Modeling rubber products- "quasi-static" finite element analyses and validation testing. (Tech Service).

A previous article (September 2002) described materials characterization for "quasi-static" rubber FEA. Tests like uniaxial tension and compression, planar and equi-biaxial tension and volumetric compression were detailed for prescribed contact conditions. Further testing and numerical simulation makes for this second article, in developing an under-the-hood sealing application. The article also helps interpret computer predictions for engineering design purposes. In particular, minimum and maximum material conditions (LMC and MMC) are defined for the case study. The former addresses sealing over of the assembly disclosed under light compression, which requires experimental establishment of minimum pressure to seal. Maximum material conditions relates to material strength, i.e., failure stresses or strains under deviatoric modes of deformation, in a true quantities meaning.

Introduction

To date, many engineered products are still developed through trial and error. Prototypes are built for testing. The results are then used to alter designs, as new prototypes are further tested until a satisfactory outcome is reached. This sequential approach delays the time to bring goods to market. Moreover, any analysis after prototyping tunas out to be highly expensive, as often times calculations change locus from optimizing products to understanding failure of prototypes. In the end, the limited integration of CAE leads to inefficiency and a lack of design creativity.

A modern product development approach integrates materials testing to CAD, CAM and CAE. Still, products need to go through "what if?" scenarios. However, these operations take place in the "virtual world": They are computer generated, through a technology referred to as finite element analysis or FEA. Design through FEA has helped large organizations improve the performance and quality of their finished products. It has also helped them reduce the timetable to bring ideas to the market, while making appropriate choices of materials. By and large, PEA minimizes weights, specifies the structural integrity of goods before prototyping and reduces overall costs of development and production.

However, with rubber components FEA is fully nonlinear. Rubber deforms significantly under load or straining. Its reaction to deformation is nonlinear, and it is often used in contact. The analysis reaches a higher level of difficulty when dealing with many materials of special constitutive equations, and several contact bodies, some of which are rigid, others deforming. Defining friction adds further complications to assembling components, besides pinpointing leakage, interacting fluids with structures and establishing an onset to failure.

Design of rear retainer for under-the-hood

A push in Detroit to produce parts lighter, faster and at a lower cost has somewhat created a migration from conventional materials to polymer-based composites, even under-the-hood. However, metal to plastic conversion requires a far better understanding of mechanical, chemical and rheological properties of resins. Besides strength and modulus, parameters such as creep, fatigue and degradation in the working environments are crucial. Thermal and mechanical compatibility with metallic components, like inserts at bolt holes (ultrasonically welded in post-molding operations or placed in molds prior to injecting resins), is also necessary.

Interestingly, designing plastic parts for interference calls for least and maximum material conditions between rubber and plastic. While interference ensures sealability in the long run, over-compressing a gasket promotes viscoelastic effects (stress relaxation and creep), and generates high reaction of rubber on plastic housings. Hence, plastic parts performance is best left to FEA. Least material conditions analysis defines sealability, for which leak testing and time effects are important. Adversely, MMC analysis defines material strength and assembly requirements. Testing aged robber under deviatoric modes of deformation is important. Equally important is the testing of plastics to failure under true stress-strain conditions, allowing the establishment of material strength. Flow simulation ensures that no stress concentration superposes weak material areas. Friction testing permits the quantification of assembly force requirements.

Ford Motor selected WIDL to assess the feasibility to convert a heavily machined aluminum rear retainer to epoxy vinyl ester composite (figure 1). Molding tolerances led to disagreements between plastic and rubber parts suppliers. A program of laboratory tests and computer analyses was thus set at a neutral/arbitral company.

[FIGURE 1 OMITTED]

Rear retainer and associated components were parametrically built in ProlEngineer (figure 2). The geometry was then passed to Mentat (ref. 1) for meshing and model setting. Figure 3 presents an FEA mesh in axi-symmetric elements, and pinpoints materials involved. Fully nonlinear analyses of rear retainer assembly used MARC (ref. 1).

