New bogie suspension concept

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New bogie suspension concept

Philip Sjöstrand

Mechanical Engineering, master's level 2019

Luleå University of Technology

Department of Engineering Sciences and Mathematics

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Thanks

This project was not a one man’s job. Without guidelines and help through the project, there wouldn’t be any results. Major gratitude for all the help and support from the people at Volvo CE in Bra˚as and my mentor at LTU. A special thanks is directed at:

• Marcus Andersson, mentor at Volvo CE.

• H˚akan Stigsson, constructor at Volvo CE.

• Amir Abdou Mahmoud, CAD support at Volvo CE.

• Anders Pettersson, mentor at Lule˚a University of Technology.

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Summary

There is always a desire to develop and offer the best and most profitable products on the market. This master thesis in mechanical engineering investigates the possibility to reduce the costs of the bogie suspension on Volvo’s articulated haulers. The so called stays in the existing bogie suspension are significant components that connects the axle housings to the frame. The existing solution consists of stays that are expensive, heavy and time consuming to manufacture. Concepts in CAD will be compared to each other and a final concept will be evaluated in more detail.

Totally five concepts were generated and modelled. They were compared regarding strains on rubber parts, required stay dimensions, collision between different parts and axle movements.

Two proceeded concepts for further development after the evaluation and two new concepts were generated. A new comparison was made with additional tests.

Simulations confirmed that it was only possible to proceed with one of the two developed concepts because one of the concepts would require large dimensions to manage the applied forces. The selected concept was redesigned and adapted to be as realizable as possible.

Bushing kits, reinforcements, and detailed designs of parts were considered. Simple FEM calculations was only made on parts that wasn’t depending on components on the frame since these calculations would be too advanced and time consuming. The resulting concept needs more work to be realizable since there are geometry optimization on molded components left as well as advanced calculations when integrating the solution on the frame. A weight loss of approximately 95kg and a cost reduction of 3700SEK was made. Further investigations has to be done to determine if it’s possible to obtain a positive business case with the new bogie suspension.

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1 Introduction

Volvo Construction Equipment is a leading manufacturer that produces vehicles with high quality, environmental care and safety for the construction market. One of their products are articulated haulers, which they where first in the business with back in 1966. Nowadays, they are considered to be the top of the line manufacturer compared to its competitors and offers a selection of different models. The model range stretches from the base model A25 that can load 25 short tons and up to the top model that can load 60 short tons, called the A60. The production of these machines are located in Bra˚as, Sweden.

To reduce the standard cost for the parts in the bogie suspension of Volvo’s A30 model, this master thesis will investigate if a new concept can achieve a significant cost reduction. The solution of today is robust, but some of the components are expensive and time consuming to manufacture. Therefore, a new concept that will decrease the total cost of the axle suspension is desired without influencing the overall quality and robustness in a negative way. A proven way to combine robustness and economical benefits is to use pipe stays, which will be applied here.

1.1 Aims

An alternative concept for the bogie suspension of the two wheel pairs on the rear frame of the articulated hauler will be investigated and developed. A model in CAD to prove that the concept can fit and replace the existing construction will be generated. Related calculations and evaluations that specifies the concepts strength and reliability will be presented to ensure that the concept is practicable. A motion simulation to compare the solution of today with the new concept are also results that the thesis will deliver. This simulation will also provide data of the strains of the flexible parts, which will be compared to the existing solution. The aim is to decrease these values to increase the life time of each flexible part.

The final concept has to have a lower total cost than the existing solution. An economical calculation to compare the present and the new solution will be done as well as a weight comparison. The quality can´t be lower than the solution of today either as well as the overall properties. Otherwise this new concept is not interesting and is therefore unnecessary to proceed with. If a successful concept would result, each component will be specified from suppliers or have support to be realizable.

1.2 Project limitations

The design of the axle suspension for the front wheel pairs are quite similar to the wheel pairs at the rear, which means that they are also relatively expensive. Therefore, they are also in the need of a new design. This thesis is however focused on the rear. Since the time is limited to 20 weeks, there is no time for evaluating the concept by building a prototype or test it in an advanced calculation model.

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1.3 Existing bogie suspension

The existing solution consists of some components that are welded sheet metal parts, which are called A-stays. These stays handles the longitudinal forces and the moment around the axle housings on the axle suspension. These occupy a lot of space on the construction and needs a lot of material. As mentioned earlier, they are also expensive and time consuming to manufacture. Side forces are handled by the so called cross stays which are mounted at the back of each axle housing. The cross stay for the front axle housing is a molded part and has a very special geometry in order to fit in the construction. The rear cross stay is a simple pipe stay. The rear frame with the stays that the existing bogie suspension consists of is presented in figure 1 and are coloured in red.

Figure 1: The rear frame seen from the side/below with the existing bogie suspension in red.

The so called ”bogie beams” are attached to the rear frame on a console called ”bogie mounting”. A rotation around the bogie beam’s centers are possible. There are stops above their endpoints in order to limit the rotation. Otherwise, the tires will collide severely with the basket. Between the axle housings and the bogie beams are rubber dampers located, these are called ”elephant foots”. The components that were described are presented in figure 2. The bogie beam in the figure is tilted to one of its maximum rotation configuration to illustrate their movements.

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Totally four extreme cases can result from the bogie beams maximal rotation configurations.

The first two is when the bogie beams are tilted in the same direction forward and backward (parallel). The last two is when they are tilted in the opposite direction forward and backward (diagonal). These configurations will later be used to estimate the strains on the rubber and flexible parts on the generated concepts. In order to simplify further indices when comparable variables are presented, the front axle housing is from now on named A and the rear axle housing is named B.

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2 Theory

2.1 Resulting forces and moments

There are forces that acts along and across the axle housings on a bogie suspension. The resulting force that acts in the direction j on a rigid body can be summed and calculated as in equation 1.

F_res,j=

∞

X

i=1

F_i,j (1)

Moments are also acting on the axle housings. The resulting moment around a rigid body p can be summed and calculated as in equation 2. There can also be contributions to the resulting moment in the form of a force F and a lever x, which is also presented in the equation.

M_res,p=

∞

X

i=1

M_i,p =

∞

X

i=1

F_ix_i (2)

2.2 Strain on a circular pipe

The force that a circular pipe can handle which has a material with a yield point σ_y and a cross sectional are A_cs can be expressed as equation 3.

