Optimization of Brake Calliper Design: Model Parameters and Instructions

Task 1 – Hand calculation (30 Marks)

Details and information of the essential model parameters

As a freelancer, you can only afford one Altair Hypermesh FE License as such you have to maximize the computational resource at your disposal. Also, when analysing and optimizing the Calliper adhere to the following instructions:

Perform a three-dimensional analysis and optimization in the tasks below,

Statements in your report must be precise and concise, with valid justification for design decisions, Assume that the Calliper’s material operates in the linear elastic region,

The company has advised that the Calliper would be made from either of the Aluminium alloys shown in Table 1. This complies with strict regulations in the formula one industry, which has an upper limit of 80GPa for the Young’s modulus of Calliper materials.

Use the last digit of your student identification (SID) number to determine your material from Table 1. The peak stress in the final Calliper design must not exceed 75% of the Yield Strength.

Table 1: Material properties

The boundary conditions experienced by the Calliper is shown in Fig. 3, The internal surface of the hollow cylinder is fixed,

When the driver presses the brake pedal, the pistons moves out of their housing, clamping the disk in proportion to which the pedal is displaced. This cause the internal surface of the Piston housing and surfaces in contact with the brake Pads to experience a pressure P, shown in

Fig.  Please assume the magnitude of P to be 6MPa,

It is your responsibility to determine surfaces that experience this pressure and the direction of the pressure. With the information given please, proceed to attempt the tasks described below.

(Task 1 consists of two hand calculations Q1 and Q2 and the first part of the finite Element Analysis (CW1))

--- The value of q is the last two digits of your SID ---

Q1: For the structure in Figure Q1,

1. Discretise the structure with the least possible number DOFs and produce a table of element types and properties [2 marks]
2. Calculate all the element stiffness matrices in the global CSYS [4 marks]
3. Assemble the global structure stiffness matrix (with elements contribution) [3 marks]
4. Write the reduced stiffness matrix after the boundary conditions [3 marks]
5. Find the unknown displacements (in mm) [2 marks]
6. Find the unknown reaction forces (in N) [1 marks]

Nodes and elements numbers are given in Figure Q1 and You MUST use the labelling provided.

Q2: The structure in Figure Q2 is made of 2 horizontal members

1. Discretise the structure with the least possible number DOFs and produce a table of element types and properties [2 marks]
2. Calculate all the element stiffness matrices in the global CSYS [4 marks]
3. Assemble the global structure stiffness matrix (with elements contribution) [3 marks]
4. Write the reduced stiffness matrix after the boundary conditions [3 marks]
5. Find the unknown displacements/rotations (in mm/deg) [2 marks]
6. Find the unknown reaction forces/moments (in N/Nmm) [1 marks]

Nodes and elements numbers are given in Figure Q2. You MUST use the labelling provided.

1.1 Although the company is interested in the structural analysis of the Calliper, can you think of any other engineering phenomena (e.g. Fatigue, electromagnetism, heat transfer, vibration) which must be considered when designing the Brake Calliper. Remember to discuss why you think this phenomenon is important. Also, stating how finite element can be used to determine the performance of the Calliper with regards to your chosen phenomena.

1.2 The domain shown in Fig. 2 was constructed in the manner that prevents the Calliper from colliding with adjacent mechanical parts. The company would like you to perform an initially finite element assessment of the domain to confirm if there are indeed opportunities to create a better more efficient calliper. Using information given in the previous section:

1. Perform an FEA on the domain,
2. Complete a mesh convergence study for the domain while fixing nodes on the fixed surface for all degrees of freedom,
3. Repeat your convergence study by constraining the fixed surface with RBE3 elements,
4. Plot both convergence graph in a chart and compare and discuss the results
5. Discuss the maximum deflection and stresses in the domain making sure the domain is not already exceeding the deflection criteria nor is it exceeding the yield stress.
6. Explain six mesh quality metrics (e.g. aspect ratio, Jacobian) from your finest mesh in the RBE3 models,
7. Report the initial volume of your Calliper domain.
8. Carry out vibration analysis on the Calliper domain. The vibration analysis should simulate the scenario when Calliper domain is constrained (constraining the fixed surface) and setup to vibrate naturally - without any external excitation loads 

The Company wants you to conduct a single objective topology optimization of the domain using information given in the previous section. The objective is to minimize the weight or volume of the Calliper with a displacement constraint. The Company want the maximum displacement of the Calliper to be less than or equal to 0.5mm and are quite particular about this constraint. They will reject your optimized Calliper if it violates this constraint!

2.1 Discuss the relevance of this constraint on the performance of the Calliper,

2.2 Perform a topology optimization on the Calliper domain with appropriate parametric setting,

2.3 Decide on an appropriate density threshold and extract an optimized solution,

2.4 Analyse the performance of the optimized Calliper upholding the integrity of your results with a convergence analysis and discussing the performance of your results.

2.5 Discussing concisely the most suitable route for manufacturing your optimized solution.

The Company anticipate that vibration could be an issue with the topology-optimized solution.

2.6 Carry out vibration analysis on the Calliper optimised domain. The vibration analysis should simulate the scenario when Calliper domain is constrained (constraining the fixed surface) and setup to vibrate naturally - without any external excitation loads

2.7 Compare and discuss the maximum Calliper stress against the yield and estimate a factor of safety.