Exercise bike

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(Mechanical Analysis)
(Mechanical Analysis)
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== Mechanical Analysis ==
== Mechanical Analysis ==
A mathematical analysis was done to calculate the inertia of the flywheel and study the chosen weight, weight distribution and their effects on driver perception of on-road cycling.  
A mathematical analysis was done to calculate the inertia of the flywheel and study the chosen weight, weight distribution and their effects on driver perception of on-road cycling.  
 +
 +
The following assumptions were made in the calculations:
 +
1. The flywheel has uniform density
 +
2. There is no major friction loss in the chain and bearing
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3. The width if the flywheel is negligible compared to its diameter.
 +
 +
We analyze the weight distribution of the wheel by dividing it into two sections: a solid disc and a hollow ring. We define the following variables:
 +
 +
r<sub>ring,o</sub> = Outer radius of ring (m)
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r<sub>ring,i</sub> = Inner radius of ring (m)
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r<sub>disc</sub> = Radius of disc (m)
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h<sub>ring</sub> = Width of ring (m)
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h<sub>disc</sub> = Width of disc (m)
 +
m<sub>ring</sub> = Mass of ring (kg)
 +
m<sub>disc</sub> = Mass of disc (kg)
 +
m<sub>total</sub> = Total mass of wheel (kg)
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I<sub>ring</sub> = Moment of Inertia of ring about the shaft (kg.m<sup>2</sup>)
 +
I<sub>disc</sub> = Moment of Inertia of disc about the shaft (kg.m<sup>2</sup>)
 +
I<sub>total</sub> = Moment of Inertia of wheel about the shaft (kg.m<sup>2</sup>)
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w<sub>input</sub> = Revolutions per minute (rpm) of rider (rpm)
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w<sub>wheel</sub> = Revolutions per minute (rpm) of flywheel (rpm)
Weight of flywheel  m = 19.5kg
Weight of flywheel  m = 19.5kg

Revision as of 19:50, 22 September 2008

Contents

Executive Summary

In order to understand the product design behind this exercise bike, a thorough analysis was required. Our analysis includes which stakeholders are involved, how the product functions and is used, and a comprehensive product dissection. This is followed by a study of how the bike was designed for manufacturing and assembly, while considering the design's overall environmental impact. Finally, we analyze the bike's possible areas of failure and include a detailed mechanical analysis of inertial effects of the flywheel.

During the analysis of the product, we discovered that problems with the product were not severe enough to consider for improvement. Instead, through the mechanical analysis of the system, the energy produced was large enough that it could be used for other purposes, such as regenerating the power to offset the greenhouse gases from power generation in production.

Stakeholders

There are 5 main stakeholders in the exercise bike: Users, Fitness centers, Maintenance crew, Manufacturers and Sporting Goods stores. The requirements and needs that each has is listed below:

  • Users
Easy to use
Storage
Safety
Cheap
  • Fitness centers
Reliability
Life of product
Inexpensive
  • Maintenance crew
Accessible
Safety
  • Manufacturers
Compact
Simple design and components
  • Sporting Goods stores
Storage
Aesthetics
Price

Product Function

Once the user is mounted on the bike and his/her feet are positioned firmly in the pedal cages, manual energy is used to provide an angular momentum to the rear disc. This rear disc has teeth at the circumference and is connected to a shaft at the front of the bike by a chain. As the rear wheel continues to rotate due to the momentum provided by the user, the momentum is transferred to the front shaft via the chain. The front shaft also has a heavy flywheel mounted onto it over a bearing. As the shaft rotates it causes the flywheel to rotate. The weight of the flywheel creates resistance to this rotation and this is transmitted back down the system to the user, giving the sensation of on-road cycling.