F = σ_yA_cs. (3)

With outer radius R and inner radius r, the cross sectional area A_cs can be expressed as equation 4.

A_cs = π(R²− r²) (4)

Using a safety factor n and combining equation 3 and 4, the force that a circular pipe can handle can be expressed as in equation 5.

F = π(R²− r²)σ_y

n (5)

If the force, yield point, safety factor and inner radius are known, equation 5 can be rearranged to express the outer radius as seen in equation 6.

s

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2.3 Buckling

The stays in the construction will be exposed to a risk of buckling. The formulas that are presented in this section is taken from a collection of formulas that are presented in the book H˚allf asthetsl¨ara[1] by Malemdahl.

The moment of inertia for a pipe[6] with outer diameter D and inner diameter d can be calculated with equation 7.

I = π(D⁴− d⁴)

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The radius of gyration for a pipe with cross sectional area A can be expressed as in equation 8.

k = rI

A = s

4I

π(D²− d²) (8)

For a pipe with buckling length L, the slenderness factor can be calculated with equation 9.

λ = L

k (9)

Elastic buckling occurs for certain values for λ. The condition for elastic buckling is described in equation 10.

λ < λ0 (10)

The variable λ₀ is the limit for elastic buckling and can be calculated together with the modulus of elasticity E with equation 11.

λ0 = π

s E

0, 85σ_y (11)

Equation 10 determines whether elastic or nonelastic buckling occurs. Euler´s buckling formulas can be used to describe the elastic case and Tetmajer´s method can be used to calculate the nonelastic case. For the buckling cases in this thesis, only nonelastic cases occurred. The strain at which buckling occurs can be calculated using Tetmajer´s method and is presented in equation 12.

σ_T = a − bλ + cλ² (12)

The material for the pipe that is exposed to buckling determines the values for the constants a, b and c in equation 12. Using steel SS1412, the values for the constants becomes a = 322, b = 0, 88 and c = 0 [3].

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The buckling strain σT will be compared to the yield point σy when the dimensions for the pipe is calculated. The parameter that has the lowest value will determine the final dimensions, otherwise the pipe will fail.

2.4 Cardan shaft design

When designing a bogie suspension it’s important to consider how the cardan shaft will fit in the construction. The relation between the operating angles on the cardan shaft should be as similar as possible in order to achieve optimal conditions [5]. The operating angles are presented in figure 3.

Figure 3: Simplified cardan shaft with its operating angles.

If the angles differ too much, there will be a displacement between the phase of the incoming rotational speed and the outgoing rotational speed. The outgoing speed will vary in an inconsistent behaviour compared to the incoming. In other words, the outgoing speed will speed up and slow down in intervals while the incoming speed is held constant. This will result in noise and vibrations if the relationship is larger than a certain value. The condition that should be fulfilled for optimal conditions[2] is described in equation 13.

| θ_A²− θ_B² |< 10 (13)

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3 Method

The procedure of this work follows mostly the stage-gate model presented in the book by Ulrich Eppinger [4]. The different steps that were used are presented in this section.

3.1 Planing

This thesis was a full time study of 20 weeks. A spreadsheet containing activities and deadlines was made to structure the work and to ensure that it would be finished until the final deadline. The planning was checked by the mentor of the university and Volvo. It was after that changed in a more suitable way. This document is found in appendix A.

3.2 Collecting information

The application for the new concept is in a very rough environment, including high loads and unpredictable terrain. This means that designs used for heavy duty applications are of interest. To find information about bogie suspensions suited for these circumstances, a research on the internet was made. Websites of trucks, terrain vehicles, articulated haulers and manufacturers of heavy duty axle suspensions were visited. The solutions for these were investigated for inspiration for the coming concept generation.

The frame of the articulated hauler where the new concept for the axle suspension should be placed was studied. A CAD model of the frame was used to see the degrees of freedom and the shapes of the frame. These properties and shape of the frame contributes to limited design possibilities and must be considered.

3.3 Concept generation round 1

Different solutions to the problem were initially sketched by hand and was complimented by text to clarify the functions and features of each idea. A first primitive evaluation of each idea were made to summarize its potential advantages and disadvantages. The process was iterated several times until no more ideas were found. The thought about the sketching was to obtain a ”base idea” and the sketches were held at a low level of detail. The following step was to summarize and sift all the ideas into complete concepts. These held a level of detail high enough to be modelled in CAD.

To discover if a concept would fit into the present frame on the articulated hauler it was realized in CAD. This resulted in a model of each concept that was ensured to fit in the frame. The concept models would then be ready for an individual evaluation from Volvo.

The following step was to realize the movements for each concept and apply the feedback that was mentioned by Volvo. The degrees of freedom for the system of components were carefully considered to achieve a successful motion model. These models were then presented

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to Volvo for a further evaluation. The concepts was updated and changed until Volvo was satisfied with the CAD models of the concepts.

3.4 Concept evaluation round 1

After all the concepts were developed to a final version, each concept were investigated carefully to collect values of different properties that would later on be used for a comparison with the existing solution.

Depending on the design of the concepts, different properties of strength and robustness resulted. A free body diagram was made for each concept and they were complimented by calculations based on these diagrams, using equation 1 and 2. All concepts used pipe stays and the thickness that was needed to handle the forces was important to know. To handle the torques and forces that acts on the axle housings, there needed to be stays above and under it. The forces and moments that were used was maximum values that has been measured in real tests. The stays that were located above were separate parts from the under placed stays. This means that the two kinds of stays could have different dimensions.

To save time, a script was made in Matlab. The input was the dimensions for the over stays and the inner diameter of the under stays. The outer radius of the under stays could then be computed, using the calculations of the free body diagrams and equation 6. Several combinations for the input parameters were tested to achieve reasonable dimensions for the thickness of the under stays. The yield point for the material that is used for Volvo´s pipe stays and their safety factor was considered in the calculations. However, the yield point for the material may not be the critical strain. It is possible that the buckling strain may be lower than the yield point. Therefore the buckling strain had to be controlled after an iteration with the script. The generated dimensions were inserted in an Excel spreadsheet that calculated the buckling strain using the equations of section 2.2. If it was lower than the yield point, the buckling strain was used in the script instead of the yield point. A new thickness would then result and the process was iterated until satisfactory results were achieved. The results of this script only gives a hint regarding the dimensions, more advanced simulations and calculations must be done in order to achieve better precision.

