Abstract

Nonlinear Finite Element Analysis (FEA) has revolutionized the elastomeric seal design process by minimizing the costly trial-and-error prototyping and pre-production testing. Now a design can be conceived, drawn up, and then modeled by computer using FEA to determine results before the part is built. This allows design iterations to be made, results obtained, and perhaps an optimum design developed before tooling begins. Even though testing is still necessary to verify the results, a more predictable and cost-effective part can be developed in a more timely fashion.

Some examples where FEA has made significant contributions to the design and development of some of Parker's products are discussed. These examples include a rod seal for a piece of exercise equipment, a bumper used to stop a pneumatically accelerated piston, and a custom u-cup used in a snowmobile brake system.

Introduction

The Parker Packing Division of Parker Hannifin's Seal Group has a main focus of manufacturing dynamic seals for hydraulic and pneumatic applications. We have a large number of plastic and rubber compounds for various sealing applications.

As shown in the following examples, Parker uses FEA in the development of new products as well as in the design optimization of existing products. The included analyses use static, two-dimensional, axis-symmetric models with Full & Herrman elements. The material is characterized by the Ogden model. The Bulk Modulus is used as a measure of the materials compressibility.

The left side of the included FEA figures is the inner diameter and the right side is the outer diameter of the part's cross section. The shaded contour bands show the stress values throughout the part. The darker shades correspond to higher compressive stresses; while the lighter shades correspond to lower compressive stresses.

Example 1

A leading exercise equipment manufacturer came to us with the problem of a leaking hydraulic seal on a particular piece of exercise equipment. The leak rate on this seal was about 3 to 5 percent, which made for some very unsatisfied customers. Even though Parker did not make this unsatisfactory seal, we accepted the opportunity to determine the problem and find a solution.

To help determine why the existing seal was leaking, we modeled its cross section with FEA. A sketch of the seal installed in the cylinder is shown in Figure 1. A spring is installed against the pressure side of the seal to help keep the seal tight.

Figure 1

Figure 2 shows an FEA model of the seal installed in the cylinder. The color contours correspond to the true stress in the radial direction. This model determined that the last lip does not contact the rod and the third lip only contacts the rod slightly. The first two lips have about the same contact force on the rod.

Figure 2

The angle on the top of the seal is such that the lip on the outer diameter of the seal is non-pressure actuated. Also, the mold code is located at the bottom the seal. Both of these items facilitate leakage around the outer diameter of the seal.

Now that the seal has been modeled, several new design proposals can be modeled with FEA. The design that ultimately was chosen has three lips. The first lip is the least aggressive and the last lip is the most aggressive. Also, all of the new seal's outer diameter is the same as the previous seal's outer diameter lip. This causes more force on the sealing lips. This higher force gives more sealing power at the cost of higher friction and higher wear. The higher friction force is not a concern because it just adds to the resistance of the exerciser. The material has been changed from a nitrile to a polyurethane to give the seal higher wear resistance.

Another design change consists of two small bumps added to the bottom of the seal. These bumps will assist in preventing leakage around the outer diameter of the seal. Figure 3 shows this seal design installed in the cylinder.

Figure 3

This design has been used to make prototype parts for the customer. The customer performed testing and was very impressed. This part outlasted the previous part many times over.

Example 2

Along with hydraulic and pneumatic seals, Parker Packing Division also makes bumpers to stop the pneumatically accelerated pistons in nail and staple guns. Many of these polyurethane bumpers have failed prior to the customer's expected number of cycles. Such failures may be due to certain design parameters, which may be addressed with FEA.

Following are the deformed geometries of three different designs. A cross section of each design is shown. The left side is the inner diameter and the right side is the outer diameter. The shaded contour bands show the first component of Cauchy Stress (the true stress in the axial direction). The darker shades correspond to higher compressive stresses; while the lighter shades correspond to lower compressive stresses. The FEA code had difficulties determining when contact occurred with the radius on the piston that comes in contact with the top inner diameter of the bumper. For this reason, the corner is modeled as a sharp corner instead of rounded. Each model is shown compressed as far as the program would allow. An outline of the undeformed bumper is also shown.

