- Email: [email protected]
Design and Manufacturing of Variable Stiffness Mattress
Available online at www.sciencedirect.com Available online at www.sciencedirect.com
ScienceDirect ScienceDirect
Procedia Manufacturing 00 (2018) 000–000 Available online atatwww.sciencedirect.com Available online www.sciencedirect.com Procedia Manufacturing 00 (2018) 000–000
ScienceDirect ScienceDirect
www.elsevier.com/locate/procedia www.elsevier.com/locate/procedia
Procedia Manufacturing 26 (2018) 132–139 Procedia Manufacturing 00 (2017) 000–000 www.elsevier.com/locate/procedia
46th SME North American Manufacturing Research Conference, NAMRC 46, Texas, USA 46th SME North American Manufacturing Research Conference, NAMRC 46, Texas, USA
Design and Manufacturing of Variable Stiffness Mattress Design and Manufacturing of Variable Stiffness Mattress
Manufacturing Engineering Society Conference 2017, MESIC Ruinan Xie, ChadInternational Ulven, Ph.D., Bashir Khoda, Ph.D.*2017, 28-30 June 2017, Vigo (Pontevedra), Spain Ruinan Xie, Chad Ulven, Ph.D., Bashir Khoda, Ph.D.* North Dakota State University, Fargo, 58104 USA North Dakota State University, Fargo, 58104 USA
Costing models for capacity optimization in Industry 4.0: Trade-off between used capacity and operational efficiency
* Corresponding author. Tel.: +1-7012318071; fax: +17012317195. * Corresponding Tel.: +1-7012318071; fax: +17012317195. E-mail address:author. [email protected] E-mail address: [email protected]
A. Santanaa, P. Afonsoa,*, A. Zaninb, R. Wernkeb
Abstract Abstract a University of Minho, 4800-058 Guimarães, Portugal b Sleep quality are found to be decreased in the past decades from several surveys. And researches conducted that uncomfortable Unochapecó, 89809-000 Chapecó, SC, Brazil Sleep quality areone found to be decreased in the causing past decades fromproblems. several surveys. Andpresents researches uncomfortable mattress can be of the important reasons sleeping This paper the conducted design andthat manufacturing of mattress be one of the important reasons causing presents design and manufacturing of variable can stiffness mattress with cellular structure to sleeping maintainproblems. uniform This body paper support. The the relation between the hexagonal variable stiffness mattress with cellular structure to maintain uniform support. relationtobetween the digitize hexagonal honeycomb thickness and stiffness is studied and tested. The author appliesbody image analysisThe technique extract and the honeycomb is studied and The author analysis and hexagon. digitize the Abstract information thickness from the and bodystiffness load distribution map.tested. Voxelization is applies used to image determine the technique thickness to of extract each unit A information from thethe body load distribution Voxelization is used istogiven determine of each under unit hexagon. A comparison between designed mattress andmap. current existing mattress basedthe on thickness their deformation same load. comparison between mattress current existing mattress isbe given on be theirincreasingly deformation under same toload. With thethe study of the the unit cell and voxelization technique, our designed mattress hasbased less variation on deformation compare the Under concept of designed "Industry 4.0", and production processes will pushed to interconnected, With themattress studybased of which theon unit voxelization mattress has less on deformation to the uniform indicates we have more control onour the designed deformation with this proposed information a cell realand time basis and,technique, necessarily, much more efficient. Invariation this methodology. context, capacity compare optimization uniform mattress indicates moremaximization, control on the deformation with thisfor proposed methodology. goes beyond thewhich traditional aimwe ofhave capacity contributing also organization’s profitability and value. © 2018 The Authors. Published by Elsevier B.V. Indeed, lean management continuous © 2018 The Authors. Publishedand by Elsevier B.V. improvement approaches suggest capacity optimization instead of © 2018 The under Authors. Published by Elsevier B.V. committee of NAMRI/SME. Peer-review responsibility of the scientific maximization. The study of capacity optimization and costing models is American an important research Research topic that deserves Peer-review under responsibility of the scientific committee of the 46th SME North Manufacturing Conference. Peer-review under responsibility of the scientific committee of NAMRI/SME.
contributions from both the practical and theoretical perspectives. This paper presents and discusses a mathematical Keywords: Cellular structure; Variable stiffness; Mattress design model forCellular capacity management based Mattress on different Keywords: structure; Variable stiffness; design costing models (ABC and TDABC). A generic model has been developed and it was used to analyze idle capacity and to design strategies towards the maximization of organization’s value. The trade-off capacity maximization vs operational efficiency highlighted andcompelling it is shown that capacity 1. Introduction which isisone of the most problems in the 1. Introduction which is one of the most compelling problems optimization might hide operational inefficiency. industrialized world. Furthermore, sleep isin the an © 2017 The Authors. Published B.V. industrialized world. Furthermore, sleepof is Humans spend one third by ofElsevier their lifetime in bed essential factor in the health and the quality life an of Peer-review under responsibility of committee Engineering Society International Conference spend one thirdwith of the their lifetime in fact, bed of the Manufacturing essential factor in the health quality lifethe of [1] Humans and directly interacting thescientific mattress. In an individual. Research studyand hasthe pointed outofthat 2017. [1] and directly interacting with the mattress. In fact, an individual. Research study has pointed out that the in industrialized western cultures everyone spends quality of a mattress is the most important factor in a in industrialized western cultures everyone spends quality of a mattress is the important in a more time sleeping in a bed than in any other single sleep environment [3]. Themost ergonomics of factor a mattress Keywords: Cost Models; ABC; TDABC; Capacity Management; Idle Capacity; Operational Efficiency more time sleeping in a bed than in any other single sleep environment [3]. The ergonomics of a mattress activity, during the course of everyday living [2]. An should also prevent back-pain, lumbago, and hence activity, during the course of everyday livingthe [2].body An should lumbago, and factors hence appropriate mattress may correctly support improvealso the prevent quality back-pain, of life. Three dominant appropriate mattress may correctly support the body improve the quality of life. Three dominant factors which will bring relaxation and quality sleep. are commonly considered in mattress design process: 1. Introduction which will back bringsupport relaxation and low-back quality sleep. are commonly considered in mattress design process: Insufficient can cause pain, Insufficient back support can cause low-back pain, The cost of idle capacity is a fundamental information for companies and their management of extreme importance in modern systems. In general, it isB.V. defined as unused capacity or production potential and can be measured 2351-9789 ©production 2018 The Authors. Published by Elsevier 2351-9789 2018responsibility The Authors. Published by Elsevier B.V.hours Peer-review of the scientific committee of NAMRI/SME. in several©under ways: tons of production, available of manufacturing, etc. The management of the idle capacity Peer-review underTel.: responsibility the761; scientific committee NAMRI/SME. * Paulo Afonso. +351 253 of 510 fax: +351 253 604of741 E-mail address: [email protected]
