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Cost reduction of the Genius
Standards Carriage
C.A.L. Aerts (Corné)
DCT 2006.12
Rapport second internship
Supervisors:
Dr. Ir. P.C.J.N. Rosielle
Ir. H. Steijaert
COMPANY CONFIDENTIAL
Eindhoven, January 2006
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Preface In my former projects the financial consequences of a design were not in the scope of the study. During my internship at Frencken Mechatronics an interesting study is done on one of their products. In this case a design is required that is cost efficient. For this purpose collaboration is of great importance. At the start of a project a lot of information is required to understand the product and to get the specs. Cees Bakker and Jan van Endschot from Philips Medical Systems provided the required information with great enthusiasm. The contacts and internal briefings are also important. Hans Steijaert guided me in the internship and also through the company. Feedback from Hans himself and also from meetings with the whole engineering team helped in developing a new design. Also the briefings at the TU/e with Nick Rosielle and the students gave good ideas for the project. As mentioned before, the costs of the design can’t be neglected. Cost Engineer Johan Corbijn helped with analyzing concepts at their costs. Already at an early stage he was involved in the design. The cost price calculations were very useful. The own estimations for costs were also compared with a quotation from a sheet metal company in Heeze. Those people from Bumet were quite co-operative and were enthusiastic to talk about the design. It was very instructive to work with a variety of people. All these people have ideas and visions that have to be taken in account. Combining these visions is quite a task, but important for the development of the product. All in all it was a successful internship.
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Summary Nowadays the carriage of the Genius Standard is a Cast-Iron part. In this study the possibility for cost reduction is analyzed. Several design rules are formulated for achieving this. The rules are based on minimizing mass and on minimizing operations on heavy and large parts. . For this purpose a concept study is done. This lead to a basic construction. After this is done the main parts of the design are elaborated. To prevent wear to the runners, the alignment of the parts is important. Also wear to the drive wheel of the motor is prevented with a new construction. The new construction is evaluated at it’s costs and at it’s specs. A cost reduction of 15% is achieved. An other property of the construction is its mass, which is almost 40% lower.
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Contents
1. Introduction 4 2. The Carriage in its surrounding 5 3. Interfaces 6 4. Mechanical specifications for the carriage 8 5. Cost price reduction 10 6. Concept study 12 6.1. Moments and forces 12 6.2. Basic design 12 6.3. Beams 13 6.4. The hub 15 6.5. Welding 15 6.6. The three concepts 16 7. Design study 17 7.1. Runner beams 18 7.2. Motor suspension 21 7.3. Design of the hub 23 7.4. Assembly 24 7.5. Stress Analysis 28 8. Cost price calculation 29 9. Efficiency of cost reduction 34 10. Conclusions and recommendations 35 11. References 36 Appendixes
A1. Tolerances 37 A2. L-arm 39 A3. Rail system 40 A4. Shock Impact 41 A5. Length of mortise and tenon joints in the leg 42 A6. Alternative designs 43
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1. Introduction Frenken Mechatronics is a supplier of mechatronic modules and equipment. The focus is on Design For Manufacturing and Design For Assembly supported by active cost reduction programs. One product that is assembled at this company is the L-arm with it’s carriage. This product is a part of the Genius Standard of Philips Medical Systems. In the next chapter an overview is given for this product. In this rapport a better look is given at the carriage. The main target is to lower the cost price of this product. First an overview of the whole system is given (Ch 2,3). The mechanical specifications will be derived from the carriage’s interfaces and functions (Ch 4). Then certain design rules are formulated for achieving cost reduction (Ch 5). With these rules, a concept design can be made and later on, this design is translated into a new carriage (Ch6,7). The new product is evaluated at its costs and its specs to be able to decide if the cost price reduction reaches the target (Ch 8). Costs for development and tooling are taken into account to see if it’s possible to make the carriage at a lower price (Ch 9).
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2. The Carriage in its surrounding The carriage is part of the Cardio Vascular Scan System of Philips Medical Systems. A set up of these products can be seen in the picture below. Several products are designed or partly manufactured by Frencken Mechatronics.
Figure 1 Cardio Vascular Scan
System
Picture above: A. Genius Standard B. Patient table. C. Monitor panel Picture left: 1. Rail system 2. Longitudinal Carriage 3. L-arm 4. C-arc Figure 2 Genius Standard
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3. Interfaces The Carriage has two main interfaces. They are the L-arm and the rail system. They are described in appendix A2 and A3. An overview of the other interfaces in the Cast-Iron design is given in the picture below and in the picture on the next page Top view
Figure 3 Interfaces of carriage 1/2
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Bottom view (part that faces the ceiling)
Figure 4 Interfaces of carriage 2/2
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4. Mechanical specifications for the carriage In this part the mechanical specifications are derived.
Purpose carriage The carriage has to transport the Genius Standard longitudinal from parking position to working position. The travel distance is approximately 2,5 meter. In working position, a rotation between carriage and L-arm is provided.
