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In brake systems, where the components are exposed to mechanical and thermal loads, the numerical analysis is very helpful. The main function of the brake system is to control or reduce vehicle’s speed by transformation of kinetic and potential energy in thermal energy. Using finite element method and Abaqus application, the present work proposed a model to study the impact of these loads on the performance of a pneumatic S cam drum brake’s friction material. The model included the effects of the rivet process; brake torque and warming in one of the 17 t bus front brake lining. Areas where the stresses vary with considerable amplitudes during temperature increase and brake application were identified. Also, it was possible to compare results of the numerical model to vehicle’s experimental measurements and understand its proximity to real braking events. By the application of the methodology and using the numerical model, proposed in this work, it will be possible to contribute considerably for a more accurate design of the friction material, besides undertake a better selection of the sub-compounds which it is made of.

During pneumatic brake system actuation, the vehicle’s driver, by application of the brake pedal valve [

In a typical commercial vehicle application, brake system is actuated several times in a repetitive way [

Numerical works on the effects of mechanical loads on these components have been published by some au- thors, as described for instance, on reference [

Neglecting the wear, considering perfect contact between lining and drum during braking and using the energy conservation principle, in accordance to the references [

On the other hand, friction material subcomponents selection, including its quantity and relative volume, will also be easier to be determined, once known the effects of mechanical loads and temperature distribution on the whole composite.

In the present work, the thermal and mechanical effects, including de riveting process and the temperature increase due to successive braking actions, on the brake lining, are studied and presented. The friction material, in this work, was numerically molded as an orthotropic material (due to its manufacturing process) [

In urban buses applications, where the brakes are applied with high frequency, the cooling intervals are not larger enough and the convective effect on the drums is not efficient, the temperature level can cause reduction of mechanical resistance, increase of wear and may provide considerable impact on the friction material stress distribution.

On

Based on that, the subject of this work is to build and validate a numerical model that could help engineers to:

・ Correctly design (dimension and develop) brake’s friction material;

・ Understand thermo-mechanical phenomena on brakes in order to turn new composites development easier;

・ Understand mechanisms of failure on friction materials during durability tests after consecutive cycles of brake application.

The numerical model was built up with applicative Abaqus 6.12 and the input data was calculated based on field urban bus braking application experimental measurements.

Development of this work has consisted on the following steps (

A 17 t load capacity bus, equipped with S cam drum brakes has percussed a typical 23 km total extension urban route in Osasco, SP, Brazil. During this percuss driver has applied vehicle’s brake pedal several times in order to keep its velocity the same and stop at bus stations and transit lights, making the brakes to accumulate thermal energy until completing the whole route.

The total time of the route was approximately 2 hours (7200 s). During this time some data was acquired by special equipment:

・ Vehicle’s velocity: v;

・ Vehicle’s altitude: h;

・ Pneumatic pressure inside front mechanical brake actuator:

・ Averaged temperature of front brake’s friction material:

・ Temperature of front brake’s friction film: T;

・ Environment temperature:

The instant of highest actuator pressure and brake torque has occurred during a braking performed between 6935 s and 6965 s of vehicle’s percuss. During this interval, the friction film temperature, T, measured by ther- mocouple positioned 1 mm from the drum’s internal surface [

Variation of the vehicle’s linear velocity, v, and altitude, h, during this braking was also obtained. It’s presented on

In this section, the basic theory applicable to the work is presented. Calculation of the data necessary for the numerical simulation and preparation of the model are also part of this section.

The maximum contact pressure on the friction material during the braking in S cam brakes is defined by the Equation (1), where W is the lining width and

The expressions

On the other hand, the brake torque, _{0} [

The angles

The contact pressure on the friction material’s surface varies with the angular position,

It’s easy to observe that the maximum contact pressure will take place at

Consider the drum brake system diagram defined on

The element of friction force,

After splitting both sides of Equation (4) by the element of area,

where:

1) Mechanical Energy Conservation

The heat generated on the brakes can be calculated by the mechanical energy conservation principle. Neglecting optical, noise, particles pulverization and other forms of energy [

where m is the vehicle mass, g is the local gravity acceleration and k is the rotational elements inertia factor. Typical values of k are between 1.03 and 1.60 [

2) Energy Absorbed by the Brakes

The quantity of energy absorbed by the brake,

The averaged heat flux,

Part of brake energy is absorbed by friction material and part by the drum. Based on the energy conservation principle and considering perfect contact, it’s possible to describe:

where _{} denotes the averaged heat flux through the drum and _{} and

In short braking events, the convective effect during brake’s actuation on both components can be neglected, then

where

Once determined heat flux through friction material and drum, it’s possible to define the concept of energetic factor,

3) Distribution of Friction Material’s Heat Flux per Unit of Area

The brake potency can be determined for each instant of the braking once known the brake torque,

Then, the instantaneous friction material’s heat flux can be calculated using the concept of energetic factor:

The brake torque, function of time,

That leads to:

The friction material’s heat flux distribution per unit of area is obtained splitting Equation (19) by the element of area,

Then, it’s defined, for one brake lining, in accordance with the references [

where:

All data related to the brake design, vehicle’s characteristics and calculation of the loads can be found on the Appendix A.