2351-9789 © 2017 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the scientific committee of the Manufacturing Engineering Society International Conference 2017. 2351-9789 © 2018 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the scientific committee of the 46th SME North American Manufacturing Research Conference. 10.1016/j.promfg.2018.07.016
2
Ruinan Xie et al. / Procedia Manufacturing 26 (2018) 132–139 Ruinan Xie, Chad Ulven, Bashir Khoda/ Procedia Manufacturing 00 (2018) 000–000
i) materials, ii) sleeping poster or ergonomics and iii) interaction interface between mattress and body. The quality of sleep is affected by a synergy of psychological, physiological, and physical conditions [4]. Various factors influence the interaction between the human body and the sleep system. Contributing factors include body dimensions, distribution of body weight, and stiffness of the sleep system across the mattress surface [5]. Most of the identified studies that have dealt with objective measurements were concerned with the healing of wounds or the prevention of bed sores for those who are bedridden [2]. Sleep ergonomics have recently become especially crucial and deals with the body posture and position during sleeping. The scientific literature includes a number of works focusing on human body’s categorization. These categories depend on their morphological type, some of them dealing with the modeling of mattresses [6]. However, the available research that looks at sleep quality on different bedding systems remains very vague on the actual bed properties, using terms such as soft, firm, medium-firm, (un)comfortable, etc. without further specification. Also, the rise of several new bedding technologies has made it increasingly difficult for the consumer to select a proper sleep system [5]. Thus, there is a disconnection between material, ergonomics and interface interactions research and combining the knowledge in designing the mattress is currently missing. Bad quality sleep can cause both physiological and psychological illness including back pain, scoliosis and depression. People studied the sleep quality on different bedding system and figure out the design of the mattress makes lot of difference in improve the sleeping quality [3, 7]. A good sleep system should provide proper body support and avoid peak pressure [8]. Synthetic cellular structures are introduced in many application and area including high stiffness structures [9], energy absorption [10], thermal insulation [11] and bio-printing [12]. The material efficiency of the cellular structure can be enhanced by doing topology design of variable performance cellular structure. Ajdari [10] studied the functional graded cellular structures and its energy absorption performance. The results show that introducing the density gradient will significantly improve the performance. However, the performance can be stochastically distributed along the structure, so the study of the performance distribution is very important.
133
In this paper, a systematic approach is proposed to design a customized mattress with cellular structure considering the body load distribution to provide uniform supports. The methodology of designing variable stiffness mattress is shown as roadmap in Figure 1. An image analysis technique is applied to quantify the body load distribution in pixel-sized level. And voxelization is introduced to determine the cell parameters resulting controlled spatial stiffness following the body contour.
Fig. 1. Framework of design variable stiffness mattress.
Ruinan Xie et al. / Procedia Manufacturing 26 (2018) 132–139 Ruinan Xie, Chad Ulven, Bashir Khoda/ Procedia Manufacturing 00 (2018) 000–000
134
3
* s
2. Hexagonal Honeycomb Structure Honeycomb structure is the most commonly used closed cellular structure in both natural and synthetic domain. It has been selected as 3D printing infill pattern and core of sandwich structures due to the high material efficient. Many researchers have studied and proved that honeycomb structures obtain high strength under both in-plane and out-of-plane loads [13]. Honeycomb cell shapes including square cell, equilateral triangles, regular hexagonal and diamond, etc. This research will focus on regular hexagonal honeycomb which is a regular array of hexagonal prismatic nest together to fill a space. And its performance under out-of-plane (along longitudinal cell axes) load will be tested and analyzed. Here we consider Smooth-on Mold Star 15 Slow silicone which has a Young’s Modulus Es 0.3792MPa . This material has the property that matches commercially available mattress material. First, we determined the relationship between the cell parameter with the mechanical characteristics of the material. Then using this relationship, the variable stiffness is achieved in our design.
The parameters of hexagon are given below in Figure 2. The relative density of the regular hexagon,
* is evaluated which is a function of the edge s lengths, l and k , arbitrary cell wall angle and thickness t . By simplifying its geometry, the relationship between relative density and the parameters are derived neglecting the quadratic term [13]：
t l k l 2 s 2 cos k l sin
* s
Ө
k
W
t
Fig. 2. Hexagon parameters.
2 t * s 3l
(2)
The relationship can be further simplified (equation 2) when the cells are considered regular i.e. h l; 30 . In this case, two parameters will be needed to define a regular hexagon, the length, l (mm) and wall thickness, t (mm). 2.2. Sample Fabrication and Mechanical Test
2.1. Structure Characterization
*
l
(1)
Test specimens are designed with 3x3 hexagonal prismatic that has edge length of 20 mm, height of 45 mm. Four different thicknesses are considered as shown in the Table 1. The relative density is then calculated from the Equation 2 and listed in table 1 as well. Table 1. . Design of Experiment of Regular Hexagonal Honeycombs. Edge Thickness(t) Experiment Length(l) (mm) (mm) 1 20 2 2 20 3 3 4
20 20
4 5
Relative Surface Area Density (mm^2) 11.55% 17.32%
8.314E+03 8.314E+03
23.09% 28.87%
8.314E+03 8.314E+03
Specimens are made by casting process and the molds were 3D printed with Makerbot Z18 printer. The design of the mold is shown in Figure 3, where inner hexagons are printed separately from the base and the boundary for easy demold. Bolts and nuts are used to locate the hexagons in right positions.
4
t l h l 2 2 cos h l sin
Ruinan Xie et al. / Procedia Manufacturing 26 (2018) 132–139 Ruinan Xie, Chad Ulven, Bashir Khoda/ Procedia Manufacturing 00 (2018) 000–000
135
Mechanical testing of the specimens is done with Instron 5567 universal test machine. The compression load is applied at the rate of 50mm/min along z direction until compressed 50% of original height (22.5mm). The deformation example of a 5mm thickness specimen during the test are shown below in Figure 5.
2 t 3l
When the cells are regular( h l ; 30 );
2 t * s 3l Fig. 3. Specimen casting process: (a) the designed CAD model of mold, (b) mold printing with Makerbot z18, (c) pouring silicone with syringe into the mold, (d) demold the cast after curing for 4 hours.
