American DJ Aftershock Party Light

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Figure 1: American DJ Aftershock

Contents

Description

The main purpose of the Aftershock is to provide beat sensitive party lighting that is capable of sufficiently lighting up a party space. The purpose of this wiki is to provide insight into the internal workings of the light.

How It Works

The Aftershock uses an internal microphone in order to capture low frequency sounds. Using a circuit board it transfers and amplifies the signal to an electric motor at the opposite end of the light. The motor is rigidly attached via a bracket assembly (see figure 2) to a mirror, and contains a weight on its axle to provide uneven interial loading to the assembly. The shake table assembly is then bound in a neoprene diaphragm that allows relatively limited motion of the shake table.

Figure 2: Bracket Assembly

Why It Works

Every component in the assembly has a life expectancy due wear generated by constant friction and other forces acting on the parts. This expectency varies between individual parts based on the location, direction and magnitude of the forces acting on the part and also the geometery and material compositon of the part.

For the force requirement on the gears to rotate the grind wheel at 10,000 RPM, the power consumption of the grinder was researched. From the power consumption the torque was calculated to be 0.315 Nm, which equates to about 2.61 lbs of force on the workpeice from the grind wheel. This calculates to 12.4626 N of force at the gears to rotate the grind wheel at 10,000 RPM.

To calculate the stress in the gears, a stress equation was used from the Fundamentals of Machine Components Design by Robert C. Juvinall. The velocity factor was caluated with the assumption that the gears were precision shaved and ground. The overload factor was calculated with the assumption that the source of power is uniform and the driven machinery is assumed to have moderate shock. Both gears were overhung, which gave a mounting factor of 1.25. The calculated stress in the smaller gear was 613.601 PSI and the stress in the larger gear was 442.438 PSI.

To calculate the life of the bearing a life expectancy equation was used from the Fundamentals of Machine Components Design by Robert C. Juvinall. It was found that common practice was to use a dynamic load for a like of 9X10^6 seconds. Assuming the grinder will be used constantly the bearing will last 3.33*10^7 years before failure. If the grinder will be used six hours every day, 365 days a year then the bearing will last 1.33*10^8 years. Under the more realisitic assumption that the grinder will be used six hours a day, five days a week, the bearing will last 1.86*10^8 years.

Parts

The table belows lists the Bill of Materials for the American DJ Aftershock:

Table 1: American DJ Aftershock Bill of Materials
Part # Part Name # Category Function Material Picture
1 Grounded AC Power Supply Input Allows the light to be powered off of a standard wall outlet Plastic casing with steel and copper prongs
Aftershockoutlet.jpg.png
2 Transformer Input Changes the AC power input to DC power Copper wiring used for coils
Aftershocktransformer.png
3 Internal Microphone Input Differentiates low frequencies sounds Steel with a rubber housing
Aftershockmic.png
4 Geared Motor Output Rotates the reflector Steel gears
AftershockGearedMotor.png
5 Shake Table Motor with Added Destabilizing Weight Output Allows for the motor to spin unevenly since the distribution of weight is lopsided Steel nuts, weight and screw
AftershockShakeTableAssembly.png
6 Fan with Motor Output Cool the inside of the light and prevent overheating Steel casing and fan blades
Aftershockfan.png
7 Diaphragm Structural Components Holds shake table and weighted motor in place Steel plates, nuts and screws

Rubber or neoprene for the diaphragm

AftershockDiaphragm.png
8 Reflector Other Rotates on the geared motor and the light hits the various reflective mirrors on the lens Steel Disc with glued, colored glass lenses
Aftershockreflector.png
9 Magnifying Lens Other Magnifies the light off reflected off of the reflector Glass magnifying lens
Aftershocklens.png
10 Mirror Other Redirects magnified light outward Glass Mirror with Steel Supports
Aftershockmirror.png

Engineering Specifications

The table belows details the convective cooling rate of the fan:

