ROBUST DESIGN METHODOLOGY FOR THE DEVELOPMENT OF 
COMMERCIAL VEHICLE BRAKING SYSTEMS 
 
1Kemmler, Stefan*, 2Leopold, Tobias, 2Fricke, Jens, 1Bertsche, Bernd 
1University of Stuttgart, Germany, 2Knorr-Bremse Systeme für Nutzfahrzeuge GmbH, 
Germany 
 
KEYWORDS – Robust Design Methodology, Axiomatic Design, SMART, Reliability, Air 
Disk Brake 
 
ABSTRACT 
 
Today’s product requirements demand an ever increasing functionality for the same space and 
usually the same number of components. Thereby, the quality, reliability and robustness of 
these products should be preserved or even be increased. This target conflict cannot be solved 
without compromises. The research community between the Institute of Machine 
Components (IMA), University of Stuttgart, and the Knorr-Bremse Systeme für 
Nutzfahrzeuge GmbH is seeking for new solutions for these challenges. The new approaches 
for designing robust and reliable products are being implemented directly in a current 
development project of an innovative Air Disc Brake (ADB). 
 
With “Systematic Method for Axiomatic Robustness-Testing” (SMART), reliability methods 
and the basic concept of Robust Design methodology are related to the Taguchi Method. 
SMART is based on three phases: System, Parameter and Tolerance Design; accordingly, the 
sample phases of VDA (Association of German Automotives) are used as milestones. In the 
System Design, SMART focuses on the decreasing complexity according to the functional 
dependences of the DPs, thus precluding early random failures. In the Parameter Design 
phase, SMART gives the developer an approach for modeling an adaptive simulation model 
(SIM-SMART). This model also enables the simulation of random and possible fatigue 
failures in addition to the nominally robust DPs. In the early stage of product development, 
reliability predictions are possible. In the iterative Tolerance Design phase, the final tolerance 
limits for robust and reliable products are defined with consideration of compromises in terms 
of costs, quality and technical feasibility. 
 
With the application of SMART, a design concept of a new generation of an ADB with less 
complexity is created. The extensive functions for flexible function studies are modeled with 
the objective of SIM-SMART. Accordingly to this model, parameter studies for determination 
of the nominal adjustment levels can be performed and their random and fatigue failures 
modeled. In conclusion, more accurate reliability test strategies are recommended using the 
definition of tolerance limits. The cost aspect and technical feasibility are also taken into 
account. 
 
So far, SMART has not been added to the iterative Tolerance Design phase. With this paper, 
the method is not only extended to this phase, but also sufficiently validated. In addition, 
SMART can predict and analyze random failures. With its three coherent and iterative phases, 
it is an as yet unpublished and unimplemented approach for designing even more robust and 
reliable products. Robust Design Methodology and reliability methods are fundamental 
building blocks for products with high quality requirements. SMART presents an approach to 
support the designing of robust, reliable, highly functional and innovative ADB.  
TECHNICAL PAPER 
 
INTRODUCTION 
 
Today’s requirements for products and processes are, in addition to low cost and development 
time, also potentials for savings for their production and processing with increasing functional 
performance. This means that the same or an even larger number of functions has to be 
fulfilled in a smaller space. Hence more functions are transmitted to the individual 
components, which in turn leads to an increased functional density, and thus to an increased 
complexity in the system. To accomplish this, serial system structures are generally 
implemented depending on the safety criterion. The demand for reliable and robust products 
and processes increases with these serial system structures and with the realization of high 
functional density. Consequently, a good compromise between requirements and technical 
feasibility must be determined: see Figure 1. 
Due to the high density function within a system, correlations between Functional 
Requirements (FR) and their Design Parameter (DP) have to be systematically structured in 
the early stages of product development (Concept Phase) and their relationships and 
interactions have to be known. In addition, conscious and thus manageable compromises 
regarding the system complexity must be deferred to. Requirements such as less space and 
lower costs are necessary for economically successful products and processes. However, the 
focus should remain on the quality; it therefore forms the top priority in the development of 
robust and reliable products and processes. For this reason, design tradeoffs and the resulting 
restriction of the components’ degrees of freedom have to be made. 
 
