topology optimization used to achieve frequency … kingdom... · anexisting bracket design and...

Copyright © Altair Engineering Ltd, 2000 9 / 1

TOPOLOGY OPTIMIZATION USED TO ACHIEVE FREQUENCY TARGETS OF AN ENGINE BRACKET

LOTUS ENGINEERING B J G Kidd

Principal Project Engineer Lotus Engineering, Lotus Cars Ltd

Hethel, Norwich, NR14 8EZ Abstract : Topology optimisation technology is becoming increasingly used in the design process of automotive

components. This technology can be applied very effectively to simultaneously achieve static compliance and frequency targets for structural designs. The paper provides an industry perspective on how this technology is applied to a production bracket and the important role the designer and engineer play in converting the optimised material layout into a component which can be manufactured. It is demonstrated that the combination of topology optimisation and design knowledge can provide a design solution which could not otherwise have been achieved.

Keywords : Topology Optimization, Engine Bracket Design, OptiStruct 1.0 INTRODUCTION In the highly competitive automotive industry, there is a continual initiative to reduce the design cycle time. Optimisation technology provides a scientific method for automatically determining the most efficient ideal design. Application of this technology can reduce the design cycle time and produce economic designs without compromising functionality or fitness for purpose. The technology was applied to development of an automotive engine mounted bracket. An earlier design of the bracket had been shown to be unable to reach the natural frequency targets imposed on the new design. Topology optimisation software was applied to the development of the new bracket design. Noise and vibration, stiffness and durability requirements provided the constraints on the design. Package space for the component was dictated by surrounding engine components and positions of the attached items. An optimised shape for the part was derived from assessing both static and natural frequency performance simultaneously. Considerable manufacturing constraints existed for the component and re-definition of the idealised shape was required to provide the final design.


2.0 OPTIMIZATION METHODOLOGY The process of developing a prototype design from initial package space definition and design constraints has four main phases (Figure 1). Phase I requires definition of the package space and the designable and non-designable portions. Non-designable volumes would usually apply at bolt locations and fixing points. Phase II requires definition of the design optimisation problem. The global objective, load cases and constraints are defined in this phase. In the case of the bracket problem documented here, the global objective is to minimise the global compliance of the system for static loads and modes, subject to minimum natural frequency constraints, without increasing the mass of the bracket significantly above the original design. Phase III covers post processing of the results and visualization of the idealised shape. An iso-surface plot of model densities is generated using HyperMesh [2]. Sections through the optimised shape are also generated in HyperMesh using the cutting plane functionality. In the final phase, phase IV, modifications to the final shape are made to meet the manufacturing constraints. This is a very interactive process and requires human skills and knowledge from analysis, design and manufacturing engineers to finalise the shape. 3.0 APPLICATION OF METHODOLOGY 3.1 Description of Bracket The bracket component is required to be an aluminium alloy pressure die casting. The bracket is mounted on the front of an engine block at four bolt locations. Mounted on the lower half of the bracket with three

bolted connections is an air conditioning compressor. Attached with three bolts through a flanged connection at the top of the bracket is a power steering pump. The material for the bracket is Aluminium with the properties summarised in Table 1.

Figure 1: Optimization Methodology


Property Value

Young’s Modulus (GPa)

Poisson’s Ratio

Density (kg/m3)

75

0.32

2,750

Table 1: Material Properties

Loading of the system is from belts connected through pulleys to both the Pump and the Compressor. Engine vibration provides the source of dynamic loading to the bracket transmitted through the bolted mounting positions. 3.2 Definition of Optimization Model The model was defined to include the attached components, pump and compressor, the periphery of anexisting bracket design and design space inside and outside the periphery.

Transfer of geometric data defining the non-designable volumes of the system was performed digitally using 3D CAD interfacing to HyperMesh. Meshing was performed in Hypermesh using linear tetrahedral elements for volume definitions and four-noded linear quad elements for simplifications of the attached components. Idealisation of the attachments of the compressor and pump to the bracket was made using rigid elements. The model is shown in Figure 2. The geometry for the design space was defined by inspection of the bounds defined by surrounding components available through real assemblies and 3D CAD data. Design space is identified in Figure 3. Two load cases were defined for the model. Belt loads (Table 3) were defined in a linear static load case. An eigenvalue extraction load case was used to find the first four modes of the system. Topology optimisation was performed using OptiStruct [1]. OptiStruct uses the homogenisation

Figure 2: Optimization Model Including Attached Components


method to optimise material layout. The optimisation problem was defined as follows: Global objective function: minimise compliance. Lower bound natural frequency constraints: i) First mode natural frequency, 420 Hz ii) Second mode natural frequency, 440 Hz iii) Third mode natural frequency, 460 Hz The topology optimisation was used to minimise the system compliance for the static and modal extraction load cases simultaneously. 3.2 Visualization of results The results from the optimisation analysis of greatest importance are element densities. A threshold surface can be defined which bounds all material volumes with densities above a value of 30%. This allows three-dimensional visualisation of the optimised shape computed by the solution procedure. The optimised shape for the bracket is shown in Figure 4. Sections through the component are provided (Figure 5a to 5b) showing contours of material density. Red areas indicate 100% density and blue areas indicate 0% density (no material). The white hatched region indicates the section predicted by OptiStruct .

The natural frequencies for the optimised design are provided in Table 2 and are compared with the results for the periphery bracket (original design without stiffening, Figure 2) and a previous stiffened design. The lowest natural modes for the system occur due to global oscillations of the pump and compressor supported on the bracket stiffness. A significant improvement was found in the first mode natural frequency of the optimised bracket over the previous stiffened design for a similar total weight.

