Analytical Prediction of the Brake Caliper Seal- Groove Performance

Transcription

1 Analytical Prediction of the Brake Caliper Seal- Groove Performance Okon D. Anwana, Hao Cai Delphi Corporation Excerpts taken with Permission from SAE and SAE SAE International Abstract: It is well known that the design of the seal groove assembly in the brake caliper greatly influences the braking performance. The rubber seal performs the dual function of sealing the piston bore and retracting the caliper piston after a brake apply. However, the seal function is affected by the configuration of the seal groove, as well as the friction at the piston/seal and groove/seal interfaces. The material properties of the rubber seal are also important design parameters. Issues such as fluid displacement, piston retraction, piston sliding force, and brake drag are some of the critical brake performance/parameters that must be considered in every brake caliper design. Presently, the brake caliper seal-groove design is still based on empirical rules established mainly from past experience and its performance is achieved through prototype testing. Indeed, an analytical model that offers some predictive estimate of the seal groove contributions to the braking performance is needed. This will enhance the optimization of the seal groove design and reduce the need for product prototyping. In this paper, we attempt to identify the critical design parameters in the seal/seal groove assembly and quantify their impact on the brake performance. In addition, numerical models are presented for evaluating the effects of the seal groove, housing, and lining on caliper performance. These models provide reliable and timely design predictions for a brake caliper design with considerable savings in product development time and costs. 1. Introduction Figure 1 shows a typical disc brake system comprising of a caliper and a rotor. The caliper usually consists of housing, piston, shoe and lining assemblies. Within the piston bore in the housing is the seal groove where a seal fits to seal the brake fluid. During brake apply, fluid pressure activates the piston towards the rotor, which forces the linings to rub against the rotor and generate braking torque. The caliper housing is deflected during brake apply and springs back into its undeformed shape after brake release. 23 ABAQUS Users Conference 1

2 Fluid displacement during brake apply and drag torque after brake release are two important performance characteristics of a caliper design. Displacement is the extra brake fluid volume needed to achieve a certain braking pressure. Higher displacement means longer travel of the brake pedal. Drag is the residual torque on the rotor after the brake is released. It hurts fuel efficiency, lining life and may induce pulsation. The caliper housing stiffness, lining compressibility and seal/groove design all play important roles on drag performance and fluid displacement. The seal groove is designed to perform dual functions of sealing the piston bore during brake apply and retracting the caliper piston at brake release. Piston retraction is the distance a piston retracts into the bore of the caliper housing after a certain brake apply. Both drag and displacement performances of a caliper depend on piston retraction. The greater the retraction, the less the drag and the more the displacement, or vice versa. Piston retraction is greatly affected by the profiles of the rubber seal and groove [1, 2]. The need to increase piston retraction to alleviate drag often conflicts with the requirements to reduce piston travel (i.e. reduce displacement) during brake apply. This is one of the major challenges in the seal-groove design. Acceptable caliper performance can be achieved by judicious selection of these component designs. Presently, brake engineers rely on prototype testing and empirical rules for seal groove design [4, 9]. These empirical rules are usually limited to a few design parameters and cannot be reliably applied to predict the seal behavior in a quantitative sense. Our focus in this paper will be to develop some analytical design tools for estimating the influence of the caliper components on the braking performance. In the literature, there is little or no published information regarding the analytical prediction of the seal groove behavior and its interaction with the caliper housing and lining. A number of studies on the rubber material properties for seal applications [2, 7, 8], as well as the experimental estimates of friction effects in the caliper bore and piston [11] have been reported. A statistical evaluation of seal groove design parameters [12] based on the Taguchi approach has assessed the effect of design tolerances on the seal groove assembly. Additionally, the capabilities of commercial analysis software codes for rubber analysis was reviewed that also included estimates of to the load-displacement relationship for a given seal groove design [5]. A recent analytical study [3] conducted by the authors provided the qualitative link between the response of the rubber seal within the prescribed groove boundaries and the expected retraction performance of the seal groove design. Subsequently, the analysis model used in [3] was extended to include the effects of the caliper housing and linings [6]. This resulted in an analytical tool for relating sealgroove design parameters to brake performance with due consideration of the effects of the caliper housing and shoe lining. In this paper, we essentially summarize the results of the study published in References 3 and 6 with some modifications. We begin with a brief description of the seal groove, and the analysis considerations for quantifying the critical design parameters in the seal/seal-groove assembly. Following this, analytical models are presented that include the effect of caliper housing and lining in the brake performance estimates. Analytical predictions from these models are provided and compared with test data. The strengths and limitations of the analysis models are also discussed. We note that temperature and brake service conditions also affect the rubber seal behavior, and consequently the braking performance. But for simplicity, the temperature and environmental parameters are not considered in the analysis ABAQUS Users Conference