The strains of the rubber of the bushings and the elephant foots for each concept were evaluated. These strains occurs when the bogie beams reaches their maximum parallel and diagonal configurations. Conical deflections, torsional deflection, bendings and displacements were measured on the CAD models and was then inserted in a table. This made it easier to compare the concepts relative each other. Since the dimensions can vary between the over and under stays, their strains were presented separately from each other. The upper stays are all stays located above the axle housings and the under stays are all stays that are located below the axle housings. The existing solution has no over stays, only under stays which are the A-stays and the cross stays. The method to measure these strains are explained in table 1.

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Table 1: Method to measure the angles for strain evaluation.

Symbol Unit Description Method of measurement

φ ^◦ Conical deflection Angle between center line of stay and center line of fixing

λ ^◦ Torsional deflection Angle between center line of stay and plane of fixing

τ ^◦ Ball joint conical deflection Angle between ball joint plane and stay plane

γ ^◦ Bending angle elephant foot Angle between top plane and bottom horizontal plane of elephant foot ω ^◦ Torsional deflection elephant foot Angle between top and bottom

vertical plane of elephant foot

mm Shear distance elephant foot Distance between top middle point and bottom middle vertical plane of elephant foot

The different composition of stays will result in different behaviours regarding the movement of the axle housings. They have to be checked if they rotate or if they don’t move horizontally relative each other. The tires are a critical parts depending on the axle movements, these will affect if they collide with each other. There is also a risk of a collision between the tires and the basket. To check for these collisions, the tires and the basket was inserted in each concept assembly.

When all the data was measured, it was compiled into tables were the values could be easily compared between each concept. The different values were presented to Volvo and they were discussed. The concepts that didn’t show potential for further development where discarded and concepts that would be interesting to proceed with were kept.

3.5 Concept generation round 2

After evaluating which concepts to proceed with, they were developed further. The design that was beneficial was implemented and new concepts where generated. These were modelled in Volvo´s CAD software apart from previous concepts which were modelled in the CAD program that was provided by LTU.

3.6 Concept evaluation round 2

In addition to the strains that was measured in the first concept evaluation, some strain measurements were added for the evaluation of the developed concepts. One of them was the strains on the cardan shaft. The axle movement will affect its operating angles and is therefore important to consider. Unfortunate movements like non parallelism between the axles or rotation will affect the cardan shaft negatively and hence the durability. The cardan shaft was therefore inserted in the assemblies for the concepts to enable an analysis of its

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operating angles and displacement. The method to meassure these variables is described in table 2

Table 2: Method to determine the angles for strain evaluation.

Symbol Unit Description Method of measurement

ξ mm Displacement cardan shaft Distance between the flexible parts on the cardan shaft

θ ^◦ Operating angle cardan shaft Angle between center line of rotation disc on axle housing and center line of cardan shaft

Another thing that was considered was the collision risk between the bogie mounting and the tires. There can be different sizes and types of tires for the A30 model, so to investigate the worst case scenario, the largest tires that are available were used. The bogie beams were tilted to their different configurations to investigate when or if a collision would occur. If a collision occurred, a cross sectional picture was captured. Otherwise, the clearance was captured as an ordinary image to illustrate the magnitude of the clearance.

If a concept was assessed to have doubtful force handling properties, a simulation model was made for the concept to investigate how the forces affected the construction. This made it possible to identify where the forces were concentrated and determine the magnitude. The joints affection was also considered which contributed to a reliable evaluation method.

3.7 Concept selection

When all the wanted data was measured from the criterias of the concept evaluation 2, the concepts could be compared to each other and a selection could be done. The selection process did however not only rely on the measured data. Meetings were held at Volvo to discuss additional problems and benefits that was not considered in the criterias of the concept evaluation. A simple cost calculation was done to provide a perception whether the chosen concept would be profitable enough to proceed with.

3.8 Final design

After choosing which concept to proceed with, a detail construction could be initiated. It’s beneficial to use existing or available components provided by Volvo´s suppliers for many reasons, but mainly for reducing costs. The geometries were optimized to consider the properties listed below:

• Minimize strain concentrations and maximize strength

• Access of spraying paint

• Assembly properties

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Since Volvo already has a working bogie suspension, the new concept needs to be compatible at as many properties as possible.

3.9 Final evaluation

Since the chosen concept was designed in more detail, its properties may vary from its predecessor. It was therefore necessary to redo some of the evaluations and comparisons that was made before. These were:

• Strain on rubber parts

• Strain on cardan shaft

• Axle movements

• Collision basket - tire

• Collision bogie mounting - tire

These properties will be measured/compared in the same way as described in section 3.4 and 3.6. FEM calculations was also done on some parts to confirm that they could manage the loads. The applied loads was based on the maximum values that were measured from real tests.

An estimation of the final cost will also be done to investigate whether the concept is worth realize or discard. This estimations considers the cost of the different parts including manu- facturing and material but not the cost of the assembly at Volvo. The cost of each individual part will not be presented due to secrecy. The weight of the concept will also be measured and compared to the existing solution.

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4 Results

The results of the different steps in the thesis are presented in this section.

4.1 Concept generation round 1

When the first concept generation was finished, five concepts resulted and each had an associated CAD model that were implemented in the rear frame. The level of detail was relatively low but high enough to ensure that they could be realizable.

Concept K1

The first concept reduces the pair of A-stays and also the two cross stays. This means that all the fixings that supports the cross stays can be eliminated. The fixings of the A-stays could also be eliminated.

Axle fixings are mounted on both sides of the under part of each axle housing. A pipe stay for each axle fixing connects them to an individual fixing which are located on consoles that are welded to the under side of the frame. The consoles are relatively high for more beneficial force handling in the longitudinal direction. The consoles are located as close to the middle as possible to provide a beneficial angle for the under stays to handle the side forces. All joints are spherical.

To increase the robustness and strength, a pipe stay connects the top of each axle housing with the frame. The joints on the frame can only rotate around their axle but the joints on the axle housing are ball joints and hence spherical to enable the desired motion. These stays in collaboration with the stays at the under part handles the resulting moment on the axle housing and the longitudinal forces.

