Bachelor Final Project
Designing a foosball table actuator
Technical University of Eindhoven Department of Mechanical Engineering
Dynamical System Design – Control Systems Technology Student: Erik G. Hijkoop Student number: 575617 Coach Ir. W. Aangenent Supervisor Prof. dr. ir. M. Steinbuch
25 December 2007
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Table of content 1 Introduction ..........................................................................................................................4 2 Demands and requirements ................................................................................................6
2.1 The game ........................................................................................................................6 2.2 The table .........................................................................................................................6 2.3 The location.....................................................................................................................7 2.4 Forces and moments.......................................................................................................7
2.4.1 Forward...................................................................................................................7 2.4.2 Midfield .................................................................................................................10 2.4.3 Defending .............................................................................................................10
2.5 Demands summary .......................................................................................................12 3 Principles of actuation .......................................................................................................14
3.1 Axial...............................................................................................................................14 3.1.1 Performance .........................................................................................................14 3.1.2 Various demands..................................................................................................14
3.2 Radial ............................................................................................................................15 3.2.1 Performance .........................................................................................................15 3.2.2 Various demands..................................................................................................15
4 Choosing the motors .........................................................................................................16 4.1 Direct drive versus indirect drive ...................................................................................16 4.2 Axial Movement.............................................................................................................16
4.2.1 Slide......................................................................................................................17 4.2.2 Maglev ..................................................................................................................17 4.2.3 Conclusion ............................................................................................................18
4.3 Radial movement ..........................................................................................................18 5 Design................................................................................................................................19
5.1 Spline Shaft ...................................................................................................................19 5.2 Bearing attachment .......................................................................................................19 5.3 Linear motor bearings ...................................................................................................20 5.4 Displacement sensor.....................................................................................................20 5.5 Cogwheel position .........................................................................................................21 5.6 Safety tubes ..................................................................................................................21
6 Results...............................................................................................................................22 7 Conclusions .......................................................................................................................23 8 Recommendations.............................................................................................................24 9 References ........................................................................................................................25 Appendix A: Measurements ...........................................................................................................27 Appendix B: Estimation of Mass moment of inertia........................................................................28 Appendix C: Advantages and disadvantages of actuator principles ..............................................29
Axial............................................................................................................................................29 Radial .........................................................................................................................................31 Direct drive vs. indirect drive ......................................................................................................33
Appendix D: Resulting mass, mass moment of inertia and costs ..................................................34 Appendix E: Bearing house design ................................................................................................35 Appendix F: Cogwheel selection ....................................................................................................36 Appendix G: Danaher Motion DBL4H00750 Datasheet .................................................................37 Appendix H: Danaher Motion IC11-100 Datasheet ........................................................................38 Appendix I: Bosch Rexroth MKR 20-80 Datasheet ........................................................................40 Appendix J: Datasheet SE1............................................................................................................42 Appendix K: Engineering Drawings ................................................................................................44
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Nomenclature
ω Angular velocity
mb Mass of the ball
x Distance
a Acceleration
t Time
v Speed
F Force
T Torque
J Mass moment of inertia
ω(dot) Angular acceleration
Phi Angle
ωe Angular velocity at the end of shooting
N Newton
Fh Horizontal force
Θ Angle between vertical and foosball player
Table 0.1: The meaning of the symbols used in this report.
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1 Introduction Imagine you are in a bar with some friends. After some beers you decide to play a game of table foosball. After five times losing with zero points, you discover you are a bad table foosball player. To impress your friends next week it’s time to practice, off course without noticing your friends. The only player you have is your little brother who is even a worse player than you. You have a problem. Building a robotic side of the foosball table will do the job. This may sound easy but it would cost more than one week. A camera is needed to find the ball in combination with some computer programs. This computer also has to calculate the trajectory. In the meantime the bars need to be positioned. To tackle this last problem, positioning the bars, a solution is proposed in this report. So to be able to play foosball an existing foosball table needs to be actuated. The Lehmacher Tecball is chosen, some of the characteristic measurements can be seen in figure 1.1. (The open arrows are the movements from the shaft and the closed arrows are fixed distances) This is done earlier by the University of Freiburg and was called KIRO.[9] The disadvantage of there system is the high moving mass and the use of belts as can be seen in figure 1.2. The disadvantage of this construction is that the belts will be compressed and strained when moving around. This will lead to errors in the positions and a limitation on moving acceleration and speed. Possible improvements for these problems are the lowering of the moving mass by excluding the motors from the moving part of the construction. Next to that the transmission should be made more rigid by using cogwheels or even using direct drive on the bars.
Figure 1.1 Dimensions of the Tecball
33 mm.
740 mm.
164 mm.
112 mm.
185 mm.
356 mm.
150 mm.
1430 mm.
1120 mm.
200 mm.
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Figure 1.2: Kiro construction Next to Kiro, Rice University build foosbot, which is also an automated table foosball system. Foosbot is different from Kiro because no camera is used. The ball is found by using infrared beams crossing the field. At the Milwaukee School of Engineering a similar table to the Foosbot is designed. In Denmark the Technical University of Denmark builds a table with a camera above the table. The constructions used for these tables are all quite similar to the Kiro table, so the advantages and disadvantages are also the same.[10] The report is build up in the following manner. Firstly the demands will be formulated, after that some choices are made considering actuators and principles. Subsequently some designs are discussed, followed by the performance achieved, the conclusion and some recommendations.
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2 Demands and requirements There are some limitations in the design of the actuators. This is due to the available space, acceleration and the fact the table is positioned in a pub. Of course the actuator construction is meant to outlive the table itself. So it should be designed properly taking into account all limitations. Next to that the table should be safe for human beings and although the university has a lot of money they would like to have an indication of the building cost. Issues needed to take into account are:
• The table should be safe
• Indication of building cost
2.1 The game
Due to regulations not everything is allowed, the ball must be hit after maximum one rotation of the bar and after hitting again only one entire turn is allowed. To be able of shooting like humans do it is necessary a pinshot and snakeshot can be made. When a pinshot is used the ball is clammed under the feed of the player and from there positioned under the bar. Immediately the player moves back and forward hitting the ball in this movement. This leads to a limited acceleration angle of around 60 degree. When the snakeshot is used the player is holding the ball and is rotated 360 degrees around the bar to shoot.[12] This shot needs the bar to rotate and translate at the same time. Concluding the following demands are mentioned here:
• Maximum acceleration angle of 60°.
• Rotating and translating at the same time.
2.2 The table Automatically by choosing the Tecball as the table, the distances are constrained. When we take the construction in mind there is a limiting factor by the distance between the bars. There is 15 cm space between two of them, this gives a 15 cm building space.(figure 2.1) The depth is limited by the ‘smoothness’ of the construction. Taking into account a maximum stroke needed of 356 mm(figure 1.1) the space behind the table becomes quickly quite big. The height of the table is also fixed so the dimensions can be seen in figure 2.2.