Overview main specs for carriage Rotational Stiffness: minimal 9e6 Nm/rad Vertical Stiffness: runner has to be able to move 0,4 mm vertically due
to gravity Design: Philips Design approved Reproducibility at ISO-center: 5 mm transitional and 0,20 rotational Safety: Design for infinite life, Shock proof. Technical life: 12 years, 120.000 cycles for L-arm position Gravitational load: 900 kg plus weight of carriage. Moment at hub: 6500 Nm plus 2000 Nm for scan mode. Dimensions: 880 x 1070 x 165
Derivation Rotational Stiffness This stiffness is important for the reproducibility of the system.
Properties of L-arm and Rail Looking at the stiffness of the L-arm, the minimal rotational stiffness of the carriage has to be 9e6 Nm/rad. (See appendix A2)
Scan mode: The rotation and angulation of the C-arc has to have a reproducibility of 0,20. In scan mode, the C-arc has to have an angulation of 550 in 1 second. Acceleration and deceleration provide a moment of approximately 1800 Nm. If 10% error of 0,20 is caused by stiffness, this will lead to 1800 Nm/3,5e-4=5e6 Nm/rad. Position of C-arc The moment at the hub is between 4500 and 6500 Nm. This is because of the different positions of the center of gravity of the C-arc. If 10% error of this reproducibility is due to the difference in moment, 2000 Nm/ 3,5e-4 rad = 5,8e6 Nm/rad is necessary. At calibration, this error can be eliminated. 10% error of reproducibility due to stiffness is not achievable. The error will probably be between 20 and 30%.
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Vertical Stiffness In the Cast-Iron design this is in the order of 100 KN/mm. It’s more or less dependent on the rotational stiffness. Decoupling of the two stiffnesses is possible but will lead to higher stresses. The carriage consists of 4 main runner blocks. One of these blocks has to be pulled towards the rail for tenths of millimeters. The Cast-Iron design has a value of 0,4 mm. This is caused by position errors and by bending of the construction. Therefore the stiffness can’t be to high. The tolerance of position error is also dependent on this stiffness. Design The appearance of the carriage can’t be changed drastically. It has to be Philips Design approved. A cowling can be used to achieve this. Interfaces The design of the carriage is dependent on all the interfaces. Changing some parameters can affect the working of the system. Only where necessary the product can be refined. Safety
Design for infinite life of the construction.(= 1e6 cycli). Due to changing the positions of C-arc and L-arm, the moment applied to the hub of the carriage is changed in direction and in magnitude. Also changes of stress arise if the side runners have to keep the carriage on the rail. If a maximum stress of +/- 30 Mpa is allowed for the applied moment and +/- 30 Mpa for the applied force at the side runners, almost every type of weld can be chosen. Safety factors Overall: 2,4 Weld spots: 4,0 (UTS) Shock Impact For normal use the deceleration at the end stop is 3,8 m/s2. For excessive use a deceleration of 7,6 m/s2 is taken. Earthquake The gravitational force is 4,5 m/s2 extra for X and Z and 1,5 m/s2 extra for Y (= vertical).
Stationary load The carriage has to hold the L-arm and it’s components. The mass of these parts is 900 kg. Because the center of mass is not in the centerline of the hub, a moment of 6500 Nm is introduced.
Dimensions The Carriage has to be able to go through doorways. The dimensions are fixed Tolerances The main tolerances are for the longitudinal movement of the carriage. The squareness of the L-arm on the carriage is of less importance, because this error is compensated at calibration.
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5. Cost price reduction The purpose of the study is to achieve a cost price reduction. This means that the method of production has to be investigated. There are basically two ways to make the carriage:
- Casted carriage: Casting itself is a very cheap process. The most costs are for machining and for coating. That’s because of the large heavy part that has to be handled. Usually the foundry can deliver these operations for a relatively low price. A disadvantage of a cast model, is the possibility of large defects in the material.
- Welded construction from plate and tube. The variety of possible processes is large. The advantages will be discussed next.
For cost reduction there are several design rules or possibilities. The following items are discussed:
a) Minimize use of material b) Machining operations in smaller handy pre-fabrications c) Finishing operations on smaller parts d) Minimize operations at all e) Dependency on practical circumstances
a) Minimize use of material This means that there is a need for an Optimal design with a high stiffness/mass ratio. This ratio is already improved by the choice of material. Construction steel has an higher Young’s modulus compared to the one from cast iron GG25 (2e11 N/m2 compared to 1,14e11 N/m2). An other solution can be found with the TRIZ contradiction method1. This is a method that delivers solutions that are derived from successful patents. In this case the contradiction is between stiffness and mass. This means that if strength has to be improved, the mass will rise. A few possibilities are given to prevent this. - Segmentation: use of smaller parts to create the product. In this case use of
smaller prefabs is possible. Also smaller parts give less waste of material when it’s cut from plates. Because of assembly not too many parts are allowed.
