Material Selection of an Elastomer Capable of Absorbing Vibrations Actuated by a 4D Movie Theater
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Abstract
The objective was to investigate possible vibration isolator solutions for a 4D entertainment theater. The paper focused on resolving a vibration leakage issue experienced by customers of Company A which manufactures tactile motion actuators for 4D theater entertainment purposes. The investigation started by utilizing Cambridge Engineering Selector software to determine the value of the mechanical loss factor for given materials. Elastomers had the best mechanical loss coefficient, specifically polyurethanes. While considering the specifications provided by Company A, certain parameters such as nominal load withstanding and prices were considered. After investigating the materials thoroughly, Sorbothane showed the best performance along with suitable prices. The vibrational system investigated resulted in a frequency ratio of 6, and a transmissibility of 2.86% at normal conditions, which indicates that the material selected was suitable. Sorbothane material at shore 00 and durometer 50 showed its capability to withstand maximum nominal loading at 635 kg (1400 lbs). This was 57% higher than the targeted loading. The mechanical loss factor was 0.52 at 50Hz excitation frequency, which was high enough to dissipate excessive vibrations.
Keywords
Ashby’s charts Polyurethanes Mechanical loss coefficient TransmissibilityIntroduction
The objective of this paper was to investigate possible vibration isolator solutions for a 4D entertainment theater. The approach was to conduct a material selection search within the elastomers family to resolve a vibration leakage issue claimed by customers of Company A. This company manufactures a vibratory system that actuates vibrations transmitted from an amplifier in order to provide a 4D experience while watching movies. The device manufactured by Company A operates as a vertical tactile motion actuator that transforms electrical signals into mechanical vibration motion.
Specification list by Company A for square pad
Properties  SI units  Imperial units 

Resonant frequency  20–80 Hz  20–80 Hz 
Geometry  12.7 × 12.7(+5.1–0) cm  5″ × 5″(+2″–0″) 
Thickness  0.254–1.27 cm  0.1–0.5 inches 
Nominal load for pad  1779 N  400 lbs 
Maximum load for pad  3559 N  800 lbs 
Maximum price  $15.00 each  $15.00 each 
Specification list by Company A for circular rubber feet
Properties  SI units  Imperial units 

Resonant frequency  20–80 Hz  20–80 Hz 
Geometry (diameter)  5.1–10.2 cm  2–4″ 
Thickness  0.254–1.27 cm  0.1–0.5 inches 
Nominal load for pad  445 N  100 lbs 
Maximum load for pad  890 N  200 lbs 
Maximum price (minimum order quantity 1000 pcs)  $5.00 each  $5.00 each 
Background
The main idea behind this study was to select a material that is high in damping. Highly damped materials have the capability to absorb vibrational energy and damp it thoroughly. The best known vibration isolation materials are elastomers. Those materials have a significant mechanical loss factor coefficient, η, and yet have the least Young’s modulus values [1].
Materials and Methods
Various elastomer prices and mechanical properties [2]
Material  Price (USD/lb; USD/Kg)  Young’s modulus (psi; Kpa)  Mechanical loss coefficient 

Polyurethane  (2.82–3.76 USD/lb) (6.2–8.3 USD/Kg)  (2.9–7.25 psi) (19.99–49.98 Kpa)  0.5–1.0 
Polypropylene  (0.898–0.988 USD/lb) (1.979–2.178 USD/kg)  (43.5–72.5 psi) (299.92–499.87 Kpa)  0.2–0.5 
Butyl/halobutyl rubber  (1.71–1.88 USD/lb) (3.769–4.144 USD/kg)  (102–218 psi) (703.27–1503.06 Kpa)  0.5–0.9 
Melamine  (4.7–6.58 USD/lb) (10.36–14.506 USD/kg)  (14.5–29.0 psi) (99.97–199.95 kPa)  0.3–0.5 
Materials selected based on price and mechanical loss coefficient from CES [2]
Material  Price (USD/lb)  Young’s modulus (psi; Kpa)  Mechanical loss coefficient 