The friction material is usually fixed on the brake shoe surface by rivets. The rivet process consists in applying an instantaneous peak of load on the rivets, making them to deform and compressing the joint components each other.

The peak of force on the rivets,

It was assumed that the friction material was orthotropic with isotropy on the plans orthogonal to its manufacturing process compression direction [

Characteristics | Unit | Value |
---|---|---|

Rivet’s body diameter―d_{r} | [m] | 6.70 × 10^{−3} |

Rivet sectional area―A_{r} | [m^{2}] | 3.53 × 10^{−5} |

Peak of force on the rivets―F_{p} | [N] | 8829.00 |

Pressure distribution on rivet’s extremities―p_{p} | [MPa] | 250.40 |

Characteristics | Unit | Value |
---|---|---|

Fibers relative volume―Glass E-type | [%] | 40% |

Matrix relative volume―Phenolic Resin + other compounds | [%] | 60% |

Friction material’s resistance stress at fibers direction―σ_{RL} | [MPa] | 94.16 |

Friction material’s resistance stress at compression direction―σ_{Rt} | [MPa] | 85.39 |

Friction material’s Poisson coefficient between fibers and compression directions―ν_{Lt} | - | 0.28 |

Friction material’s Poisson coefficient between compression and fibers directions―ν_{tL} | - | 0.12 |

Friction material’s Poisson coefficient on the isotropic plan, Lz―ν_{z} | - | 0.20 |

Friction material’s young modulus at fibers direction―E_{L} | [GPa] | 4.08 |

Young’s modulus on compression direction (t)―E_{t} | [GPa] | 1.82 |

Friction’s material Shear modulus between L and t directions―G_{Lt} | [GPa] | 2.31 |

Friction material’s thermal expansion coefficient at fibers direction―α_{L} | [K^{−1}] | 5.90 × 10^{−6} |

Friction material’s thermal expansion coefficient at compression direction―α_{t} | [K^{−1}] | 1.20 × 10^{−5} |

Numerical analysis of the braking was thermal coupled with mechanical (plan strain state). All the simulation was split in three steps, representing respectively the riveting process, the warming of the brakes until the begin- ning of the braking and the braking.

Before the steps, the initial temperature of the components, as well the model anchorage was defined. The initial temperature of lining, brake shoe and rivets were all set as environment, T_{∞} = 22˚C.

On the first step, the peak of pressure on the rivet’s heads and basis were applied. It was necessary to input the plasticity curve of the rivet material in the model (SAE 1020) [

On the second step, the friction film temperature was fixed in 322˚C during all the time that preceded the braking (6935 s), establishing a heat flux through the brake components, making them to warm, up to the ther- mal equilibrium was attained.

The braking event was simulated on the third step.

Before performing simulation, it was necessary to enter calculated data (Appendix A), to define material pro- perties: rivet, isotropic―SAE 1020; shoe, isotropic―EN-GJS-500-7 and friction material, orthotropic

The convective coefficient, h, has corresponded to the natural convection. Conductance between different com- ponents was compatible with the materials [

After simulation, temperature distribution and most critical contact shear stresses were obtained. They are presented on the following sections.

Temperature distribution are presented for both thermal equilibrium and braking steps.

The minimum and maximum temperature of the assembly at the end of Step 2 were respectively 243˚C (516 K) and 319˚C (592 K).

During the braking, the hottest area of the friction material is near to the angular position

It’s possible to observe on graphic of

The next graphics (

All of these nodes have presented contact shear stresses with considerable magnitude variations, however, the highest amplitudes were verified on nodes 85,763 and 85,491, near to

During thermal equilibrium step, stress variation on node 85,763 due to temperature increase (from 22˚C to 255˚C) was 23.50 MPa. During this time it’s possible to verify inversion of the stress orientation around the node. The amplitude of contact stress during the braking was 9.30 MPa on the opposite orientation.

On the node 85,491 the contact stress variation during thermal equilibrium was 14.70 MPa. When the brakes were applied the stress was reduced in 12.70 MPa, showing that during braking application, there is also chang- ing of the contact shear stress orientation.