Table 2.1: Convective Cooling Rate for the 400-W Incandescent Bulb
1 Engineering Specification (description, target value, direction of improvement) and related User requirement. A fan is used to circulate air through the apparatus and cool the bulb. How much direct heat removal through the air (not convection/conduction/convection through the casing) is necessary for steady-state operation? The more heat that can be removed via air cooling the lower the steady state temperature inside the apparatus will be resulting in longer operating times. Therefore, the direction of improvement for this specification is increasing the convective heat transfer. The target value is a minimum of one quarter (25%) of the total heat output being removed via air cooling. This specification relates to the safety user requirement.
2 Design decisions/parameters affected Higher fan speeds, and therefore higher air flow rates, involve more expensive equipment, higher power requirements, more noise and larger forces. A balance must be struck between these considerations and the ultimate goal of heat removal. This decision will affect the maximum temperature experienced in the light, the lifetime of the circuitry, and the maximum runtime of the light without overheating.
3 Key geometric, inertia, and material properties Fan speed, inlet size, outlet size, inlet and outlet placement
4 Type of Analysis and method of obtaining results. List relevant equations and describe how they relate to the design decisions A psychrometric analysis of the air being used to cool the system was conducted to determine the amount of heat transfer out of the light via direct convection. The volumetric flow rate of the air was calculated by V= v*A, where V is the volumetric flow rate, v is the velocity of the air at the fan inlet, and A is the cross sectional area of the fan inlet. The enthalpies of the air at the inlet and outlet were found through measurements of air temperature and relative humidity followed by use of the ASME psychrometric chart. The total heat transfer in the air was then determined by multiplying the mass flow rate of air (calculated by m=V/v, where m is the mass flow rate, V is the volumetric flow rate, and v is the specific volume of air at the inlet) by the change in enthalpy between the inlet and outlet per unit mass (Q= m*(h_outlet-h_inlet)), where Q is the rate of heat transfer, m is the mass flow rate, and h is the enthalpy of the air at various sites). The total heat generated by the bulb was equal to 0.95 times the bulb wattage (incandescent bulbs convert 95% of their input energy into waste heat).
5 Boundary Conditions and Loading No significant mechanical stresses were placed on the system in this analysis. The light bulb presented a thermal load of 380W.
6 Quantitative Results (plots, calculations). How do these relate back to the engineering specifications? How do they verify the quality of the design? Experimental observations of the aftershock under steady-state operating conditions showed the inlet velocity to be 2.55 m/s (Inlet diameter was 10.16 cm). The inlet temperature was 20.8oC with a relative humidity of 34.7 %; this led to an inlet enthalpy of 35 kJ/kg. The outlet temperature was 24.8oC with a relative humidity of 26.7 %; these conditions specify an outlet enthalpy of 39.5 kJ/kg. Once all data was calculated as described above it was found that the convective heat transfer out of the system via air cooling was approximately 112 W. This represents approximately 29.4% of the total thermal load of the system. Therefore, the remaining 268 W of thermal loading are being dissipated through the metal casing of the system.
7 What changes could be made to improve the quality of this design with respect to this engineering specification? What trade-offs would this introduce? The use of a higher fan speed would allow for a higher mass flow rate of air through the system. This would result in a higher amount of convective heat transfer out of the light, and therefore a lower operating temperature. However, given that the light can already run uninterrupted for hours at a time the costs associated with installing a more powerful fan likely do not make it a worthwhile investment.


The table belows explains the caclation of the force on the gears:

Table 2.2: Force on gears
1 Engineering Specification (description, target value, direction of improvement) and related User requirement. The maximum angular deflection of the mirror determines the size of the area the lighting effect will cover, as well as the complexity of the light patterns that can be produced. Coverage area and pattern complexity increase with increasing maximum deflection, hence the direction of improvement for this specification is larger maximum deflection. The target value for this specification is 20 degrees from the centerline axis of the governing diaphragm.
2 Design decisions/parameters affected The geometry of the shake table will determine the magnitude of the loading on the diaphragm. This in turn will affect the maximum deflection seen in the mirror. The maximum speed of the motor will also have an effect on the deflection of the mirror.
3 Key geometric, inertia, and material properties The shape of the shake table and connection point to the diaphragm determines the magnitude of the diaphragm loading. The materials used in the shake table design will affect the moments of inertia for the assembly, and consequently the maximum deflection of the mirror.
4 Type of Analysis and method of obtaining results. List relevant equations and describe how they relate to the design decisions
5 Boundary Conditions and Loading
6 Quantitative Results (plots, calculations). How do these relate back to the engineering specifications? How do they verify the quality of the design?
7 What changes could be made to improve the quality of this design with respect to this engineering specification? What trade-offs would this introduce?
Figure 3: Angular Deflection of the Mirror
Figure 3: Pro/E Model of the Diaphragm