Figure 2.1: Available building space bar. Figure 2.2: Available building space side view This gives us the extra demands:
• 150 mm. width building space.
• The construction should be as small as possible.
150 mm.
25 mm.
224 mm.
35 mm.
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2.3 The location Bearing in mind most people play table foosball in a pub, the table must deal with the environments in the pub. The temperature is quite high, say in a hot summer day 40+ degrees Celsius. Friction will heat up the bearings even more. Next to that there won’t be 400 Volts power available, so only 230 Volt motors can be used. Next to that safety is an issue. Systems with a lot of energy in it are not preferred because when the system fails the energy can be pointed in the wrong direction. Clearly poisoning oils or gasses are not permitted, again because of safety. So the demands caused by the playing position are:
• Working properly until at least 50° Celsius
• 230 V power supply available.
• Less energy in the system is better, due to safety.
• Poisoning oils and gasses should not be used.
2.4 Forces and moments The ball does not move without an impulse. So a force must act on the ball. This force is delivered by the rotational actuator. This force can be determined when the speeds and accelerations are known. To determine the limits of the forces we should check where the highest speeds are needed. The highest shooting speed is needed when attacking because otherwise the opposite party can defend more easily. At the defending side the sideward speed is crucial because this is the only way you can defend and the faster you can defend the better. The midfield needs to be moderately fast at both degrees of freedom, because next to defending this line is passing the ball trough to the front or may even score [13]. Now the needs of speed will be determined for the attacking and defending stroke.
2.4.1 Forward Starting with the demanded shooting speed the maximum velocity needed is 10 m/s. For good players this is the upper limit in speed they can reach.[9] This is also obtained by measuring the time and distance when shooting as fast as possible from one side of the table to the other side. In figure 2.3 the ball moves from left to right. The distance covered is 933 mm. which lead to velocity of 9.33 m/s. To be sure humans are matched the limit of 10 m/s is taken.
Figure 2.3 The time difference between the two pictures is 0.1 seconds. (20 frames with a 200 fps camera) [15] To obtain the time available the critical distance is required. This distance, between the attackers and the goalkeeper, is at least 300 mm combining the speed of 10 m/s with this distance the
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maximum reaction time to defend is determined. This leaves just 30 ms when assuming the speed of the ball does not drop in this 300 mm. There are several ways of calculating the shooting forces of the ball. Impulse moment is used to calculate this as can be seen in equation 2.3. Herein mball is the mass of the ball, dv the difference in speed of the ball, F the force acting on the ball and dt the time in which the collision takes place.
dtFdvmball ** = (2.3)
The collision time can be determined by calculating the angle the foosball player has contact with the ball. Because the required turning speed of the rod is specified, due to the maximum forward speed, the time can be calculated.
Figure 2.4 The available acceleration angle and the trajectory of the feet of the foosball player. The shooting angle is approximately 60° (figure 2.4), bearing in mind a small possible error in positioning the foot compared to the ball. The horizontal movement is 71 mm combining this with the speed of 10 m/s gives the available time, 0.0071 seconds. This leads to a turning speed of 147 rad/s. Now it is possible to calculate the mean force with equation 2.3, using the weight of the ball of 19.7 grams. The mean force then becomes 27.7 N. If the average length of the touching point is taken at 66.5 mm, the torque needed is 1.84 Nm. This is the moment needed to shoot the ball, not to accelerate the bar. This will be discussed in the next paragraph. One of the rules at table foosball is the amount of degrees the bar is allowed to rotate. This is limited at 360° before or after hitting the ball. Although mostly this is large enough, a pin shot has to be considered too. In that case the bar can only turn around 60° to accelerate from 0 to 147 rad/s. Calculating the moment needed in this case equation 2.4 is used. Herein J is the mass moment of inertia of the shaft including peripherals, which must be as low as possible. This is one
71 mm.
61 mm.
64.3°
71 mm.
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of the factors that can differ a lot from the estimated 1.2E-3 kgm2 and thus have a lot of influence.
(See table 2.1) Description Amount J (kgm
2) Total J (kgm
2)
Bar (Main with puppets) 1 5.96 E-4
5.96 E-4
Bar (connection) 1 6.16 E-5
6.16 E-5
Cogwheel big (r =34 mm) 3 1.66 E-4
4.98 E-4
Cogwheel small (r = 10 mm) 1 1.24 E-6
1.24 E-6
Motor(Faulhauber 4490) 1 1.3 E-5
1.3 E-5
Total 1.17 E-3
Table 2.1 Estimation for the mass moment of inertia which is based on the Kiro foosball table. (See also Figure 1.2 and Appendix B)
wJT &*= (2.4)
With
π
π
*2*)360/(
*2
1
*
**2
1*2*)360/(
2
2
phi
w
w
gives
w
wttww
twphi
e
e
e
=
=⇒=
=
&
&&
&
(2.5)
Using equation 2.5, the acceleration becomes 10178 rad/s
2. Combining the mass moment of
inertia and the acceleration a moment of 12.4 Nm is needed using formula 2.4. This is not totally true because of the angle the player is making with the shooting direction. (The plane of the table floor) see figure 2.6. To compensate for this, the torque should be multiplied by 1.07. This factor gives the same area as the 27.7 N line in the plot of the horizontal force (figure 2.5). This all leads to a torque of 13.2 Nm.
-20 -10 0 10 20 30 4020
22
24
26
28
30
Shooting angle θ (degree)
Horizonta
l shooting f
orc
e (
N)
Figure 2.5 The horizontal shooting force acting on the ball. Figure 2.6 Force partitioning The sideway movement is only used when shooting a snakeshot or playing from one attacker to another. The snakeshot movement is the fastest, so taking this one in consideration the
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acceleration becomes 32.4 m/s2
using equation 2.6. The sideward movement (x in equation 2.6) then is only 0.02 meter in the time one turn is made, with the angular acceleration of 10178 rad/s
2(a in equation 2.6). This time is 0.035 seconds.
2**5.0 tax = (2.6)
The stroke needed to cover the entire field is 185 mm. as can be seen in figure 1.1, this is an additional demand because otherwise the game could not be played well. This gives us the following requirements (taking a mass moment of inertia of 1.2 E
-3 kgm
2):
• Forward velocity of the ball of 10 m/s o Gives an angular acceleration of 10178 rad/s
2
• Linear movement: acceleration of 32.4 m/s2
• The torque needed is 13.2 Nm
• A stroke of 185 mm. is needed.
2.4.2 Midfield The midfield only plays the ball forward to the attackers or backwards to the defenders but do not have very demanding tasks to handle. This gives no limiting speeds and accelerations to this bar, so the accelerations (linear and angular) could be moderate compared to the attackers and the defenders. The stroke needed for the midfield is 112 mm. Summarizing this demands give us:
• The stroke needed is 112 mm.
• The accelerations of the defending and attacking bars are sufficient for the midfield to use.