Lubricant is applied on the inner surface of the boundary and outer surface of hexagons to smooth the demold process. Silicones are poured into the mold with syringe and no degassing needed for this low viscosity rubber. The silicone needs 4 hours to cure at room temperature before demolding. To better keep shape of the samples, all specimens are left overnight for curing.
Fig. 5. Compression test applied on silicone hexagonal structure (a) no load applied (b) applying load to the structure (c) 50% deformation happened to the structure.
The same testing protocol is applied to all the specimens successively with same machine setup to minimize the test-induced variation. And the results are shown below in Figure 6. The performances have larger variation when the relative density is lower but getting more stable when thickness increased.
2.3. Mechanical Test Honeycombs are stronger and stiffer under out-ofplane load where only axial stress applied to the walls. Changing the thickness of the wall will cause change in relative density and mechanical properties. A compression test is designed to determine the relationship between Young’s modulus and its relative density. The compression load is applied along Z direction as shown in Figure 4. Z
Y
Fig. 6. Compression test result of all specimens with different thickness, (a) t 2 , (b) t 3 , (c) t 4 and (d) t 5 (unit: mm).
X
Fig. 4. Compression load applied on hexagonal honeycombs along Z direction.
This may have caused by different failure mode behavior during the compression test. We observed that all the specimens are failed because of buckling, but when the thickness is relatively low ( t 2mm ), it buckled inward. And when thickness increased to 3mm, some of the walls start buckled outward. As the
Ruinan Xie et al. / Procedia Manufacturing 26 (2018) 132–139 Ruinan Xie, Chad Ulven, Bashir Khoda/ Procedia Manufacturing 00 (2018) 000–000
136
wall thickness keep increasing, only outward buckling is shown under the test. This observation tells that the failure mode has some relationship with the wall thickness, and the change of buckling direction happened when the wall thickness is around 2mm and 3mm.
5
Wall Relative Specimen Specimen Specimen Specimen Specimen Thickness Mean Density 1 2 3 4 5 (mm) 2 3 4 5
0.1155 0.1732 0.2309 0.2887
0.7949 2.7704 3.0706 4.1276
0.7782 2.2833 4.0623 4.3325
0.9501 2.1624 3.2689 4.1529
Fitted Line Plot
0.7756 3.5984 2.7510 4.5015
1.0505 2.3314 3.3108 5.6930
0.8699 2.6292 3.2927 4.5615
Stiffness per cell (N/mm)_1 = 9.36905 + 0.038968 / 'Relative Density' + ... 5
Stiffness (N/mm)
4
3
2
1 0.10
0.15
0.20
0.25
0.30
Relative Density
Fig. 8. Plot of the stiffness vs. relative density.
Fig. 7. Failure mode for different thickness, (a) 2mm, (b) 3mm, (c) 4mm, (d) 5mm.
After the load deflection curves are plotted, stiffness 𝐾𝐾′ of all the specimens are found by using Equation 4 where F is the applied load in Newton and ∆ℎ is the deformation under the compression load. A refers to the apparent area of the sample which is the area closed by the boundary. Apparent area is a function of the cell edge length as shown in Equation 3. h is the height of the hexagonal prismatic.
A
3 3 2 l 2
𝐾𝐾′ =
(3)
𝐹𝐹 ∆ℎ
(4)
The stiffness is actually the slope of the first stage deformation, the results are listed below in Table 2. Mean value of three specimens are calculated for each sample and used as the modulus for that thickness. The data points are plotted in a graph and a nonlinear pattern is observed. A non-linear regression model is then fitted as shown in Equation 5. Table 2. Single cell stiffness of all silicone hexagon specimens. Stiffness (N/mm)
𝐹𝐹
∆ℎ
= 9.36905 +
0.038968(√3 𝑙𝑙) 2𝑡𝑡
+ 4.07695 ln (
2𝑡𝑡
√3 𝑙𝑙
)
(5)
Equation 5 represents the relationship between the relative density and stiffness, this model will be used in Section 3 to predict the relative density with desired stiffness. 3. Variable Stiffness from Load Map In this section, a methodology is proposed to design the variable stiffness mattress with honeycomb structure, load distribution map will be used as input for image analysis to extract the body weight distribution information. Then the mattress will be voxelized to satisfy the stiffness that calculated from the weight and spine shape. Unit cells will then fitted to the voxels to create a variable stiffness mattress. 3.1. Image Data Extraction and Digitization A full body pressure distribution map gained from Tekscan’s Body Measurement System website [14] provides the 2D pressure data across the entire body as shown in Figure 9. The image is an array of pixels Px,y [ Px, y ] , where Px, y is the intensity value of the
pixel at location x, y . The pixel values vary spatially and can be mapped as a function of x and y , so the image will be represented as a single value
6
Ruinan Xie et al. / Procedia Manufacturing 26 (2018) 132–139 Ruinan Xie, Chad Ulven, Bashir Khoda/ Procedia Manufacturing 00 (2018) 000–000
function I : [1, , m] [1, , n] , where m and n are the pixel numbers along X and Y directions, respectively.
137
For a given cell length l ， the bounding box parameter l x and l y is calculated from the following Equation 7. l x 3l; l y 2l
(7)
All force values inside this outer hexagon is found as Fxk, y [ Fx ,...,Fx m1 ] [ Fy ,...,Fy n1 ] where m1 and Fig. 9. Load distribution map on mattress [14].
n1 are the number of pixels along x and y direction
The pixel intensity values of image I are then normalized and the body weight W is distributed accordingly to generate the applied forces Fx, y in
for k th cell/voxel respectively. The total force value 𝐹𝐹 𝑘𝑘 is calculated by summing each pixel
each pixel using following equation. This process results in a set of discrete iso-intensity value regions in the image which is assumed to possess approximately same physical properties.
combining the equations listed above, the value of t becomes a function of load and deformation at each voxel which is represented in Equation 5.
Fx , y
W m n
Px, y
Px, y
(6)
x 1 y 1
3.2. Voxelization The thickness (t ) of the hexagon structure is changed in this design to get the relative density which will result the desired stiffness. A hexagon prismatic is made with two wall as shown below in Figure 10. Two bounding box is needed to define the thickness of the hexagon which is the offset distance between them.
Fk
x m1 y n1
Fx, y and used as the load indicator. By x
y
By solving Equation 5, the thickness, the inner hexagon size can be determined. The voxel parameters lix and liy will be calculated from Equation 8.
li l
t
(8)
3
lix 3l t; l y 2l
2t 3
(9)
Figure 11 shows the voxelization method applied on the virtual mattress domain with parameters h 45mm, l 20mm， h 0.3mm .