Figure 3: Design Space Definition

Figure 4: Optimised Shape Defined by OptiStruct


Section 2

Section 1

Section 3

Section 4

Section 5

Section 6

Section 7

Section 8

Figure 5a: Section Locations

Figure 5b: Optimised Bracket Geometry Sections


1. Periphery Bracket Mode No. Frequency Mode Shape Description

1 2 3

240 322 387

Lateral Pump

Lateral Pump / Vertical Compressor Vertical Pump / Vertical Compressor

2. Optimised Bracket

1 2 3

420 453 478

Vertical Pump / Vertical Compressor

Lateral Pump Lateral Pump / Lateral Compressor

3. Previous Stiffened Design

1 2 3

339 367 410

Lateral Pump

Vertical Compressor Vertical P/S Pump

3.3 Design Modifications The design produced by OptiStruct could not take into account the restrictions imposed by the manufacturing process, which could not simply be defined as non-designable areas of the design space. The manufacturing process chosen for the part required vertical ribs and geometry, which could be cast efficiently using a single upper and lower die. The OptiStruct results provided a clear indication of where material was required to provide a design which would meet the frequency targets. The design was re-interpreted to provide an equivalent ribbed design. This process involved several important phases. i) The optimised geometry of the component was studied by the design team. The isosurface

plot produce by HyperMesh was used for this purpose and provided in a form which could be viewed in a 3D graphics environment. Mode shapes were investigated to understand the dynamic response of the idealised shape so that this could be replicated using a ribbed design equivalent. A typical mode shape for the pump and compressor is shown in Figure 7.

ii) An initial ribbed design was defined based on the understanding of the required material

distribution and re-analysed to extract new mode shapes. The optimised shape concentrates material in areas A and B. In area A, a closed section is introduced, ideal for providing maximum efficiency for torsional stiffness, increasing the lateral mode frequency of the pump. The ribbed design replicated this stiffness by introducing the highest possible concentration of horizontal ribs in this area and vertical ribs running to mounting points to hold all ribs in position


during deformation. In area B, an array of ribs was introduced to replicate the stiffness of the material introduced by the optimisation software. The maximum number of ribs was introduced in this area and their efficiency maximised by tying them to adjacent mounting points.

The frequency results from redefinition of the design are summarised in Table 3. It was found that the design target of 400 Hz was met within 1% (396 Hz) for the final design. Since the final design natural frequencies were so close to the required target values, the final stage of application of size and shape optimisation was not performed (Figure 1). This process can be used to adjust rib thickness to fine-tune the efficiency of the structure.

Mode No. Frequency (Hz) Description

1

2

3

396

433

456

Vertical/Lateral Pump / Vertical Compressor

Lateral Pump / Vertical Compressor

Vertical Pump / Pump Flywheel / Lateral

Compressor

Table 3: Summary of Natural Frequencies and Mode Shapes for Revised Design

Figure 6: Revised Design Figure 7: First Mode Natural Frequency Displacement Contours


The original and revised designs following the optimization process are shown in Figure 8. The contrasting rib layouts illustrate how the idealised material layout generated in the topology optimization analysis have been re-interpreted to produce a new design meeting the frequency targets. Most notably, additional ribbing has been introduced in regions A and B to provide higher generalised stiffness in the AC compressor and pump modes respectively. Modal testing has been performed on the bracket and excellent correlation achieved (tested first mode natural frequency 396 Hz, simulated natural frequency 396 Hz), demonstrating the value of introducing finite element based methods early in the design process. 4.0 STRESS ASSESSMENT A further design modification was defined following the design optimization process. A pulley boss was introduced (Figure 9). This was introduced to the verified finite element models and the opportunity taken to apply operational and fault load cases to the bracket to assess the peak stress amplitudes in the component. Stress results are given in Figure 10. The maximum value was compared with the fatigue limit stress for the die cast Aluminium and confidence gained in the durability performance of the component. The low cyclic stresses resulting from engine vibration excitation resulted from the low dynamic amplification factors – a direct result of the increased first mode natural frequency.

Figure 8: Cast Brackets Before and After Optimization

Figure 9: Finite Element Model of Revised Bracket

Design


5.0 CONCLUSIONS Topology optimisation has been used to define an idealised material layout for an engine bracket component, which has exceeded the design requirements for stiffness and natural frequencies. It has been necessary to re-define the idealised material layout of the bracket to allow use of economical and well established manufacturing techniques. This process had to be carefully controlled so that the benefits of the optimised layout could be maintained in the revised ribbed design. Efficient communication of optimised geometry and revised geometry between the members of the design team was vital for the efficiency of this process. Efficient meshing algorithms for developing new finite element models of the revised bracket design were also extremely important in this process. Design and manufacturing experience together with a full understanding of the optimised shape allowed re-definition of the shape to meet the manufacturing constraints whilst maintaining the frequency requirements. At the end of the work a final design had been developed, which could be manufactured using similar procedures to those used for previous designs, which met challenging new natural frequency and durability requirements. 6.0 REFERENCES [1] Altair OptiStruct Version 3.2, 1998. Altair Computing , Inc.

[2] Altair HyperMesh Version 3.0, 1998. Altair Computing , Inc.

Figure 10: Peak Stress Amplitudes from Combined Load Cases

topology optimization used to achieve frequency … kingdom... · anexisting bracket design and...

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