STATEMENT OF THE PROBLEM 
 
As a result of the increasing competition in industry and economy, the quality and time to 
market of a product or process has become a more central and important demand. The quality 
attributes can have different variations around their mean value and specification limits, 
which can lead to unexpected deviations from the required function. To control this effect, the 
Robust Design Methodology (RDM) by Genichi Taguchi (16) has been developed (12). 
According to (4) and (7), the quality of a product or process is essentially defined by the 
customers and their satisfaction. For this purpose, two aspects must be considered: the 
function of a product / process, and the ability of the product/process to perform this function 
at any time under the determined environmental conditions. 
 
 
Figure 1: Scale between Robust Design and product requirements. 
According to Park (13), there are three RDMs: the Taguchi Method (TM), the Axiomatic 
Design (AD) and the Robust Design Optimization (RDO). According to Genichi Taguchi 
(16), robustness is a state, whereas the performance of a product or process is minimally 
sensitive to the factors that cause variations and the one with the lowest possible 
manufacturing costs. Two steps have to be taken to find robustness (16): first, the smallest 
variation of the objective function has to be determined, and then the mean value has to be set 
to the required target value. In contrast, N.P. Suh (15) describes, in his approach of AD, a 
robust design as a design that meets his FRs despite large tolerances of the DPs and of the 
process variables during production and assembling. The third method is the RDO, which 
mainly deals with numerical solutions of the optimization of a design. For this purpose, the 
robustness aspect is already integrated during the optimization process (10). In contrast to the 
TM, the RDO has two main objectives: on the one hand, the robustness of the objective 
function has to be maximized, which is influenced by the tolerances of the design variables. 
On the other hand, it should guarantee that the entire tolerance range of the design variables 
all constraints are always satisfied (12). Despite the different approaches, all three methods 
have the main objective of RDM: the insensitivity of products and processes to variations 
(12). 
 
However, the mentioned RDMs currently have a limited distribution in the industry, due to 
lack of information on methods of integration into the existing development process. In 
addition, there is little understanding of the use of the individual RDMs, and a lack of RDM 
techniques starting already in early product development phases and also in the integration of 
the aspect of reliability (1). General approaches of (5) and (6) exist, but no systematic 
approach to product development has been formulated. 
 
SMART gives a systematic approach for designing robust products (8). This RDM was 
developed in the research cooperation between the Institute of Machine Components (IMA), 
University of Stuttgart, and the Knorr-Bremse Systeme für Nutzfahrzeuge GmbH and is 
described in the following chapter. 
 
SYSTEMATIC METHOD FOR AXIOMATIC ROBUSTNESS-TESTING (SMART) 
 
The need for a holistic and systematic approach, which efficiently uses the benefits of AD in 
the concept development, as well as the benefits of TM or RDO in the optimizing of 
parameters, derives from the missing RDM approach for the systematic implementation in the 
product development, as described in the previous chapter. This knowledge is the essential 
motivation for the development of the Systematic Method for Axiomatic Robustness-Testing 
(SMART)-Method; see Figure 2. 
 
The Robust Design method SMART is aligned with the four chronological phases of the 
Product Development Process (PDP) of VDI (Association of German Engineers) Guideline 
2221 (17). SMART also combined the System, Parameter and Tolerance Design phases with 
the PDP. The adaptive RDM provides an entry at any point in the development process, but 
with decreasing scope of design options (9). 
 
