com-pact density Effect of the axial formation pressure onice compact density was investigated for producing the icecompact having high density of ρ > 0.83g · cm−3. The den-sity of the ice compact is not homogeneous and varies lo-cally. So, in the following, the average value of the icecompact will be evaluated and used. Photographs of theice compacts that were compressed by the axial pressure,pz = 1.0 and 5.0 MPa are shown in Fig. 10. The formerfor pz = 1.0 MPa has some air voids at all over the points.But in the latter for pz = 5.0 MPa, the void size becomessmaller than in the former one.

Relation between ice compact density and axial forma-tion pressure is shown in Fig. 11. In the figure, variation ofthe density of the ice compact is shown as a function of theaxial formation pressure pz. The density data as shown bysolid circle • are same one used in Fig. 9. The snow and theice compact density obtained in the previous study [1] arealso shown in the figure as a comparison. As can be seenfrom the figure, the ice density of the present study has aquite large variation. However, the average of the ice den-sity increases as increases of the axial formation pressurepz, and then it saturated at ρ ≈ 0.84g · cm−3. And, it is seen



(a) pz = 1.0Mpa ρave = 0.79g · cm−3

(b) pz = 0.5Mpa ρave = 0.84g · cm−3

Figure 10: Photographs of the ice compacts compressed bythe axial pressure pz = 1.0 and 5.0 MPa.

that the axial formation pressure pz of 3.0 MPa is needed forobtaining the high density ice compact for ρ > 0.83g · cm−3.In this study, the value of the maximum ice density was ob-tained as ρ ≈ 0.84g · cm−3. The value is not higher than theprevious reported one having ρ ≈ 0.90g · cm−3 [1]. Thisnumerical difference is attributed to the difference in thecompaction formation way of ices. In this study, the icepieces were compressed once at the given formation pres-sure, and then the pressure was not maintained at the value.And stress relaxation [17] is assumed to occur during theice compaction formation of the present study. But in theprevious report [1], the ice pieces were pressed iterativelyup to the indicated pressure value by using manual pressmachine. And, the maximum formation pressure was main-tained at least for 5 seconds during the compaction forma-tion. Thus the ice compact density in the present study islower than the previous study’s one [1].

5.3 Effect of the mean normal stress on the ice compactdensity during compression formation The effect ofthe mean normal stress on the ice compact density duringcompression formation was investigated. The mean normalstress σm was given by following equation (3).

σm =σ1 + σ2 + σ3

3[MPa] (3)

Here, σ1, σ2, σ3 were principle stresses in Cartesian co-ordinate. Specifically, the first principal stress equals to −pz

Figure 11: Relation between ice compact density and axialformation pressure.

and the second and the third principal stresses are given asσ2 = σ3 = −pr. The values of pz and pr shown in Fig. 9were used to calculate the mean normal stress σm.

Relation among ice compact density, axial formationpressure and absolute value of mean normal stress duringcompression test are shown in Fig. 12. It show the changesof the ice compact density ρ as a function of the axial forma-tion pressure pz and of the absolute value of the mean nor-mal stress |σm|, respectively. As seen from Fig. 12(b), thereis a positive linear relationship between the ice compactdensity ρ and the absolute value of mean normal stress |σm|.The data scatter of the density ρ in the region |σm| > 1.5MPabecomes smaller than that in |σm| < 1.5MPa. Ice compactwith a high density of ρ ≤ 0.84g · cm−3 can be obtainedat the condition of |σm| ≤ 2.50 MPa and at the strain rateε ≈ 0.05s−1. It was found that the value of the averagenormal stress 2.50 MPa needed for making the high den-sity ice compact under high speed compression formation.It is ten times larger than that in the case of the slow speedcompression formation of the natural ice sheet [9]. Further,at the high speed compression formation of the ice at theregion ε ≤ 0.05s−1, to use the mean normal stress insteadof the axial pressure is appropriate because of reducing thedata scatter of the ice compact density ρ.

6. ConclusionsFor designing and developing durable compression ma-chine, the radial pressure generated at the inner surface ofthe steel pressure vessel during the ice compression testwith strain rate ε ≈ 5.0 × 10−2s−1 was investigated. Theresults obtained are summarized as follows.

1. It is possible to evaluate the generated radial pressureby measuring the circumferential strain at the center inheight of the pressure vessel. The validity of the evalu-ation procedure was confirmed by FEM simulation andcompression test of water.



(a) Axial formation pressure pz

(b) Absolute value of mean normal stress |σm |

Figure 12: Photographs of the ice compacts compressed bythe axial pressure pz = 1.0 and 5.0 MPa.