3 2. Seal Groove Analysis 2.1 Background A seal groove assembly has three main components - rubber seal, piston and caliper groove. Figure 2 shows the cross-section of the typical seal groove assembly components in the undeformed state, in which x denotes the radial direction and y denotes the axial direction. By design, the seal outer diameter is larger than the groove outer diameter. Hence the rubber seal is squeezed between the groove and the caliper piston when assembled. Rubber squeeze in the seal groove assembly and its deformation during brake apply are critical parameters for evaluating seal performance and pis ton retraction. To study the effect of seal groove geometry on brake performance, we select a seal of known material and configuration. A nomogram of the seal material properties had been established from testing for a range of temperatures (-4 F to 23 F), frequency and load rates [2]. Coulomb friction was assumed at the seal interfaces with the piston and the groove. The temperature was set at room temperature (under ambient conditions). By fixing the seal material, seal geometry, the lubricant, piston material and geometry, we implicitly standardize the material, friction, contact and environmental design parameters. Under such considerations, one can make judicious changes in seal groove geometry (i.e. in the geometry parameters) and monitor their effects on the braking performance under room temperature conditions. The modeling approach used for finite element analysis (FEA) of the seal groove assembly is described in the next section. 2.2 Static FEA Modeling The analysis model presented here is axisymmetric with the cross section of the seal groove components in the undeformed state as shown in Figure 2a. The piston and groove surfaces in contact with the rubber seal are considered as rigid surfaces since they are much stiffer than the seal material. The rubber seal material is modeled with 8-node biquadratic, hybrid elements (CAX8H) with linear pressure. The second order Ogden model is used to describe the material hyperelastic behavior, while the material viscoelastic response is approximated by the Prony series. Convergence studies conducted outside the scope of this paper showed a global mesh size of.3mm was adequate To capture the pressure loading during a brake application, the fluid space in the caliper piston is modeled as fluid cavity with the hydrostatic pressure as the only degree of freedom. The braking load is applied in the form of pressure. But where analysis convergence is not feasible with pressure loading, the brake apply is implemented as a concentrated force on the piston. Coulo mb friction laws are applied between seal/groove and seal/piston interfaces. The static analysis is performed in two steps using the Abaqus/ Standard commercial finite element software. First, the rubber seal is installed in the groove-piston assembly (Figure 2b). The installation is initiated by moving the groove and piston into their assembly positions such that the rubber seal is enclosed within their prescribed boundaries. Kinematic contact between rubber seal and the groove or piston is enforced. Then the braking action is simulated by moving the piston in the brake apply direction a certain distance equal to the piston travel (Figure 2c). 23 ABAQUS Users Conference 3