Fig. 10. Voxel size parameter. Fig. 11. Voxelization of mattress.
Ruinan Xie et al. / Procedia Manufacturing 26 (2018) 132–139 Ruinan Xie, Chad Ulven, Bashir Khoda/ Procedia Manufacturing 00 (2018) 000–000
138
7
3.3. Fitting Unit cell Once the voxel is generated, hexagonal cell needs to be fitted in them using Equation (11). Figure 12 shows an example of fitting hexagons into the voxels. Figure 12(a) is the designed voxels where blue boxes are the outer box and blacks are the inner boxes. Hexagons are drawn using the parameters calculated from Equation 10. Filling the space between two hexagons creates the walls of the hexagonal honeycomb. Figure 13 is Designed mattress with fitted hexagons.
Fig. 14. Model of uniform hexagonal mattress. ∆ℎ𝑘𝑘,𝑦𝑦 =
9.36905 +
hk minhk , y
Fig. 12. Hexagon unit cell fitting into voxel, (a) an example of voxelization result, (b) hexagon outlines are drawn with the equation, (c) the real honeycomb structure with variation thickness.
𝑘𝑘 𝐹𝐹𝑥𝑥,𝑦𝑦
0.038968(√3 𝑙𝑙) 2𝑡𝑡 + 4.07695 ln ( ) 2𝑡𝑡 √3 𝑙𝑙
(11) (12)
The deformation profile in Figure 15 shows the max deformation along the vertical column of the hexagonal cell. The deformation of the designed mattress is then plotted (red curve) and compared with the deformation in the uniform mattress (blue curve) which is shown in Figure 15.
Fig. 15. Comparison of deformation between two designs. Fig. 13. Fitting variable thickness hexagons into voxels.
l
lx 3
;l
ly 2
(10)
4. Evaluation The comparison between the proposed designed mattresses with a uniform design is simulated here to evaluate the proposed design, with the deformation alignment constructed form body contour image. A uniform hexagonal mattress is modelled (shown in Figure 14) and the deformation is calculated using Equation (12) which is also shown in Figure 15. The material, cell height, and edge length is kept same as the proposed design which are h 200, l 20, t 2.
The plot shows that the proposed design will have less variation in deformation, which achieves the uniform support. On the other hand, the uniform hexagonal mattress shows significantly higher and wide range of deformation which could be uncomfortable and may increase the possibility of causing pressure ulcers. 5. Conclusion In this paper, design and manufacturing approaches of variable stiffness mattress with hexagonal honeycomb structure has been developed. A designed mattress has been evaluated by comparing to the existing mattress. In this study, an image analysis technique is used to extract weight distribution information. And the relationship
8
Ruinan Xie et al. / Procedia Manufacturing 26 (2018) 132–139 Ruinan Xie, Chad Ulven, Bashir Khoda/ Procedia Manufacturing 00 (2018) 000–000
between the cell parameters and performance are also given by designing, manufacturing and mechanical testing on samples. Voxelization is applied to determine the cell size and unit cells are then fitted into the voxels respectively. The design methodology is performed considering single sleeping posture. However, multiple postures will be considered in our future work. The methodology can be applied to design seat cushion, shoe sole, and other similar deformationdriven applications. It can also be widely used into aerospace applications since weight of the structure is reduced but the mechanical properties are maintained compare to solid objects. Also, the highlight of the methodology is to create controlled-performance based cellular structure which optimized the mechanical performance of the structure. In conclusion, a topology design of variable performance cellular structure is achieved to enhance the performance and material efficiency. This makes the topology optimization become an effective approach on enhance cellular structures behaviors. Acknowledgement The authors would like to thank financial supports provided by the National Science Foundation Grant # IIA-1355466 and by Research ND Grant#17-08-G191. We thank Comfort King LLC for providing support, specimen and information for this research. References 1. LI, Y.-q., et al., Mechanical Properties of Palm Fiber Mattress, in Advanced Material Science and Engineering (AMSE2016). 2016, WORLD SCIENTIFIC. p. 100-107. 2. DeVocht, J.W., et al., Biomechanical evaluation of four different mattresses. Applied Ergonomics, 2006. 37(3): p. 297304. 3. Park, S.J., et al. Evaulation of Mattress for the Koreans. in Proceedings of the Human Factors and Ergonomics Society Annual Meeting. 2001. SAGE Publications Sage CA: Los Angeles, CA. 4. Lee, H. and S. Park, Quantitative effects of mattress types (comfortable vs. uncomfortable) on sleep quality through polysomnography and skin temperature. International Journal of Industrial Ergonomics, 2006. 36(11): p. 943-949. 5. Verhaert, V., et al., Modeling human-bed interaction: the predictive value of anthropometric models in choosing the correct bed support Work, 2012. 41(1). 6. Palmero, C., et al., Automatic Sleep System Recommendation by Multi-modal RBG-Depth-Pressure Anthropometric Analysis. International Journal of Computer Vision, 2016: p. 1-16. 7. Hsu, H.-C. and R.-C. Lo, A new mattress development based on pressure sensors for body-contouring uniform support.
139
arXiv preprint arXiv:1308.2196, 2013. 8. Verhaert, V., Ergonomic Analysis of Integrated Bed Measurements: Towards Smart Sleep Systems (Ergonomische analyse van geïntegreerde bedmetingen: op weg naar slimme slaapsystemen). 2011. 9. Bauer, J., et al., High-strength cellular ceramic composites with 3D microarchitecture. Proceedings of the National Academy of Sciences, 2014. 111(7): p. 2453-2458. 10. Ajdari, A., H. Nayeb-Hashemi, and A. Vaziri, Dynamic crushing and energy absorption of regular, irregular and functionally graded cellular structures. International Journal of Solids and Structures, 2011. 48(3): p. 506-516. 11. Valdevit, L., et al., Optimal active cooling performance of metallic sandwich panels with prismatic cores. International Journal of Heat and Mass Transfer, 2006. 49(21): p. 38193830. 12. Ahsan, A.N., R. Xie, and B. Khoda, Direct Bio-printing with Heterogeneous Topology Design. Procedia Manufacturing, 2017. 10: p. 945-956. 13. Wang, A.-J. and D. McDowell, In-plane stiffness and yield strength of periodic metal honeycombs. Journal of engineering materials and technology, 2004. 126(2): p. 137-156. 14. Pressure Image. 06/05/2017]; Available from: https://www.tekscan.com/applications/pressure-imagingmattress-design.