SMART is launched, in principle, at the beginning of the Parameter Design with the 
construction of the P-diagram. If, however, there is no design concept at the beginning, a 
suitable design should be conceived initially as part of the System Design. Therefore, the 
Functional Requirements (FRs) are derived from the Customer Requirements (CRs) and the 
corresponding Design Parameters (DPs) are defined. Then the design matrix is set up for a 
clear dependency description and arranged with reference to the laws of reorganization in 
(11). Thus, the application of the independence axiom (15) is possible. If this is not  
Is the information 
satisfactory?
Set up of the 
transfer matrix 
[A]
Redefining
the Design 
Parameter (for 
draft part 
concerned)
Comparison on
the basis of
the information 
axiom
Application of
the information 
axiom
Introduction
of new draft 
levels
Defining the
functional 
requirements and 
design parameters 
from the customer 
requirements 
determined
Is the draft
already 
available?
Is the
transfer matrix 
satisfactory?
Application
of the 
independence 
axiom
Reorganization of 
the transfer matrix
Design of 
Experiment
Carrying out
the experiment
Analysing the 
experiment
Axiomatic Design to 
disclose any draft 
errors that may 
have occurred, and 
to remedy them
Setting up the
P-diagram
Determination 
of the predicted 
reliability
Was the 
confirmation 
experiment 
successful?
Optimization 
possible?
Carrying out the 
confirmation 
experiment
Was the 
confirmation 
experiment 
successful?
Are the optimum 
nominal values
for the 
Design
parameter 
known?
Starting the 
contemplation of 
the system
Is the
reorganization of the 
transfer matrix 
possible?
Optimizing the 
draft on the basis 
of the results
Are there
several drafts
and thus
transfer
Matrices
available?
Tolerance 
synthesis
Technical
feasibility possible?
Analysis using 
statistical
methods
Optimization
of tolerance 
costs using 
weighting 
factors
Set up
Quality Loss
Function
Robustness 
criteria 
satisfies?
Best possible 
costs?
Limit sample test
Determining the 
reliability
Recommending 
the steps of 
action
Variance 
decomposition
Design of 
Experiment
Tolerance 
analysis
customer 
requirements
functional 
tolerances
Technical
Feasibility
possible?
Main workflow
1. Loop
2. Loop
Yes
No
based
on the planned 
process 
capability
that remove the 
couplings
 
 
Figure 2: Systematic Method for Axiomatic Robustness Testing (9). 
accomplished, new DPs are determined as appropriate, or a redesign has to be carried out. 
 
In the next step, the analysis and the comparison of the available design alternatives are 
performed by the information axiom (15). If an adequate design using its information content 
is found, the next phase, the Parameter Design, and the deployment of the P-diagram, (8) 
begins. 
 
The target of the Parameter Design phase is to determine a robust and reliable design, in terms 
of its nominally adjusted DPs with respect to the objective function. If there is already a 
design at the beginning of SMART, using AD is nevertheless recommended in this context as 
a system analysis tool to uncover any opportunities for improvement and potential 
weaknesses of the design. All required parameters are divided in control factors, signal 
factors, confounding factors and objective function in the P-diagram by their features and for 
the subsequent design of experiment (DOE). The knowledge of the previous AD can be 
helpful thereby and, for example, already provide information about which parameters are to 
be considered critical and need to be examined in the DOE. The implementation of the 
statistical tests can be done classically or by RDO, which should be decided on for each 
specific problem. For this reason, SMART provides open space to the developer. The 
evaluation and clarification of whether an optimization of the design can be accomplished and 
whether it is technically feasible are made afterwards. If both requirements are met, and the 
subsequent confirmation experiment is successful, first reliability predictions in the form of 
random and fatigue failure (2) can be determined. If these match with the required reliability 
parameters, the Tolerance Design phase follows. 
 
After an adequate reliability prediction, or if optimal nominal parameter levels for the DPs are 
already present at the beginning of SMART, the optimal and robust tolerance limits are 
determined in the subsequent Tolerance Design, and the actual mean value and the variance of 
the objective function considering the cost aspect and the technical feasibility are defined. 
DPs, which have no significant performance fluctuations with regard to the target size, can be 
expanded in their tolerance limits. DPs with significant performance fluctuations, however, 
are constrained accordingly. If the DPs and the resulting objective function are clearly 
defined, confirmation experiments are conducted: Which makes it possible to make additional 
reliability tests. If the design accomplishes the required reliability requirements, then further 
guidance can be defined. 
 