There is also a provision to forcefully reduce the rotation of the front wheel. This is done by two soft pads that are connected to the either face of the flywheel. In their starting position, the pads are not in contact with the flywheel and hence do not impede motion. They are connected to each other by a spring. When it is required to reduce the rotation of the flywheel, this spring is compressed and it causes the distance between the pads to reduce and creates contact between them and the flywheel. The resistance due to this contact slows down the flywheel and eventually brings is to a halt.

Product Use

The product is a stable platform used for cycling practice as well as a smooth, intense workout. The user mounts the bike, sitting on the seat. Feet rest on the pedals and hands on the rubber handles to the front of the bike. While holding the handles, feet on the pedals and sitting on the seat, the rider is provided a stable riding position. To ride, the user pedals forward (backward is not recommended by Schwinn) exerting significant effort to build momentum in the heavy flywheel. Once user reaches a comfortable speed their effort levels to a steady pace. There are a few ways to stop, all not very intuitive to basic bike riders. There is a knob on the frame that can be turned to apply a clamp-brake to the flywheel that will slow the wheel down. The user can also completely remove their legs from the pedal assembly, but this is not recommended since it is dangerous and the momentum in the wheel is too high and will spin for a very long time. The user could also cool down by gradually reducing their pedal speed till it becomes slow enough to dismount. This is recommended anyway in any strenuous workout, stopping abruptly is not good for the body.