ScienceDirect ScienceDirect
Procedia Manufacturing 00 (2018) 000–000 Available online atatwww.sciencedirect.com Available online www.sciencedirect.com Procedia Manufacturing 00 (2018) 000–000
ScienceDirect ScienceDirect
www.elsevier.com/locate/procedia www.elsevier.com/locate/procedia
Procedia Manufacturing 26 (2018) 132–139 Procedia Manufacturing 00 (2017) 000–000 www.elsevier.com/locate/procedia
46th SME North American Manufacturing Research Conference, NAMRC 46, Texas, USA 46th SME North American Manufacturing Research Conference, NAMRC 46, Texas, USA
Design and Manufacturing of Variable Stiffness Mattress Design and Manufacturing of Variable Stiffness Mattress
Manufacturing Engineering Society Conference 2017, MESIC Ruinan Xie, ChadInternational Ulven, Ph.D., Bashir Khoda, Ph.D.*2017, 28-30 June 2017, Vigo (Pontevedra), Spain Ruinan Xie, Chad Ulven, Ph.D., Bashir Khoda, Ph.D.* North Dakota State University, Fargo, 58104 USA North Dakota State University, Fargo, 58104 USA
Costing models for capacity optimization in Industry 4.0: Trade-off between used capacity and operational efficiency
* Corresponding author. Tel.: +1-7012318071; fax: +17012317195. * Corresponding Tel.: +1-7012318071; fax: +17012317195. E-mail address:author. [email protected] E-mail address: [email protected]
A. Santanaa, P. Afonsoa,*, A. Zaninb, R. Wernkeb
Abstract Abstract a University of Minho, 4800-058 Guimarães, Portugal b Sleep quality are found to be decreased in the past decades from several surveys. And researches conducted that uncomfortable Unochapecó, 89809-000 Chapecó, SC, Brazil Sleep quality areone found to be decreased in the causing past decades fromproblems. several surveys. Andpresents researches uncomfortable mattress can be of the important reasons sleeping This paper the conducted design andthat manufacturing of mattress be one of the important reasons causing presents design and manufacturing of variable can stiffness mattress with cellular structure to sleeping maintainproblems. uniform This body paper support. The the relation between the hexagonal variable stiffness mattress with cellular structure to maintain uniform support. relationtobetween the digitize hexagonal honeycomb thickness and stiffness is studied and tested. The author appliesbody image analysisThe technique extract and the honeycomb is studied and The author analysis and hexagon. digitize the Abstract information thickness from the and bodystiffness load distribution map.tested. Voxelization is applies used to image determine the technique thickness to of extract each unit A information from thethe body load distribution Voxelization is used istogiven determine of each under unit hexagon. A comparison between designed mattress andmap. current existing mattress basedthe on thickness their deformation same load. comparison between mattress current existing mattress isbe given on be theirincreasingly deformation under same toload. With thethe study of the the unit cell and voxelization technique, our designed mattress hasbased less variation on deformation compare the Under concept of designed "Industry 4.0", and production processes will pushed to interconnected, With themattress studybased of which theon unit voxelization mattress has less on deformation to the uniform indicates we have more control onour the designed deformation with this proposed information a cell realand time basis and,technique, necessarily, much more efficient. Invariation this methodology. context, capacity compare optimization uniform mattress indicates moremaximization, control on the deformation with thisfor proposed methodology. goes beyond thewhich traditional aimwe ofhave capacity contributing also organization’s profitability and value. © 2018 The Authors. Published by Elsevier B.V. Indeed, lean management continuous © 2018 The Authors. Publishedand by Elsevier B.V. improvement approaches suggest capacity optimization instead of © 2018 The under Authors. Published by Elsevier B.V. committee of NAMRI/SME. Peer-review responsibility of the scientific maximization. The study of capacity optimization and costing models is American an important research Research topic that deserves Peer-review under responsibility of the scientific committee of the 46th SME North Manufacturing Conference. Peer-review under responsibility of the scientific committee of NAMRI/SME.
contributions from both the practical and theoretical perspectives. This paper presents and discusses a mathematical Keywords: Cellular structure; Variable stiffness; Mattress design model forCellular capacity management based Mattress on different Keywords: structure; Variable stiffness; design costing models (ABC and TDABC). A generic model has been developed and it was used to analyze idle capacity and to design strategies towards the maximization of organization’s value. The trade-off capacity maximization vs operational efficiency highlighted andcompelling it is shown that capacity 1. Introduction which isisone of the most problems in the 1. Introduction which is one of the most compelling problems optimization might hide operational inefficiency. industrialized world. Furthermore, sleep isin the an © 2017 The Authors. Published B.V. industrialized world. Furthermore, sleepof is Humans spend one third by ofElsevier their lifetime in bed essential factor in the health and the quality life an of Peer-review under responsibility of committee Engineering Society International Conference spend one thirdwith of the their lifetime in fact, bed of the Manufacturing essential factor in the health quality lifethe of [1] Humans and directly interacting thescientific mattress. In an individual. Research studyand hasthe pointed outofthat 2017. [1] and directly interacting with the mattress. In fact, an individual. Research study has pointed out that the in industrialized western cultures everyone spends quality of a mattress is the most important factor in a in industrialized western cultures everyone spends quality of a mattress is the important in a more time sleeping in a bed than in any other single sleep environment [3]. Themost ergonomics of factor a mattress Keywords: Cost Models; ABC; TDABC; Capacity Management; Idle Capacity; Operational Efficiency more time sleeping in a bed than in any other single sleep environment [3]. The ergonomics of a mattress activity, during the course of everyday living [2]. An should also prevent back-pain, lumbago, and hence activity, during the course of everyday livingthe [2].body An should lumbago, and factors hence appropriate mattress may correctly support improvealso the prevent quality back-pain, of life. Three dominant appropriate mattress may correctly support the body improve the quality of life. Three dominant factors which will bring relaxation and quality sleep. are commonly considered in mattress design process: 1. Introduction which will back bringsupport relaxation and low-back quality sleep. are commonly considered in mattress design process: Insufficient can cause pain, Insufficient back support can cause low-back pain, The cost of idle capacity is a fundamental information for companies and their management of extreme importance in modern systems. In general, it isB.V. defined as unused capacity or production potential and can be measured 2351-9789 ©production 2018 The Authors. Published by Elsevier 2351-9789 2018responsibility The Authors. Published by Elsevier B.V.hours Peer-review of the scientific committee of NAMRI/SME. in several©under ways: tons of production, available of manufacturing, etc. The management of the idle capacity Peer-review underTel.: responsibility the761; scientific committee NAMRI/SME. * Paulo Afonso. +351 253 of 510 fax: +351 253 604of741 E-mail address: [email protected]