Despite absent of a methodology acceptable for friction material fatigue resistance determination, it’s possible to

elaborate a hypothesis based on the numerical results.

After comparing the friction material of the vehicle’s front brakes after durability tests (

numerical model (Figures 13-15), it was possible to associate the failures to accumulation of damage, due to cyclic contact stresses resulting from successive braking actions, on the interface between friction material and rivet.

The contact shear stresses at nodes 75,978 and 85,763 change in value and in sense, during the period of thermal equilibrium, as can be seen in

The

In this topic is presented a comparison between numerical results and experimental measurements performed on an urban bus with same type of brakes.

Area Analysis | Thermal Equilibrium (Step 2) | Braking (Step 3) | |||
---|---|---|---|---|---|

Temperature Variation | Stress Variation | Temperature Variation | Stress Variation | ||

Near to S cam | Node 76030 | 228˚C | 6.00 MPa | 0˚C | 3.00 MPa |

Node 75978 | 233˚C | 4.00 MPa | 0˚C | 0.70 MPa | |

Near to | Node 85763 | 238˚C | 23.50 MPa | 0˚C | 9.30 MPa |

Node 85491 | 238˚C | 14.70 MPa | 0˚C | 12.70 MPa |

The experimental deformation was measured by two one-directional strain gages (S_{2} and S_{3}) installed on the bus front brake friction material in different angular and radial positions (see

_{2} and S_{3}.

As it is possible to observe, experimental radial deformation along the time was in good agreement with numerical.

Temperatures were measured by thermo-couples

Experimental temperature distribution on front brakes was obtained after stabilization of the friction film

temperature [

Comparison between numerical and experimental temperature after stabilization shows a very good agreement. As can be observed _{1} (stabilization temperatures were 237.80˚C and 248.30˚C respectively for experimental and numerical data).

Comparison between numerical friction film temperature, obtained during simulation of the braking (Step 3) and experimental one, measured during the route of the bus in Osasco, SP (

The error verified during maximum torque instant and at the end of the braking was respectively 4.20% and 0.30%, as can be seen on

・ The main subject of the work, a numeric model and a methodology available and validated to be used by engineers, mentioned on Section 2, was attended because:

a. Critical areas, in terms of stress, identified on the model, have corresponded to areas where historically failures are observed during brake lining development tests. These stresses are related to the effects of the combination of thermal and mechanical load cycles on the surface contact between lining and rivets.

b. Numerical results are in good agreement with experimental data.

・ Friction material is vulnerable to cycling contact shear stresses on the interface between friction material and rivet’s head, mainly on the area with highest contact pressure, friction force and heat flux per unit of area

・ With a friction material fatigue resistance limit determination methodology available, it is going to be possible to estimate the life of it, once the quantity of braking cycles and temperature are known. This will be feasible by adjusting the S x n curve by Goodman method and counting the damage cycles by rain flow technic [

・ Nodes where highest amplitudes of stresses were verified concur with vertices (intersection of rivet holes walls and the plans in contact with rivet’s heads). This means that improvements on brake lining geometry, such as, elimination of the vertices by cutting sharp edges, could be applied.

・ Numerical model presented, built with Abaqus applicative, will find practical application in the automotive industry in analysis related to brake’s system projects, including new friction materials development. The model will bring the following benefits:

a. The effects of the vehicle’s application brake temperature combined with brake torque loads on the friction material can be previously predicted without necessity of vehicle’s road tests. This will save development costs and time;

b. Assuming hypothesis that friction material is orthotropic, simulations using this model will contribute to design of the composite friction material and its composition;

c. Development of improved brake lining geometry and relative volume of the composite compounds.

・ As suggestion for next works, it’s highlighted.

a. Improvement of numerical model, including other components, like brake drum, S cam and brake’s anchors and rolls [

b. Include variation of elastic properties of friction material with temperature.

c. Extend model to simulate effects of air convection through brake components during intervals between braking.

d. Include the effect of damage related to loss of lining materials resulting from brake action in the performance of the material in subsequent braking.

The authors are grateful to Smart-Tech for the discussions during development of the numerical model and out- put data analysis and to CAPES/MEC for the support to PPGEM/UFF.