2.4.3 Defending Now the defending bars are considered; again the speed and acceleration in axial direction (of the bar) should be determined. Before calculating these, the distance covered is obtained. The width of the goal is 200 mm (See also figure 1.1). This width can be reduced heavily as can be seen in figure 2.3. Here only the case of a attack trough the middle is taken into account because this is the smallest distance from the attacker towards the goal. Off course when the ball is shot from aside the goalkeeper and the defender should be positioned a bit towards the side where the shot is coming from. Firstly the goal width is divided in two, so the keeper and the defender will both cover one half of the goal. After that the ball is bounced when the player is hitting the ball, this happens when the ball and the player are at max the radius of the ball away from each other. Therefore this radius is removed at both ends of the stroke a player is taken (these are the dotted lines at figure 2.7). This leaves a distance to cover of 54.1 mm for the goalkeeper and only 9 mm for the defender. The distance to cover can be reduced by a factor two when we assume the players are positioned at the middle of this distance. This leaves a distance to overcome of 27 mm. or 4.5 mm. respectively. Both will be examined.
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Figure 2.7 Reduction of covered distance by the goalkeeper. The available time to move is calculated using equation 2.7, herein the distance the ball has to travel (x) is 150 mm for the defender and 300 mm. for the goalkeeper as shown in figure 2.7. The maximum speed the ball can travel is determined in chapter 2.4.1 at 10 m/s. Using these figure gives us 0.015 seconds (defender) up to 0.030 seconds (goalkeeper). So the distance the goalkeeper has to move is 27 mm, combining this with the time calculated, the acceleration needed for the goalkeeper becomes 60 m/s
2 using equation 2.6 again. The
acceleration the defender has to reach is 40 m/s2, using the calculated available time of 0.015
seconds and the distance to cover of 4.5 mm.
v
xt = (2.7)
Since the table is a real object, it is impossible to have instant acceleration. When we consider a third order set point an acceleration of 67 m/s
2 is needed instead the 60 m/s
2 calculated earlier,
when a jerk of 20000 m/s3 is reached.
Herein twice the distance and time is taken to be sure the maximum speed is reached at the collision point. This is shown in figure 2.8. Herein we can find a maximum speed needed of 1.8 m/s.
54.1 mm.
150 mm.
150 mm.
33 mm.
9 mm.
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Figure 2.8 Third order set point of the moving goalkeeper. (Made with a Ref3 block) Because the defenders and the goalkeeper only have to play the ball to the midfield there is no demand to the angular acceleration. So the demands needed for the defending bar are as follows:
• A stroke of 356 mm. is needed
• The linear acceleration needed is 40 m/s2
And the demands for the goalkeeper are the following:
• A stroke of 164 mm. is needed
• The linear acceleration needed is 67 m/s2 (using a jerk of 20000 40 m/s
2)
• A maximum speed of 1.8 m/s is needed.
2.5 Demands summary When we summarize the demands for the foosball table the following has to be taken into account while designing.
• The table should be safe.
• Building cost must be estimated.
• Building space must be as small as possible.
• 150 mm. width building space for the construction.
• Rotating and translating at the same time.
• Working properly until at least 50° Celsius
• 230 V power supply available.
• Less energy in the system is better, due to safety.
• Poisoning oils and gasses should not be used. Attacker
• The attacker stroke needed is 185 mm.
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• Minimum acceleration angle of 60°.
• Forward velocity of the ball of 10 m/s o Gives an angular acceleration of 10178 rad/s
2
• The torque needed is 13.2 Nm
• The linear acceleration needed is 32.4 m/s2 (using a jerk of 20000 m/s
3)
Midfield
• The midfield stroke needed is 112 mm. Defender
• The defender stroke needed is 356 mm.
• The linear acceleration needed is 40 m/s2 (using a jerk of 20000 m/s
3)
Goalkeeper
• The goalkeeper stroke needed is 164 mm.
• The linear acceleration needed is 67 m/s2 (using a jerk of 20000 m/s
3)
• The minimum linear speed needed is 1.8 m/s. When we take the same motors for all bars the highest accelerations should be the benchmark for the motors. So the next demands are the one taking in consideration when selecting the motors for all bars.
• Forward velocity of the ball of 10 m/s o Gives an angular acceleration of 10178 rad/s
2
• The torque needed is 13.2 Nm
• The linear acceleration needed is 67 m/s2 (using a jerk of 20000 m/s
3)
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3 Principles of actuation Several principles exist to move something like a bar. Hydraulic, pneumatic and electromechanical actuators are all available and considered in this comparison. Because the demands have been determined in chapter 2 the best suitable actuation principle per movement can be selected. The different principles are evaluated and the advantages and disadvantages are presented.
3.1 Axial
3.1.1 Performance When we take a look for the performance demands for the axial movement we can conclude that hydraulics actuators would not be a likely option because the highest speeds possible are somewhere around 1 m/s which is a big difference from the demand of 1.8 m/s. [5] Electromechanical and pneumatics could easily match this requirement. When we consider the acceleration this three principles are capable of reaching a high enough acceleration of 67 m/s
2.
[11] So hydraulics has the disadvantage compared to both electronic and pneumatic actuators. [1, 2, 6]
3.1.2 Various demands Considering safety hydraulics are not that safe, oil is needed, which can cause some environmental hazards. Safety issues are also at hand due to the high pressure needed. Furthermore a massive amount of mass (cylinders and oil) is moving around, which gives a hazard for humans also. The energy in the system is also taken into account because this energy can be very harmful for humans playing a game. When this energy is released in the wrong direction, because of the failure of a tube for example, this energy should not be dissipated into the player. Hydraulics will be come to a hold quite soon when pressure drops fast. Pneumatics does not have this advantage and will move faster still, compared to hydraulics, because of the smaller relative pressure drop in the system. Electronics has the advantage in this case because when a wire is broken the system will not function at all or does stay in boundaries of the system. Counteracts are possible in this case. Although then the problem must be observed by the table. When we consider costs, pneumatics has an advantage of hydraulics and electromechanical systems. These last two are more expensive than the first one. Next to that the three options are all capable of working in a 50° Celsius environment. The building space is getting bigger when pneumatics are used, this is due to the complex controller valves, which are needed because the controller should be physical (compared to the electromechanical) and do a very good job because of low damping in the system itself. Hydraulics has the advantage this controller valves can be less complex and so take less space. [3, 4, 5, 7] An electromechanical system needs an amplifier but no pump and tubing so the hydraulics and electromechanical systems will take around the same building space, taking into account the free placing of the pump and some tubing. So flexibility of placing is considered too here. Concluding table 3.1 is made with the (dis)advantages for the principles.
Axial Performance Electromechanical Pneumatic Hydraulic
Speed + + -
Acceleration 0 0 + Various
Safety + 0 -
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Building costs 0 + -
Building space + 0 +
Working temperature
+ + +
Energy in the system
+ - 0
Environment + + -
Table 3.1 Table of advantages and disadvantages of the axial movement. (The entire table of comparisons can be found in appendix C.)