Concept K1 is coloured in orange and is presented in figure 4, 5, 6 and 7.

Figure 4: The rear frame seen from the side/below with concept K1 in orange.

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Figure 5: The rear frame seen from below with concept K1 in orange.

Figure 6: The rear frame seen from the side with concept K1 in orange.

Figure 7: The rear frame seen from above with concept K1 in orange.

Concept K2

The second concept consists of fewer modifications compared to concept K1. Instead of

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eliminating the cross stays, this solutions keeps them and their associated fixings. The support to manage side forces are thereby covered. The A-stays are however replaced, which means that their fixings can be eliminated. The overall result is a construction that minimize modifications.

Fixings are mounted on both sides of the under part of the front axle housing. In front of the axle housing are fixings on each side which are mounted directly on the frame. These fixings are connected to the fixings on the axle housing by pipe stays. The joints are spherical to enable the desired motion. The cross stay that is used on the front axle housing on the existing solution is as mentioned earlier kept and used on this concept.

On the rear axle housing, fixings are located just like the front housing. In front of these fixings are fixings that are located on the bogie mounting. They are connected with pipe stays. Spherical joints are usedl. The cross stays are kept from the present solution.

The top of each axle housing is connected to the frame by circular pipe stays. Both joints are ball joints and are spherical. These stays with help from the stays on the under part handles the moment that results around axle housing and the longitudinal forces.

Concept K2 is presented in figure 8, 9, 10 and 11. The parts that are new are coloured in orange and the parts that are kept from the existing solution are coloured in red.

Figure 8: The rear frame seen from the side/below with concept K2 in orange and red.

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Figure 9: The rear frame seen from below with concept K2 in orange and red.

Figure 10: The rear frame seen from the side with concept K2 in orange and red.

Figure 11: The rear frame seen from above with concept K2 in orange and red.

Concept K3

The third concept eliminates both A-stays as well as the cross stays and their associated

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fixings. This concept uses the least number of parts and is inspired by the solution that is commonly used on heavy duty trucks.

Axle fixings are mounted on both sides of the under part of each axle housing. A pipe stay for each axle fixing connects the axle housing to fixings that are located on each bogie mounting. The fixings on the bogie mountings have a design that is optimized for beneficial force absorption in the longitudinal direction. All joints for the stays are spherical to enable the desired motion.

The top of each axle housing is connected to the frame by V-stays. Each joint has to be spherical to enable the desired motion. The V-stay handles all the side forces. The V-stay in collaboration with the stays on the under part handles the ´moment of the axle housing and the longitudinal forces.

Concept K3 is coloured in orange and is presented in figure 12 13, 14 and 15.

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Concept K4

This concept is an improvement of concept K1. The straight stays that connects the top of the axle housings with the frame are replaced by V-stays compared to K1. This provides an increased resistance against side forces. Concept K4 is coloured in orange and is presented in figure 16 17, 18 and 19.

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Concept K5

The last concept shares components and design with concept K3. The common components are the stays at the under part and their fixings. The under part of this concept is also complimented with the existing cross stays from the present solution to handle the resistance against side forces.

The V-stay on the top is replaced by a straight circular pipe stay which has spherical joint on both ends. This is a cheaper solution and the side support that the V-stay gives is no longer needed due to the implementation of the cross stays.

Concept K5 is presented in figure 20 21, 22 and 23. The parts that are new are coloured in orange and the parts that are kept from the existing solution are coloured in red.

Figure 20: The rear frame seen from the side/below with concept K5 in orange and red.

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Figure 21: The rear frame seen from below with concept K5 in orange and red.

Figure 22: The rear frame seen from the side with concept K5 in orange and red.

Figure 23: The rear frame seen from above with concept K5 in orange and red.

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4.2 Concept evaluation round 1

The free body diagram that was made for each concept can be found in appendix B and corresponding Matlab code in appendix C. The forces and moments that was applied on the calculations were brought by the calculation team at Volvo. These are presented in table 3.

Table 3: Forces used in the calculations.

Axle housing Longitudinal force [kN] Side force [kN] Torque [kNm]

A 153,52 174,00 109,00

B 108,45 235,00 77,00

After iterations of testing different combinations of dimensions on the pipe stays, a suggestion of suitable dimensions was obtained. These dimensions are presented in table 4

Table 4: Suitable dimensions for pipe stays.

Concept Over stay dimensions [mm] Under stay dimensions [mm]

K1 D62, d48 D66, d48

K2 D58, d48 DA60, dA48, DB47, dB38

K3 D62, d48 D74, d48

K4 D48, d38 D47, d38

K5 D31, d22 D32, d22

Some of the dimensions in the table above does not exist, so the dimensions has to be rounded up when applied to a final solution. All of the concepts had the buckling strain as their critical strain which implied larger dimensions.

The results of the axle movement evaluation are presented in figure 24

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Figure 24: Axle movements for each concept including the existing solution.

All of the concepts were investigated to determine if the tires would collide with the basket and was compared to the existing solution. The parallel configuration of the bogie beams resulted in a good clearance for all concepts. The diagonal configuration was on the other hand worse for the concepts. The tires of the concepts without cross stays hit the rear part of the basket slightly. The case was different for concepts with cross stays, including the existing solution. The tires hit the basket severely both at the front and rear part of the basket. The cross section view that shows the collision between the tires and the baskets for the concepts with and without cross stays are presented in figure 25 and 26. The cross sections are displayed in green and the collision in red.

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Figure 25: Collision between tire and basket for concepts with cross stays and for the existing solution.

Figure 26: Collision between tire and basket for concepts without cross stays.

Because of these collisions, there is no possibility to increase the bogie beam rotation which would also increase the ability to drive in hard terrain . A conclusion can be made that the concepts without cross stays are better for the passability in hard terrain.

The results of the strain measurements of the flexible parts are presented in figure 27. The green cells are the best result of each measured category and the red are the worst result. Note that the measured values for the over stays of the existing solution are zero. This because there are no over stays on the existing solution. The ball joint for the existing solution is the joint on the front of the A-stays. The other concepts has a ball joint located on top of the axle housings.

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Figure 27: The results of the strain measurements on the flexible parts.

