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MCE 464 Vibrations
Working Model computer Assignment # 2
Accelerometer Design

An accelerometer is an instrument that measures the acceleration of a vibrating body. Such instruments are widely used for vibration measurements in machine and structural applications. The instrument consists of a mass m, and spring k, and a damper c inside a cage, which is rigidly fastened to the vibrating body (see schematic). With such an arrangement, the bottom support of the spring and dashpot will have the same motion as the cage, y(t), while the suspended mass will undergo a different motion, x(t). The relative motion of the suspended mass with respect to the cage, z(t) = x(t) - y(t), can be calibrated and measured electronically using piezoelectric technology. The device operates under the principle that with z(t) known, the motion of the device(object) y(t) can be determined.

Recall that the basic equations governing this problem are (see text, pp 636-641)

From these results we find that the acceleration of the base, |y''(t)| is given (with the exception of the phase angle) by |-wn2z(t)| if the term 1/[(1-r2)2 + 2(zeta)r)2]½ = 1. Figure 10.13 in the text illustrates the behavior of this term. If the base motion consists of a single harmonic, the phase angle will not be of importance. The problem is to design and build an accelerometer using Working Model with following constraints:

  1. To be used for machinery running in range 250-500rpm.
  2. Case size limited to 20 mm <= b & h<=30 mm.
  3. Steel case mass not to exceed 2g.
  4. Steel sensing mass range: 0.2M <= m <= 0.7M.
  5. Recorded motion (acceleration, |-wn2zmaz(t)|) must be within 5% of cage motion |w2ymax(t)| over the required frequency range.
Construct a Working Model accelerometer by making appropriate choices for the device parameters; k, m, c, M, b, h and the case thickness. Machine or base excitation should be produced by a length actuator. Include an output window of the vertical motion of the sensing mass and the cage(case). Make WM runs for each end of the required operating frequency range, and save each WM simulation data set in Excel. Using Excel, calculate the relative motion wn2|zmax(t)| and compare it with wn2|ymax(t)| in order to satisfy condition 5. Submit a write up describing your design and include: