# Mechanical Engineering Lab Report

Experiment 1: Inertia of a Compound Gear Train

Abstract

Usually, there is a change in total system inertia when a geared system accelerates or decelerates. This increase or decrease is dependent on the ratio of the speed from various system parts.

Objective

To demonstrate the theory of the prediction of the motion of rotors connected by gears. The gear system is in the form of a compound train with four gears.

Using the equation P x R = I x a + T_{f}

But P = m (g-a)

Results

Gear 3cc | |||

P | 1m | ||

R | 6cm | ||

a | |||

Tf | |||

Nd | 90 teeth | ||

Time (s) | Mass (N) | Length (m) | radius (mm) |

0.47 | 10 | 1 | 61.83 |

0.45 | 15 | 1 | 61.83 |

0.23 | 20 | 1 | 61.83 |

0.2 | 25 | 1 | 61.83 |

Gear Total | |||

P | 1m | ||

R | 6cm | ||

alpha | |||

Tf | |||

Nd | 45 teeth | ||

Time (s) | Mass (N) | Length (m) | radius (mm) |

15.01 | 10 | 1 | 61.83 |

12.12 | 15 | 1 | 61.83 |

8.3 | 20 | 1 | 61.83 |

7.12 | 25 | 1 | 61.83 |

Experiment 2- Deflection of beams

Objective

To determine the laws relating to the deflection of a simply supported beam when carrying a central load.

Apparatus

- Cast iron bed
- Adjustable simple supports
- Mild steel beam (with 4 differing cross section measurements.)
- Stirrup
- Mass hanger
- Individual mass items
- Dial gauge indicator

Theory

The deflection of a simply supported beam carrying a central concentrated load, varies if the following change:

- Load
- Span
- Breadth of cross section
- Depth of cross section

Procedure

The appropriate material was selected and the apparatus was arranged to satisfy the following conditions;

- L=1m, b=20 mm and d=14mm. Load was then applied in increments of 25N, from 0N to 150N and the deflection was measured at each stage.
- W=150N, b=20mm and d=14mm. L was adjusted in increments of 0.1m, from 0.6m to 1.2m and the deflection was measured at each stage.
- W=150 N, L=1 m and d=20 mm. The material was altered under test so in each instance it is only the breadth of cross section that changes, and the deflection at each change was measured under these conditions. This was completed with each different beam provided.
- W=150 N, L=1 m and b=20 mm. The material was altered under test so in each instance it is only the breadth of cross section that changes, and the deflection at each change was measured under these conditions. This was completed with each different beam provided.
- Following this activity, the experimental values of a were determined.
- The values obtained in the experiment were compared with theoretical values expected under similar conditions. Additionally, the role of K within this relationship was speculated.

Results

Beam 1 | ||||

width | 19.66mm | |||

thickness | 13.87mm | |||

length | 1m | |||

Mass (N) | Deflection (mm) | log (mass) | Log (deflection) | a |

25 | 0.53 | 1.40 | (0.28) | |

50 | 1.08 | 1.70 | 0.03 | |

75 | 1.63 | 1.88 | 0.21 | 1.01 |

100 | 2.18 | 2.00 | 0.34 | |

125 | 2.73 | 2.10 | 0.44 | |

150 | 3.28 | 2.18 | 0.52 | |

Beam 3 | ||||

width | 19.89mm | |||

thickness | 11.8mm | |||

length | 1m | |||

Mass (N) | Deflection (mm) | log (mass) | Log (deflection) | a |

25 | 0.29 | 1.40 | (0.54) | |

50 | 1.14 | 1.70 | 0.06 | |

75 | 2.02 | 1.88 | 0.31 | 1.32 |

100 | 2.42 | 2.00 | 0.38 | |

125 | 3.81 | 2.10 | 0.58 | |

150 | 4.7 | 2.18 | 0.67 |

Beam 2 | ||||

width | 40mm | |||

thickness | 9.75mm | |||

length | 1m | |||

Mass (N) | Deflection (mm) | log (mass) | Log (deflection) | a |

25 | 0.71 | 1.40 | (0.15) | |

50 | 1.44 | 1.70 | 0.16 | |

75 | 2.06 | 1.88 | 0.31 | 0.99 |

100 | 2.8 | 2.00 | 0.45 | |

125 | 3.56 | 2.10 | 0.55 | |

150 | 4.34 | 2.18 | 0.64 | |

Beam 4 | ||||

width | 14.81mm | |||

thickness | 15.87mm | |||

length | 1m | |||

Mass (N) | Deflection (mm) | log (mass) | Log (deflection) | a |

25 | 0.07 | 1.40 | (1.15) | |

50 | 0.44 | 1.70 | (0.36) | |

75 | 0.76 | 1.88 | (0.12) | 1.32 |

100 | 1.12 | 2.00 | 0.05 | |

125 | 1.48 | 2.10 | 0.17 | |

150 | 1.86 | 2.18 | 0.27 |

- Codecogs.com. (2018).
*Dynamics of Geared Systems – Theory Of Machines – Engineering Reference with Worked Examples*. [online] Available at: http://www.codecogs.com/library/engineering/theory_of_machines/dynamics-of-geared-systems.php [Accessed 16 Mar. 2018]. - Selfridge, R. (1980). Compound gear trains of minimum equivalent inertia.
*Mechanism and Machine Theory*, 15(4), pp.287-294.