- Counterweight: This item is not possible in the design. Counter weighting will enlarge the mass of the whole system and secondly there is no room for it.
- Composite materials: This is basically done by building out of plates with baffle plates in between.
- Dynamicity: Make more parts movable. In this case, this is basically the same as building as statically determined as possible.
1 Msc. Valeri Souchkov, ICG training & consulting Ir. Jacques Stevens, stevens idé partners, Systematisch
innoveren met Triz: de contradictiematrix. Constructeursnieuws 10-2005, p16, Uitgeverij Nassau
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b) Machining operations in smaller handy pre-fabrications It’s quite expensive to have a large product that needs a final process. This is because of it’s mass that has to be lifted and the need for a large bench for clamping. If the assembly consists of smaller prefabs, this can be eliminated. With a good assembly order and with smart welding, this is possible. c) Finishing operations on smaller parts Coating of a huge heavy part is expensive. This is for the same reasons as described in the last item. Especially when the coated product needs a treatment in an oven. Also a lot of screening is necessary when parts of the product can’t be painted. Low weight cover plates can be used on the carriage to minimize these costs. A primer for the covered parts will do. d) Minimize operations at all It’s not the material that costs a lot. It’s more the effort that is taken to build a product. Minimize the hours of manufacturing is important. This can be done by: - Using small welds and mortise and tenon joints for the alignment - Using self-aligning in stead of long adjusting protocols - Minimizing wrong assemblies by use of clear variety of parts e) Dependency on practical circumstances Unfortunately cost reduction is also dependent on the practical circumstances. There is already a product that is sufficient for it’s function and that is running. A new product means a whole trajectory of designing, effectuation, tooling and testing. Furthermore the product has an end of life. Al these costs have to be accounted for.
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6. Concept study In this study, the base construction of the carriage is determined. First the moments and forces are described. Then the basic design and it’s components are given. Also a statically determined construction is described and some details about welding and stresses are taken in account.
6.1. Moments and forces First the Cast-Iron design was analyzed with a FEM program called Algor. The load of the L-arm and the C-arc can be described with a force and a moment on the hub. The force is a constant; the moment can change in direction and in magnitude. For the new design, the minimal torsional stiffness is almost the same as that of the Cast-Iron design. The vertical stiffness of the current design is 100 KN/mm.
Figure 5 Torsional and vertical stiffness
6.2. Basic design The base of the design is a hub with 4 legs. The force paths are as short as possible. The cross section of the hub is a square box of 120x120 and has a thickness of 6 mm.
Figure 6 Basic design: 4 legs on a hub
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6.3. Beams Several beams were analyzed. For the limited height, a beam with minimal mass and required stiffness is chosen. The following formulas were implemented in a Matlabscript Bending of a beam Torsion
)(
)(2
2
xEI
xM
x
V=
∂
∂ (1)
)(xGJ
T
x=
∂
∂θ (2)
The beams are loaded at the end with a force of 5000 N. That is the same as setting a moment of 6500 Nm on the hub, with the direction of the moment perpendicular on the legs. First the global measurements of the beam are taken. The thickness of the wall is altered. In the diagram lines of weight and deflection are drawn for different thicknesses.
Figure 7 Beamdesign
In stead of taking a straight beam, a wedge can be chosen. The stiffness/mass ratio is slightly better. With wedges, the connection with the hub is more convenient.
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Deflection of the beam (triangle) With a load of 5000 N, a deflection of 0,5 mm is allowed. Approximately 60% of the total deflection is done by the beam, the other 40% is assumed to be provided by the hub. This can be seen in the schematic diagram below. This diagram gives the derivative of the deflection. The area below the curve is the total deflection.
Figure 8 Deflection of the beam and hub
In the next table the deflection V and the weight of a specific beam are given. This value is +/- 60% of the total deflection
Table 1 Deflection for different configurations of the beam
Changing B doesn’t affect the result very much. In the design a beam with overall thickness 6 is chosen. With this beam the stiffness is 1,5 times the required one, but the stress will be lower.
h1xb1xL [mm3] H x B V [mm] Weight [Kg] 120 x 100 x 400 6 x 2 0,15 5 3 x 1 0,2 3 100 x 100 x 400 6 x 2 0,20 5 3 x 1 0,27 3
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6.4. The hub To get an optimal use of material, the legs have to be connected tangentially to the hub. This can be seen in the picture on the right. Some baffle plates in the hub provide a good transmission of the forces.