Experimental brake torque curve was calculated by Equation (2) for each instant of braking using measured pressure inside mechanical actuator,

Per convenience, experimental brake torque curve was approached into linear and continuous functions,

The brake torque could be obtained for each instant of the braking, using the functions,

In a similar way, the maximum friction force per unit of area,

All the values are plotted in

It’s possible to calculate the heat generated on the brakes using Equation (7), data related to the vehicle (m = 17,000 kg and

The averaged heat flux through lining, ^{3} and 2050 kg/m^{3}. Using

On the other hand, angular velocity of the vehicle’s wheels, measured during the route, necessary to determine heat flux distribution on the lining surface, was approached into linear and continuous functions defined, per convenience, within the braking interval [0 s, 31 s], as shown on

The wheel’s angular velocity was calculated for each instant of braking by the functions,

Braking Time [s] | Torque T(t) [Nm] | p_{max}(t) [MPa] | F_{d}"_{max}(t) [N/mm^{2}] | Braking Time [s] | Torque T(t) [Nm] | p_{max}(t) [MPa] | F_{d}"_{max}(t) [N/mm^{2}] |
---|---|---|---|---|---|---|---|

0 | 0.00 | 0.0000 | 0.0000 | 15 | 5053.40 | 0.5415 | 0.2166 |

1 | 32.10 | 0.0034 | 0.0014 | 16 | 3926.70 | 0.4207 | 0.1683 |

2 | 446.10 | 0.0478 | 0.0191 | 17 | 2800.00 | 0.3000 | 0.1200 |

3 | 860.10 | 0.0922 | 0.0369 | 18 | 2800.00 | 0.3000 | 0.1200 |

4 | 1274.10 | 0.1365 | 0.0546 | 19 | 2800.00 | 0.3000 | 0.1200 |

5 | 1688.10 | 0.1809 | 0.0723 | 20 | 2800.00 | 0.3000 | 0.1200 |

6 | 2102.10 | 0.2252 | 0.0901 | 21 | 2800.00 | 0.3000 | 0.1200 |

7 | 2516.10 | 0.2696 | 0.1078 | 22 | 2800.00 | 0.3000 | 0.1200 |

8 | 2640.00 | 0.2828 | 0.1131 | 23 | 2800.00 | 0.3000 | 0.1200 |

9 | 2640.00 | 0.2828 | 0.1131 | 24 | 2800.00 | 0.3000 | 0.1200 |

10 | 2640.00 | 0.2828 | 0.1131 | 25 | 2576.00 | 0.2760 | 0.1104 |

11 | 2640.00 | 0.2828 | 0.1131 | 26 | 2016.00 | 0.2160 | 0.0864 |

12 | 2640.00 | 0.2828 | 0.1131 | 27 | 1456.00 | 0.1560 | 0.0624 |

13 | 3490.50 | 0.3740 | 0.1496 | 28 | 896.00 | 0.0960 | 0.0384 |

14 | 4908.00 | 0.5258 | 0.2103 | 29 | 336.00 | 0.0360 | 0.0144 |

14.50 | 5616.80 | 0.6018 | 0.2407 | 30 | 0.00 | 0.0000 | 0.0000 |

Characteristics | Unit | Value |
---|---|---|

Heat generated on the vehicle’s brakes―q | [J] | 2929780 |

Front brake’s absorbed energy―E_{n} | [J] | 798365.10 |

Front brake’s averaged heat flux― _{n} | [W] | 25753.70 |

Friction material’s averaged heat flux― _{L} | [W] | 2293.30 |

Friction material energetic factor―P_{L} | - | 0.09 |

Braking Time [s] | Angular Velocity ω(t) [s^{−1}] | q_{L}"_{max}(t) [mJ/mm^{2}s] | Braking Time [s] | Angular Velocity ω(t) [s^{−1}] | q_{L}"_{max}(t) [mJ/mm^{2}s] |
---|---|---|---|---|---|

0 | 0.00 | 0.00 | 15 | 2.00 | 7.99 |

1 | 15.44 | 0.39 | 16 | 0.52 | 1.61 |

2 | 15.78 | 5.57 | 17 | 0.10 | 0.22 |

3 | 16.12 | 10.96 | 18 | 0.10 | 0.22 |

4 | 16.46 | 16.58 | 19 | 0.10 | 0.22 |

5 | 16.80 | 22.42 | 20 | 0.10 | 0.22 |

6 | 15.32 | 25.46 | 21 | 0.10 | 0.22 |

7 | 13.84 | 27.53 | 22 | 0.10 | 0.22 |

8 | 12.36 | 25.80 | 23 | 0.10 | 0.22 |

9 | 10.88 | 22.71 | 24 | 2.04 | 4.52 |

10 | 9.40 | 19.62 | 25 | 2.04 | 4.16 |

11 | 7.92 | 16.53 | 26 | 2.04 | 3.25 |

12 | 6.44 | 13.44 | 27 | 2.04 | 2.35 |

13 | 4.96 | 13.69 | 28 | 2.04 | 1.45 |

14 | 3.48 | 13.50 | 29 | 2.04 | 0.54 |

14.50 | 2.74 | 12.17 | 30 | 0.00 | 0.00 |