3.2 Radial
3.2.1 Performance Now we take a look at the radial movement. Speeds (147 rad/s at top speed) obtained are feasible for al principles. Although for pneumatics the limit is close. Taking into account the accelerations, an acceleration of 10178 rad/s
2 is needed, we conclude that the hydraulics is the
best option although again all principles can reach the requirements.
3.2.2 Various demands Again the safety is best preserved by the electrical systems and the worst by the hydraulic systems, due to oil in the system and the hazard of leakages. Also the energy in the system is the most with the pneumatics and less considering the electromechanical system. Building costs are the highest with the hydraulics although the same pump could be used when one and the same principle is taken to drive the axial and the radial movement. This is preferred because costs, space and complexity is reduced. Pneumatics are using up most available space because of the controller valves and tubing needed to control the system. [3, 8, 11] Table 3.2 is gives an overview of the disadvantages and advantages for the principles used for radial movement.
Radial Performance Electromechanical Pneumatic Hydraulic
Speed + 0 +
Acceleration 0 0 + Various
Safety + 0 -
Building costs 0 + -
Building space + 0 +
Working temperature
+ + +
Energy in the system
+ - 0
Environment + + -
Table 3.2. Table of advantages and disadvantages of the radial movement. (The entire table of comparisons can be found in appendix C.)
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4 Choosing the motors Selecting the motors was more difficult than expected. Motors are often bigger than the available space or can not deliver the output needed. After searching the internet, checking brochures a selection and choices were made. One of the biggest problems selecting the motors appeared to be the voltage of 230 V. High power motors mostly needs 400 V so the suitable motors are just a small part of the total selection of motors available. This will increase the space needed by the motors. Less volts means less power because there is a maximum currency possible, due to resistance of the wiring inside the motors. The axial movement and the radial movement are discussed separately in this chapter.
4.1 Direct drive versus indirect drive Next to the motor direct drive versus indirect drive must be examined. Direct drive means that the motor is directly attached to the shaft so without any cogwheels, belts or anything else. Indirect drive is the opposite of that. Direct drive initially has the preference above indirect drive because it delivers a smoother system and a lower mass moment of inertia. The main disadvantage is the more complex repairs when a direct drive system must be fixed. The advantages of indirect drive could not be neglected. The range of torque is one of the most important advantages, because the motors should be as small as possible (to get a smooth system again). So when the motor has its maximum output point at higher (or lower) speeds, than the maximum speed needed at the bar, it is possible to change this point to the ideal speed. The comparison and the differences may be clearer when taking a look at table 4.1. The choice for indirect drive is made when the force the motor can deliver is insufficient for his task. (The demands are determined in chapter 2)
Aspect Direct Drive Indirect Drive (decrease in speed - increase in speed)
Torque Low High – Low
Force Medium High – Low
Friction Low Low – High
Build(complex, easy) Easy Complex
Speed Medium Low – High
Stiffness High High – Low
Maintenance Easy/Medium Medium Table 4.1 Properties of indirect and direct drive.
4.2 Axial Movement For the axial movement an acceleration of 67 m/s
2 is required. Considering a weight of 3 kg for
the shaft, because the striving is to accelerate only the shaft, the force needed to accelerate at full power will be at least 201 N. This is based on the approximated weight of the shaft used in Kiro. (See also appendix B) For this several options are available. After some selection, only a mechanical slide and a magnetic train system, like the maglev, are left. The selection is made considering available force, maximum speed, maximum acceleration and the interface (voltage). The in chapter 3 determined demands are used as selection criteria. So acceleration (also available force), speed, safety (also environment), building space and building cost are used in this order.
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4.2.1 Slide Firstly the Rexroth Linear Module MKR 20-80 (see also figure 4.1 and appendix I) was selected. Between limits, this unit has the option to attach quite a lot of motors to its ingoing shaft. The maximum speed available is 2 m/s. [14] This is just good enough. The module works with an internal belt which is driven by the shaft and moves the slide on top of it. The biggest plus of this system is the easy mounting options to the table itself and the option of an inbuilt position sensor. All the parts used are easy to replace due to the simple design. The downside is the space required, it would be 494 mm longer then the stroke needed. Every stroke can be determined separately so the distance which is not needed is not build in, so it’s cheaper than using for similar modules.
Figure 4.1 MKR 20-80 Belt drive Figure 4.2 Danaher Iron Core 11 motor
4.2.2 Maglev Next to this option the Danaher IC11-100A5 (Appendix H) appears, this is a motor based on the principle of electromagnetic forces. It uses a track of magnets, and the motor consist of inductors. So at the base it is the similar principle as a stepped rotation electromotor, only folded out. This motor has a moving part of 6.5 kg which is of course a disadvantage. On the other hand the total building space is 701.9 mm (consisting of two MC100-256 and one MC100-064 magnet way) in total, which is only 346 mm more than the stroke of 356 mm needed so the construction stays relatively compact. An advantage of this system appears when the four modules are made because the stroke can be changed easily per motor without making big design changes. This combining with the fact the magnets ways are modular a higher number of one kind of part can be ordered so possibly a cheaper price can be arranged. The Danaher IC11-100A5 is capable of moving the 9.5 kg of the motor and shaft with the needed 67 m/s
2. The force needed then is 637
N. This can be reach easily because the peak force is 1250 N. The peak force can be taken for this for the reason that the high speed movements are only needed when defending. Attacking with these accelerations would be nice, but with a continuous force, of 599 N, delivered by the motor the acceleration will be 63 m/s
2. [20] This should be sufficient for the normal movement of
the midfield and defender shafts when playing a game.
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4.2.3 Conclusion In table 4.3 the advantages and disadvantages of the two options are weighted to each other according to the requirements.
Demand MKR 20-80 Danaher IC11-100
Acceleration (force) 0 +
Speed + +
Safety(environment and human) + +
Building space 0 0
Building cost 0 0
Table 4.3 comparison between MKR 20-80 and Danaher IC11-100 Now it can be seen that the Danaher IC11-100 is a slightly better choice then the Rexroth MKR 20-80 slide. This motor is used for the axial movement.
4.3 Radial movement According to chapter 2 a torque of 13.2 Nm is needed. This is too much when direct drive should be used. There are no motors available which can handle the speeds and the torque. This is why indirect drive was chosen. Choosing the Danaher DBL4H00750 (see appendix G) the maximum speed is 3000 rpm with a torque of 6.4 Nm. [20] At lower speeds the torque increases to 7.5 Nm at standstill. This leads to a ratio between 2.07 (torque is the limiting factor at zero speed) and 2.14. (Speed is the limiting factor, 1400 rpm) So the ratio is something around 2.1 and will be 2 when taking the best suitable cogwheels considering the design. Respectively 28 and 14 cogs are used. Bigger cogwheels do not fit the 150 mm. width available, which can be found in chapter 2, considering the cogwheels of Köbo. Next to that the use of bigger cogwheels give a higher moment of inertia and that is exactly the opposite of what we like. To be exact the 4A400140 and the 4a400280 are used.[19] The width of the biggest cogwheel is 120 mm. the module used is 4, because the small amount of cogs (14) combined with the small cog width gives a smaller maximum torque throughput. In appendix F the selection tables (SN) can be found. Using cogwheels the mass moment of inertia becomes high but this seams to be the best option.