Bill of Materials

Part/Sub-assembly Part # Part Name QTY Weight (g) Function Manufacturing Process Material Image
Seat 1 Seat 1 428 Allows user to sit on bike press fit/lay over cloth and stitch foam, plastic, stainless steel
- 2 bolt 1 25 Assembles seat to seat support forging, thread rolling stainless steel
- 3 sm. washers 2 15 Assembles seat to seat support stamping stainless steel
- 4 lg. washers 2 15 Assembles seat to seat support forging, thread rolling stainless steel
- 5 nuts 2 5 Assembles seat to seat support casting thread tapping stainless steel
- 6 u-clip 1 50 Assembles seat to seat support stamping, bending stainless steel
- 7 solid support 1 1725 Connects seat assembly to seat attachment square extruded tube cut/welded to machine bent circular tube stainless steel
Seat Attachment 8 seat attachment 1 1795 Connects seat attachment to bike frame cut square extruded tubing/weld together stainless steel
Handle Bars 9 handle bars 1 1795 Connects seat attachment to bike frame cut square extruded tubing/weld together stainless steel
Outer Casing 10 outer casing for chain 1 1377 Protects bike chain while pedaling stamping stainless steel
- 11 screw 3 2 Assembles outer casing to bike frame heading, thread rolling stainless steel
- 12 washers 3 1 Assembles outer casing to bike frame stamping stainless steel
Brakes 13 brake pads 2 23 Directly contacts wheel to brake injection molding, press fitting, thread insertion brass, wool, plastic
- 14 springs 2 1 Absorbs force on the brake pads coiling stainless steel
- 15 rod, spring and clip 2 42 Connects brake control to brake casting stainless steel
- 16 toothed half-pipe w/hole 1 4 Assembles brake support to bike frame casting stainless steel
- 17 sm. washers 4 <1 Assembles brake pads to brake support stamping stainless steel
- 18 lg. washer 1 <1 Assembles brake pads to brake support stamping stainless steel
- 19 spacer 2 <1 Assembles brake pads to brake support injection molding plastic
- 20 lg. nut 1 1 Assembles brake pads to brake support casting, thread tapping stainless steel
- 21 sm. nuts 2 <1 Assembles brake pads to brake support casting, thread tapping stainless steel
- 22 sm. bolts 2 3 Assembles brake pads to brake support heading, thread rolling stainless steel
- 23 lg. semi-threaded bolt 2 6 Assembles brake pads to brake support heading, thread rolling stainless steel
Brake Supporters 24 brake pad link 2 33 Squeezes brake pads to wheel casting,stamping stainless steel
- 25 spring wound 2 5 Absorbs force on the brake pad links coiling, stamping stainless steel
- 26 u-center 1 33 Centers brake pad assembly over wheel stamping stainless steel
- 27 washers 4 <1 Assembles brake supporters stamping stainless steel
- 28 nuts 2 1 Assembles brake supporters casting, thread tapping stainless steel
- 29 sm. bolts 2 8 Assembles brake supporters heading, thread rolling stainless steel
- 30 lg. bolt 1 15 Assembles brake supporters heading, thread rolling stainless steel
Chain 31 bike chain 1 358 Links sprocket on pedals to wheel sprocket stamping, assembling steel
Inner Casing 32 inner casing 1 1487 Protects bike chain while pedaling stamping stainless steel
Frame Supports 33 front leg 1 1607 Supports bike frame and allows transport cut square extruded tubing/weld together stainless steel
- 34 back leg 1 1290 Supports bike frame in the back cut square extruded tubing stainless steel
- 35 bolt 2 18 Assembles frame supports heading, thread rolling stainless steel
- 36 washers 4 2 Assembles frame supports stamping stainless steel
- 37 nuts 2 4 Assembles frame supports casting, thread tapping stainless steel
Wheel Assembly Supports 38 brackets 2 260 Supports and attaches wheel to bike frame stamping, bending stainless steel
- 39 bolts 2 12 Attaches brackets to bike frame heading, thread rolling stainless steel
- 40 washers 2 <1 Assembles wheel support stamping stainless steel
- 41 nuts 2 12 Assembles wheel support casting, thread tapping stainless steel
Wheel Sub-Assembly 42 *wheel sub-assembly 1 18144 Wheel-Provides resistance to user's pedaling machining large steel stock Steel
- 42a clutch 2 - Friction based transmission of torque from pedals allows slip if torque is too high cutting composites
- 42b wheel sprocket 1 - Allows chain to lock to wheel axle stamping steel
- 42c spring 1 - Maintains high pressure for clutch to function properly coiled stainless steel
- 42d bolt 1 - Besides wheel assembly, the bolt functions as the axel of the wheel thread rolling stainless steel
- 42e nuts 4 - Assembles wheel sub-assembly casting, thread tapping stainless steel
- 42f retainer 1 - Locks wheel sub assembly together injection molding plastic
- 42g right bearing 1 - Minimizes friction of flywheel while spinning extruding, casting various steel components, grease
- 42h left bearing 1 - Minimizes friction of flywheel while spinning extruding, casting various steel components, grease
Frame 43 bike frame sub-assembly 1 18759 Core structure of bike assembly cut square extruded tubing, weld together stainless steel
- 43a main frame 1 - Core structure of bike assembly cut square extruded tubing, weld together stainless steel
- 43b sprocket 1 - Locks chain to pedal crank allowing the transmission of the pedal rotation to the wheel stamping steel
- 43c pedal crank 2 - Provides the link arm from the pedals to the sprocket casting stainless steel
- 43d pedals 2 - Force from users feet is loaded onto the pedals, which connect to the pedal cranks stamping, bending stainless steel
- 43e bolts 2 - Assembles pedal cranks and sprocket to bike frame heading, thread rolling stainless steel
- 43f nuts 2 - Assembles pedal cranks and sprocket to bike frame casting, thread tapping stainless steel


* We were not able to dissect the wheel sub-assembly due to the high pressure that the assembly is under at all times. Dissecting the wheel would be extremly dangerous, and once it was dissected, getting the wheel under the same high pressure would have requried special tools that we do not have access to. The conclusion that dissection was not a good idea was supported by the expert machinists in the Carnegie Mellon machine shop in Hamerschlag Hall.
** Removing the bike pedals from the bike frame was not a possibility for our group due to the need of a special bike-specific tool called a crank arm extractor. More information can be found by watching this video: http://www.youtube.com/watch?v=H6aHvq4oD9o. In addition, the sprocket is welded to the pedal crank, making it impossible to remove.