Polyurethane filter foam (open cell, 0.019)  (4.7–7.52 USD/lb) (10.36–16.58 USD/Kg)  (6.38–7.52 psi) (43.99–51.84 Kpa)  0.5–1 
Polyurethane foam (elastomeric, open cell, 0.065)  (2.82–3.76 USD/lb) (6.17–8.29 USD/Kg)  (2.9–7.25 psi) (19.99–49.98 Kpa)  0.5–1 
Polyurethane foam (elastomeric, open cell, 0.028)  (2.82–3.76 USD/lb) (6.17–8.29 USD/Kg)  (2.03–4.35 psi) (13.99–29.99 kPa)  0.5–1 
Polyurethane foam (elastomeric, open cell, 0.024)  (2.82–3.76 USD/lb) (6.17–8.29 USD/Kg)  (1.45–2.9 psi) (9.99–19.99 kPa)  0.5–1 
The polyurethanes shown in Table 4 illustrate the best possible solutions for the selection. An initial selection has been made on the polyurethane foam (elastomeric, open cell, 0.024) based on its relatively low Young’s modulus and low cost compared to other polyurethanes shown in Table 4. Hence, the 0.024 in the polyurethane name means the relative density value of the material. Once polyurethane foam (elastomeric, open cell, 0.024) was selected, the selection was suggested to Company A to find the raw material in the market, to create a mold design and to find a supplier. However, Company A was unable to find a supplier for the raw materials as well as a mold design creation. Therefore, Company A requested to research other possible sources besides Ashby’s charts in order to find a supplier willing to provide a rubber molded by their unique design. A research online has been conducted to find a rubber that is specifically suitable for vibration isolation applications. The research resulted in finding out that there was a modified polyurethane composition owned by Sorbothane Company, which carries the same name, but shows a better performance than unmodified polyurethane in controlling mechanical vibrations and is suitable for vibration damping operations. Sorbothane is a viscoelastic polymer (polyurethane) that has low transmissibility verifying its damping superiority over other elastomers [3].
Results
Sorbothane material properties [3]
Durometer  Shore 30  Shore 50  Shore 70 

Tensile strength at break  (110 psi) (758 Kpa)  (172 psi) (1186 Kpa)  (173 psi) (1193 Kpa) 
Elongation at break  645%  653%  395% 
Tear strength  (16 lb/in) (286 kg/m)  (20 lb/in) (357 kg/m)  (31 lb/in) (554 kg/m) 
Bulk modulus  (4.71 Gpa) (683 Kpsi)  (3.84 Gpa) (557 Kpsi)  (4.14 Gpa) (601 Kpsi) 
Poisson’s ratio  0.4066  0.4856  0.4947 
Density  (81.91 lb/ft^{3}) (1312 kg/m^{3})  (81.78 lb/ft^{3}) (1310 kg/m^{3})  (82.28 lb/ft^{3}) (1318 kg/m^{3}) 
Mechanical loss coefficient (tan delta) for Sorbothane [3]
Mechanical loss coefficient  Durometer (shore 00)  

30  50  70  
Mechanical loss coefficient at 5Hz excitation  0.58  0.4  0.2 
Mechanical loss coefficient at 15Hz excitation  0.64  0.46  0.28 
Mechanical loss coefficient at 30Hz excitation  0.68  0.5  0.33 
Mechanical loss coefficient at 50Hz excitation  0.69  0.52  0.36 
Data analysis
Natural frequency (Hz)  50 
Interference frequency (Hz)  300 
Transmissibility  2.86% 
Frequency ratio  6 
Shape  Dimensions (inches; cm)  Quantity  Durometer shore 00  Price (USD)  Total price (USD) 

Hemisphere  (1 × 1 × 0.5 inches) (2.54 × 2.54 × 1.27 cm)  8  50  1.87  14.99 
Circular  (2.2 × 2.2 × 2.0 inches) (5.59 × 5.59 × 5.1 cm)  8  50  2.49  19.99 
Square  (5 × 5 × 0.5 inches) (12.7 × 12.7 × 1.27 cm)  2  50  12.245  24.49 
Small square pad  (0.5 × 0.5 × 0.2 inches) (1.27 × 1.27 × 0.51 cm)  36  50  0.6375  22.95 
Shape  Dimensions (inches; cm)  Durometer shore 00  Load (lbs; Kg) 