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5 Design Several choices have already been made to come to a final design. But not everything is illuminated. Most of the missing parts are described in this chapter. For example the linear bearing of the motor for the axial movement, displacement sensor which is not integrated in the linear motor and the attachment of the shaft to the bearing are discussed.
5.1 Spline Shaft To move the shaft separately in linear and axial direction a spline shaft is needed. This is just a linear bearing on a shaft which can pass on torque. This is a critical part of the construction and is attached in line with the shaft. The part is produced by KERK and is capable of handling the torque. This is true using a hollow shaft with a 19.05 mm diameter. [23] This part is only available in inches, this is a small problem. Every other part in the construction is produced in SI so this part has to be attached using a bearing measured in inches too. Drag from the shaft is only 1.5 N so negligible.
Figure 5.1 Spline shaft: KERK SS12
5.2 Bearing attachment Cogwheels and bearings can be attached in two ways. One of them is to push the bearing over the shaft with huge force. Heating the cogwheel or bearing is the other and preferred way. The cogwheel clamps itself at the shaft and would not require any locknuts. Considering the bearing for both cases one side of the bearing is pushed against a small wall and the other side is locked with a locknut. This helps to secure the bearing. [16, 17] Because the bearing should be attached not only to the shaft but also to the linear motor an attachment part should be made. This is a tube attached to a metal plate which is attached to the motor with some bolts. Also in this case the housing must be heated so it can slot over the bearing. Again a locknut is necessary. The fitting must be K5, which means a fit of +0.002 mm. to +0.013 mm. [22], so the bearings can handle the forces acting on it in all directions and still have a long life. A housing unit must be produced because the standard housing units are quite heavy. Figure 5.2 show the housing unit needed and the attachment with the bearing and the bearing with the shaft. In appendix E some extra information and figures can be found. Appendix K contains some engineering drawings.
20
Figure 5.2 The bearing attachments, outside(left) and inside(right).
5.3 Linear motor bearings The electromagnetic motor has no guidance of it self and consist of two different blocks who must be lined out because otherwise the motor does not work properly. This is done using a linear bearing as can be seen in figure 5.3. When the motor is not attached to the housing the linear motor would turn around the shaft when the ball is shot, due to friction in the bearing, and damage the magnet ways in its movement. The forces to hold the slide horizontal are not big so an easy construction could do the job. By mounting this guidance several, degrees of freedom are fixed. The turning around the direction in the length of the table as well as the movement is that direction is fixed. The movement in the upwards direction is set too. The only degree of freedom is the direction in line with the shaft itself. The guidance selected is the INA KUME 12C, an easy build linear bearing. [21]
Figure 5.3 The construction with the INA KUME12C included.
5.4 Displacement sensor The absence of a displacement sensor in the linear motor is solved by the fitting of an external one. The SE1 displacement sensor is selected. (Figure 5.4) This one uses a cable and sends pulses to its output. So the displacement can be determined. The maximum acceleration or deceleration possible is 30 g so the demand of 67 m/s
2 is obtained easily. [18] The sensor has a
deviation of 1.3 mm. at max. This is not a problem because the foosball player has a feet width of 20 mm. and with this deviation the ball is still hit.
INA KUME
Mrotation
Mrotation
21
The angle of the bar can be determined with an integral sensor in the radial motor itself. So another external sensor is not necessary. See also appendix J.
Figure 5.4 The SE1 displacement sensor, in the construction and photo(right).
5.5 Cogwheel position The cogwheel attached to the shaft must be kept in place. Otherwise there would be more wearing of the cogwheels and the cogwheels would definitely lose contact with each other when moving in linear direction. This is done by attaching the bush, of the spline shaft, to the construction. This is shown in figure 5.5. This bearing should cope with axial and some radial forces. The radial forces are generated by bending of the shaft. Next to that the spline shaft in inches from KERK is fitted into the construction easily this way.
Figure 5.5 Attachment of the bush Figure 5.6 Drawing of the safety tube
5.6 Safety tubes To keep the risks for human beings small a tube must be produced to slide over the out coming shaft at the other side of the table. Otherwise the player could be hit by the moving shaft with a mass of 9.5 kg. The construction is quite simple; a shaft with a hollow end is attached to the table around the moving shaft. This hole is necessary because otherwise the pressure will change in the tube when moving fast and influence the results. At the opening a grid is made so fingers can not penetrate the tube. This can be seen in figure 5.6.
22
6 Results The result can be seen in figure 6.1 but this picture does not say anything about it performance. To give a good idea of the performance the accelerations are calculated now. Therefore the mass moment of inertia is needed. When this is combined with the available torque the maximum angular acceleration is determined. Furthermore the moving mass will be calculated and combined with the force delivered by the motor. The total moving mass increased to 11.33 kg. This is higher then the in chapter 4 approximated 9.5 kg. Also the mass moment of inertia is a lot higher then estimated in chapter 2. It became 2.5E-3 kgm
2 instead 1.2E-3 kgm
2.
80% of this mass moment of inertia is caused by the two cogwheels used. The total costs for one actuated bar would be around € 4390. The calculations can be found in appendix D, just like the calculations of the moving mass and mass moment of inertia. Here it can be seen then motors alone will cost around € 2000. The parts that have to be made will cost approximately € 1600 and the other parts like the cogwheels, sensor, and bearings will be charges at around € 800. The maximum available axial peak force is 1250 N and continuous force is 599 N which can be found in chapter 4 and appendix H. The maximum acceleration of the axial movement then becomes 110 m/s
2 at peak performance and 52 m/s
2 when using the continuous force. For the
radial movement the mass moment of inertia is 2.5E-3 kgm2, and the maximum torque becomes
7.5 Nm at standstill and 6.4 Nm at 3000 rpm. This combined with the gear ratio of 1:2 the torque becomes 15 Nm and 12.8 Nm. When we now calculate the acceleration, with the worst case of 12.8 Nm, it becomes 5120 rad/s
2. Now the shooting speed drops till 7.46 m/s or 103.6 rad/s.
because the motor can deliver more torque the faster is goes, the shooting speed will be slightly more. The extra space needed for this construction is 594 mm. in the depth of the table, 150 mm. between the bars and 235 mm. considering height. The table dimensions must be added to this to have the entire dimensions needed to place a table. Some extra things are done for safety reasons, a bar is added to encase the sliding bar. Next to that electromechanical actuators are used which gives no extra hazards like high pressurized oils and smaller effects when a cable is malfunctioning.
