# American DJ Aftershock Party Light

Figure 1: American DJ Aftershock

## 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 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.

## 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
2 Transformer Input Changes the AC power input to DC power Copper wiring used for coils
3 Internal Microphone Input Differentiates low frequencies sounds Steel with a rubber housing
4 Geared Motor Output Rotates the reflector Steel gears
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
6 Fan with Motor Output Cool the inside of the light and prevent overheating Steel casing and fan blades
7 Diaphragm Structural Components Holds shake table and weighted motor in place Steel plates, nuts and screws

Rubber or neoprene for the diaphragm

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
9 Magnifying Lens Other Magnifies the light off reflected off of the reflector Glass magnifying lens
10 Mirror Other Redirects magnified light outward Glass Mirror with Steel Supports

## 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. Force on the Gears in a tangential direction, the target value is the lowest possible value to achieve 10,000 rpm at the grind wheel, direction of improvement is ↓, the user requirements related are tool life and grinding ability.
2 Design decisions/parameters affected Torque required at the motor, type of gears used, design of gears
3 Key geometric, inertia, and material properties Gear Ratio (31:9), Strength of gear
4 Type of Analysis and method of obtaining results. List relevant equations and describe how they relate to the design decisions We looked up the power requirement for the grinder using P=IV. Then using P=Tω we found the torque provided by the motor. Knowing the radii of the gears we found the tangential force on the gears.
5 Quantitative Results (plots, calculations). How do these relate back to the engineering specifications? How do they verify the quality of the design? P=IV (5.5 amps/2)*120V = 330 Watts

P=Tω ω = (10,000*2*pi) / 60 T = 330/ω = 0.315 Nm

.315/0.05715 = 5.51 kg 5.51 * 9.81 = 12.4626 N at the gears

6 What changes could be made to improve the quality of this design with respect to this engineering specification? What trade-offs would this introduce? Lowering the force on the gears would improve this engineering specification. This would allow the motor to be smaller as well as the grinder to be more compact. The draw backs of this is that it decreases RPM’s at the grinder wheel which would decrease the performance of the grinder.

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

Table 2.3: Stress on gears
1 Engineering Specification (description, target value, direction of improvement) and related User requirement. Stress in the gears that could lead to failure, below 100 ksi (yield stress of steel) ↓, the related user requirement is tool life
2 Design decisions/parameters affected Type of material used, gear design
3 Key geometric, inertia, and material properties Gear Ratio (31:9), Strength of gear
4 Type of Analysis and method of obtaining results. List relevant equations and describe how they relate to the design decisions σ = (FtP/bJ)KvKoKm where Ft is the tangential load in pounds, P is the diamertral pitch at the large end of the tooth, b is the face width, J is the geometry factor, Kv is the velocity factor Ko is the overload factor and Km is the mounting factor. 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.
5 Quantitative Results (plots, calculations). How do these relate back to the engineering specifications? How do they verify the quality of the design? From figure 16.13 in the Juvinall book, J for the little gear was found to be 0.2, and J for the big gear was found to be 0.18. Kv was calculated by using the equation (50 + sqrt(v))/50. Calculating a V in ft/min. V=rω, V=10,000(2*pi)(0.075) = 4712.389 ft/min. Ko was found to be 1.25 from table 15.1 in the Juvinall book. Km was found to be 1.25 from table 16.1 in the Juvinall book. P = Np/dp. For the smaller gear, P = 16.216 and for the larger geat P = 17.22. Combining all of this with a force of 12.4626 N or 0.2248 lbs the calculated stress in the smaller gear was 613.601 PSI and the stress in the larger gear was 442.438 PSI.
6 What changes could be made to improve the quality of this design with respect to this engineering specification? What trade-offs would this introduce? Many changes could be made in the design of the gears to decrease the stress in the gears. For example, P, or the ratio of the number of teeth to the diameter of the teeth could be decreased. This would directly lower the stress in the gears. Another example would be increases the face width of the gears, this would increase the surface for the force on the gears to be transmitted, also directly decreasing the stress in the gears. Also utilizing a different geometry would ultimately change the stress in the gears. The trade-offs would be that most of the examples of how to decrease stress, increase the material needed. This will increase the weight of the gears as well as increase the production cost.