Shock Response of a Motherboard

Electronic equipment often has to certified to function after having been subjected to a specified shock loading. Performing a numerical simulation is cheaper, and has a lower turnaround time, than doing the actual physical testing. In many cases, it is not necessary to perform a full nonlinear contact analysis. Rather, the requirement is specified in terms of a certain given acceleration history.

A common such specification of a shock is that the acceleration behaves as a half sine function with a given period and peak amplitude.

In this example, the effect of a 50g half-sine shock load with a duration of 11 ms on a computer motherboard is investigated using two approaches: response spectrum analysis and direct time stepping using mode superposition.

Model Definition

GEOMETRY

Figure 1 shows a motherboard with a design that is typical for smaller computer devices such as game consoles, for example.

Figure 1: Motherboard geometry.

A processor (CPU) and a graphics chip (GPU) are covered by massive heat sinks used for passive cooling. Memory chips are located next to the CPU unit. A number of cylindrical capacitors of various sizes are scattered over the motherboard. Several connectors for peripherals are located along the motherboard edges. The board is attached to the housing via six mounting bolts. The latter are not modeled explicitly.

Material

The board itself is made of a generic PCB material. The heat sinks are made of aluminum. The chips are modeled as made of silicon. The connectors are modeled as rectangular blocks made of plastic. Some effective material properties are used to represent the capacitors.

Constraints

All six mounting holes have fixed constraints on their cylindrical boundaries.

Loads

For the response spectrum analysis, the loading is represented by a pseudoacceleration spectrum as shown in Figure 2.

Figure 2: Vertical spectrum for 50g shock load with 11 ms duration.

During the transient computations, all parts of the motherboard are subjected to a transient body load (gravity load) with 50g magnitude and 11 ms duration:

(1)

Mesh

Figure 3 shows the mesh used.

Figure 3: Mesh.

The discretization using this mesh together with quadratic serendipity elements results in approximately 100,000 degrees of freedom (DOF) being used in the eigenfrequency analysis.

Results and Discussion

As a first step, the lowest fifteen eigenfrequencies have been computed. Figure 4 shows their distribution together with the values of the participation factors for the corresponding eigenmodes.

Figure 4: Participation factors for Z-translation for all the eigenmodes.

The sum of the effective modal mases for all computed eigenmodes is around 0.94. Thus, the modes account for about 94% of the vertical dynamic forces of the system.

Figure 5 shows the values of the vertical shock spectrum computed at the eigenfrequencies.

Figure 5: Vertical shock spectrum input at eigenfrequencies.

Thus, the first and third modes have the largest participation factor for vertical translation. The eigenfrequency for the third mode is also located close to the maximum of the input spectrum, so these two modes seem important for the response. The modes are shown in Figure 6 and Figure 7 below.

Figure 6: The 1st eigenmode.

Figure 7: The 3rd eigenmode.

The response spectrum evaluation is based on the eigenvalue solution, and it is performed during postprocessing using a dedicated dataset called Response Spectrum.

In Figure 8, the vertical displacement response, as computed using the CQC mode combination method with damping of 5% is shown.

Figure 8: Vertical displacement, as a result of the response spectrum evaluation.

Figure 9 shows the stress distribution computed using the response spectrum analysis. The plot shows rather high stress level at the memory chips.

Figure 9: Stress in the motherboard components.

For comparison, the same analysis is also performed in the time domain, using a Time Dependent, Modal solver. Figure 10 shows the vertical displacement of the system after 11 ms of transient loading.

Figure 10: Dynamic response of the system at the end of the shock pulse.

The maximum displacement computed over a 60 ms long transient simulation is shown in Figure 11.

Figure 11: Maximum vertical displacement.

Note that the maximum is computed pointwise, so that Figure 11 does not correspond to a state of the system at some particular time instance. Rather, it gives an estimation of the worst deformation response in each point. In this sense, the plot presents a similar information as the computations of the shock spectrum response, and can be compared with Figure 8. Both methods indicate a maximum displacement of about 8 mm.

Notes About the COMSOL Implementation

The two methods used here has different merits. The response spectrum method only provides an approximate solution, whereas the time stepping is exact (within the limits given by time discretization and truncation of higher modes). On the other hand, you will have to store a full solution for all time steps in order to find the maximum values when using time stepping. This will cause large file sizes.

Note that the maximum response can occur significantly later than the end of the shock, particularly for systems with low damping. During the time stepping, a few periods of the lowest eigenfrequency should be covered. Here, the end of the time stepping is set to 60 ms, which is about three full periods of the first eigenmode.

For the time-dependent analysis, you enter the function for the load by entering the factor:

50*sin(2*pi/22[ms]*t)*(t<11[ms]) in the input field available in the node’s settings. The body load set up via the node will be multiplied by this factor, giving an effective load magnitude of 50g.

Structural_Mechanics_Module/Dynamics_and_Vibration/motherboard_shock_response

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