Figure 6.1 The foosball table
23
7 Conclusions In the end some of the demands have been realized, others are not. This can be seen quite easily in the following table 7.1. Although the specified demands are not fully fulfilled, the machine comes close. A shooting speed of 7.5 m/s in a 60 degree acceleration angle is still quite fast. The shooting speed goes up to 10 m/s when the shot can be taken in a bigger angle. The speed of the bar moving from one place to another is fast enough, 2 m/s with a 110 m/s
2 acceleration, and
should be capable of defending fast shots. The construction has a high moving mass of 11.33 kg. this is 2 kg. more then estimated but does not harm the performance to much. The mass moment of inertia is more then two times as much as estimated which give a performance problem as can be seen in table 7.1. Performance Demands Reached
Axial
Acceleration 67 m/s2 110 m/s
2
Speed 1.8 m/s 2 m/s Radial
Acceleration 10178 rad/s2 5120 rad/s
2
Speed 147 rad/s 103.6 rad/s Various
Building costs - € 4390 per bar
Building space As small as possible 594 x 150 x 235 mm
Working temperature 50° Celsius+ 50° Celsius+
Moving mass 9.5 kg (estimated) 11.33 kg.
Mass moment of inertia 1.2E-3
kgm2 (estimated) 2.5E
-3 kgm
2
Voltage 230 V 230 V
Attacker stroke > 185 mm. 360 mm.
Midfield stroke > 112 mm. 360 mm.
Defender stroke > 356 mm. 360 mm.
Goalkeeper stroke > 164 mm. 360 mm.
Table 7.1 Comparison between the required and the reached demands. When we take a look at some other demands like the costs we can conclude that the estimate for the costs for one actuated bar would be around € 4390. Also safety is taken into account, mostly by adding a safety bar at the player side of the table. Next to that the environment is not harmed by oils. By using the spline shaft the rotation and translation can be made at the same time, which results in fast combination foosball.
24
8 Recommendations Although the demands are almost achieved, the radial movement has his problems still. Some solutions could be examined further. One of these is making of some holes in the cogwheels so the mass moment of inertia is lowered significantly. This should be done in collaboration with the manufacturer of these cogwheels, because it may influence the strength of them. Next to this option other connections could be investigated more, belt drives and chains are not being investigated that much but may be capable of doing the job quite well, without being very noisy or inaccurate. Another option to improve the performance is to change the ratio of the cogwheels. This is an option because the top speed of the motor is not reached in the design anymore, 2100 rpm instead of 3000 rpm. Another option is the mass of the entire construction. It would be better when the machine weighed less because there will be four of them hanging at the foosball table. This will make the table less stable and a lot heavier to move. It would be better when the spline shaft could be replaced by another one with more reaction of the manufacturer. The distributor has contacted them but no real reaction was coming from them. The shaft could handle the job although it was made of aluminium, nevertheless when problems occur it is recommended to make the shaft from steel. Another recommended design change contains trying to use the magnets of the linear motor as sensor, so the extra position sensor is not needed anymore. This gives more space and fewer parts to be made and bought.
25
9 References
1. Isermann, R. (2003) Fundamentals of mechatronic systems. Berlin, Springer. ISBN: 1-85233-693-5 2. Silva, C. W. de. (2005) Mechatronics an integrated approach. London, CRC Press. ISBN: 0-8493-
1274-4
3. Aizerman, M. A. (1968) Pneumatic and hydraulic control systems. London, Pergamon.
4. Walters, R.B. (1991) Hydraulic and electro-hydraulic control systems. London, Elsevier Applied Science. ISBN: 1-85166-556-0
5. Guillon, M. (1968) Hydraulische Regelkreise und Servosteuerungen. Hanser.
6. Backe. W. and Roth, J. (1986) Servohydraulik. Aachen, Rheinisch-Westfaelische Technische
Hochschule Aachen.
7. Goetz, W., Haack, S and Mertlik, R.(1999) Electrohydraulic proportional and control systems. Ditzingen. ISBN: 3-933698-05-7
8. Krivits, I. L. and Krejnin, G. V. (2006), Pneumatic actuating systems for automatic equipment :
structure and design. London, CRC, Taylor & Francis. ISBN: 0-8493-2964-7
9. Thilo Weigel and Bernhard Nebel, Universität Freiburg, Informatik (2003), Kiro – an autonomous
table socces table. Pages 384-392. Berlin/ Heidelberg, Springer. ISBN: 978-3-540-40666-2. Link: ftp://ftp.informatik.uni-freiburg.de/documents/papers/ki/weigel-etal-robocup-02-kiro.pdf
10. Foosbot and other alternative autonomous foosball tables.
Link: http://www.answers.com/topic/foosbot
11. R.Richardson, A.R.Plummer and M.Brown. Modelling and simulation of pneumatic cylinders for a physiotherapy robot. Leeds (UK), School of Mechanical Engineering, University of Leeds (UK). Link: http://intranet.cs.man.ac.uk/robotics/research/medical/modelling.pdf
12. Definitions of snakeshot and pinshot.
http://forum.tischfussball-online.com/ftopic162.html
13. Rules of table foosball. Lehmacher Soccer Netherlands (2004), Wedstrijd en Toernooi Reglement 2004-2005.
14. Bosch Rexroth (2003) Robotic Erector Systems for Linear Modules. Bosch Rexroth. RE 82
402/2003-10 15. A.J.P.van Engelen and C.J.Zandsteen (2007), Vision Controlled Foosball. Eindhoven, TUE.
And the following supplier and parts websites: 16. SKF mounting instruction website:
http://webtools.skf.com/mountingnew
17. SKF mounting information: http://www.skf.com/skf/productcatalogue/jsp/viewers/tableViewer.jsp?tableName=1_0_t26&mai ncatalogue=1&lang=en\
18. Compact String Encoder, SE1, Celesco Transducer Products, Inc. July 2006.
http://www.celesco.com
19. Cogwheel manufacturer http://www.kobo.nl
26
20. Datasheets of Danaher motors http://www.danahermotion.de/http://danahetmotion.com
21. Schaeffler group/INA Miniature ball monorail guidance systems, KUME ..-C.
http://ww.ina.de/media-service 22. Schaeffler/FAG Angular contact ball bearings, 32..-B-2RSR. June 2007.
http://www.fag.de/media-service
23. Kerk Motion spline shaft manufacturer. http://www.kerkmotion.com
24. Bearingshops
http://www.detechnoshop.nl http://eshop.adoz.cz/detail/17571
25. Spline shafts supplier
http://www.elmeq.nl
26. Encoder shop http://www.ece.clemson.edu/crb/students/vilas/projects/octor/docs/octor_bom_v6.xls
27
Appendix A: Measurements Description Measurement
Length foosball player 115 mm.
Length legs foosball player 72 mm.