ADJUSTER UNIT 
 
Trucks in Europe are nowadays equipped almost entirely with air disc brakes (ADBs) (3). A 
defined clearance between brake disc and brake pad has to be present for a reliable braking 
function. In this case, this clearance should not be set too small, so that a constant grinding or 
even an overheating of the brake will be avoided. In addition, the clearance must be set at a 
sufficiently large interval so that tumbling of the brake disc does not lead to contact and thus 
to uneven deterioration. 
 
The clearance must also be adequately protected against thermal expansion of the 
components. The clearance should be designed in such a way that all possible working 
conditions of the vehicle are covered. ADBs have usual ranges from 0.5 to 1.1 mm. The 
adjustment path per brake stroke is shown in Figure 3 and is defined as follows (3): 
 
 ℎ𝑁 = 𝑓𝑁(ℎ𝑖𝑑𝑙𝑒 − 𝑠𝑐𝑐) (1)  
 
The constant adherence to the nominal value of 0.8 mm within the specification limits is 
implemented by a mechanical adjusting unit. The active adjustment process only takes place 
if there is no contact between the brake pad and the brake disc. Once a braking force on the 
threaded spindle and on the brake pads acts on the brake rotor, each adjusting movement is 
stopped. The actuator for the adjusting movement is the lever, which is coupled by a positive 
connection with the adjuster. A defined brake lever travel is executed without any adjustment 
upon each brake actuation. 
 
The drive movement of the lever only acts on the adjuster after a certain amount of clearance, 
and a drive torque is initialized. The defined stroke (hidle) is referred to constructive clearance 
and essentially determines the clearance that has to be adjusted. The amount that is adjusted 
during the actuation of the brake (hN) is proportional to the difference of the stroke (hidle) and 
the constructive clearance (scc), which is referred to as excess travel, and adjustment factor of 
the brake (fN), see Equation 1. The adjustment factor (fN) is an important quality criterion of 
an adjusting unit and should be defined in addition to the constant clearance as an objective 
function in the development of adjustment units. It is a measure of the speed at which too big 
clearance over the number of brake actuations can be corrected (9). 
 
SMART SYSTEM DESIGN 
 
At the beginning of the System Design phase, defining all requirements holistically is strictly 
required, both from a customer’s point of view and from the company-internal perspective. 
 
 
Figure 3: Adjustment speed according to (3). 
Mode 1:
Overcome constructive clearance
Mode 2:
Adjust-
ment
Mode 3:
Overload -
decoupling
Designparameter (DP)
F
u
n
ct
io
n
al
 R
eq
u
ir
em
en
ts
 (
F
R
)
Designparameter (DP)
Mode 
4:
Retract
-ing 
move-
ment
 
   (a)           (b) 
Figure 4: Design-Matrix organized (a), reduced and reorganized (b). 
This will be done with a kind of function requirement specification, in which the parameters 
are divided in control factors, signal factors and confounding factors. A classification of the 
parameters with their specification limits in the P-diagram is useful for a better overview of 
all factors. In terms of a functional block diagram, a system-based approach is before the 
design matrix is set up is advantageous. In this diagram, all components within the system 
boundary “Adjuster” are shown with regard to their connection property as well as their 
degrees of freedom. The consideration of the cause-effect relationship is, as a result of the 
operating modes, essential for the simulation strategy out of the Parameter Design and for 
arranging the design matrix. 
 
This classification into the various operating modes in the diagram of the cause-effect 
relationship gives a very clear understanding of the cause-effect relationship of the individual 
components and their functions among the components of each mode of operation. The 
different operation modes of the adjuster are listed below: overcome the constructive 
clearance, brake press (adjustment), overload mode (decoupling), release brake (rear rotary 
motion) and service function. The latter mode occurs only during maintenance of the brake 
and therefore is not applicable in the regular operation of the adjusting unit (9). 
 
After the determination of the operating modes and of the top level of the design matrix, these 
can be arranged. A viewing depth to the third or, at most, the fourth level, is advisable, which 
means that the quantified DPs out the function requirement specification should be in the last 
level, e.g. the maximum overload torque. It appears that such a complex product, with its high 
demands, results in a very large and confusing matrix; see also Figure 4a. 
 
