TBR Technical Corner: Optimized Braking System Sizing by means of a Parametric 1D Brake Model (Part 1 out of 3)

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Source: Applus IDIADA

This article is the first of three TBR Technical Corners by Narcis Molina, Project Manager, Braking Systems in Applus IDIADA, about finding the optimal braking system for a vehicle.

This article presents a methodology that incorporates a 1D (non-geometric) brake model, together with conventional vehicle tests, into the solution of problems associated with the sizing of a braking system.

The 1D tool is aimed at predicting the main braking attributes, such as pedal feel or thermal capacity under repeated snubs, and the fulfilment of the legislative requirements —service, emergency and parking brake performance. The model recreates a parametric brake system, and thus allows engineers to understand the impact a parameter (e.g. a specification) might have on the overall performance when it is altered. This calculation provides valuable assistance when sizing a braking system.

The methodology presented succeeds in reducing the number of vehicle test iterations throughout the brake sizing stage, thus being more cost-effective and less time-consuming than the usual trial and error approach to select the off-the-shelf components available from suppliers.

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The vehicle under study, an off-road car, suffers from unacceptable pedal feel (deemed as ‘spongy’) and, most importantly, does not satisfy the requirements laid down in UNECE Regulation No. 13 for the secondary braking system.

Brake-pedal feel primarily refers to the perceived relationship between the force applied on the pedal by the driver’s foot and the pedal travel, as well as the deceleration experienced by the vehicle —and, by extension, the driver’s body (1). It is fundamental to guarantee the customer’s confidence in the braking performance of the vehicle (2). Several authors have presented a number of methods for predicting brake pedal feel at the design stage: in-depth studies that focus on the influence of the vacuum booster specifications (3) or the frictional material properties (4), and other holistic works that incorporate several system components characteristics (5) (6) (7).

Brake performance, on the other hand, has become a very important factor because of legislative safety standards such as UNECE Regulation No. 13 (8) —or its Indian counterpart, AIS-150 (9). These regulations specify the minimum requirements to bring the vehicle safely to rest under normal conditions —service braking— and if a failure occurs —secondary braking.


The methodology presented below is divided into three phases:

  • Phase 1: vehicle and brake specifications are gathered in order to model the problem by means of the 1D tool. Once the simulation is completed, prediction results are correlated using the previously-measured vehicle test data.
  • Phase 2: it consists of modelling the available replacement off-the-shelf components, thus reducing associated costs and getting shorter lead times; the outcome is a gap analysis, i.e. exploring the relative impact that each modified component has on the critical attributes.
  • Phase 3: the new components are tested on the vehicle; newly-obtained evidence is compared against the baseline experimental results in order to check whether the targeted improvements are successfully met.


Phase 1

Tables 1 to 4 summarize the vehicle and brake specifications for the baseline configuration. Note that none of the listed parameters needs to be specifically measured, as they are design (nominal) specifications that can be easily obtained from the component supplier or the OEM itself.

Table 5 lists the test results obtained with the baseline vehicle configuration. The test procedures and requirements strictly adhere to the UNECE Regulation No. 13[1] for a vehicle of category N2 under GVW condition. When the actual result is not objectively recorded, the corresponding value is left as ‘NA’.

[1] UN ECE Reg. No.13 is aligned with the Indian standard “AIS-150: Requirements for Approval of Vehicles of Categories M2, M3, N and T with regard to Braking”.

As indicated in Table 2, the baseline vehicle uses an I-brake split, where the primary circuit feeds the front brakes, whilst the secondary circuit corresponds to the rear axle. Note that the MFDD of the primary fail test —braking only with the rear brakes— is 1.8 m/s2 and, hence, does not comply with the minimum deceleration of 2.2 m/s2.

Besides the legislative breach, the brake pedal feel of the baseline vehicle also raises concerns. No objective data is available, but the feel is subjectively deemed by an expert driver as ‘spongy’: the pedal stiffness is too soft, meaning that —under a ramp application— the pedal travel / vehicle deceleration relationship is poor.

The absorption of a brake component is the volume of brake fluid that is ‘consumed’ per pressure level. Its judgment is fundamental in order to characterize the brake pedal travel and, ultimately, understand the customer’s confidence in the vehicle’s braking performance.

For its measurement, a ramp apply is conducted while measuring the system pressure and the pedal stroke —baseline condition. Then, both brake circuits are sequentially closed (by means of taps) at different points in order to isolate each component. For each condition, the ramp apply is repeated and both pressure and stroke, recorded. As shown in Figure 1, the front brakes (1) are firstly closed, followed by the rear brakes (2), the front hoses (3) and the rear hoses (4). The remaining volume of brake liquid corresponds to the piping and the ABS module.

The output of the test relates, for each circuit condition, the pedal stroke and the brake line pressure. Hence, volume is not a direct measurement, but an estimation based on the actual pedal travel and the theoretical dimensions of the master cylinder and the pedal box.

Table 6 shows the actual absorption values of the different components that make up the braking system. Note that ‘front’ and ‘rear’ consider the volume consumed by the components on both sides of the axle; ‘piping + ABS’ takes into account all the pipes and the ABS module.

About Applus IDIADA

With more than 25 years’ experience and 2,450 engineers specializing in vehicle development, Applus IDIADA is a leading engineering company providing design, testing, engineering, and homologation services to the automotive industry worldwide.

Applus IDIADA has locations in California and Michigan, with further presence in 25 other countries, mainly in Europe and Asia.

[1] UN ECE Reg. No.13 is aligned with the Indian standard “AIS-150: Requirements for Approval of Vehicles of Categories M2, M3, N and T with regard to Braking”.

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