2351-9789 © 2017 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the scientific committee of the Manufacturing Engineering Society International Conference 2017. 2351-9789 © 2018 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the scientific committee of the 46th SME North American Manufacturing Research Conference. 10.1016/j.promfg.2018.07.016
2
Ruinan Xie et al. / Procedia Manufacturing 26 (2018) 132–139 Ruinan Xie, Chad Ulven, Bashir Khoda/ Procedia Manufacturing 00 (2018) 000–000
i) materials, ii) sleeping poster or ergonomics and iii) interaction interface between mattress and body. The quality of sleep is affected by a synergy of psychological, physiological, and physical conditions [4]. Various factors influence the interaction between the human body and the sleep system. Contributing factors include body dimensions, distribution of body weight, and stiffness of the sleep system across the mattress surface [5]. Most of the identified studies that have dealt with objective measurements were concerned with the healing of wounds or the prevention of bed sores for those who are bedridden [2]. Sleep ergonomics have recently become especially crucial and deals with the body posture and position during sleeping. The scientific literature includes a number of works focusing on human body’s categorization. These categories depend on their morphological type, some of them dealing with the modeling of mattresses [6]. However, the available research that looks at sleep quality on different bedding systems remains very vague on the actual bed properties, using terms such as soft, firm, medium-firm, (un)comfortable, etc. without further specification. Also, the rise of several new bedding technologies has made it increasingly difficult for the consumer to select a proper sleep system [5]. Thus, there is a disconnection between material, ergonomics and interface interactions research and combining the knowledge in designing the mattress is currently missing. Bad quality sleep can cause both physiological and psychological illness including back pain, scoliosis and depression. People studied the sleep quality on different bedding system and figure out the design of the mattress makes lot of difference in improve the sleeping quality [3, 7]. A good sleep system should provide proper body support and avoid peak pressure [8]. Synthetic cellular structures are introduced in many application and area including high stiffness structures [9], energy absorption [10], thermal insulation [11] and bio-printing [12]. The material efficiency of the cellular structure can be enhanced by doing topology design of variable performance cellular structure. Ajdari [10] studied the functional graded cellular structures and its energy absorption performance. The results show that introducing the density gradient will significantly improve the performance. However, the performance can be stochastically distributed along the structure, so the study of the performance distribution is very important.
133
In this paper, a systematic approach is proposed to design a customized mattress with cellular structure considering the body load distribution to provide uniform supports. The methodology of designing variable stiffness mattress is shown as roadmap in Figure 1. An image analysis technique is applied to quantify the body load distribution in pixel-sized level. And voxelization is introduced to determine the cell parameters resulting controlled spatial stiffness following the body contour.
Fig. 1. Framework of design variable stiffness mattress.
Ruinan Xie et al. / Procedia Manufacturing 26 (2018) 132–139 Ruinan Xie, Chad Ulven, Bashir Khoda/ Procedia Manufacturing 00 (2018) 000–000
134
3
* s
2. Hexagonal Honeycomb Structure Honeycomb structure is the most commonly used closed cellular structure in both natural and synthetic domain. It has been selected as 3D printing infill pattern and core of sandwich structures due to the high material efficient. Many researchers have studied and proved that honeycomb structures obtain high strength under both in-plane and out-of-plane loads [13]. Honeycomb cell shapes including square cell, equilateral triangles, regular hexagonal and diamond, etc. This research will focus on regular hexagonal honeycomb which is a regular array of hexagonal prismatic nest together to fill a space. And its performance under out-of-plane (along longitudinal cell axes) load will be tested and analyzed. Here we consider Smooth-on Mold Star 15 Slow silicone which has a Young’s Modulus Es 0.3792MPa . This material has the property that matches commercially available mattress material. First, we determined the relationship between the cell parameter with the mechanical characteristics of the material. Then using this relationship, the variable stiffness is achieved in our design.
The parameters of hexagon are given below in Figure 2. The relative density of the regular hexagon,
* is evaluated which is a function of the edge s lengths, l and k , arbitrary cell wall angle and thickness t . By simplifying its geometry, the relationship between relative density and the parameters are derived neglecting the quadratic term [13]：
t l k l 2 s 2 cos k l sin
* s
Ө
k
W
t
Fig. 2. Hexagon parameters.
2 t * s 3l
(2)
The relationship can be further simplified (equation 2) when the cells are considered regular i.e. h l; 30 . In this case, two parameters will be needed to define a regular hexagon, the length, l (mm) and wall thickness, t (mm). 2.2. Sample Fabrication and Mechanical Test
2.1. Structure Characterization
*
l
(1)
Test specimens are designed with 3x3 hexagonal prismatic that has edge length of 20 mm, height of 45 mm. Four different thicknesses are considered as shown in the Table 1. The relative density is then calculated from the Equation 2 and listed in table 1 as well. Table 1. . Design of Experiment of Regular Hexagonal Honeycombs. Edge Thickness(t) Experiment Length(l) (mm) (mm) 1 20 2 2 20 3 3 4
20 20
4 5
Relative Surface Area Density (mm^2) 11.55% 17.32%
8.314E+03 8.314E+03
23.09% 28.87%
8.314E+03 8.314E+03
Specimens are made by casting process and the molds were 3D printed with Makerbot Z18 printer. The design of the mold is shown in Figure 3, where inner hexagons are printed separately from the base and the boundary for easy demold. Bolts and nuts are used to locate the hexagons in right positions.
4
t l h l 2 2 cos h l sin
Ruinan Xie et al. / Procedia Manufacturing 26 (2018) 132–139 Ruinan Xie, Chad Ulven, Bashir Khoda/ Procedia Manufacturing 00 (2018) 000–000
135
Mechanical testing of the specimens is done with Instron 5567 universal test machine. The compression load is applied at the rate of 50mm/min along z direction until compressed 50% of original height (22.5mm). The deformation example of a 5mm thickness specimen during the test are shown below in Figure 5.
2 t 3l
When the cells are regular( h l ; 30 );
2 t * s 3l Fig. 3. Specimen casting process: (a) the designed CAD model of mold, (b) mold printing with Makerbot z18, (c) pouring silicone with syringe into the mold, (d) demold the cast after curing for 4 hours.