The table belows explains the lifetime of the diaphragm:

Table 2.3: Maximum Cycles of Diaphragm
1 Engineering Specification (description, target value, direction of improvement) and related User requirement. The rubber diaphragm that constrains the shake table motion is subject to a repeated, varied, cyclical loading. The diaphragm should be able to withstand 10.8 million loading cycles (at three cycles per second this corresponds to 1000 hours of operating time). The direction of improvement for this specification is an increasing number of load cycles. This specification relates to the durability user requirement.
2 Design decisions/parameters affected The stiffness of the rubber and the size of the diaphragm are both important design considerations. The stiffness of the rubber determines how effectively the diaphragm dampens the motion of the shake table. A stiffer rubber will produce a larger dampening force, allowing for a smaller diaphragm. However, a smaller diaphragm will experience a greater stress, and therefore have a shorter lifetime. Additionally, consideration must be given to the diaphragm geometry. The shape of the diaphragm will govern whether the dampening of the shake table motion is symmetric or not. A circular diaphragm was used to ensure symmetric dampening.
3 Key geometric, inertia, and material properties Rubber type, modulus of elasticity, diaphragm shape, diaphragm size
4 Type of Analysis and method of obtaining results. List relevant equations and describe how they relate to the design decisions The shake table assembly was modeled in Pro/Engineer and ported into the ADAMS environment for a stress analysis. The diaphragm was modeled as a system of eight grounded springs connected to a massless disc in the shape of the actual diaphragm. All mass and inertial properties of the system were determined in Pro/Engineer and applied in ADAMS. The rotating weight was given an angular velocity of three rotations per second (equal to the maximum angular velocity in real-life operating conditions). The stiffness of the springs was then set such that the angular displacement of the mirror matched the real life operating conditions (angular displacement of approximately 20 degrees from the centerline axis).

ADAMS’ postprocessor was then used to determine the maximum force experienced in each spring. This force was found to be approximately 1 Newton. An order of magnitude analysis was then performed to get a rough estimate of maximum lifetime cycles.

5 Boundary Conditions and Loading The actual diaphragm consists of two pieces of rubber pressed between steel plates. The plates were designed such that only a 3-in diameter section of the diaphragm could move. The loading the diaphragm experiences is due to gravity and the shake table motion. This loading resulted in a 1 Newton force when modeled in ADAMS. See Figure 4 for Diaphragm geometry.
6 Quantitative Results (plots, calculations). How do these relate back to the engineering specifications? How do they verify the quality of the design? Equations could not be found to calculate the exact stress experienced by the diaphragm, but the use of s=F/A, where s is stress, F is the force, and A is the area of the diaphragm, predicts the stress to be on the order of 102 Pa. Experimental data from Mars and Fatemi’s paper, Multiaxial Stress Effects on Fatigue Behavior of Filled Natural Rubber, indicates a 50 million cycle lifetime at a stress of 7.5*105 Pa. Given that the stress in the diaphragm is three orders of magnitude smaller it is reasonable to say that failure due to fatigue will not happen. The rubber will decay through simple aging far before sufficient cycles would be reached for fatigue failure.
7 What changes could be made to improve the quality of this design with respect to this engineering specification? What trade-offs would this introduce? The diaphragm size and rubber stiffness could be changed, allowing for different diaphragm geometries. However, it makes no sense to change the diaphragm given the robust nature of the design in resisting cyclic failure. The diaphragm is extremely well suited to this particular application.
Figure 5: Front, Right, Isometric Views for the Shake Table Assembly

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