4 2.3 Rubber Seal Forces In the assembled position (see Figure 2b), the seal rubber is subjected to normal force F n, a tangential force F t, and moment M. The magnitude of the normal force (F n ) at the piston/seal interface is a measure of rubber squeeze in the seal assembly. The effect of radial squeeze on rubber deformation is shown in Fig. 3a and 3b. In this plot, the rubber squeeze is defined as the radial factor (in percentage) that quantifies the undeformed and deformed dimensions of the seal in relation to the geometry of the other components in the seal groove assembly. The higher the magnitude of the squeeze force, the higher the value of the squeeze factor. Piston sliding occurs when the tangential force (F t ) is exceeded during brake application. Depending on the effects of friction and groove configuration, slippage between rubber seal and the piston can occur during the apply-and-release processes. The variations in the seal squeeze and sliding forces with brake apply is depicted in Figure 4 for a production seal groove design. At zero sliding force, the reference point on the piston is at point A1 for the seal groove assembly with high squeeze and at point A2 for the lower squeeze assembly. By comparing the piston and rubber seal positions before, during, and after brake application, we can estimate the piston travel and retraction, which is a key contributor to brake drag and fluid displacement. Thus, the energy quantities associated with the brake apply and release are easily determined. It is worth noting that, after brake release, the piston retracts but not necessarily to its assembled position. 2.4 Piston Retraction To evaluate a seal/groove design based on its analysis results, it is necessary to understand why the piston is not fully retracted after brake release. Consider groove/seal/piston assembly as a system. During brake apply, outside energy is transferred into this system to displace the piston. Rubber seal deforms as a result of the energy imparted to it from the piston displacement. Part of the imparted energy is reserved in the seal due to its deformation. The remaining part of the energy is dissipated through friction and viscous material flow. So when the brake is released, the energy reserved in the rubber seal is not enough to retract the piston all the way back to its original position. Hence, there is a residual displacement of piston. When the piston is not retracted sufficiently, it will still contact the brake pad, which is pushed against the rotor and consequently, induces drag. Based on this understanding, we hypothesize that the energy loss during brake apply is an indicator of how much the piston would retract after brake release. The greater the energy loss, the less the piston will retract, resulting in increased brake drag and less displacement. By calculating energy loss during brake apply from FEA results, one can evaluate the performance of different seal groove profiles before making any prototypes. 2.5 Energy Loss Hypothesis Verification To validate the energy loss hypothesis, the performance of a brake caliper was analyzed with three different groove configurations which, for proprietary reasons, are designated as groove A, B and C. The brake caliper system was designed for small truck applications. Fig 5 shows the analytical predictions to this brake caliper design. Analysis results show that the energy loss is the highest for groove A and lowest for groove C among the three grooves (Fig. 5a) ABAQUS Users Conference

5 Groove B is very close to C. This suggests that, for the given caliper design, changing the groove configuration from A to B then to C should decrease the residual drag torque of the caliper correspondingly. Test data support the analytical predictions (Fig. 5b). To further confirm the model, the analysis was repeated for various caliper designs with varying piston sizes and groove profiles. Again, the analysis predictions for these cases were in good agreement with test data. The static model is quite effective in developing the groove profiles. It offers a tool for predicting the performance of a new groove design relative to the designs we already know. With this modeling approach, one can tailor a seal groove design for a specific caliper rather than resort to trial and error techniques. Note that every caliper has its unique system stiffness, which usually requires a unique configuration of the seal groove to meet performance requirements. Using analysis approach, various combinations of seal groove profile can be quickly evaluated for a particular caliper application. This technique has already been applied in Delphi for developing caliper designs with various system stiffness and performance requirements. 3. Caliper Performance Modeling It is worth noting that the caliper housing and lining function as springs in the mechanical system of the caliper. During brake apply, the caliper housing is forced to open and the shoe lining is compressed by the hydraulic pressure acting on the system. Once the hydraulic pressure is released, they also tend to release the elastic energy stored in them as they recover from the deformations. For the caliper housing, this recovery occurs almost instantaneously in the form of spring back motion. This effect is not accounted for in the previous results in section 2.3. For improved analytical predictions, the effects of the caliper housing and shoe lining must be included in an analytical model and the model must be a dynamic one, since the housing springback action is dynamic. Inclusion of the caliper housing and shoe lining in the analysis model is important for other reasons. The caliper housing and lining stiffness have the greatest impact on caliper drag. Making the housing and lining as stiff as possible is always the first choice. However, a more compliant caliper housing design or softer lining material is sometimes selected for reasons such as minimizing lining taper wear or brake noise. Typically, the greater the compliance of the caliper housing or shoe lining, the higher the brake drag. Hence, in a caliper system with compliant housing or lining, the seal/groove design is usually modified to compensate for the increased drag. To capture the comprehensive effect from changes to the housing, lining and seal/groove designs, we need an analysis model that includes all these factors. Additionally, design changes to the seal/groove that reduce drag often lead to increased fluid displacement. Reducing the stiffness of the caliper housing or lining material also tend to increase fluid displacement since the bulk of the displacement comes from the housing deflection and lining compression. It is essential that the caliper system still meets both the displacement and drag requirements after any design changes. Only by including the housing and lining in the model can we properly estimate caliper displacement. 23 ABAQUS Users Conference 5

