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Clock Timing Analysis

Avoiding Mistakes in Engineering Analysis is Critical

  • Mistakes can cost money, hurt careers, and result in injury or lost lives.
  • We want a systematic approach to analysis that will catch errors.
  • See consequence of unit conversion error of the Gimli Glider
  • See consequence of miscommunication and unit error in Mars Climate Orbiter that was lost.
  • To avoid mistakes we will use 3 approaches described below in the Clock Timing Analysis, and these same methods should be used whenever possible for all important analyses.


Clock Timing Analysis

 

The challenge of the clock timing analysis is to predict how fast your clock will tick before you actually measure it (each pendulum will tick at a different speed due to the shape variations amount pendulums). In real-world design projects, the cost of building a device is typically high, so it is essential that analysis is correct. Therefore we will emphasize use of the following analytical approaches to catch errors and should be used in all design projects:

Clear Documentation:

All values should be shown with units, and unit conversions should be clearly done (see unit conversion tips). Show only the proper number of significant digits in results and not more than warranted by accuracy of your measurements. Clear documentation is essential in design projects so that team members can check one's work. In the clock project we will use the MathCAD software that shows the equations, values, and units in a report format (see worksheet example).

Multiple Methods of Analysis: 

Calculate results using different approaches to see if both methods yield similar results. Approximate estimations complement more accurate calculation methods, since they allow one to find large errors. In the clock project we will use both the point-mass and ridig-body methods to calculate the natural frequency of the pendulum.

Intermediate Verification:

One would always like to catch any error early on when it is less expensive to fix. Whenever one can measure an intermediate result, this is a very valuable way to validate the analysis. In the clock project we use intermediate verification by weighing the pendulum after it is cut, and by balancing it on our finger to get an approximate center of mass. 

Computer-Aided-Analysis

The clock timing will use CAD to help determine the mass properties of your pendulum, and MathCAD to perform the calculations. 

 

Natural Frequency of a Point-Mass Pendulum

The first step in analysis is often to consider a simplified case that can be easily verified. For the pendulum analysis we initially assume that the mass of the pendulum is concentrated at a point.

Deliverables

·       Problem Description

·       Objectives

·       Assumptions

·       Free Body Diagram

·       Basic Equations

·       Center of Mass Analysis for Pendulum without Bolts

o      Intermediate Analysis and Verification   

·       Center of Mass Analysis for Pendulum with Bolts

o      Intermediate Analysis and Verification

·       Point Mass Pendulum Frequency Calculation

·       Comparison of Calculated Time to Actual Time


Natural Frequency of a Rigid Body Pendulum

A more accurate method for calculating the natural frequency of a pendulum is to consider the whole body of the pendulum and include the effect of the rotational inertia. The rotational  inertia cannot be as easily verified as the center of mass, but it is more accurate.  

Deliverables

·       Problem Description

·       Objectives

·       Assumptions

·       Free Body Diagram

·       Basic Equations

·       Center of Mass Analysis for Pendulum without Bolts

o      Intermediate Analysis and Verification   

·       Center of Mass Analysis for Pendulum with Bolts

o      Intermediate Analysis and Verification

·       Rotational Inertia Analysis for Pendulum without Bolts

·       Rotational Inertia Analysis for Pendulum with Bolts    

·       Rigid Body Pendulum Frequency Calculation

·       Comparison of Calculated Time to Actual Time

 

Values Used In Timing Analysis

 

 Value Name
 Variable Numerical value (SI)
 Numerical Value (English)
 Weight of a single nut Wn 1.15 g
 0.04 oz
  Weight of a single screw Wb 1.6 g
 0.06 oz
 1/2 in long #8 bolt with 2 nuts  3.9 g
 0.14 oz
 Density of acrylic
   1.1754 g/cm^3  0.6865 oz/in^3

Ċ
Michael Tolley,
Apr 6, 2015, 10:00 AM
Ċ
Nate Delson,
Oct 14, 2015, 12:38 PM
Ċ
Nate Delson,
Oct 13, 2015, 8:42 PM
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