Design for Manufacture and Assembly (DFMA)

Design for Manufacture

This product is heavy and rugged. Looking at all of the components, several design choices were made for manufacturability of Spinners in batch quantities.
The frame consists largely of steel square tubing and is cut at different angles to be welded together. Therefore the frame is very rigid, since almost all joints are welded instead of fastened. The main goal of the frame is to be stable. Therefore the design strategy we see that considered manufacturability is:

  • Keep the frame simple and cost effective
    • Used inexpensive and simple tubing
    • Cut pieces at angles to be welded, no bending
  • Use heavy material to add to stability of frame
    • Steel tubing

The handle and seat assembly have curved steel pieces. Mounting to the frame could have been complicated but instead were designed very simply, not only for assembly but for the sake of manufacturing separate parts at a lower cost. This way only a small piece of material had to be bent in part 7. The handles (part 9) have a large amount of bending required, but this may be due to the requirement of good ergonomics and worth the additional manufacturing cost.

  • Complicated parts were made simple by using multiple parts
    • These parts assemble easily (pull pins)
  • Requires less machinery in-house, more importing of material/components

Along a similar line, many of the other components were bought off the shelf because manufacturing them in-house would be very costly and inefficient. Things like bolts, nuts, washers, and springs would most likely have been purchased from a supplier whose expertise is mass producing such components. This greatly saves costs as long as Spinners are made in batch sizes. If these bikes were in large-scale mass production then some of these common parts would be made in house, but Spinners are special items and not produced in large enough quantities to warrant mass production manufacturing techniques.

Design for Assembly

It became apparent while dissecting the product that the design for assembly of the Schwinn Spinner exercise bike was carefully planned as well as pragmatic. This made the dissection and re-assembly process relatively easy and safe.

In terms of safety the bike is designed so that the heaviest object, the 40 pound wheel, cannot slip out of its supports after any one particular piece is removed. There is at least a second line of defense to support the wheel. If this were not the case, it would be easy for anyone to get hurt or break the bike not knowing which particular piece held the wheel. Once that piece was loosened, the wheel could easily slip and crack another part of the bike or fall on someone’s hand or foot.

It is important to note that the assembly makes it easy to remove pieces which would do not have easy access. For example, the back casing which is sandwiched between the pedal cranks and the bike frame can be slipped out from behind due to its design, which incorporates slots into the axle holes. This allows the user to remove the casing without completely removing everything else from the axles.

Many of the bike parts are sub assemblies themselves which is a great DFA because it creates a layering affect for dissection. In order to replace a small part on the bike there is never a time when the entire bike would need to be taken apart. Instead, the user would remove the particular sub-assembly the part belongs to and then dissect that assembly, keeping the remainder of the bike intact. The design also follows a format of high-quality DFA by minimizing the part count and using larger, welded parts rather than piecing these larger parts together with nuts and bolts. In most cases, the large welded parts like the handlebars and seat assembly have easy attachment and adjustment to the base frame with a pin and slot design.

FMEA

The Failure Mode and Effects Analysis is used to find problems with the existing product design, suggest improvements to decrease the severity and/or the occurrence of the specified problem and improve the ability to recognize a problem during the manufacturing process. The effect of the change on the product is predicted by the analyst.