Concept K1 resulted in gross dimensions on its pipe stays. This is however logical since its under stays handles the side forces with no help from the over stays. Dimensions on

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but nothing to consider as unacceptable. The movement of the axle housing was in contrast very disadvantageous. The axles moved horizontally, but they became very angled when the bogie beam had the diagonal configuration. The concept K1 was eliminated due to the need of gross pipe dimensions and the bad behaviour of the axle movements.

Even though the second concept could be constructed with available dimensions on the pipe stays, it showed bad results at many criterias. Strains on the flexible parts were severe and showed the worst results compared to the rest of the concepts. The tires hit the basket severely and the axles didn’t rotate horizontally relative each other when the bogie beam was moving, which has an negative effect on the rolling. Another thing that was a big disadvantage with this concept was the fixings on the bogie mountings. This part is not built to handle the longitudinal forces that arises from this concept. Advanced calculations and potential major changes on the frame makes this concept hard to develop further. All these reasons led to an elimination of this concept.

The largest required dimensions on the pipe stays compared to all the other concepts was concept K3. The ability to handle the moments and the longitudinal forces were good, but the side forces are only handled by the V-stays on the top of the axle housings. Due to the construction of the frame and to achieve the desired motion, the angle in the V became very small and hence is the support for side forces weak. The tires hit the basket for the diagonal configuration of the bogie beam slightly, just as K1. The strains on the flexible parts were mediocre and resulted in a middle score compared to the others. The movements of the axles were however exemplary. They did not rotate and moved horizontally. This property is desired and a conclusion can be made that a set up of the stays like this on the under part is beneficial for the axle movement. Therefore, this was noted for further concept generation but the total concepts was eliminated due to the weak construction.

The design of the stay setup of concept K4 resulted in a robust construction that can handle the acting forces and torques. Small dimensions on the stays could thereby be applied. The tires hit the basket, but not considerably much. Many angles on the strain measurements for the flexible parts were good in comparison, there were also no worst case values for this concept. A severe tilting on the axles resulted, compared to the previous concept. The axles were however horizontal relative each other, which is good. A way to decrease the tilting is to move the console that holds the under stays outwards, like in concept K3. This would lead to a worse protection against side forces, but is possible since the required dimensions for this concepts are small. A development of this concept is interesting when all the resulting properties are summarized.

The last concept required the lowest dimensions on its pipe stay compared to all concepts.

The main issue about this concept is the fixing of the under stays that are placed on the bogie mountings. The longitudinal forces from each axle housing would act on the bogie mounting in the same direction and hence expose the component to a very high strain. The eventual major changes to be able to handle the upcoming forces and the advanced calculations to confirm this makes this concept hard to choose as it is. Like concept K2, the tires hit the basket severely. The strain evaluation did not show positive results either. However, like concept K3 the movement on the axles are beneficial. With this in mind as well as the need of small dimensions on the stays, the advantages was be kept in mind and was developed further.

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4.3 Concept generation round 2

The first concept that was developed further was K4. The new name for the developed concept was K4b. The difference between them are the location of the console, this concept locates the console further from the middle. The reason was to achieve similar beneficial behaviour of the axle movements which occurred for K3. Therefore, the geometry of the under part was inspired by K3. The angle becomes smaller and the protections against side forces decreases. However, the previous calculations for K4 indicated that small dimensions could be used which means that a decrease in side protection is possible. The console is now integrated with existing parts on the frame, which will save weight and costs. The space on the under part of the frame is also better. Concept K4b is coloured in orange and is presented in figure 28 29, 30 and 31.

Figure 28: The rear frame seen from the side/below with concept K4b in orange.

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Figure 29: The rear frame seen from below with concept K4b in orange.

Figure 30: The rear frame seen from the side with concept K4b in orange.

Figure 31: The rear frame seen from above with concept K4b in orange.

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Concept K5 was also developed and the new concept was named K5b. The main problem was the fixings for the stays at the under part. This concept removes these fixings and uses the same console as in concept K4b. Otherwise, the concept is the same as K5. The concept K5b is coloured in orange and red and is presented in figure 32 33, 34 and 35.

Figure 32: The rear frame seen from the side/below with concept K5b in orange and red.

Figure 33: The rear frame seen from below with concept K5b in orange and red.

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Figure 34: The rear frame seen from the side with concept K5b in orange and red.

Figure 35: The rear frame seen from above with concept K5b in orange and red.

4.4 Concept evaluation round 2

The longitudinal and side forces that were presented in table 3 were used to investigate the strengths of the concepts. The free body diagrams that were made for each developed concepts predecessor could be used to investigate the required dimensions for the new concepts.

This was done by changing the angles that described the tilting of the under stays. Based on calculations for the free body diagram, the required dimensions for the stays for each concept is presented in table 5. The corresponding Matlab code can be found in appendix D.

Table 5: Suitable dimensions for pipe stays.

Concept Over stay dimensions Under stay dimensions

K4b D58, d48 D58, d48

K5b D38, d28 D38, d28

The strength results shows the same behaviour as for the predecessors. Concept K4b can be built with dimensions on its stays that are available by Volvo and K5b can use even smaller

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dimensions. This behaviour also resulted for the axle tilting when the bogie beams are in their diagonal configuration. The comparison between them are presented in figure 36.

Figure 36: Axle movements for K4b, K5b and the existing solution.

The movement of the axles are more beneficial for K5b. The axles are parallel and doesn’t tilt or rotate which is desired. K4b has parallel axles, but has a large tilting. These behaviours results in different properties regarding the collision between the tire and the basket, the comparison can be seen in figure 37.

Figure 37: Collision between tire and basket for K4b, K5b and existing solution.

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when comparing figure 36 with 37 is that a low tilting angle on the axles results in a major collision while a high tilting angle gives a minor collision. These properties are all depending on whether cross stays are used or not.

Both concepts managed to avoid a collision between the tires and the bogie mountings when the bogie beams were in their parallel configuration. The diagonal configuration were however different for the two concepts. K4b collided with the bogie mounting slightly but K5b managed to keep a small clearance. The existing solution had a minor collision for the diagonal configuration. The cross sectional view for the collision of K4b, the existing solution and the clearance of K5b are presented in figure 38.

Figure 38: Collisions and clearance displayed in the red circles.

The results of the strain measurements of the flexible parts are presented in figure 39. The green cells are the best result of each measured category and the red are the worst result.