There were many failures with the inner diameter of design A. Under a compressive load, the inner diameter of the bumper "kinks" or "buckles" as shown by the arrow in Figure 4. It is believed that the part fails before the desired number of cycles due to the high stress which is evident in the buckled region.

Figure 4. Design A with 0.170 inches compression and 1841 lbs. axial force

Design B is shown in Figure 5 and is similar to design A, but has a smaller inner diameter. This smaller inner diameter prevents the "buckling" that occurred in design A. From FEA results, it is expected that design B will have a longer life than design A.

Figure 5 Design B with 0.165 inches compression and 1751 lbs. axial force

There has been some concern expressed about the bumper grabbing the piston. When an axial load is applied to the bumper, it is compressed radially, causing it to grab the piston. With this in mind, several design iterations have been done to come up with a design where radial contact is postponed as long as possible. The result is design C, shown in Figure 6.

Design C has the same outer diameter as the other designs. Following is a list of differences between design C and the other designs:

1. The bottom has a steeper angle toward the inner diameter that joins a shallow angle at about the middle of the cross section.
2. The top is angled so the inner diameter is higher than the outer diameter. When the bumper is initially compressed there is a stress concentration at the top inner diameter. However, as the bumper is compressed farther, the stress concentration moves toward the outer diameter. The angled top allows the force to be distributed over more area resulting in lower stress.
3. The bottom inner diameter is smaller than the top inner diameter with a gradual change between them. This allows the top to move in as the bumper is compressed, and postpones radial contact between the bumper and piston.

Figure 6 Design C with 0.146 inches compression and 1841 lbs. axial force

The FEA code was unable to compress design C as far as the other designs. However, the analysis does show some benefits of design C. These benefits are:

1. The bumper does not contact the piston radially until it is compressed 0.140 inches. This will reduce the amount the bumper will grab the piston.
2. The contact area on top of the bumper is larger. Therefore the force is spread out more and the stresses are lower. To illustrate this, notice from Figures 4 and 6 that a force of 1841 pounds is placed on both designs. However, the maximum axial compressive stress is about 2000 psi less in design C than design A.
3. Design C stops the piston with less travel. The 1841 pounds compressed design A 0.170 inches, and it compressed design C only 0.146 inches. This may or may not be a benefit, depending on the customers desires.

Design B is currently being supplied to the customer as an easy fix for the high stress concentration on the inner diameter. Design B has satisfactory results and a tool has not yet been made for Design C. Therefore the performance difference between Designs B and C is still unknown.

Example 3

Another example where nonlinear FEA has proved beneficial is with the design of a custom U-Cup for the brake system for a major snowmobile manufacturer.

Figure 7

Figure 7 shows the cross section of the seal installed on the piston. The pulling of the brake lever pressurizes the seal. This pressure then actuates the brake.

The customer has two qualifications for this seal. The seal cannot leak and the outer lip must be short enough to not cover a small port when the brake lever is pulled.

Three unsuccessful seal designs were made (shown in figures 8 - 10) before FEA was involved. The seal design in Figure 8 failed because it extruded around the outer diameter of the piston. The extrusion point in Figure 8 is the bottom right corner. This problem can now be avoided by implementing FEA to design the seal so that the stress as a function of pressure is much less at this location.

Figure 8

The seal in Figure 9 leaked because the outer diameter lip was not aggressive enough. Figure 9 shows the seal installed without any pressure applied. This is where the most leakage occurs. This problem can be corrected by using FEA to install the new design and measuring the contact force of this lip against the bore of the cylinder.

Figure 9

The outer diameter lip in Figure 10 is too long and covers the port in certain field tests. This problem can be avoided by measuring the contact length of the seal's outer lip, compare this to the position of the port and then add a safety distance to allow for variances in the port position.

Figure 10

The key parameters for the new seal design that were established by linking FEA results and test results of these three seals, are now used to design the new seal. The seal was made and has proven to be successful in lab and field tests by the customer. The FEA model of this successful seal is shown in Figure 11.

Figure 11

Conclusions

These three examples show how nonlinear finite element analysis help solve design problems of elastomeric parts. Parker Hannifin's Packing Division relies heavily on FEA to produce better products at a better price in the best possible time.