6 3.1 Dynamic model description Two springs representing the caliper housing and shoe lining respectively are implemented in the above static model, as shown in Figure 6. One spring with the stiffness of the caliper housing is attached to the analytical rigid surface representing the seal groove. The other spring with the stiffness of a set of shoe and lining assemblies is connected to the piston. There is a gap between the lining and a fixed end simulating the initial gap between linings and rotor. The housing spring is linear while the lining spring is non-linear. The lining spring stiffness increases non-linearly with the increase in compression, but its tension stiffness is zero because lining can never be under tension during caliper s whole working sequence. Usually, the analysis with the dynamic model is performed in three steps. In the first step, the rubber seal is installed in the seal groove as in the static model, such that there are no loads in the model springs (Figure 6a). Second, equal but opposite loads are applied on the piston and groove to simulate braking (Figure 6b). Groove travel here represents the housing deflection. This step is performed by static analysis. During the third step, the applied loads are released and dynamic analysis is adopted to evaluate the response of the groove and piston to the spring back motion of the caliper housing and lining. Appropriate material damping is employed in this step. Note that after dynamic release, the lining usually won t return to its starting position, which leaves the gap between lining and rotor smaller than what it was before load apply (Figure 6c). The apply-andrelease load sequences described in the second and third steps can be repeated at different load levels to simulate the braking action at different pressures. The piston and housing (groove) travels during loading are defined by their relative positions before and after the braking load sequence. Using the total travel of the piston and housing during brake apply determined by analysis and the piston area, one can easily obtain the fluid displacement curve of the caliper as a function of hydraulic pressure. We can also take the gap between lining and rotor after brake release as an index to drag torque. The wider the gap, namely the farther away the lining is from the rotor, the lower the drag. If a coordinate system located at the face of the rotor is used as reference such that the initial lining position is -1mm (Fig. 7a), we can easily monitor the variations in the gap between lining and rotor after brake release using the lining displacement δ. It is our considered opinion that the functional relationship between the said gap and applied pressure can be correlated with the drag. 3.2 Dynamic Model Verification To benchmark the predictive capabilities of the dynamic model, we analyze a caliper system with different seal groove configurations, shoe lining materials and caliper housing Effect of seal groove on caliper performance The dynamic model was used to analyze the same caliper system described in Section 3.1. Fig 8 shows the analytical predictions for fluid displacement based on the dynamic model. These predictions are presented on the plot by square markers connected with thin lines. The comparative test data are also shown in the plot as thicker solid lines. Clearly, the test data verify the accuracy of the analytical predictions. The analytical results for groove C is omitted in the plots due to lack of test data ABAQUS Users Conference

7 Figure 9 compares the residual drag torque obtained from test with the analytical predictions of the gap between the lining and rotor after brake release for the same caliper system. The analysis predictions shown in Figure 9b indicate that the gap between the rotor and lining decreases as pressure increases, which is consistent with drag behavior with applied pressure derived from tests (Figure 9a). The results also confirm that groove configuration A produces higher drag in the caliper system than groove B. Furthermore, a direct correlation is established between brake drag and the gap between the lining and the rotor after brake release. In retrospect, drag torque is friction force acting on a radius and this friction force depends, among other things, on the degree of contact (or lack of gap) between the lining and rotor. Hence the gap between the lining and rotor after brake apply can be used as a consistent predictor for drag during caliper design Effect of Shoe Lining on Caliper Performance The same caliper system considered in Section was reanalyzed with two different lining materials using the dynamic model. Figure 1 shows the compressibility of the two lining materials evaluated. Both are made of non-asbestos organic materials. Lining II is stiffer than lining I. According to analytical results with the dynamic model, lining II should have a lower drag performance than lining I (Figure 11b). This conclusion is verified by test data in (Figure 11a). Figure 12 is the fluid displacement curve determined from the analysis of the caliper system with different lining materials. No corresponding test data is available. Even though lining II deforms less than lining I under the same brake load (Figure 1), there is no significant difference between the fluid displacements calculated for these two linings. However, a closer look reveals that lining II leaves a wider gap between the lining and rotor after brake release than lining I (see Figure. 11b). So lining II yields slightly higher displacement at lower pressure because more fluid is needed to cover the wider initial gap. Lining I yields higher displacement at higher pressures which is consistent with its higher deformation at these loads. The ability of the analysis model to relate a design change in lining material to brake performance is very useful for caliper product development Effect of Housing Stiffness on Caliper Performance A caliper system, with two different housing stiffnesses, was analyzed to assess the relative impact of caliper housing on brake performance. The stiff housing (labeled Stiff HSG), with 15% improvement in stiffness, is a revised version of the soft housing (Soft HSG) on the same caliper system (Figure 13). Analysis results of displacement and drag for the caliper with soft and stiff housings are shown in Figure 14. According to these results, both the displacement and drag values decrease with increase in the housing stiffness. Although there are no corresponding test data, these conclusions are consistent with engineering experience. In a related study, the dynamic model has been used to evaluate other caliper systems in which the seal-groove diameters and/or rubber seal configurations were varied. Although the results of this study cannot be provided at the present time, it is worth noting that all the analytical predictions agree with engineering experience. 23 ABAQUS Users Conference 7