Note that the measured values for the over stays of the existing solution are zero. This because there are no over stays on the existing solution.

Figure 39: Strains for rubber parts and cardan shaft.

The results of the strain measurements differs a lot. Two categories of strains that are considerably better for the concepts than for the existing solution is the the properties of the cardan shaft and the sheer distance of the elephant foots. It is more important for the stays

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to have a low conical deflection than a torsional since this is more beneficial for the rubber parts. The solution with the best properties for this category did however vary a lot. The conical deflection for the ball joint at the over stays were highest for K4b and lowest for the existing solution.

Since K5b is constructed with existing cross stays there is no reason to investigate whether the concept can handle the side forces. The stays that are used are proven and have dimensions large enough to handle the forces. The case is different for K4b. The configuration of stays is not proven to work, neither by Volvo or any of the competitors. It was therefore necessary to simulate how the forces acts on the concept. The model that was made for this simulation is presented in figure 40.

Figure 40: Simulation model for K4b.

Side forces were applied to the model with a magnitude of 100kN, which acted along the center line of the axle housing. The joints that were investigated were divided in to under stay joints and V-stay joints. The V-stay joints corresponded to the over stay joints. These are presented in figure 41.

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The results of the forces that arose in the V-stay and the under stays are presented in figure 42.

Figure 42: Simulation results for K4b.

The results of the figure above shows that a negligible part of the side force is handled by the under stays. The concept can thereby not rely on that the under stays can handle any forces from the side.

4.5 Concept selection

Each concept had different strengths and weaknesses. A summary of these properties was made to simplify the selection of which concept to proceed with. The summary is compared to the existing solution and is presented in figure 43.

Figure 43: Summary of concept evaluation round 2.

Even though concept K4b showed better potential for some important categories, like being more economical beneficial than K5b, it was eliminated. The simulation of the force distribution in the previous section showed that only a small amount of the total force is handled

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by the under stays. The calculations from before assumes that there are similar conditions regardless of what type of stays. It is unsure to proceed with K4b and therefore K5b was chosen to be developed further.

4.6 Final design

After considering limitations and optimization, a final concept could be constructed. The new developed concept was named K5c and is a developed version of the concept K5b. The CAD model could move in the same way as the previous solution. The resulting design of K5c is presented in figure 44 and 45.

Figure 44: K5c seen from above.

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Just like the previous concept, this solution uses the same type of stays as the rear cross stay for the exiting bogie suspension. Since the supplier of the rear cross stays didn’t have a CAD model with smaller dimensions, the same cross sectional dimensions as the rear cross stay was used. The design of the stays that was used for the concept is presented in figure 46.

Figure 46: Over and under stay designs of K5c.

The design of the under and over stays are the same, the cross sectional area, the length and the size of the bushings at the end of the stays separates them. The bushing kit is also the same as for the existing solution, but its size variate. This bushing kit is shown in figure 47.

Figure 47: Bushing kit for the stays of K5c.

The fixings for the under stays on the axle housings were completely redesigned. The total volume and geometry were minimized to save weight and space. They are now integrated in the axle housings and can thereby be cast in the same mold. The processing on the axle housings that was made for the A-stays can be eliminated on one side. The processing of the other side is necessary for the cross stays, so it has to remain. The bushing kit is merged

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to the fixings by screws and bolts. The hole for the screws in the fixings were horizontal to avoid shearing. The depth of the hole is three times the hole diameter in order to obtain a desired strain on the screw. The hole isn’t centered on the fixing because it would increase the risk of collision between the fixing and the stay when the stays are moving. Therefore, the hole of each fixing are displaced to the side that is the closest to the other hole. The new design for this component is presented in figure 48.

Figure 48: Under stay fixings on the axle housings of K5c.

The conical and torsional deflections on the ball joint for the fixings for the over stays on the axle housings were relatively low, see figure 39. This made it possible to use the same type of joint as for the cross stays. Thereby is the same type of bushing kit used. The fixing is molded in to the cast of the axle housing. The bushing kit is merged to the fixing by screws and bolts. The hole in the fixings for the screws were horizontal for the same reason as for the under stay fixings. The depth of the hole is also three times the hole diameter to obtain a strain on the screw. The displacement of the holes are the same as for the previous fixing.

The design can be seen in figure 49.

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Figure 49: Over stay fixings on the axle housings of K5c.

The over stay fixings for the frame was adapted to the busing kit of the cross stays. This made it possible to use a simple pipe stay as a over stay. The fixings were made thicker compared to the solution of the predecessor. A hole was made through the component which made the screws and bolts for the merge of the bushing kit resistant to shearing. Like before, the depth is three times the hole diameter. It is a molded component and it is located on a transverse plate and they are merged by welding. This is presented in figure 50.

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Figure 50: Over stay fixings on the frame of K5c.

The transverse plate that was mentioned in the previous paragraph is an important part of the construction. It handles side forces and has a considerable importance to stabilize the frame. There are two of these plates and they connects both sides of the frame as well as between the top and the bottom plate of the frame. Since the over stay fixing components are located on these plates, they will be exposed to forces that acts were they are week. To increase stability, two more plates were added to the construction. These are perpendicular to the other plates and handles the longitudinal forces that arises from the forces on the fixings.

To enable screws and bolts for the merging of the bushing kit on the fixing, the longitudinal plates were not located in the same line as the fixings which would otherwise give optimal force absorption properties. Instead they had an offset from this line. A screw plate was added to the construction because of better conditions for the workers of the assembly line.

This component was meant for the screws and bolt for the bushing kit. It fitted in the design by cutting a section of each side of the longitudinal plates. The different plates are presented in figure 51.

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Figure 51: Stabilization plates and screw plate of K5c.

A reinforcement structure is needed to handle the forces that arises from the fixing of the front cross stay. This is solved by a cut plate that is bent to a U-shape that is welded to the bottom and the top plate of the frame. This component is presented in figure 52.

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Figure 52: Reinforcement plate of K5c.