6.5. Welding The construction will be welded together. That means choosing the right weld at the
right positions. Furthermore it’s important to minimize the number of them and to gain good access to the weld spots. Alignment of the parts is done by means of mortise and tenon joints. The minimal total length of these joints in the legs is derived in appendix A5. Small but welds are used. At some places fillet welds are used. Their fatigue strength is lower. Fatigue Weld fatigue is due to cyclic changes in stress. In this case it’s mainly caused by the change in direction of the moment on the hub. It is chosen to design for infinite life. This means that the carriage is designed for one million cycles. In practice approximately 120.000 cycles are made. A weld fatigue strength of approximately 60 Mpa2 is taken for this cyclic load (1e6 cycles, 50% probability of failure). This is for the worst case weld. This means that the stress caused by the moment of 6500 Nm has a maximum of +/- 30 Mpa. This stress is approximately 70% or 80% of the total stress that also includes the gravitational load. The stress range is a very safe one. At some spots in the construction higher stresses are allowed: Connection between plates with thickness t
Fatigue strength x
4 22t
Longitudinal welds Fatigue strength x 2 If 120.000 Cycles were made Fatigue strength x 2 With St37 as material, and with safety factor 4 the maximum stress is 90 Mpa. The stress due to the moment has to be below 60 Mpa.
2 S.J. Maddox, Fatigue strength of welded structures, second edition, Woodhead Publishing Ltd, 1991, ISBN 1
85573 013 8
Figure 9 Tangentially placed legs
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6.6. The three concepts
Table 2 The concepts
1. Optimal lines of force 2. Beams 3. Combo
The paths of forces are as short as possible. The beams are placed tangentially to the hub.
The carriage is built out of standard beams. In the middle a plate with a thickness of 10 mm is needed. This will lead to thick welds.
Near the main runners, a lot of functions come together. With two beams attached to the inner body, it’s easy to make the interfaces at those spots
The first concept is the optimal design. With pole positioning, the normal force at the contact of the main runners with the rail won’t create a moment into the construction. Because the side wheels have to be attached, it’s not easy to create an appropriate construction at that spot. With concept three this problem is eliminated. Some stiffness is provided by bending stiffness of the two beams. The construction of beams consists of standard beams with typically thicknesses of 10 mm. This thickness is necessary because of the limited height near the hub. The square plate with hole requires a washer plate. The thickness is also needed for bending stiffness. Thick welds are needed. (weld speed is approximately 4 meter/hour). The base construction, without cowling and motor suspension is in the order of 160 kg. The torsional stiffness is in the order of 16e6 Nm/rad. First estimations lead to cost reduction, but probably more reduction is possible with the third concept. The third concept is build out of plates with a thickness of 6 mm. Weld joints can be made at conveniently situated positions. With mortise and tenon joints, only small welds have to be made. The same stiffness as for the former concept is achievable. The mass is typically less than 125 kg for the basic construction. The last concept is the base for the design
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7. Design study The design rules for cost reduction and the concept study lead to a design of the carriage. The design consist of a base plate with on it the runner beams and the inner body that holds the hub. The base plate is convenient for alignment and for positioning of the parts. Furthermore the motor suspension and two other interfaces are placed on it. The alignment of the parts will take place by means of mortise and tenon joints. The mass of the construction with cowling is in the order of 140 kg.
Figure 10 Base plate with parts on it
In the next part the following items will be discussed: - Runner beams - Motor suspension - Design of the hub - Assembly - Stress distribution
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7.1. Runner beams The design will consist of two runner beams, with in between them the body with the hub. The main runners have to be in line with the rail. A skewness of 0,20 is allowed. This number is an outcome of tests at Philips Medical Systems. If these runners can be placed into the runner beams without tolerance errors, a squareness of 3 mm is allowed. In practice, there is some tolerance and the squareness will be in the order of a mm. In appendix A1 a situation is given were a squareness of 2 mm is acceptable.
The runner beams will bend due to the forces acting on the carriage. This beam can’t be to stiff,
because the rail already bends due to the normal contact force. This can be described as
approximately 9e5 N/rad at the contact spot (see appendix A3)
Figure 11 Squareness of runner beams
Figure 12 Bending of runner beam
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The side runners have to hold the carriage onto the rails. The main runner has to be pulled towards or pushed away . This will create a moment on the beam. The arm has to be as short as possible. The maximum force is estimated as 5000 N. This means a maximum moment of 500 Nm. Also here the stress has to be below 30 Mpa. The strip with the side runners on it will bend a little bit. The bending is in the same order as the one for the Cast-Iron design. Stiffness at the siderunners should be in the order of 50 KN/mm (derived form Cast-Iron design).
For the estimation of the force: Maximum load for normal use: 15000 N Friction coefficient: 0,33 Force: 5000 N
Figure 13 Side runner
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Concepts for placement side runners A few ideas where made for eliminating the moment. This becomes interesting if the runner beams are not in the design. Because they are already necessary for alignment and for bending stiffness, these ideas are not implemented.
Table 3 Concepts for side runners
Concept 1/2 : Side runner in main runner block
Concept 2/2: side runners on arc
One side runner is placed into the main runner block. The other one is placed like in concept 2, on a U-beam An axle has to be placed through the side runner. Replacement of the runner is difficult.