Lubricant is applied on the inner surface of the boundary and outer surface of hexagons to smooth the demold process. Silicones are poured into the mold with syringe and no degassing needed for this low viscosity rubber. The silicone needs 4 hours to cure at room temperature before demolding. To better keep shape of the samples, all specimens are left overnight for curing.
Fig. 5. Compression test applied on silicone hexagonal structure (a) no load applied (b) applying load to the structure (c) 50% deformation happened to the structure.
The same testing protocol is applied to all the specimens successively with same machine setup to minimize the test-induced variation. And the results are shown below in Figure 6. The performances have larger variation when the relative density is lower but getting more stable when thickness increased.
2.3. Mechanical Test Honeycombs are stronger and stiffer under out-ofplane load where only axial stress applied to the walls. Changing the thickness of the wall will cause change in relative density and mechanical properties. A compression test is designed to determine the relationship between Young’s modulus and its relative density. The compression load is applied along Z direction as shown in Figure 4. Z
Y
Fig. 6. Compression test result of all specimens with different thickness, (a) t 2 , (b) t 3 , (c) t 4 and (d) t 5 (unit: mm).
X
Fig. 4. Compression load applied on hexagonal honeycombs along Z direction.
This may have caused by different failure mode behavior during the compression test. We observed that all the specimens are failed because of buckling, but when the thickness is relatively low ( t 2mm ), it buckled inward. And when thickness increased to 3mm, some of the walls start buckled outward. As the
Ruinan Xie et al. / Procedia Manufacturing 26 (2018) 132–139 Ruinan Xie, Chad Ulven, Bashir Khoda/ Procedia Manufacturing 00 (2018) 000–000
136
wall thickness keep increasing, only outward buckling is shown under the test. This observation tells that the failure mode has some relationship with the wall thickness, and the change of buckling direction happened when the wall thickness is around 2mm and 3mm.
5
Wall Relative Specimen Specimen Specimen Specimen Specimen Thickness Mean Density 1 2 3 4 5 (mm) 2 3 4 5
0.1155 0.1732 0.2309 0.2887
0.7949 2.7704 3.0706 4.1276
0.7782 2.2833 4.0623 4.3325
0.9501 2.1624 3.2689 4.1529
Fitted Line Plot
0.7756 3.5984 2.7510 4.5015
1.0505 2.3314 3.3108 5.6930
0.8699 2.6292 3.2927 4.5615
Stiffness per cell (N/mm)_1 = 9.36905 + 0.038968 / 'Relative Density' + ... 5
Stiffness (N/mm)
4
3
2
1 0.10
0.15
0.20
0.25
0.30
Relative Density
Fig. 8. Plot of the stiffness vs. relative density.
Fig. 7. Failure mode for different thickness, (a) 2mm, (b) 3mm, (c) 4mm, (d) 5mm.
After the load deflection curves are plotted, stiffness 𝐾𝐾′ of all the specimens are found by using Equation 4 where F is the applied load in Newton and ∆ℎ is the deformation under the compression load. A refers to the apparent area of the sample which is the area closed by the boundary. Apparent area is a function of the cell edge length as shown in Equation 3. h is the height of the hexagonal prismatic.
A
3 3 2 l 2
𝐾𝐾′ =
(3)
𝐹𝐹 ∆ℎ
(4)
The stiffness is actually the slope of the first stage deformation, the results are listed below in Table 2. Mean value of three specimens are calculated for each sample and used as the modulus for that thickness. The data points are plotted in a graph and a nonlinear pattern is observed. A non-linear regression model is then fitted as shown in Equation 5. Table 2. Single cell stiffness of all silicone hexagon specimens. Stiffness (N/mm)
𝐹𝐹
∆ℎ
= 9.36905 +
0.038968(√3 𝑙𝑙) 2𝑡𝑡
+ 4.07695 ln (
2𝑡𝑡
√3 𝑙𝑙
)
(5)
Equation 5 represents the relationship between the relative density and stiffness, this model will be used in Section 3 to predict the relative density with desired stiffness. 3. Variable Stiffness from Load Map In this section, a methodology is proposed to design the variable stiffness mattress with honeycomb structure, load distribution map will be used as input for image analysis to extract the body weight distribution information. Then the mattress will be voxelized to satisfy the stiffness that calculated from the weight and spine shape. Unit cells will then fitted to the voxels to create a variable stiffness mattress. 3.1. Image Data Extraction and Digitization A full body pressure distribution map gained from Tekscan’s Body Measurement System website [14] provides the 2D pressure data across the entire body as shown in Figure 9. The image is an array of pixels Px,y [ Px, y ] , where Px, y is the intensity value of the
pixel at location x, y . The pixel values vary spatially and can be mapped as a function of x and y , so the image will be represented as a single value
6
Ruinan Xie et al. / Procedia Manufacturing 26 (2018) 132–139 Ruinan Xie, Chad Ulven, Bashir Khoda/ Procedia Manufacturing 00 (2018) 000–000
function I : [1, , m] [1, , n] , where m and n are the pixel numbers along X and Y directions, respectively.
137
For a given cell length l ， the bounding box parameter l x and l y is calculated from the following Equation 7. l x 3l; l y 2l
(7)
All force values inside this outer hexagon is found as Fxk, y [ Fx ,...,Fx m1 ] [ Fy ,...,Fy n1 ] where m1 and Fig. 9. Load distribution map on mattress [14].
n1 are the number of pixels along x and y direction
The pixel intensity values of image I are then normalized and the body weight W is distributed accordingly to generate the applied forces Fx, y in
for k th cell/voxel respectively. The total force value 𝐹𝐹 𝑘𝑘 is calculated by summing each pixel
each pixel using following equation. This process results in a set of discrete iso-intensity value regions in the image which is assumed to possess approximately same physical properties.
combining the equations listed above, the value of t becomes a function of load and deformation at each voxel which is represented in Equation 5.
Fx , y
W m n
Px, y
Px, y
(6)
x 1 y 1
3.2. Voxelization The thickness (t ) of the hexagon structure is changed in this design to get the relative density which will result the desired stiffness. A hexagon prismatic is made with two wall as shown below in Figure 10. Two bounding box is needed to define the thickness of the hexagon which is the offset distance between them.
Fk
x m1 y n1
Fx, y and used as the load indicator. By x
y
By solving Equation 5, the thickness, the inner hexagon size can be determined. The voxel parameters lix and liy will be calculated from Equation 8.
li l
t
(8)
3
lix 3l t; l y 2l
2t 3
(9)
Figure 11 shows the voxelization method applied on the virtual mattress domain with parameters h 45mm, l 20mm， h 0.3mm .