FMEA Table

Item and Function Failure Mode Effects of Failure S Causes of Failure O Design Controls D RPN Recommended Action Responsibility and Deadline Actions Taken S' O' D' RPN'
Pedals-User applies force to drive product Torsional stress failure Product no longer functions 8 Inadequate welding 2 Post-welding stress testing at different rotational speeds 3 48 -Higher-quality welding -Welder in manufacturing process N/A 8 1 4 32
Gear #1-Converts user-driven tranlational energy to rotational energy Wear from chain contact Increased slippage 3 Lack of proper maintenance 4 Fretting-wear testing at different speeds 5 60 -Lubricant coating to prevent wear -Gear #1 Designer -Manufacturer N/A 3 3 5 45
Chain-Converts Gear #1 rotational energy to translational energy Slippage Loss of energy, possible consumer injury 4 Radical change in speed 6 Record instances of slippage at different speeds, accelerations 3 72 -Increase surface contact between gear and chain -Chain Designer -Manufacturer N/A 3 4 3 36
Wear from gear contact Increased slippage 3 Lack of proper maintenance 4 Fretting-wear testing by measuring friction at different speeds 6 72 -Lubricant coating to prevent wear -Chain Designer -Manufacturer N/A 3 3 5 45
Pin shearing Chain breaks, product is unable to function 6 Poor choice of pin material 2 Apply different forces upon chain, measure results 4 48 -Change pin material -Increase pin diameter -Chain Designer -Manufacturer N/A 6 1 4 24
Gear #2-Converts Chain translational energy to rotational energy Wear from chain contact Increased slippage 3 Lack of proper maintenance 4 Fretting-wear testing by measuring friction at different speeds 6 72 -Increase surface contact between gear and chain -Gear #2 Designer -Consumer N/A 3 4 3 36
Gear #2-to-Wheel Shaft-Translates Gear #2 rotational energy to Wheel Torsional stress failure Product no longer functions 8 Poor choice of shaft material 1 Torsional stress testing by measuring deformation at different angular velocities 2 16 -Add safety cage around wheel and shaft assembly to prevent injury -Gear #2-to-Wheel Shaft Designer N/A 4 1 2 8
Shear stress failure Product no longer functions 8 Poor choice of shaft material 1 Shear stress testing by measuring deformation with different wheel weights 2 16 -Change shaft material -Gear #2-to-Wheel Shaft Designer N/A 6 1 2 12
Handlebar-Assembly-User comfort Loose casing Slightly uncomfortable for consumer 2 Vibrations from use of product 9 Measure vibrational results of different speeds, assembly dimensions 1 18 -Revision of assembly dimensions -Handlebar-Assembly Designer -Frame Designer N/A 1 9 1 9
Seat-Assembly-User comfort Loose casing Slightly uncomfortable for consumer 2 Vibrations from use of product 9 Measure vibrational results of different speeds, assembly dimensions 1 18 -Revision of assembly dimensions -Seat-Assembly Designer -Frame Designer N/A 1 9 1 9
Spring in Wheel-Helps prevent slippage caused by rapid deceleration Broken spring Overloads spring, no longer prevents slippage 6 Excessive rapid deceleration 2 Measure stress in spring under a variety of pressure to identify actual stress limit 5 60 -Increase length of spring -Increase thickness of spring -Change spring material -Spring Designer N/A 6 1 5 30

Design for Environment (DFE)

Design for environment is an important factor to consider in the contemporary world and in order to asses the total effect a product has on the environment completely, both production and use of the product need to be taken into consideration. To run an analysis on the effect that production of the exercise bike has on the environment the economic input-output life cycle assessment(EIO-LCA) was used. Using EIO-LCA, the sector which best represented an exercise bike was 336991 Motorcycle, Bicycle, and Parts Manufacturing. This U.S. industry comprises establishments primarily engaged in manufacturing motorcycles, bicycles, tricycles and similar equipment, and parts.

Some examples of activities in this sector are:

  • Bicycles and parts manufacturing
  • Mopeds and parts manufacturing
  • Motor scooters manufacturing
  • Motorcycles and parts manufacturing
  • Tricycles, metal, adult and children's, manufacturing
  • Vehicle, children's, metal manufacturing

Although there is no exact exercise bike activity, the best fit activity to the exercise bike in this sector is bicycles and parts manufacturing. This activity is a fairly accurate representation of the exercise bike product. Both products use roughly the same amount of steel from similar frames, handlebars and pedals. The main differences stem from the base of the exercise bike and the wheels between the two products. The exercise bike is stationary and so it requires additional steel to form a base at the bottom of the frame. The bicycle has two wheels while the exercise bike only has one, but the one wheel on the exercise bike has a significantly greater amount of mass than the two wheels on a regular bicycle.