2. The axial, circumferential and radial strains that weregenerated in the water compression test were ranged10 − 100 micro strain. These strains can be predictedprecisely by using FEM. Good agreements were con-firmed between FEM and experimental data. The dif-ference between them was ranged ± 10%.

3. The radial pressure pr increases with an increase of theaxial formation pressure pz. In the case of the ice com-pression test performed at fast strain rate ε = 0.05s−1,the maximum value of the radial pressure pr is lessthan 60 % of the axial formation pressure pz.

4. There is a positive linear relationship between the icecompact density ρ and the mean normal stress |σm|.Ice compact with a high density of ρ ≤ 0.84g · cm−3

can be obtained at the condition of |σm| ≤ 2.50 MPaand at the strain rate ε ≈ 0.05s−1. Further, at the high

speed compression formation of the ice at the regionε ≤ 0.05s−1, it was found that to use the mean normalstress instead of the axial pressure is appropriate be-cause of reducing the data scatter of the ice compactdensity ρ.

7. AcknowledgementsThis study was started December, 2010. Many thanks to allthe students who studied in Ishiguro’s laboratory. Thanksalso to the staff related to this project. The authors ex-press their thanks to President K. Nagahama and Chair-man K. Matsui at the Kanaya Co. Ltd, Toyama prefectureand Toyama first bank to their supports and helps. Thisstudy was supported by JSPS KAKENHI Grant NumberJP16K01338, which is appreciated very much.

References

[1] M. Ishiguro, “Rapid Continuous Extrusion Procedure forSnow Removal”, Journal of Japan Society for Design En-gineering, 50- (12), pp. 668-673 (2015).

[2] Planning section, Snow management office, Construction bu-reau, city of Sapporo, “Picture book of snow in Sapporo”,pp.1- 46 (2006). (in Japanese )

[3] Planning section, Snow management office, Construction bu-reau, city of Sapporo, “For snow removal measures businessin Sapporo”, pp.1-41 (2013). (in Japanese)

[4] N. Takamiya and Y. Sato, “A study of the impact onthe public economy of snow removal market in Sapporo”,Hokkaido Development Association Grant Research, pp.97-132 (2012). (in Japanese)

[5] A. Ono, “Introduction to Mountain Village’s EnvironmentalSociology Marginal Villages and Cooperative Managementof Basin Area”, ISBN: 4-540-04299-8 (2005). (in Japanese)

[6] T. Ebinuma and N. Maeno, “Studies on the densificationof snow as a pressure sintering process”, Seppyo, 46-(4),pp.153-161 (1984). (in Japanese)

[7] T. Ebinuma and N. Maeno “Experimental studies on densi-fication and pressure-sintering of ice”, Annals of glaciology,6-(1), pp.83-86 (1985).

[8] N. Maeno and T. Ebinuma, “Pressure sintering of ice andits implication to the densification of snow at polar glaciersand ice sheets”, The Journal Physical Chemistry, 87-(21),pp.4103-4110 (1983).

[9] D. S. Wilkinson “A pressure-sintering model for the densifi-cation of polar firn and glacier ice”, Journal of Glaciology,34-(116), pp.40-45 (1988).

[10] K. Sakai and M.Yoshida, “Introduction of Mitsubishi snowto ice converter, Cold region technology conference ’88”,pp.530-535 (1988).

[11] T. Adachi, H. Kawamoto, M. Sasaki, M. Narita and H. Ya-mada, “The properties of ice block made by SIC and appli-cation for snow festival”, Cold region technology conference’87, pp.56-61 (1987).



[12] J. H. Faupel, “Yield and Bursting Characteristics of Heavy-wall Cylinders”, Transactions of the ASME, 78-(5), pp.1031-1064 (1956).

[13] J. H. Faupel, “Pressure Vessels of Noncircular Cross Sec-tion”, Transactions of the ASME Journal of Pressure VesselTechnology, 101-(3), pp.255-267 (1979).

[14] M. Hamada, R. Yokoyama and H. Kitagawa, “An estimationof maximum pressure for a thick-walled tube subjected tointernal pressure”, International Journal of Pressure Vesselsand Piping, 22-(4), pp.311-323 (1986).

[15] P. Xin, M. Ando, N. Kondo, M. Amano, H. Ohtsuka, K.Enomoto and E. Hasebe, “Evaluation of Compaction Char-acteristics for Powder with Uniaxial Pressing Test”, Taik-abutsu, 53-(11), pp.618-623 (2001). (in Japanese)

[16] W. R. D. Manning, “Bursting Pressure as the Basis for Cylin-der Design”, Transactions of the ASME, Journal of PressureVessel Technology, 100-(4), pp.374-381 (1978).