Fig. 10. Voxel size parameter. Fig. 11. Voxelization of mattress.
Ruinan Xie et al. / Procedia Manufacturing 26 (2018) 132–139 Ruinan Xie, Chad Ulven, Bashir Khoda/ Procedia Manufacturing 00 (2018) 000–000
138
7
3.3. Fitting Unit cell Once the voxel is generated, hexagonal cell needs to be fitted in them using Equation (11). Figure 12 shows an example of fitting hexagons into the voxels. Figure 12(a) is the designed voxels where blue boxes are the outer box and blacks are the inner boxes. Hexagons are drawn using the parameters calculated from Equation 10. Filling the space between two hexagons creates the walls of the hexagonal honeycomb. Figure 13 is Designed mattress with fitted hexagons.
Fig. 14. Model of uniform hexagonal mattress. ∆ℎ𝑘𝑘,𝑦𝑦 =
9.36905 +
hk minhk , y
Fig. 12. Hexagon unit cell fitting into voxel, (a) an example of voxelization result, (b) hexagon outlines are drawn with the equation, (c) the real honeycomb structure with variation thickness.
𝑘𝑘 𝐹𝐹𝑥𝑥,𝑦𝑦
0.038968(√3 𝑙𝑙) 2𝑡𝑡 + 4.07695 ln ( ) 2𝑡𝑡 √3 𝑙𝑙
(11) (12)
The deformation profile in Figure 15 shows the max deformation along the vertical column of the hexagonal cell. The deformation of the designed mattress is then plotted (red curve) and compared with the deformation in the uniform mattress (blue curve) which is shown in Figure 15.
Fig. 15. Comparison of deformation between two designs. Fig. 13. Fitting variable thickness hexagons into voxels.
l
lx 3
;l
ly 2
(10)
4. Evaluation The comparison between the proposed designed mattresses with a uniform design is simulated here to evaluate the proposed design, with the deformation alignment constructed form body contour image. A uniform hexagonal mattress is modelled (shown in Figure 14) and the deformation is calculated using Equation (12) which is also shown in Figure 15. The material, cell height, and edge length is kept same as the proposed design which are h 200, l 20, t 2.
The plot shows that the proposed design will have less variation in deformation, which achieves the uniform support. On the other hand, the uniform hexagonal mattress shows significantly higher and wide range of deformation which could be uncomfortable and may increase the possibility of causing pressure ulcers. 5. Conclusion In this paper, design and manufacturing approaches of variable stiffness mattress with hexagonal honeycomb structure has been developed. A designed mattress has been evaluated by comparing to the existing mattress. In this study, an image analysis technique is used to extract weight distribution information. And the relationship
8
Ruinan Xie et al. / Procedia Manufacturing 26 (2018) 132–139 Ruinan Xie, Chad Ulven, Bashir Khoda/ Procedia Manufacturing 00 (2018) 000–000
between the cell parameters and performance are also given by designing, manufacturing and mechanical testing on samples. Voxelization is applied to determine the cell size and unit cells are then fitted into the voxels respectively. The design methodology is performed considering single sleeping posture. However, multiple postures will be considered in our future work. The methodology can be applied to design seat cushion, shoe sole, and other similar deformationdriven applications. It can also be widely used into aerospace applications since weight of the structure is reduced but the mechanical properties are maintained compare to solid objects. Also, the highlight of the methodology is to create controlled-performance based cellular structure which optimized the mechanical performance of the structure. In conclusion, a topology design of variable performance cellular structure is achieved to enhance the performance and material efficiency. This makes the topology optimization become an effective approach on enhance cellular structures behaviors. Acknowledgement The authors would like to thank financial supports provided by the National Science Foundation Grant # IIA-1355466 and by Research ND Grant#17-08-G191. We thank Comfort King LLC for providing support, specimen and information for this research. References 1. LI, Y.-q., et al., Mechanical Properties of Palm Fiber Mattress, in Advanced Material Science and Engineering (AMSE2016). 2016, WORLD SCIENTIFIC. p. 100-107. 2. DeVocht, J.W., et al., Biomechanical evaluation of four different mattresses. Applied Ergonomics, 2006. 37(3): p. 297304. 3. Park, S.J., et al. Evaulation of Mattress for the Koreans. in Proceedings of the Human Factors and Ergonomics Society Annual Meeting. 2001. SAGE Publications Sage CA: Los Angeles, CA. 4. Lee, H. and S. Park, Quantitative effects of mattress types (comfortable vs. uncomfortable) on sleep quality through polysomnography and skin temperature. International Journal of Industrial Ergonomics, 2006. 36(11): p. 943-949. 5. Verhaert, V., et al., Modeling human-bed interaction: the predictive value of anthropometric models in choosing the correct bed support Work, 2012. 41(1). 6. Palmero, C., et al., Automatic Sleep System Recommendation by Multi-modal RBG-Depth-Pressure Anthropometric Analysis. International Journal of Computer Vision, 2016: p. 1-16. 7. Hsu, H.-C. and R.-C. Lo, A new mattress development based on pressure sensors for body-contouring uniform support.
139
arXiv preprint arXiv:1308.2196, 2013. 8. Verhaert, V., Ergonomic Analysis of Integrated Bed Measurements: Towards Smart Sleep Systems (Ergonomische analyse van geïntegreerde bedmetingen: op weg naar slimme slaapsystemen). 2011. 9. Bauer, J., et al., High-strength cellular ceramic composites with 3D microarchitecture. Proceedings of the National Academy of Sciences, 2014. 111(7): p. 2453-2458. 10. Ajdari, A., H. Nayeb-Hashemi, and A. Vaziri, Dynamic crushing and energy absorption of regular, irregular and functionally graded cellular structures. International Journal of Solids and Structures, 2011. 48(3): p. 506-516. 11. Valdevit, L., et al., Optimal active cooling performance of metallic sandwich panels with prismatic cores. International Journal of Heat and Mass Transfer, 2006. 49(21): p. 38193830. 12. Ahsan, A.N., R. Xie, and B. Khoda, Direct Bio-printing with Heterogeneous Topology Design. Procedia Manufacturing, 2017. 10: p. 945-956. 13. Wang, A.-J. and D. McDowell, In-plane stiffness and yield strength of periodic metal honeycombs. Journal of engineering materials and technology, 2004. 126(2): p. 137-156. 14. Pressure Image. 06/05/2017]; Available from: https://www.tekscan.com/applications/pressure-imagingmattress-design.