[FIGURES 2-3 OMITTED]

Rubber and plastic prototypes were checked dimensionally to establish molding capabilities. Viton, making the dynamic seal in the rear retainer, was fully characterized under uniaxial tension and compression, planar tension and volumetric compression. Various strain energy density models were tried. Further characterization of rubber and plastic explored friction, minimum pressure to seal, shearing the bound holding rubber to steel, inserted in the seal, and tensile strength. Characterization also analyzed mechanical properties of epoxy-vinyl ester (Young's modulus, Poisson's ratio and tensile stress along and across the fibers). All tests were conducted at typical under-the-hood temperatures (-40 to 150[degrees]C or -40 to 302[degrees]F).

Modeling accounted for contacts seal to bore of the rear retainer, and seal to the various rigid bodies (circular spring, insertion and retention plates, and shaft) (figure 4). To expedite the modeling, only the weakest section falling in testing prototypes (as shown in figure 1), was analyzed. Friction, measured in the laboratory was coded through a subroutine in FEA.

[FIGURE 4 OMITTED

Several cases histories set spring loading within the dynamic seal, insertion of this in the plastic housing, and shaft assembly. X, y, z axes defined axial, radial and hoop directions. Model validation compared the predicted retainer's reaction to insertion of the seal to data recorded in the laboratory, under nominal interference conditions. Post-processing monitored deformation of the seal during assembly. Radial stresses, or contact pressures, are shown on figures 5 and 6 for selected time increments under LMC. A taper was used by the plastic molder to ease seal insertion, besides lubrication.

[FIGURES 5-6 OMITTED]

Radial stress contours, upon inserting the dynamic seal in the plastic housing, indicate the level of sealing; contours reaching the 9 MPa (1,300 psi) are read. Note though that sealing lines on the dynamic seal am not compressing equally, as only the plastic housing was addressed in this study.

A minimum pressure to seal was established at "time zero." A technician compresses a ring gasket on a load frame, then pressurizes its inner bore to 34.5 kPa (5 psi) of air prior to measuring any leak rate. As per Ford, 3 cc/min. (0.079 gallons/day) is considered as a sealing condition. Figure 7 shows ring gasket force deflections recorded: a minimum pressure to seal of 0.271 MPa or 39.2 psi is calculated.

[FIGURE 7 OMITTED]

Obviously, results of minimum pressure, resulting from leak testing and post processing collected data, are to substantiate with viscoelastic effects (relaxation of rubber and creep of plastic). A viscoelastic analysis was not attempted in the program set, because of a shortage of meaningful test data (degradation of shear and bulk moduli with time, in terms of Prony series). Only compressive stress relaxation (CSR) data on seal rubber and creep curves on plastic housing were available. These were factored in results of quasistatic analyses. A large safety factor against leakage is clearly inherent in the design at hand; simulation shows contact stresses an order of magnitude higher than the experimental minimum pressure to seal.

The second aspect, important to the feasibility of the plastic rear retainer, is strength. Note that parts failed in DVP&R at the weakest section. Hoop stresses were thus monitored during assembly. Figures 8 and 9 show contours of the third, or hoop, component of stress; the color code reflects plastic material strength under quasi-static conditions, using strain gauged specimens (figure 10).

[FIGURES 8-10 OMITTED]

Stresses on figures 8 and 9 are highest at the "L" shaped insert in Viton. Metal has higher modulus than rubber and plastic, and behaves linear-elastically (stress proportional to modulus of elasticity). Only stresses in the plastic weakest cross-section should be considered herein, for design purposes.

Finally, a maximum interference between the dynamic seal and inner bore of the plastic retainer was defined through FEA and materials testing in the laboratory. The data was mainly passed to the plastic molder to gauge manufacturing tolerances of the new plastic rear retainer, and ensure its compatibility with the existing dynamic seal design and dimensions.