Two side runners are placed on an arc. This arc is mounted on installation, otherwise transport isn’t possible. The arc can be held by an axle, or can glide in a slot or in a sleeve bearing. The third wheel can be mounted on a U-beam, or is placed on a bracket, that is positioned on the arc.
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7.2. Motor suspension In the Cast-Iron design, the suspension of the motor is basically a block on a plate. Deflection of this plate will lead to an angle between the drive wheel and the rail. This will cause wear. Nowadays this wear is prevented by vulcanizing the rubber drive wheel. A better solution would be preventing skewness at all.
Figure 15 Eliminating skewness
The forces of the motor and it’s jack tensioning system3 are not in one line. This will create a moment on the suspension. By adding a section that is in line with the drive wheel, this moment is excluded. This section is stiff compared to the plate. Only some small deflection in vertical direction occurs.
Figure 16 Motor configuration with motor beam
3 Motor PM6 78-35 (Groschopp K7541 2164175-1205)
Figure 14 Moment in motorsuspension
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Some other concepts for motor design
Table 4 Concepts for motor design
Sideways
The Drive wheel is on the running surface for the side runners. The motor is held between the base plate and a plate above it. The forces are directed into the plates.
Drag conveyor
The conveyor pulls the carriage. The skewness of the drive wheel with the rail is independent on the conditions of the carriage
Motor on beam
The motor is mounted on a long beam or section. The hinge is place on the front runner beam; the spring is attached to the rear runner beam. Because of it’s length, alignment is easy.
Smaller motor To gain space, a smaller motor with an appropriate speed reduction can be used
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7.3. Design of the hub The hub is a section of a steel tube with an outer diameter of 323,9 mm and a thickness of 30 mm. Usually with this thickness, the tube is seamless and relatively expensive. In the hub thread is tapped. The bolt that goes in it has to hold 5 different parts together. Most important part is the gear ring, were the load of the L-arm is. In a document of Philips Medical Systems the specs for the bolt construction are mend. Maximum axial load: 10172 N This load occurs when the C-arc collides
against it’s end stop with a speed of 30 0/s. Left prestressing force: 12000 N This force is necessary for holding the outer
ring of the gear ring in place when the L-arm rotates and collides against its end stop. Friction coefficient is 0,1
A tightening moment of 40 Nm delivers a prestressing force of 21744 N. The choice of a bolt class and the length of the thread are dependent on the material of the hub.
In the Cast-Iron design bolts of class 12.9 are used4. The thread length is 18 mm. The safety factor for wear is approximately 2,5. The safety factor for shear fracture is 4 and the factor for tensile failure is 6.
Options:
Later it will be shown, that the massive hub is quite expensive. Building the hub out of different parts could be a possibility. Another option is to use long bolts, so there is a lot of strain in them.
4 C.P.Bakker, Clea II / FD Mechanical detail design specification, 12NC: 4522 129 1172.0, Rev C, Pag 60/141,
PMSN
Figure 17 Hub design
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7.4. Assembly The order of the steps is mainly dependent on the following things:
- machining of smaller handy parts - Achieve sufficient skewness and parallelism to the runners.
Table 5 Assembly
1/8
The runner beams are build. Per runner beam the following actions are taken:
a) The U-beam is folded.
b) The main runner blocks and the side runner blocks are welded onto it.
c) A baffle plate with a thickness of 6 mm is welded onto the beam
d) The holes for the wheels are machined
2/8
The runner beams are tacked to the base plate with thickness 6 mm Tenons on the beams stick in mortises of the base plate. The base plate contains some holes for cables The wire bracket is part of the plate. The 12 small holes are for plug welds. These have a diameter of 20 mm.
Keep weldless
until step 4
25
3/8
The hub is placed The hub contains baffle plates and tapped holes (M10). It’s tacked on the base plate. The side baffle plates are placed Continuous fillet welds are used for the connection between baffle plates and beams.
4/8
The top plate is placed onto the carriage. The Mortise and tenon joints can be welded. Near the runners small longitudinal welds are used. The hub can be tacked onto the top plate. The construction can be turned around for making the plug welds, that hold the hub on the base plate.
Weld used
for
straightening.
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5/8
U-brackets can be mounted The thickness of these brackets is 6 mm. Small welds keep them in place. Frisbee is tacked onto construction The welds only have to keep the Frisbee in place. Later on bolts are used for the constructive joint. Bracket for potentiometer is placed
6/8
Suspension of the motor is placed The suspension consists of a block and a beam. Small welds are sufficient. On the other side an other section is welded up. It’s an L-beam with two holes for screws.
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7/8
The main cover plates are fixed with screws. These plates have a thickness of 1 mm and are coated. With the fixation points they have their eigenfrequency near 80 Hz. Furthermore the motor and the potentiometer can be mounted. Also the runners are placed.