Before choosing this sector as the best fit for exercise bike production analysis, the Sporting and Athletic goods manufacturing sector was considered but this sector is too broad and includes too many items that do not match well with exercise bikes. For example, fishing bait and basketballs were put under this sector, whereas the Motorcycle, Bicycle and Parts Manufacturing sector includes products which all have a resemblance of the exercise bike.

Knowing that the sector is an accurate representation of an exercise bike, the data associated with it from EIO-LCA is therefore acceptable. The greenhouse gas emission from production data can be seen in the tables below:

As the tables indicate, the section which produces the most CO2 emissions and has the greatest global warming potential by far is the power generation and supply section. This section accounts for all the CO2 emissions created to produce the electrical power needed in the entire process of manufacturing and assembling the product and produces roughly 229.1 metric tons of CO2. The bike is primarily made of steel which justifies why the CO2 equivalent for the iron and steel mill section is the second highest at 179.2 metric tons.

For a more efficient green design, the area which is dominant in CO2 production is the one which needs to be addressed. In this case, the power generation and supply is the area which needs to be addressed. This is an indirect impact since electricity is a commodity that comes from other suppliers. This means that the only way to reduce CO2 emissions from power generation and supply is to reduce the amount of electricity consumed in the production process. Using alternative energy generators such as wind turbines and solar panels would greatly reduce the CO2 emissions caused by power generation and supply. If these alternatives where able to supply all the needed electrical power, then the CO2 of power generation would be cut to zero.

Besides CO2 caused from production of a product, CO2 caused by product use should also be considered. In this case, the exercise bike does not produce any CO2 when it is being used and so the entire focus to improve DFE should be placed on product production.

Mechanical Analysis

A mathematical analysis was done to calculate the inertia of the flywheel and study the chosen weight, weight distribution and their effects on driver perception of on-road cycling.

The following assumptions were made in the calculations: 1. The flywheel has uniform density 2. There is no major friction loss in the chain and bearing 3. The width if the flywheel is negligible compared to its diameter.

We analyze the weight distribution of the wheel by dividing it into two sections: a solid disc and a hollow ring. We define the following variables:

rring,o = Outer radius of ring (m) rring,i = Inner radius of ring (m) rdisc = Radius of disc (m) hring = Width of ring (m) hdisc = Width of disc (m) mring = Mass of ring (kg) mdisc = Mass of disc (kg) mtotal = Total mass of wheel (kg) Iring = Moment of Inertia of ring about the shaft (kg.m2) Idisc = Moment of Inertia of disc about the shaft (kg.m2) Itotal = Moment of Inertia of wheel about the shaft (kg.m2) winput = Revolutions per minute (rpm) of rider (rpm) wwheel = Revolutions per minute (rpm) of flywheel (rpm)

Weight of flywheel m = 19.5kg

Riders speed = 100 rpm

M_outer = 0.35*19.5 = 6.825 kg

M_wheel = 12.675 kg

I_outer = 6.825*0.427^2 = 1.245 kg.m^2

I_wheel = 0.5*12.675*0.460375^2 = 1.343

I_total = 2.588 kg.m^2

Rpm_input = 100rpm = 0.029 rad/sec

Rpm_fly = 0.01

KE_generated = 0.5*I_tot*rpm_fly^2 = 0.01294 J

200 calories in 60 min = 0.055 J (generated by person)

References

Carnegie Mellon University Green Design Institute. (2008) Economic Input-Output Life Cycle Assessment (EIO-LCA) model [Internet], Available from: <http://www.eiolca.net/> [Accessed 21 Sep, 2008]

Johnny G Spinner Owner's Manual
<http://support.startrac.com/documents/manual_5800_5900.pdf>

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