It can be seen that the individual operation modes are stretched on the diagonal. In the 
horizontal and in the vertical, the dependencies of the FRs, and of the DPs, respectively, are 
marked with a blue field. In this matrix structure, however, is it not possible to infer a precise 
statement of the complexity of the system. Accordingly, a reorganization is performed with 
the algorithm according to (11). With the reorganization of the full design matrix, the number 
of coupling elements is significantly reduced. In addition, the clustering facilitates the 
interpretation of the matrix, because the functions belonging together are close to each other 
and are not widely scattered; see Figure 4b.The individual outliers above the diagonal must be 
considered in the next step. If these are acceptable, the independence axiom is satisfied. Since 
it is a single concept, the information axiom is omitted here and, in accordance with the 
definition of SMART, the Parameter Design phase can be skipped to. 
 
SMART PARAMETER DESIGN 
 
The new adjustment unit was developed with the use of SMART. Because of the high 
simulation effort, a new simulation method (SIM-SMART) was designed and implemented. 
This adaptive simulation method is published in (9) and will not be explained in detail. As an 
example, to investigate the robustness of the adjuster, 43 parameters, 32 control factors and 
11 noise factors were defined from the previous sensitivity analysis. Based on the simulation 
strategy, the 32 control parameters are composed of 7 Brake-Parameters (BP) and 25 Adjust-
Parameters (AP). An exclusive consideration of the adjuster with the objective function 
constant clearance or adjustment speed does not make sense, because the clearance is 
composed of the bridge way of the brake and of the adjustment path of the adjuster and thus 
contains parameters which are located outside the system boundary of the adjuster. 
 
For a high number of parameters, an optimization and robustness analysis by TM is 
recommended. The prerequisite for using the TM is present, since there is no high mixing 
(significance and effects between the parameters). As a result of any existing non-linearities, 
the Taguchi experimental design for the internal field (control factors) is planned on three 
levels (L81(3
32)). Following the principle of robust design, the external field is interpreted 
(noise factors) on two levels (L12(2
11)). This results in a number of trials, for a total of n = 
972. SIM-SMART takes about tsim = 4 min for an execution, which results in a total time of 
tsim_ges = 64.8 h. In comparison, a pure FE-simulation of the adjuster with the same number of 
attempts has an execution period of tsim_ges = 162 d. 
 
The analysis of the experimental design takes place after TM by considering the variance of 
the nominal parameter settings. For this purpose, the target value problem II nominal-the-best 
signal-to-noise ratio is applied (14) and is defined as follows: 
 
 𝑆/𝑁𝑛𝑜𝑚 = −10 𝑙𝑜𝑔(𝑠𝑖
2) (2)  
 
In Figure 5, both the mean of S/N ratios and the Mean of Means of the individual parameter 
levels of the control factors are shown. With the exception of the significant APs 23-25 and 
BPs 2 and 6, all control factors are placed at the level with the maximum S/N ratio (lowest 
diffusion), since their mean value changes marginally. With the significant parameters, a 
compromise between high S/N ratio and mean value needs to be deferred to. The exception is 
the AP 23, which has its smallest variation in the area of the mean value. BP 6 should be set 
to the lower parameter level 1 and BP 2, despite the greater dispersion, the average parameter 
level 2 should be set, analogous to the AP 24 parameter level 3. Due to the highly fluctuating 
mean value of AP 25, the parameter level 2 should be set, although it has the largest variation. 
The difference between the minimal and the maximum specification limits of the adjustment 
speed and the clearance are shown in Figure 6. The spread of the DPs, which are given to the 
Parameter Design phase, is brighter and outside of the required limits. A possible smaller 
 
 
Figure 5: An extract from the results of the nominal control factors out of the Taguchi-DoE. 
 