8/8
The ring bearing and the gear ring can be mounted The side cover plates are fixed with two screws. The plates have a thickness of 1 mm. Due to shape and fixation points the eigenfrequency is also near 80 Hz.
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7.5. Stress Analysis A simplified model is used for stress analysis. On the hub there is a load of the L-arm in it’s most inconvenient static position. The weight of the carriage is also taken into account
Figure 18 Stress distribution in carriage
The overall stress in the legs is below 30 Mpa. At the corners a stress of 40 Mpa arises. In the base plate the stresses are below 20 Mpa. In the design the top plate has some overlap. This will lead to lower stresses in the leg. Contributions to the maximum stress: Moment of 6500 Nm on hub: 70% - 80% Force of 9000 on hub: 20% - 30% Weight carriage: neglect able The following stiffnesses can be derived:
Torsional stiffness: 16e6 Nm/rad. This is an improvement with a factor 1,5 Vertical stiffness: 100 KN/mm.
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8. Cost price calculation 3 Types of design are evaluated for the costs. These are:
- Cast-Iron design - Beam design - Actual design out of plates
A sheet metal company, has made an indicating quotation for the best new configuration Cast-Iron design
Table 6 Cost price of Cast-Iron design
Description Base material Euro’s Euro/kg base material
A Casting 220 kg GG25 315,-- 1,40 B Transport &
Measurements 57,75 0,26
C Machining bearing holes and runner holes
215,-- 0,98
D Coating 172,-- 0,78 E Cover plates 2x 29,50
Total 789,25 3,45
Beamdesign
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The costprice with different configurations with beams and plates don’t differ much. For one configuration the price is estimated:
Table 7 Cost price of beam design
Description Base material Euro’s Euro/kg base material
1 Material beam 160x80x880, thickness 6 2x 42,-- 1,08 2 Material beam 120x80x700, thickness 10 2x 56,-- 1,21
3 Plate 700x500x10 1x 30,-- 1,20 4 Baffle plate 300x100x10 2x 5,-- 1,20 5 Back plates 400x100x10 2x 7,-- 1,20 6 Side runner block 200x100x20 2x 7,-- 1,20 7 Main runner block 144x64x25 4x 20,-- 2,90 8 Other plates, motor
suspension included 50,--
9 Frisbee R500x15 1x 36,-- 1,20
A Total material 253,-- 1,20 B Welding 6000 mm 2000
mm/h 120,-- 0,59
C Machining bearing holes and runner holes
160,-- 0,72
D Priming Paint 25,-- 0,12
E Cover plates 60,--
Total Excl Cowling 618,-- If Item D is not included in this design and in the Cast-Iron design, the prices are almost the same.
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Material costs are smaller than 1,30 euro/kg. Used with the mass of an assembly including wasted material will give a good indication of the price. Standard beams are relatively expensive, so bending of sections out of plate is cheaper. Item B can be minimized by using small butt welds on thin walled constructions. Item C is minimized by using handy parts that can be machined
Actual Design: First estimation
The theoretical prices are taken from the former design. For the machining operations the costs are derived from the cost per kg base material.
Table 8 Cost price of Actual design; First estimation
Description Base material Euro’s Euro/kg base material
A Base Material 140 kg + 40 kg waste 220,-- 1,20 B Welding 6000 mm, mortise and
tenon joints 2000 mm/h
120,-- 0,47
C Machining bearing holes and runner holes
Hub 30kg, Frisbee 30kg, Runnerbeams 2x15kg, motorsuspension 10kg
72,-- 0,72
D Priming Paint 25,-- 0,12 E Cover plates 4x 60,--
Total 497,-- 2,45
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Actual design: Quotation by Bumet corrected by Frencken Mechatronics B.V. For the last design a quotation is made.
Table 9 Quotation of Actual design
Description Base material Euro’s Euro/kg base material
A Base Material 180 kg inclusive waste 269,50 A+ Bending and Cutting
of plates 41,50
B Welding 46,-- C Machining bearing
holes and runner holes
210,--
D Priming Paint 25,-- E Cover plates 4x 60,--
F Set-up 900 euro / 50 products 18,--
Total 670,-- The quotation gives a price that is approximately 200 euro higher. One reason is that machining is more expensive in practice. An other reason is that some items are quite expensive. Two of these are the massive hub and the frisbee. Also other costs like bending and set-up costs were not taken in the first accounts. It’s also possible that the steel company made higher prices because it’s a new product. The expensive parts: Massive hub: 82 euro, for 30 kg. The hub is seamless. Looking at the mass, a
price of 40 euro would be acceptable. A possible solution would be building the hub out of smaller parts.
Frisbee: 90 euro. Only 10 kg of the 30 kg base material is left due to machining. A possible solution would be dividing it into 2 parts. One part only for the brake system and the other part for holding the ring gear. A sandwich plate for the brake system could be a cheap solution.
