# American DJ Aftershock Party Light

## 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 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 Black and Decker Grinder:

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 | Transmission | Transmission | Transfers energy from horizontal plane into vertical plane for grinding wheel | Metal with grease lubricant | |

8 | Internal Motor Assembly | Output | Converts the electrical energy into the horizontal mechanical energy | Metal, plastic, and ball bearings | |

9 | Outer Motor Assembly | Input | Creates the electromagnetic field that provides the power for the tool | Metal, wires and plastic | |

10 | Transmission Casing | Structural Components | Attaches the transmission to the motor and allows the shaft and transmission to run smoothly | Metal Composite with grease lubricant | |

11 | Washer | Support elements | Attaches the motor to the gears. | Metal | |

12 | Hypoid Gear | Motion Conversion Elements | Transfers power from shaft to transmission. | Metal | |

13 | Drill handle and electrical circuits | Input and support elements | Provides the electrical power to the motor and turns the grinder on and off. | Plastic and Electrical Circuits |

## Engineering Specifications

The table belows explains the life expectancy of the bearing:

1 | Engineering Specification (description, target value, direction of improvement) and related User requirement. | Life expectancy of a ball bearing, 10 years,↑, durability, customer satisfaction |
---|---|---|

2 | Design decisions/parameters affected | The major design decisions are the size of the bearing to be used and the material composition of the bearing. These decisions are interrelated in that the increasing the size of the bearing increases the durability of the bearing while increasing the strength of the material also performs the same task; so, an optimization needs to be done to maximize the performance of the bearing under the constraints of the given situation. The parameter affected by these decisions is the Dynamic load which in turn affects the acceptable load felt by the shaft. |

3 | Key geometric, inertia, and material properties | The bore of the bearing is 7 mm, the Outside Diameter is 22 mm, the bearing type is the plain- Double shield, the Material is 52100 Steel, the lubrication is Chevron SR1 #2, width 7 mm and a Dynamic Load 3300 N. |

4 | Type of Analysis and method of obtaining results. List relevant equations and describe how they relate to the design decisions | L=Lr(C/Fr)^3.33 is the one equation that governs the life expentancy of bearings. The major design considerations are the size and strength of the bearing in combination with the force exerted on the shaft. The force exerted on the shaft will probably be known before the bearing is chosen. Hence the only variables in the equation are the dynamic load and the life rating of the bearing. It seems to be common practice that the bearings are rated at a given dynamic load for a life of 9*10^6 s. The Dynamic load depends mainly upon two factors, the dimensions of the bearing and the material composition. |

5 | Quantitative Results (plots, calculations). How do these relate back to the engineering specifications? How do they verify the quality of the design? | This quantity turned to be about 1.86*108 years if the grinder was used for 6 hours a day 5 days a week. This exceeds the life requirement target of 10 years and reinforces the quality of the design. |

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? | The major changes that could be made to improve the quality of the bearing would be to increase the strength of the bearing, to increase the size of the bearings, to use higher quality lubrication and to lower the force exerted by the shaft. Lowering the force on the shaft would have a dramatic effect on the performance of the grinder and hence is not very feasible. The only negative to all the other modifications is that making these changes would increase the cost of the grinder and in any engineering decision optimizing cost is always a primary concern. |

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

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. |

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