The console that includes the under stay fixings for the frame were modified and split in to two different parts. Several things are however common, like the use of more rounded geometries to avoid strain concentrations. Another thing are the standing plates that this part consists of, they are located in the same line as the plates that the frame consists of which is more beneficial for the force absorption. On top of the standing plates is a top plate applied by welding. The top plate is molded and includes the fixings for under stays. These has smooth radius transitions to avoid strain concentrations and the hole that goes though them to enable the merging of the bushing kit is horizontal to avoid sheering. Since the same bushing kit is used here as for the cross stays, there needs to be a certain width on the top plate. This makes it necessary to use a wider geometry than the width between the standing plates. A reinforcement is needed to support the fixings and the top plate. This is solved by welding a plate that connects the top plate and the side plate. The common design of the consoles is presented in figure 53.

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Figure 53 shows the complete design of the right console. The left console uses that design as well but is complemented with an extension to integrate it with the fixing for the front cross stay. All these plates are welded together to complete part. The left console is presented in figure 54.

Figure 54: Left console of K5c with integrated cross stay fixing.

As mentioned earlier, the fixings for the under stays are in the same mold as the top plate of the console. The bushing kit is merged in the same way as before. The depth of the hole is also three times the hole diameter. The holes are displaced from the middle so they are closer together. Figure 55 shows the component.

Figure 55: Under stay fixing on the console of K5c.

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Since concept K5c eliminates the A-stays, some downsizing of the bottom plate of the frame could be done. The parts that could now be cut was earlier necessary for the fixings of the A-stays. The cut geometry is illustrated in figure 56

Figure 56: The bottom plate of the frame with the cut material displayed in red.

4.7 Final evaluation

The new concept differs a lot from the existing solution. The modifications on the frame is presented in figure Figure 57 and includes a comparison with the components on the frame with the existing solution.

Figure 57: Frame components for K5c and existing solution.

The configuration of stays and the modification of the axle housings for K5c is compared to the existing solution in figure 58.

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Figure 58: Axle housing components and stays for K5c and the existing solution.

Changed geometry on the construction and increased stay lengths led to a different result regarding the stay dimensions. A new iteration was made with the free body diagram calculations due to the changed parameters. The Matlab script in appendix D and the Excel spreadsheet containing the resulting buckling strain were therefore used again. Just as before, the buckling strain became the critical strain. Suitable stay dimensions resulted to be 44mm in outer diameter and 36mm in inner diameter for the over stays. The under stays could have 40mm as outer diameter and 30mm as inner diameter.

The stay dimensions that was suggested in the paragraph of above was tested with FEM calculations. The derivation of the applied force can be found in appendix E. It resulted to be 120kN and were applied at all FEM calculations. The result of the FEM calculation for the under and over stays can be seen in figure 59 and 60.

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Figure 59: Results of the FEM calculation on the under stays.

Figure 60: Results of the FEM calculation on the over stays.

The yield point of 355MPa is not exceeded in the simulation and that goes also for the buckling strain, which was calculated to be 272MPa for the under stays and 282MPa for the over stays. Some strain concentrations were however very close to the buckling strain. The next part that was FEM calculated were the fixings of the axle housings. Since they are very similar, one common calculation were done for both of them. This calculation is presented in figure 61.

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Figure 61: Results of the FEM calculation on the stay fixings on the axle housings.

Strain concentrations resulted on the radius transitions, but they were not close to the yield point of 355MPa for the material. The thickness of the component was enough to handle the applied force so these dimensions can be applied in reality. The last component with FEM calculations were the fixings on the top plate of the console on the frame. The result is presented in figure 62.

Figure 62: Results of the FEM calculation on the stay fixings on the axle housings.

The under stay fixings on the console handled the applied force well, but obtained some strain concentrations at the radius transitions. The strains were far from the yield point.

The axle movements for concept K5c were very similar to K5b. A comparison was however

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done with the existing solution and this is presented in figure 63. The axle movements for K5c are very good because there is a low tilting angle on the axles and the fact that they move in a parallel manner.

Figure 63: Axle movements for K5c and existing solution.

Concept K5c showed the same behaviour regarding the collision between the tires and the basket as for K5b when the bogie beams were in their diagonal configuration. Even if collisions still exists, it’s an improvement compared to the current design. A cross section view for the collision can be seen in figure 64.

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Figure 64: Axle movements for K5c and existing solution.

A clearance between the tires and the bogie mounting resulted for K5c, independently from the configuration of the bogie beams. The comparison with the existing solution is presented in figure 65.

Figure 65: The clearance of K5c and the collision of the existing solution.

The result of the strain evaluation varied a lot, but some components benefits considerably in K5c. All measured category of the elephant foot except one was better for K5c, which may lead to an increased life time of the component. The operating angles for the cardan shaft were significantly better than existing solution which may also contribute to an increased life time and better driving experience. The evaluation is presented in figure 66. Note that the measured values for the over stays in the existing solution are zero, since there are no over stays. The ball joint angles for K5c are zero because the concept no longer uses a ball joint.

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Figure 66: Strain evaluation for concept K5c and the existing solution.

The cost evaluation showed that K5c would be a more cost efficient solution than the existing.

A decrease of approximately 3700SEK could be made, which corresponds to roughly 24%.

This result will be better if stays with the calculated dimensions are used, since the calculation is based on the price of the rear cross stay which is oversized for K5c. Another positive result was the lower weight for the new concept, 95kg could be saved which is a weight reduction of approximately 22%.

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5 Discussion

5.1 Concept evaluation

It was hard to define a suitable and fair method to score each concept’s exposure of strains of their different flexible parts. A method that based the scores on each concept using the percentage deviation from the reference was tested. This percentage value was calculated by dividing the measured value from the concept with the measured value of the reference.

A high magnitude of the measured values implied a high strain on the flexible parts and a low score was therefore desired. A percentage deviation below one implied that the specific concept had lower exposure of strains than the reference. Some types of strains were worse than others which explains why the percentage value was then multiplied by a constant. The more severe strain, the higher magnitude of the constant. The result of this method was that the reference outperformed all concepts. The reason was that all the measured values on the reference was very small. Measured values on the other concepts could only differ by a few millimeters, but because of the small values on the present solution the percentages would bolt away.

The problem couldn’t be solved by dividing the measured values into equal intervals that corresponded to a certain grade either. The range started from zero up to a value that was a bit higher than the highest measured value of the concepts. This resulted in a narrow range of grades below the values of the reference and a wide range of values above. The result was two grades below the reference and nine grades above. The only solution to get an equal number of grades above and below the reference was to have more narrow intervals below the reference and wider intervals above. This is however not a fair selection method, it also resulted in an outperforming by the reference. It was in the end chosen to discard the idea of using a scoring method to compare the concepts.