8 As a subset of the dynamic model, the static model is ideal when profiling the seal groove is the only design objective. The simplicity and computational costs associated with this model renders it very efficient for design iterations. 4. Conclusions In this paper, the authors have demonstrated the application of analysis in the caliper seal groove design. In this effort, the mechanics of rubber deformation within the prescribed boundaries of the seal groove are established. Predictions on piston travel and the forces acting on the rubber seal during brake apply are also made. Numerical models are presented for evaluating the performance of the brake caliper system. The static model emphasizes groove profile contribution to caliper drag performance. It should be applied to groove profile development. The dynamic model includes all factors that affect both drag and displacement, such as housing stiffness, lining stiffness, groove geometry, seal material and dimensions. The comprehensive effect of all these factors on caliper drag and displacement is reflected in the model s analysis results. The analysis models were applied to various caliper design applications with very positive results. By taking advantage of the spring-like behavior of the caliper housing and lining as well as the hyperelastic behavior of the seal in the seal groove, the analysis models incorporate all the salient design parameters of a caliper system, and offer complimentary predictions regarding the caliper performance. As design tools, these models grant the design engineers more freedom and control in the design of the caliber system. The ability to predict piston retraction analytically (and implicitly estimate drag and other performance parameters) provides several competitive advantages, including the ability to optimize the performance of the caliper groove seal early in the design when only the design variables are known, i.e. before prototypes are made. Furthermore, with the understanding of retraction mechanism in the seal-groove, it is possible to modify other components of the brake caliper system that would otherwise be impossible to redesign late in the product design cycle. In essence, these models eliminate the current industry reliance on engineering intuition, and serve as effective tools for developing and optimizing caliper system components. Both design cycle time and prototype cost will be saved. 5. References 1. Anwana, O. D. Analytical Design of the Seal Groove Assembly Case Study in the Performance Prediction, Delphi Automotive Internal Report (21). 2. Anwana, O. D., Characterization of Rubber Material for Disk Brake Piston Seal, Delphi Automotive Systems Internal Report EWR (2). 3. Anwana, O. D., Cai, H., Chang, H. T., Analysis of Brake Caliper Seal-Groove Design, SAE Congress, Detroit, MI, Paper No. SAE , (22). 4. Baptists, T. Brake Drag Torque Measurements, Delco Moraine - GM Report No. PG5326 (1988) ABAQUS Users Conference