[17] K. F. Voitkovsky “The relaxation of stresses in ice, Physicsof snow and ice”, 1-(1),pp.329-337 (1967).

Minoru Ishiguro (Non-member) was born inYamagata, Japan, 1980. He received the B. S.and M. S. degrees in Production system engi-neering at 2002 and 2004, and the Ph. D. degreein Mechanical structure system engineer fromToyohashi University of Technology at 2007.From 2007 he has worked at Toyama NationalCollege of technology as Assistant professor.

Since 2010, he worked at National Institute of Technology, ToyamaCollege. He is presently lecturer since 2016. He has worked onmetal forming field. He is member of JSME, JSSI and JSDE.

Hiroki Hayashi (Non-member) Graduatedstudent of Mechanical system engineeringin National Institute of Technology, Toyamacollege at 2017. He received associate degree inMechanical system engineering

Shin-ichiro Kaneko (Non-member) receivedB.E. and M.E. degree in Systems Engineeringfrom Yamagata University, Japan, in 2000 and2002, respectively, and Ph. D degree from Ya-magata University, Japan, in 2005. From 2006to 2007, and 2007 to 2008, He was a researchassistant and an assistant professor, respectively,at Toyama National College of Technology in

Japan. He is currently an associate professor in Electrical andControl Systems Engineering at National Institute of Technology,Toyama College in Japan. His research interest is in biped robotsand autonomous/remote-operated mobile robots. He is a memberof the Robotics Society of Japan (RSJ) and the Society of Instru-ment and Control Engineers (SICE).

Yotsumi Yoshii (Non-member) received theB.S. and M.S. degrees in Image science fromChiba University in 1999 and 2001. He receivedthe Ph.D. degree in Artificial systems sciencefrom Chiba University in 2004. From 2004 to2005, he was a postdoctoral researcher at Uni-versity of Fukui. From 2005 to 2010, he was anAssistant Professor at Toyama National College

of Maritime Technology. Since 2010, he has been an AssociateProfessor at National Institute of Technology, Toyama College. Hiscurrent research interests include sensors, laser spectroscopy, andsignal processing. He is a member of JSAP and IEEJ.

Tomoki Tajiri (Non-member) received the B.Eng. and M. Eng. degrees in Mechanical En-gineering from Osaka City University, Japan, in2008 and 2010. He received the Ph. D degree inPhysics system of machine from Osaka City Uni-versity in 2013. Since 2013 he has been an assis-tant professor at the National Institute of Tech-nology, Toyama College. His current research

interests include autonomous mobile robots. He is a member ofJSME and RSJ.

Sotomi Ishihara (Non-member) Master de-gree, University of Toyama, 1974, Ph. D., To-hoku University, Japan, 1984, Assistant, Asso-ciate, and Full Professor, University of Toyama,Japan, from 1974 to 2013. Visiting AssociateProfessor, University of Connecticut, CT, USA,from 1992 to 1993. President of National Insti-tute of Technology, Toyama, from 2013 to 2017.

Paper Awards from Japan Society of Mechanical Engineers 2002.Fellow of the Japan Society of Mechanical Engineers 2007. Per-formance Awards from The Society of Materials Science, Japan,2010. Performance Awards from Japan Society of Mechanical En-gineers 2013. Visiting Principal Lecturer, from South Eastern Re-gional College, Great Britain, 2014. MFA Prize from HungarianAcademy of Sciences, 2015.

Kei-ichi Masuyama (Non-member) receivedthe B. Eng. and M. Eng. in Production sys-tems engineering from Toyohashi University ofTechnology, Japan. He was a Designing Divi-sion in SUGINO MACHINE Co., Ltd. in 1991to 1992, research associate in National instituteof Technology Toyama College in 1992 to 1995,research associate in Toyohashi University of

Technology in 1995 to 1997, an associate professor at Nationalinstitute of Technology Toyama College since 1997 His current re-search interests include High Pressure Torsion of Metal elements.

Sase Naoki (Non-member) received the B.Eng. and M. Eng. in Mechanical Engineeringfrom Gifu University, Japan. He was a researchassociate in Gifu University from 1987 to 1999.He received the Ph.D. degree in Mechanical En-gineering from Gifu University in 1997. From2000 to 2008 he was an associate professor, andsince 2008 has been a Professor at the National

Institute of Technology, Toyama College. His current research in-terests include mechanical elements and machining.


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