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Summary of designs and costs In next table a summary of the costs are given. The most interesting columns are those for the Cast-Iron Design and for the quotation by Bumet.
Table 10 Summary of costs
Description Cast-Iron Design
Beamdesign Actual Design: First estimation
Quotation by Bumet
A Base Material 315,-- 253,-- 220,-- 269,50 A+ Bending and Cutting of
plates 41,50
B Transport & Measurements
57,75
B’ Welding 120,-- 120,-- 46,-- C Machining bearing
holes and runner holes 215,-- 160,-- 72,-- 210,--
D Coating / Priming Paint 172,-- 25,-- 25,-- 25,-- E Cover plates 29,50 60,-- 60,-- 60,--
F Set-up 18,--
Total 789,25 618,-- 497,-- 670,--
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9. Efficiency of cost reduction In the previous chapter, the cost reduction per product is made. The efficiency to achieve this reduction is estimated here. The customer’s costs for development are not taken in account.
Table 11Efficiency of cost reduction
Products per year: 600 End of life: December 2008 Trajectory: 9 months products to make till end of life: 1350 Old cost price: € 789 New cost price: € 670 Delta: € 119 x
Total cost reduction: € 160.000 Proto and testing: (5x) 30.000 Tooling and engineering: (500 hours) 25.000 Completing TPD: (300 hours) 15.000 Total constant costs: € 70.000 -
Profit till end of life: € 90.000
The break even point is at a cost price reduction of 50 euro/product.
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10. Conclusions and recommendations For achieving cost reduction for a part that is already on the market, a lot of effort is required. The steps that are taken in this report are an example of designing in a specific cost efficient way. For cost reduction the following things have to be done:
- Minimize the use of material - machining of parts in handy prefabs - coating on smaller parts - Minimize operations at all
With these actions a design out of plates is competitive with a Cast-Iron design. Cost reduction is certainly possible. A summary of the main properties of the competitive designs are given in the next table.
Table 12 Comparison of the designs
Cast-Iron design Actual design
Material: GG25 Material: St37 Mass: 220 kg Mass: 140 kg
Rotational Stiffness: 10e6 Nm/rad Rotational stiffness: 16e6Nm/rad Vertical Stiffness: 100 KN/mm Vertical Stiffness: 100 KN/mm Cost price: € 789,25 Cost price: € 670,-- Extra improvement: motor
suspension Delta: € 119,--
Profit till end of life: € 90.000,-- Also practical circumstances are important. It’s impossible to change something without consequences. The dependency on contacts with manufacturers, developers and the interfaces of the product is huge. Cost reduction per product is nice, but also the costs for further development have to be taken in account. In this case a profit till the end of life of the product can be made of 90.000 euro. The actual design still has some parts that are quite expensive. The main parts are the hub and the Frisbee. If a better look is taken at these parts the profit will be higher.
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Recommendations There are still some minor parts that have to be looked at:
- Cable passages - Transport bracket - Interface to wire guide holder - Some drilled holes
Another great possibility for cost reduction is the motor design. A cheaper design with less material and with main forces in line is recommended. If the carriage is build in the new way, a motor on a section is probably the cheapest solution. There is also a common recommendation. This is to get in contact with all the possible partners in an early stage. There is a huge dependency on them. In this manner all the ideas and possible solutions can be analyzed and a maximum of knowledge and expertise can be used. One of these contacts is BUMET, a company that is specialized in metal working.
11. References [A] P. vd Heijden, Clea Stand incl. FDXD Functional Requirement Specifications,
12NC: 4522 129 1172.0, Rev C, Philips Medical Systems Nederland BV, Best
[B] C.P.Bakker, Clea II / FD Mechanical detail design specification,
12NC: 4522 129 1172.0, Rev C, Philips Medical Systems Nederland BV, Best
[C] S.J. Maddox, Fatigue strength of welded structures, second edition, Woodhead
Publishing Ltd, 1991, ISBN 1 85573 013 8
[D] Msc. Valeri Souchkov, ICG training & consulting Ir. Jacques Stevens, stevens idé
partners, Systematisch innoveren met Triz: de contradictiematrix.
Constructeursnieuws 10-2005, p16, Uitgeverij Nassau
A link to Triz contradiction matrix and tools can be found at the download area of
www.idepartners.nl
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A1. Tolerances
In the following two sheets, some important tolerances and measurements are given.
Figure 19 Sheet with main measurements 1 of 2
Reference R is the contact surface with the ring bearing
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Figure 20 Sheet with main measurements 2 of 2
The squareness and the
parallelism of the hole is
derived from the curvature
radius of the runners.
This tolerance influences the
squareness of the runner beam
with reference S
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A2. L-arm For a FEM analysis a simplified model is used. With the Ansys-module of Autodesk inventor 9 the stiffness is derived.