9 5. Chang, H., On a Numerical Study for Rubber Seals, SAE Transactions v.97, Paper No. SAE (1988). 6. Cai, H., Anwana, O. D., Seal/Groove Performance Models, SAE 22 Annual Brake Colloquium, Phoenix, AR, Paper No. SAE , (22). 7. Dinzgurg, B., Measurement of Rubber Elasticity and Correlation to Seal Life, SAE Congress, Detroit, MI, Paper No. SAE (1997). 8. Dinzgurg, B., The Selection of Elastomer Compounds Through Correlation of Rubber Properties to Seal Life, SAE Congress, Detroit, MI, Paper No. SAE (21). 9. Hrbek, D., Piston Seal Characteristics on a Disc Brake Caliper with a Self Adjusting Park Brake Mechanicsm, CPC, GM Report No. PG57117 (1991). 1. Lim, J., Brake Caliper Analysis of Piston Friction, CPE, GM Report No. PG51348 (1987). 11. Meada, N. and Matsuno, M., Analysis of Rubber Boot Seal Using Finite Element Method, SAE Congress, Detroit, MI, Paper No. SAE (1994). 12. Moore, D., The Friction and Lubrication of Elastomers, Pergamon Press, Shnaider, A., Authentic Involvement Design, Dept. of Mechanical Engineering, Monash University, MI, Final Report to PBR Automotive Ltd. (1996). 6. Contact For further information, please contact Okon Anwana, Engineering Technical Center, M/C E-52, 1435 Cincinnati Street, Dayton, OH Telephone: , Fax: , okon.d.anwana@delphi.com. 23 ABAQUS Users Conference 9

10 Brake Fluid Caliper Housing Piston Seal Groove Linings Rotor Figure 1. Components of a disc brake system 1 23 ABAQUS Users Conference

11 Rubber Seal Seal Groove Contour x-axis Brake Apply Direction (A) Piston y-axis F n M (B) F t (C) Apply Figure 2. Seal/Groove analysis modeling At Assembly At Assembly At N/mm 2 (15 psi) Apply At N/mm 2 (15 psi) Apply Figure 3(a). Rubber deformation in a production seal groove with 18.95% squeeze Figure 3(b). Rubber deformation in a production seal groove with 9.85% squeeze 23 ABAQUS Users Conference 11

12 Figure 4(a). Normal or Squeeze Force vs. Piston Travel During N/mm^2 Apply Pressure Normal Force (N) A1 2 A Piston Travel (mm) 9.85% Squeeze 18.95% Squeeze Figure 4(b). Shear Force (N) Sliding or Shear Force vs. Piston Travel During N/mm^2 Apply Pressure A A2.2.4 Piston Travel (mm) 9.8% Squeeze 18.95% Squeeze 2 (A) Energy Loss from Analysis 18 (B) Test Energy Loss (N mm) Drag (ft-lb) Groove A Groove B Groove C Piston Travel (mm) Figure 5. Drag torque by analysis and test ABAQUS Users Conference

13 Housing Lining Gap Housing A. INSTALL Force Lining Gap Force Housing B. APPLY Lining Gap C. AFTER RELEASE Figure 6. Dynamic analysis model Lining a. Install Lining Gap = -1 mm δ Gap Y Rotor Rotor X b. After Release Figure 7. Lining position during analysis procedure 23 ABAQUS Users Conference 13

14 Fluid Displacement.2 Displacement (cu-in).15.1 Groove A, Test Groove B, Test.5 Groove A, Analysis Groove B, Analysis Figure 8. Fluid displacement of calipers with different grooves 18 (A) Test (B) Analysis Drag (ft-lb) Gap (mm) Groove A Groove B -.4 Groove A Groove B Figure 9. Drag torque of caliper with different grooves ABAQUS Users Conference

15 Lining Compressibility Shoe&Lining Assembly with Insulator Lining Deformation (in) Load (lb) Lining I Lining II Figure 1. Compressibility of lining I and II 18 (A) Test (B) Analysis Drag (ft-lb) Gap (mm) -.2 Lining I -.3 Lining II -.4 Lining I Lining II Figure 11. Drag torque of calipers with different lining materials Displacement (cu-in) Fluid Displacement by Analysis Lining I Lining II Figure 12. Fluid displacement estimates for caliper with different linings 23 ABAQUS Users Conference 15

16 Housing Stiffness Housing Deflection (in) Soft HSG Stiff HSG Figure 13. Stiffness comparison between soft and stiff Housings Displacement (cu-in) Fluid Displacement Gap (mm) Gap between Lining and Rotor Soft HSG Stiff HSG Soft HSG Stiff HSG Figure 14. Displacement and gap from analysis with different housings ABAQUS Users Conference