Square  (5 × 5 × 0.5 inches) (12.7 × 12.7 × 1.27 cm)  30  (900–1200 lbs) (408–544 kg) 
Square  5 × 5 × 0.5 inches (12.7 × 12.7 × 1.27 cm)  50  (1200–2400 lbs) (544–1089 kg) 
Square  (5 × 5 × 0.5 inches) (12.7 × 12.7 × 1.27 cm)  70  (2400–4800 lbs) (1089–2177 kg) 
Small square pad  (0.5 × 0.5 × 0.2 inches) (1.27 × 1.27 × 0.51 cm)  30  (0.7–1.5 lbs) (0.31–0.68 kg) 
Small square pad  (0.5 × 0.5 × 0.2 inches) (1.27 × 1.27 × 0.51 cm)  50  (1.4–3 lbs) (0.65–1.36 kg) 
Small square pad  (0.5 × 0.5 × 0.2 inches) (1.27 × 1.27 × 0.51 cm)  70  (2.2–5.5 lbs) (1–2.5 kg) 
Discussion
Based on the results found, the selected polyurethane rubbers from Ashby’s charts met the criteria of selection by evaluating their mechanical loss coefficient and price initially. Yet, the best possible solution was to consider far more factors than the material properties themselves. Company A is aiming to find a supplier that can supply rubber material in an offshelf product or a unique mold designed by Company A. In addition, the company is aiming to establish a professional contract with the supplier for future business. Sorbothane as a vibration isolation solution company has a unique composition polyurethane rubber that is made specifically for vibration isolation tasks. Also, Sorbothane has a stock rubber pad that matches the exact dimensions given by the specification lists with ability to withstand excessive nominal loadings ranging between 900 and 1200 lbs (408–544 kg) for shore 00 durometer 30 and 1200–2400 lbs (544–1089 kg) for shore 00 durometer 50 [10]. Moreover, Sorbothane has circular rubber feet shape that has a similar performance and price of $2.5 for each. The mechanical loss coefficient and price were the most valuable parameters in the study. Sorbothane had a relatively high mechanical loss coefficient. The transmissibility analyzed for the viboratory system showed that the rubber lied under the isolation area having 2.86% transmissibility and a frequency ratio of 6 at occasional loadings. Also, the price if ordered by minimum order quantity is managed to be compromised if ordered in large quantities.
Summary

Material selection for a suitable vibration isolation application was found to be an elastomer.

Ashby’s charts were utilized in searching for elastomer based on three main parameters: mechanical loss coefficient, Young’s modulus and price.

Transmissibility of the vibrational system is calculated to be 2.86%, whereas the frequency ratio was determined to be 6, yielding a rubber material that lies under isolation area.

Sorbothane is selected based on its rapid performance in controlling shock and vibration compared to other elastomers.

For pad selection, Sorbothane with shore 00 durometer 50 was available at Sorbothane with dimensions matching the specification list of 0.127 × 0.127 m (5″ × 5″) and 0.0127 m (0.5″) thickness for a price of $12 for a singular pad; total savings are 19%.

For circular rubber feet selection, Sorbothane offers them with shore 00 durometer 50 with a price of $2.50 for each, saving up to 50% for specification list maximum price.
References
 1.M. Ashby, Materials Selection in Mechanical Design, 4th edn. (ButterworthHeinemann, Burlington, MA, 2011)Google Scholar
 2.Granta Material Intelligence. Cambridge Engineering Selector (CES EduPack). Cambridge, UK. Retrieved on 2015 (2015) http://www.grantadesign.com
 3.Sorbothane. Data sheet 101, Material Properties of Sorbothane, Retrieved on January 27, 2015. (2015) http://www.sorbothane.com/Data/Sites/31/pdfs/datasheets/101sorbothanematerialproperties.pdf
 4.Durometer shore hardness scale, SmoothOn Make it Now: Retrieved on 2015. (2015) http://www.smoothon.com/DocumentsDuromete/c1351_1370/index.html
 5.Sorbothane. Data sheet 102. Performance Curves. (2015) http://www.sorbothane.com/Data/Sites/31/pdfs/datasheets/102Sorbothaneperformancecurves.pdf
 6.Isolate It: Sorbothane Vibration Isolation Square Pad 50 Duro (.50″ Thick 5″ × 5″) 2Pack, Amazon, Retrieved on December 3, 2015. (2015) http://www.amazon.com/IsolateSorbothaneVibrationIsolationSquare/dp/B0042U92TE/ref=sr_1_4?ie=UTF8&qid=1449864991&sr=84&keywords=sorbothane
 7.Isolate It: Sorbothane Vibration Isolation Circular Pad 50 Duro (.25″ Thick 2.25″ Dia.)  8 Pack, Amazon, Retrieved on December 3, 2015. (2015) http://www.amazon.com/IsolateSorbothaneVibrationIsolationCircular/dp/B0042U8P9C/ref=sr_1_2?ie=UTF8&qid=1449864991&sr=82&keywords=sorbothane
 8.Sorbothane Hemisphere, IsolateIt: Material Property Data, Retrieved on December 3, 2015. (2015) http://www.isolateit.com/hemispheres/sorbothane.html
 9.Sorbothane Sheets & Pads, (0.5″ × 0.5″), IsolateIt: Material Property Data, Retrieved on December 3, 2015. (2015) http://www.isolateit.com/vibrationisolatingsheetspads16/050050soundvibrationisolatingmaterila.html
 10.Sorbothane, Isolation Pads, Sorbothane, Material Property Data, Retrieved on December 3, 2015. (2015) http://www.sorbothane.com/Data/Sites/31/pdfs/productguides/sorbothanespgisolationpads.pdf