Height between foot and field 14 mm.
Width foosball player foot 20 mm.
Width goal 200 mm.
Width table inside 680 mm.
Width table outside 740 mm.
Length table inside 1120 mm.
Length table outside 1430 mm.
Distance between goal and first attacker.
333 mm.
Distance between goal and goalkeeper.
33 mm.
Weight foosball 19,7 gr.
Diameter foosball 36 mm.
Attacker stroke 228 mm.
Midfield stroke 112 mm.
Defender stroke 356 mm.
Goalkeeper stroke 164 mm.
Table A.1 Measurements
28
Appendix B: Estimation of Mass moment of inertia The mass moment of inertia is estimated from the existing Kiro table. This table exist of the following parts Description Amount J (kgm
2) Total J (kgm
2) Total mass (kg)
Bar (Main with puppets) 1 5.96 E-4
5.96 E-4
2.8 kg
Bar (connection) 1 6.16 E-5
6.16 E-5
1.2 kg
Cogwheel big (r =34 mm) 3 1.66 E-4
4.98 E-4
0.9 kg
Cogwheel small (r = 10 mm) 1 1.24 E-6
1.24 E-6
0.02 kg
Motor(Faulhauber 4490) 1 1.3 E-5
1.3 E-5
Total 1.17 E-3
Table B.1 Estimation for the mass moment of inertia which is based on the Kiro foosball table. The mass moment of inertia J is calculated using the following equation:
4
2
****5.0
**5.0
rlJ
rmJ
πρ=
=
The ρ used is 7900 kg/m2. Furthermore the l is the depth of the part and the r the radius.
All dimensions are estimations from picture 1.2 except when it is mentioned behind the figure. This will lead to the following figures: The main bar L = 1300 mm. Rout = 16 mm. Rin = 13 mm. The connection bar L = 500 mm. R= 10 mm. Cogwheel big L = 10 mm. R = 34 mm. Cogwheel small L = 10 mm. R = 10 mm. Datasheet Faulhauber 4490 http://www.faulhaber-group.com/uploadpk/e_4490B_4490BS_MIN.pdf
29
Ap
pe
nd
ix C
: A
dva
nta
ges a
nd
dis
ad
va
nta
ges o
f actu
ato
r p
rin
cip
les
When there
are
severa
l options lik
e lo
w,
mediu
m a
nd h
igh, th
ese v
alu
es a
re m
easure
d w
ith th
e n
eed
ed f
orc
es, speeds a
nd o
ther
dem
ands.
Axia
l
A
xia
l
E
lectr
om
echanic
al
Pne
um
atic
Hydra
ulic
Accura
cy
Up to 0
.1 m
icro
mete
r lin
ear
Aro
un
d 5
0 m
icro
mete
rs
up to
1 -
5 m
icro
mete
rs
Accura
cy c
onsid
eri
ng d
em
ands
* 0.0
2 m
m
2 m
m
?
Contr
olli
ng
positio
n
Very
go
od
Med
ium
G
ood
Costs
M
ed
ium
Lo
w
Hig
h
Build
(com
ple
x, easy)
M
ed
ium
Build
M
ed
ium
Build
E
asy B
uild
Relia
bili
ty
Med
ium
/Hig
h
Hig
h
Hig
h
Repe
ata
bili
ty
Hig
h
Lo
w (
+/-
0.1
5 m
m)
Med
ium
Eff
icie
ncy
Hig
h
Lo
w,
dro
ps w
ith h
igher
pre
ssure
s
Med
ium
Volu
me n
eede
d
Lo
w
Med
ium
M
ed
ium
Ste
pped
/Ste
ple
ss m
otion
Ste
pped
, bu
t very
sm
all
ste
ps p
ossib
le
Ste
ple
ss
Ste
pped
Torq
ue
- -
-
Spe
ed
Hig
h
Hig
h u
p t
o 5
m/s
Lo
w,
up t
o 1
m/s
Forc
e
Lo
w t
o m
ediu
m
Lo
w t
o h
igh
Hig
h
En
viro
nm
enta
l C
lea
n
Cle
an
Toxic
whe
n leakage
Harm
ful fo
r people
?
No
Med
ium
, no o
il, b
ut
pre
ssure
s (
6-1
4bar)
Y
es
wh
en
leakage,
toxic
, flam
mable
o
il,
hig
h p
ressure
s
Influence t
em
pera
ture
cha
nges
Lo
w
Med
ium
H
igh
(vis
cosity c
hang
es w
ith T
)
Conta
min
ation
pro
ble
ms
Lo
w
Med
ium
H
igh
Coolin
g n
eed
ed?
Possib
le
No
No
Dam
pin
g
Good
Lo
w
Hig
h
Stiff
ness
Hig
h
Lo
w
Very
Hig
h
* S
pee
ds(
2 m
/s),
acc
eler
atio
n(1
00
m/s
2)
and
fo
rces
(10
00
N)
nee
ded
are
tak
en i
nto
acc
ount.
30
Overs
hoot
Yes, b
ut g
ood c
ontr
olla
ble
Lo
w
Very
lo
w
Lin
ear/
non lin
ear
Lin
ear
Non-l
ine
ar
Non-l
ine
ar
Friction
Lo
w
Hig
h
Hig
h
Lubricatio
n
No
Need
ed
No
Nois
e le
ve
l M
ed
ium
M
ed
ium
H
igh
Extr
a e
quip
ment necessary
N
o
Overlo
ad p
reventio
n
Pum
p
Pum
p
Oth
er
pro
ble
ms
N
ois
e p
roduction
Hig
h m
ass m
ovin
g(o
il)
C
avitatio
n
Lag, slo
w t
o c
ontr
ol
Oth
er
Advanta
ges
Lo
w m
ass m
ovin
g
Lo
w m
ass m
ovin
g
Hig
h n
atu
ral fr
equency
Possib
ility
fo
r cushio
nin
g,
wh
ich
decre
ases n
ois
e
Table
C.1
Axia
l m
ovem
ent actu
ation p
rincip
les a
dva
nta
ges a
nd d
isad
va
nta
ges
31
Rad
ial
R
adia
l
E
lectr
om
echanic
al
Pne
um
atic
Hydra
ulic
Accura
cy
Hig
h
Med
ium
H
igh
Contr
olli
ng
positio
n
Very
go
od
Med
ium
G
ood
Costs
M
ed
ium
Lo
w
Hig
h
Build
(com
ple
x, easy)
M
ed
ium
Build
M
ed
ium
Build
E
asy B
uild
Relia
bili
ty
Med
ium
/Hig
h
Hig
h
Hig
h
Repe
ata
bili
ty
Hig
h
Lo
w (
+/-
5 d
egre
e)
Med
ium
Eff
icie
ncy
Hig
h
Lo
w,
dro
ps w
ith h
igher
pre
ssure
s
Med
ium
Volu
me n
eede
d
Lo
w
Med
ium
M
ed
ium
Ste
pped
/Ste
ple
ss m
otion
Ste
pped
, bu
t very
sm
all
ste
ps p
ossib
le
Ste
ple
ss
Ste
ple
ss
Torq
ue
Lo
w/M
ed
ium
Lo
w/M
ed
ium
M
ed
ium
/Hig
h
Spe
ed
Hig
h (
more
than 5
00 r
ad
/s)
Med
ium
up to 3
5 r
ad
/s(H
igher
possib
le)
Hig
h (
more
than 5
00 r
ad
/s)
Forc
e
- -
-
En
viro
nm
enta
l C
lea
n
Cle
an
Toxic
whe
n leakage
Harm
ful fo
r people
?