Summary

This article continued a first write-up detailing rubber materials characterization at "time zero," and the post-processing of collected data for "quasi-static" FEA. Herein, more testing, mainly to run fully nonlinear assembly and failure analyses, was discussed. In particular, experiments to establish minimum pressure to seal under LMC and the inclusion of stress relaxation characteristics were discussed, along with failure assessment under deviatoric modes of deformation and MMC.

In summary, LMC ensured sufficient contact to leakage within the rear retainer assembly disclosed, while holding the dynamic seal from spinning with the rotating shaft. Maximum material condition allowed the assessment of shearing strength of rubber to metal insert bound, and that of the weakest section of the rear retainer. Analyses allowed parts to change dimensions. Moreover, they altered properties of materials with temperature.

Indeed, low temperature leak testing ring gaskets made of Viton, coupled with analyses, allowed the establishment of LMC. Forces to insert the seal in the housing compared accurately to test results under a variety of actual conditions. The weakest rear retainer bore was adjusted to withstand radial expansion under MMC and elevated temperatures. Further tests at Ford and suppliers included push and pull out, force-deflections, adhesion, bolt torque to failure, thermal cycling and vibration, torque retention analysis and DVP&R.

Final tests were on the bench as Ford run dynamometer analyses. Nevertheless, high speed cycling, Cologne durability evaluation, cold start tests, cylinder-head gasket deep thermal shock cycles, along with durability and simulated transmission shift cycle still await the design generated through FEA.

References

(1.) Anon., "ASTM Designation D638-91 (re-approved 1992) - standard test method for tensile properties of plastics," 1994 Annual Book of ASTM Standards, Vol. 08.01.

(2.) Anon., "ASTM Designation E132-86 (re-approved 1992) - standard test method for Poisson's ratio at room temperature," 1994 Annual Book of ASTM Standards, Vol. 08.01.

(3.) Treloar, L.R.G., "The physics of rubber elasticity," Second Edition, Oxford University Press, England (1958).

(4.) Treloar, L.R.G., "Stress-strain data for vulcanized rubber under various types of deformation," Trans. Faraday Soc., Vol. 40, pp. 59-70 (1940).

(5.) Gregory, M.T., "The stress-strain behavior of filled rubbers at moderate strains," Plastics and Rubber: Material and Applications (1979).

(6.) Ogden, R.W., "Recent advances in the phenomenological theory of rubber elasticity," Rubber Chemistry and Technology, Vol. 59, 361 (1986).

(7.) Rivlin, R.S., "Large elastic deformations of isotropic materials, IV. Further developments of the general theory," Phil. Trans, Royal Soc. London, A 241 (1948).

(8.) Anon., "ASTM Designation E412-87--test methods for rubber property in tension," 1994 Annual Book of ASTM Standards, Section 9 Rubber, Vol. 09.02.

(9.) Anon., "ASTM Designation D575-88--test methods for rubber property in compression." 11994 Annual Book of ASTM Standards, Section 9 Rubber, Vol. 09.01.

(10.) Anon., "MARC user's manual," version 6.2, MARC Analysis Research Corporation, Palo Alto, CA (1996).

(11.) Anon. "ABAQUS/Standard user's manual," version 5.9, Hibbitt, Karlsson & Sorensen, Inc., Pawtucket, RI (1998).

(12.) Anon, "Pro\ENGINEER user manuals," version 18, Parametric Technology Corp., 28 Technology Drive, Waterham MA (1998).

(13.) Twizell, E.H. and Ogden, R.W., "Non-linear optimization of the material constants in Ogden's stress-deformation function for incompressible isotropic elastic materials," J. Austral Math. Sot., Series B, Vol. 24, pp. 424-434 (1983).

Dr. Ben Chouchaoui is president of Windsor Industrial Development Laboratory which specializes in materials characterization and the computer simulation of product performance and manufacturing.