The parallel configurations of the bogie beams are very common when driving. The speed of the vehicle can be relatively high and this makes the operating angles of the cardan shaft very important to consider for this configuration. The high speed will result in high strains on the cardan shaft if the angles differ too much. The diagonal configuration is also important to consider, but if the choice stands between optimal operating angles between the two configurations, it’s more important for the parallel. Apart from the parallel configuration, the diagonal can’t really be a achieved when high speeds are present. It occurs in hard terrain and therefore low speeds are in most cases present. Therefore, a reasonable deviation from the optimal condition can be accepted here.

The reason why cardan shaft measurements wasn’t considered in the first evaluation round was because these were measured incorrectly. When they would be corrected, the files of the concepts could not be restored. It would require a lot of time to fix this so it was decided that it was enough to perform these measurements in the second evaluation. The investigation whether the tires collides with the bogie mounting was brought up lately so it couldn’t be done either at that stage.

The results on the suitable dimensions for the different concepts can’t be trusted completely, which is the case for both concept evaluation rounds. The calculations based on the free body

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diagrams assumes that the joints can’t move, which is a major simplification. The behaviour of how the forces are distributed over the axle housings is complicated to know, so this was also neglected. The reason with these calculations was to get an approximate estimation on the dimensions and to see which configuration of stays that would give the most robust construction. Even though the calculations was thought to be simple, there should have been more accurate calculations in order to guarantee reliable results. A simulation that considered the complex force distribution and movable joints that was done on concept K4b in the second concept evaluation round should have been done for all concepts. For example, K3 resulted in gross dimensions while K4b could be built with much smaller dimensions according to the simplified calculations. The simulation did in contrast confirm that the contribution of side forces support from the under stays was negligible on K4b. Thereby would K4b need dimensions on its over stays with magnitudes alike K3. This was one of the reasons why K3 was eliminated.

5.2 Concept selection

One of the reasons concept K3 was eliminated was because of the need of large dimensions.

The small angle on the V-stays made the concept weak to handle the side forces. However, similar design are used on heavy duty trucks so it should be noted that this concept has potential to be realizable. The angle has to be increased in order to handle the side forces and there need to be major changes on the frame to achieve this. The support that the frame needs to handle various forces will in that case be modified and to investigate this further, advanced calculations and time consuming work has to be done. The thickness of the V-stays with this modification would require a thickness of at least 9 millimeters according to the Matlab script, which returned a suggested stay dimension of D66 d48. This is a problem for the assembly of the components of the V-stays and contributes to a high weight.

Even though concept K4b showed greater potential to achieve a significant economical benefit due to its few parts, the concept was eliminated. According to the calculations, its properties to handle the side forces would be enough. But the calculations didn’t consider the real situation. The under stays have a spherical joint in both ends and the support with its corresponding angles becomes therefore week. This was illustrated by building a simple system of links in Lego. The result is that the under stays only handles the longitudinal forces and the V-stay on the top handles the side forces all alone. This would result in gross dimensions just like concept K3. The recommended dimensions that was presented in table 5 are therefore not able to handle the loads.

5.3 Final evaluation

The weight reduction for K5c is just an approximated value. A concept that is fully developed for production will for example have a modified axle housing. Some of the geometry is unnecessary and was not changed due to the lack of time. Optimizing the geometry can increase or decrease the weight and may also offer better strength properties. This component

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components are relatively easy designed and big modifications are probably not needed. The modifications would in that case not have a big impact on the total weight.

K5c resulted in a cost reduction, which was desired. The question is however if the reduction is enough to be profitable. As mentioned earlier, there is a lot more to do before the concept is realizable. The remaining cost of optimization for the concept must be included in the savings. Detailed testings should be done to investigate the properties of the concept, which will cost a lot. This may show that it is more profitable to use the existing solution instead of a new.

Different reasons exists to proceed with K5c in addition to the economical benefit. The strain evaluations on the elephant foots showed much better results compared to the existing solution. This is also confirmed by real experience from Volvo. The elephant foot on the rear part of the bogie beam generally has twice as long lifetime as the front elephant foot.

The reason is that the bending of the rear elephant foot is more gentle than in the front.

The joint of the rear A-stay is located towards the centre of the bogie, while the front A-stay is directed from the center of the bogie beam. In cooperation with the motion of the bogie beam, the strain becomes severe on the front elephant foot.

The stay dimensions that resulted are just suggested dimensions. Depending on what outer or inner diameter that is desired, it can be varied. By changing the parameters in the Matlab script, different outcomes on the stay dimensions will result. This is an iteration process that can be done if the concept would be realized and would continue until a suitable dimension is found that could for example match the selection of stays of a manufacturer. As mentioned earlier, the Matlab script is based on the free body diagrams that was made. In contrast to K4b, it assumed that the calculations of the stay dimensions are enough precise to give a estimation of the needed dimensions. This is the case because the geometry of the free body diagram is much more simple.

The measured operating angles on the cardan shaft for the existing solution at different configurations of the bogie beams were very bad. The measurement was redone and controlled by people at Volvo, but the values were not measured incorrectly. This means that the existing solution has a big disadvantage against concept K5c and will also be bad for the ride quality of the articulated hauler. This is also a reason to proceed with K5c.

The brochure from the supplier of the rear cross stay didn’t have data regarding the force handling of the bushings. This must be verified in future work. The force that the rear cross stay can handle exceeds the applied force in the FEM calculations greatly, which means that the stays on the CAD model can handle the forces in reality. Data for the conical and torsional deflections weren’t available either. The only guideline when choosing bushings were the data of the stays that Volvo used as rear cross stays. These were larger than the measured angles and the bushings will therefore work, given that the angles are measured correctly. The summary is that the rear cross stay and bushings could be applied on the solution, but it might in that case be oversized.

Components that was taken from the existing solution were not analyzed regarding strength properties, since that is already done by Volvo. K5c is thereby safe when it comes to handling side forces. To ensure that K5c will work completely, there needs to be more advanced calculations and modifications on the new components. The stabilization plates on the frame

New bogie suspension concept