No
Med
ium
, no o
il, b
ut
pre
ssure
s (
6-1
4bar)
Y
es
wh
en
le
akage,
toxic
, flam
mable
oil,
hig
h p
ressure
s
Influence t
em
pera
ture
cha
nges
Lo
w
Med
ium
H
igh
(vis
cosity c
hang
es w
ith T
)
Conta
min
ation
pro
ble
ms
Lo
w
Med
ium
H
igh
Coolin
g n
eed
ed?
Possib
le
No
No
Dam
pin
g
Good
Lo
w
Hig
h
Stiff
ness
Hig
h
Hig
h w
hen u
sin
g a
bra
ke,
mediu
m w
hen
usin
g p
ressure
V
ery
Hig
h
Overs
hoot
Yes, b
ut g
ood c
ontr
olla
ble
Lo
w
Very
lo
w
Lin
ear/
non lin
ear
Lin
ear
Non-l
ine
ar
Non-l
ine
ar
Friction
Lo
w
Hig
h
Hig
h
Lubricatio
n
No
Need
ed
No
Nois
e le
ve
l M
ed
ium
M
ed
ium
/Hig
h
Hig
h
Extr
a e
quip
ment necessary
N
o
Overlo
ad p
reventio
n
Pum
p
32
Pum
p
Oth
er
pro
ble
ms
S
pe
ed is influ
enced
by th
e load
Restr
icte
d a
ng
le w
he
n u
sin
g a
van
e t
ype
H
igh
mass m
ovin
g(o
il)
C
avitatio
n
Lag, slo
w t
o c
ontr
ol
Oth
er
Advanta
ges
Lo
w m
ass m
ovin
g
Lo
w m
ass m
ovin
g
Hig
h n
atu
ral fr
equency
Table
C.2
Axia
l m
ovem
ent actu
ation p
rincip
les a
dva
nta
ges a
nd d
isad
va
nta
ges
33
Direct drive vs. indirect drive
Direct Drive Indirect Drive (decrease in speed - increase in speed)
Torque Low High - Low
Force Medium High - Low
Friction Low Low - High
Build(complex, easy) Easy Complex
Speed Medium Low - High
Stiffness High High - Low
Maintenance Easy/Medium Medium
Table C.3 Direct drive and indirect drive advantages and disadvantages
34
Appendix D: Resulting mass, mass moment of inertia and costs The following table shows the prices for each part needed to build the table. Prices are rounded because of possible fluctuations in price.
Price* Mass Moving Mass J
**
Danaher IC11-100A5 Linear motor € 620,00 6.5 kg 6.5 kg N/A
Danaher MC100 Magnetic track(256 mm 128 mm ,64 mm)
€ 420,00 5.7 kg N/A N/A
Danaher DBL4H00750 Radial motor € 930,00 7.7 kg N/A 4.2E-4 kgm2
Köbo 4a400140 Small cogwheel € 50,00 0.3 kg N/A 1.5E-4 kgm2
Köbo 4a400280 Big cogwheel € 120,00 1.0 kg N/A 1.8E-3 kgm2
INA16006 Bearing holding cogwheel [24]
€ 10,00 0.095 kg N/A N/A
INA3204-B-2RSR-TVH Bearing linear motor [24] € 40,00 0.16 kg 0.16 kg N/A
INA KUME12C Linear bearing € 100,00 0.63 kg 0.03 kg N/A
SE1 String encoder [26] € 150,00 0.14 kg 0.17 kg***
N/A
Kerk SS12 Spline Shaft [23, 25] € 300,00****
1.5 kg 1.5 kg 6.1E-5 kgm2
Kerk/Elmeq Shaft [23, 25] € 200,00****
2.5 kg 2.5 kg 1.0E-4 kgm2
Locknuts € 30,00 0.1 kg 0.1 kg 5.0E-6 kgm2
Bolts/nults € 10,00 0.1 kg N/A N/A
Cable holder € 10,00 0.2 kg N/A N/A
Bearing house 0.4 kg 0.4 kg N/A
Front plate 1.2 kg N/A N/A
Box plate 8.0 kg N/A N/A
Holding bracket entire unit 0.3 kg N/A N/A
Holding bracket motor back
€ 1400,00*****
0.1 kg N/A N/A
Total € 4390,00 36.3 kg 11.33 kg 2.5E-3 kgm2
Table D.1 Determined costs, mass, moving mass and mass moment of inertia.
* Prices exclusive VAT. The moving mass of the string encoder is the tension in the cable.
** Using J=0.5*m*r
2 (for a circle) and a density of 7900 kg/m
3 when no J is given.
*** The moving mass of the string encoder is the tension in the cable.
**** This is an estimation after talking to Elmeq Netherlands.
***** At the GTD(Gemeenschappelijke Technische Dienst) of the TU/e it was estimated to be 40 hours of
work at a cost of €35,00 an hour.
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Appendix E: Bearing house design The inside of the bearing is hold like the specifications of the bearing, the maximum holding surface is used. This is a circle with a diameter of 25.6 mm as inner ring. The same applies for the outer ring; the maximum is there an inner ring of 41.4 mm The locks are quite simple, the inside one consist of a wall at the shaft whereto the bearing is pressed and threads in the shaft where the locknut can be screwed around. This can be seen in figure D.1 The outer locknut(picture D.2) is quite small and can be turned using pin which must be inserted in the locknut. This gives a lighter weight of the entire unit. The nut can be seen in figure D.3. The inner nut is conventional because it is quite close to the shaft so there is possibly not the space to turn the nut with some special tools.
Figure D.1 The bearing attachments inside. Figure D.2 The bearing attachments outside.
Figure D.3 Bearing house.
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Appendix F: Cogwheel selection
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Appendix G: Danaher Motion DBL4H00750 Datasheet
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Appendix H: Danaher Motion IC11-100 Datasheet
39
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Appendix I: Bosch Rexroth MKR 20-80 Datasheet
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Because only 230 V was available the last table should be the theoretical performance.
42
Appendix J: Datasheet SE1
43
44
Appendix K: Engineering Drawings (Check CD for sharper drawings)
Frontplate
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Holding bracket entire unit
46
Holding bracket motor back
47
Bearing housing
48
Box plate
49
Holding plate box