Figure 21 Forces and stress on L-arm
The L-arm has to hold the C-arc of 510 kg5. The initial deflection with this mass means a stiffness of 15 KN/mm at the centrer of gravity of the C-arc. At the hub, this stiffness can be described as a torsional stiffness of 5e6 Nm/rad With this stiffness the one for the Carriage can be derived. The minimal torsional
stiffness for the carriage has to be: radNmeradNmekg
kgkg/69/65
510
387510=⋅
+
The current Cast-Iron design has almost the same stiffness as mentioned above. Stresses due to the load have a maximum between 20 and 30 Mpa. Also an eigenfrequency can be derived:
hub
hub
J
Cf ⋅=
π2
1= 12 Hz
with Chub the torsional stiffness of the carriage and Jhub the mass inertia of the L-arm and the C-arc at the hub. Jhub is approximately 1500 kg m2
5 C.P.Bakker, Clea II / FD Mechanical detail design specification, 12NC: 4522 129 1172.0, Rev C, Pag 12/141,
PMSN
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A3. Rail system The base of the rail system are two aluminum extrusion sections. Clamps at a minimal distance of 680 mm keep them at the ceiling. Also some strips from one rail to the other provide a form closed suspension. The section can be seen as a box profile with a strip that provides the running surfaces. The thickness of the strip is 12 mm. There are several disadvantages of this design:
- The surface of the main running wheels is outside the box profile. At the contact spot the strip is bent.
- The thinness of the strip will enlarge the effect of bending. If the profile is completely fixed to the ceiling, the load at the contact gives an angle: 9e5 N/rad.
- The stiffness that is felt at the runners is dependent on the position - The minimal stiffness is in the order of 10 KN/mm for a two point roll-support
FEM analysis. If the wheelbase is 700 mm, the minimal torsional stiffness provided to the hub of the L-arm is 5e6 Nm/rad. If the rail is mounted on more points, with an offset of 680 mm, this value is 3 till 4 times bigger.
- The rail system makes creaky sounds when the L-arm is positioned from parking position towards working position.
- In most cases the straightness is accomplished by fillers with a thickness of 1 mm.
Figure 23 Bending situations of rail if it is fixed on 3 places
Figure 22 Rail deflection
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A4. Shock impact For shock impact some simple tests were done in FEM. The load is in the middle of the runner beam. The support of the base plate is eliminated.
Figure 24 deceletation at end stop
Deceleration of carriage at end stop 3,8 m/s The force on the carriage is 4500 N. Due to collision a stress occurs of 25 Mpa in the runner beam. At the legs a maximum stress of 10 Mpa arises Deceleration of carriage at end stop excessive use 7,6 m/s The stresses are as twice as high. With these results no problem for shock are expected. Earthquake The critical parts in this situation are the runners and the bearing. The parts are the same as in the Cast-Iron design, so the same effect is expected. Conclusion
The product is probably resistant for shock impact. In real the collision with the end stops is not in the middle. The stresses due to a force will be lower.
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A5. Length of mortise and tenon joints in the legs The distance between the joints and the length of them determine the cyclic stresses that occur. The total length of these welds are derived. In worst case the moment on the hub is divided over 2 beams. This moment is translated into forces. This force leads to shear stresses at the joints.
Figure 25 Shear forces due to applied moment
With a plate thickness of 6 mm the total length of the welds per beam can be estimated:
Table 13 total length of welds
mm
NLwtotal
12
32500
max ⋅=
σ (3)
with Lwtotal the total length of the welds and σmax the maximum cyclic stress at the weld. A total length of minimal 60 mm is recommended. In practice, the force in the horizontal welds is lower. A part of the forces is also distributed over the vertical welds between the hub and baffle plates.
σmax Lwtotal
30 Mpa 90 mm 45 Mpa 60 mm 60 Mpa 45 mm
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A6. Alternative designs
Some possibilities for the design that aren’t described in the main text are given here.
Statically determined construction The rather rigid construction can give problems at the contact of the rails. This can be eliminated by dividing the carriage into two parts, with a diagonal hinge line through the contact spots at the main runners. A simple saw cut at the right place could do the trick. A disadvantage is the decrease in stiffness with a factor 2 and some bending of the radial bearing. For the design it’s chosen not to use this trick. The mass of the whole system is quite large. The 4th wheel will be pulled or pushed towards the rail for approximately 0,4 mm.
Plate on crossed beams Thickness of the inner beams is approximately 10 mm. The second moment of area is in the order of 600 cm4. The Runner beams have a thickness of 6 mm.
Figure 27 Plate on crossed beams
Figure 26 Statically determined construction
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Butterfly tie Two parts are hold together with tenon and mortise joints. The inner hub is an assembly of separate plates.
Figure 28 Butterfly tie
New design, adapted. The legs are connected to higher runner beams. The wall thickness of the runner beams is 4 mm. The design has the same properties as the new design.
Figure 29 New design, adapted