 
Figure 6: Comparison of the adjustment speed and clearance of the given DPs to the Parameter Design phase and 
the nominal DPs found at the end of the Parameter Design phase. 
66,3
67
67,7
1 2 3
Brake-Parameter 6
1 2 3
Adjust-Parameter 25
1 2 3
Brake-Parameter 2
Mean of Means [mm]
1 2 3
Adjust-Parameter 24
0,8
0,88
0,96
1 2 3
Adjust-Parameter 23
Mean of SN ratios [dB]
spread within the required limits of the adjustment speed and of the clearance was found, 
based on the nominal parameter levels of APs and BPs; see above. 
 
SMART TOLERANCE DESIGN 
 
After the subsequent experiment confirms the nominal parameters levels, a nominal optimal 
design is defined, which has qualitative the lowest variations and reaches the predetermined 
target value. It can now be entered in the Tolerance Design using SMART and the existing 
variations in the system can be described quantitatively. In these last iterative phases, two 
steps are performed; see Figure 2. In the first step, the robust design, in which the actual 
variation is conformed to the desired variation with the statistical experimental design and the 
variance decomposition, is to be determined. This is implemented by means of evaluation 
factors for the production costs in combination with the variance decomposition. The last step 
is the integration of the cost aspect and its optimization (cost and loss analysis) using 
Taguchi’s Quality Loss Function. The process of both steps is separated as the primary goal:  
the development of a robust product. At the beginning of the Tolerance Design, the 
production possibility must be clarified and compared with the final frontier model 
experiment. If successful, the loop of Tolerance Designs can be exited. A testing strategy, 
which confirms the reliability required in the ideal case, is defined on the basis of given test 
potentials. 
 
DISCUSSION AND CONCLUSION 
 
The integration and association of AD with the TM in SMART make it possible to offer a 
structured approach at the functional level in the early development phase. With AD, 
functional dependencies between DPs and FRs can be demonstrated at an early stage, which 
possibly lead to complex system structures and, consequently to failure of the product. In 
addition, the functional analysis of the components in the system gives the developer a system 
analysis in hand, which in turn can be used for other applications, such as FMEA. A 
preliminary comprehensively-developed FR specification is essential, and should be present 
during the entire development phase. Using this and the AD, all necessary parameters for a 
robust and reliable design can be defined at an early stage and can be shown systematically in 
the P-diagram, which is the basis for the parametric study. Based on the P-diagram, a 
simulation model must be modeled in the Parameter Design phase, which at most captures all 
the parameters and FRs and provides a small computing time. 
 
Without this groundwork, the subsequent parametric study can not be carried out consistently 
and efficiently. SIM SMART gives a very good possibility of adaptively adding potentially 
complex simulations and thus enables a simultaneous engineering. This has the distinct 
advantage of enabling early checks of the FRs of the product. Another important point for 
modeling the simulation model is to define the simulation strategy, which must be defined 
prior to modeling. In the presented example of the adjuster, the aim of achieving a constant 
clearance and a high adjustment speed is not possible without considering the overall brake. 
Thus, the system limit has to be extended here. 
 
As SMART points out in its approach, a specific determination of the applicable method is 
not useful. SMART specifies that the developer can consider his appropriate free space on his 
own, and which methods he posits, using the procedure in the Parameter Design, by TM or 
RDO. However, SMART is a basic systematic structure of the development method in line 
with the robust design ideas. Although the current stage of the project, the RDM SMART, is 
not complete, it can be used as a complete development method based in successful 
preliminary studies.  
OUTLOOK AND FURTHER RESEARCH 
 
In the current state of the project, the methodological approach of Tolerance Design is 
implemented further by SMART after the successful validation tests or confirmation 
experiments. The method has been successfully implemented on individual components of the 
brake, for example through the overload clutch of the adjuster. Thus, it is predicted that the 
method can be successfully performed on the brake. In addition, some preliminary work, such 
as clarification of the manufacturing processes and costs, are done as indicators. 
 
Further research work is related to the implementation of reliability in terms of the failure 
modes analysis, the fatigue testing (both by simulation and real terms) and the integration of 
random failures in the Parameter Design. In addition, early reliability statements are to be 
integrated in the early System Design phase. Finally, after a successfully- completed 
Tolerance Design, SMART should be validated as an integrated development methodology 
for the robust design idea. 
 
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