Simcenter Testing Solutions Obtaining Invariant Loads: Practical Examples

In Figure 1, the inputs and outputs of each component are identified by numbered dots. Although only a single dot is shown, each dot may represent multiple connection interfaces in reality.

From this data we can virtually assemble the source-receiver system and predict its NVH performance at the response targets using a technique called FRF Based Substructuring (FBS) as shown in Figure 2:
 

Figure 2: Virtual assembly and target prediction of a source-receiver system using FBS
 

The ability to evaluate system NVH performance without building physical prototypes explains why there is currently such a high interest in C-TPA in the NVH community. However, the accuracy of C-TPA prediction results depends greatly on the quality of the input data required. Small inaccuracies tend to be amplified in the final prediction result.

One of the most challenging steps in C-TPA is obtaining high-quality invariant loads for the source components. Several methods exist for obtaining invariant loads, so some thought is required for selecting the optimal method for each application.
This article will explain what is meant by “invariant” loads, what the best methods are for obtaining them and how to apply those methods in practice for high-quality results.

2.    What are “invariant” loads?

In general, the loads acting in an assembly will depend on the impedances of the source and receiver components. These are what we call contact (interface) forces, which are used extensively in classical Transfer Path Analysis (TPA). However, in C-TPA we want to characterize our sources in such a way that we can predict the NVH performance for any receiver component. This can be achieved by obtaining loads that do not include any receiver influence, then predicting the influence of a particular receiver from its impedances. In other words: we want to obtain loads that are receiver-invariant.

The receiver influence can be excluded by connecting the source component to a receiver with a (theoretical) impedance of infinity (= rigid receiver) or zero (= free suspension). This will result in a different set of loads depending on the type of source being characterized:

Still confused about blocked forces? Check out this article which explains in detail the differences between blocked forces and contact (interface) forces, how they are calculated, and in what circumstances they are used: Blocked Forces versus Contact Forces in Transfer Path Analysis (TPA)

3.    How to obtain invariant loads?

Broadly speaking there are two main strategies for obtaining invariant loads: direct measurement and indirect estimation.

3.1    Direct invariant load measurement

In some applications the theoretical rigid receiver or free suspension conditions can be approximated to a reasonable degree of accuracy. In such cases, invariant loads can simply be measured by instrumenting appropriate sensors at the connection interfaces.

Direct measurements work best in applications where “weak” coupling between the source and receiver components can be assumed in the frequency range of interest. Weakly coupled components exhibit a significant mismatch (>10 dB) in their impedances, resulting in one system behaving as if rigidly clamped and the other as if freely suspended.

Think of impedance as a stiffness as shown the weakly coupled mass-spring system shown in Figure 3.
 

In a weakly coupled mass-spring system shown, the spring stiffness on the left side is much greater than the other springs.  As a result, the mass attached to the less stiff springs moves a greater amount than the mass attached to the high stiffness spring.

Direct blocked forces (F_blocked) can be obtained by attaching a receiver that is very stiff compared to the source component and measuring the forces at the connection interfaces using load cells. This is shown in Figure 4.
 

In practice, this approach will be limited to low frequency investigations as resonances start appearing at higher frequencies in even the stiffest structures.

Direct free velocities (a_free) can be obtained by attaching a receiver that is very soft compared to the source component and measuring the velocities (accelerations) at the connection interfaces using accelerometers. This is illustrated in Figure 5.
 

Free velocities can be converted to blocked forces using the source impedances (H_22,A) if needed. In practice, this approach will be limited to high frequency investigations as stiffness increases at lower frequencies in even the softest structures.

3.2    Indirect invariant load estimation

In most applications direct measurements cannot be applied since “strong” coupling exists between the source and receiver components in the frequency range of interest. Strongly coupled systems exhibit comparable impedances, resulting in co-dependent system behavior that includes receiver influence.

A strongly coupled system is shown in Figure 6.
 

In the strongly coupled system, all the spring elements have similar spring rates (as well as the masses in this case).  As a result, motion in one mass causes the other to move as well.

In such cases, it is still possible to obtain the invariant loads using a technique called in-situ TPA. This technique indirectly estimates the blocked forces from the receiver indicator responses (a₄) and transfer functions (H_24,AB) measured in coupled conditions (Figure 7).
 

In fact, the accuracy of this estimation improves with stronger coupling between the source and receiver components, as the transfer functions (H_24,AB) can be measured with better signal-to-noise ratio.

A major benefit of in-situ TPA is that blocked forces can be obtained with any strongly coupled receiver component. Instead of building dedicated rigid or soft test benches, very often existing test benches or even component assemblies can simply be reused.

Airborne loads are another use case for indirect load estimation. Although weak coupling can be assumed due to the impedance mismatch between air and structural materials, directly measuring volume acceleration (i.e., acoustic force, units of m³/s²) is only feasible for simple (flat) geometries. Volume accelerations are more commonly obtained using a technique called Airborne Source Quantification (ASQ) as shown in Figure 8.
 

Like in-situ TPA, this energetic approach that indirectly estimates volume accelerations (Q) by applying Matrix Inversion to indicator responses (p₄) and transfer functions (H₂₄).

More on acoustic quantity Q in this knowledge article: What is the acoustic quantity called Q?

4.    Practical case studies

We have seen that several methods are available for obtaining invariant loads to characterize source components. The optimal method for a particular application requires careful consideration of the following boundary conditions:

The location of the connection interfaces will depend on the desired component granularity in C-TPA and on which interfaces can be feasibly instrumented. For example, in road noise applications one could consider the invariant loads at the connections between the wheel (source) and wheel hub (receiver) or equally between the suspension system (source) and vehicle body (receiver).

Once the location of the connection interfaces has been defined, the type of coupling (weak vs. strong) at these interfaces will determine whether direct or indirect invariant load estimation methods should be applied. Strong coupling is generally assumed unless a significant impedance mismatch (>10 dB) exists in the frequency range of interest.

The following case studies illustrate how this workflow can be put into practice. 

5.    Electric Drive Unit (EDU) loads

This section explains how to characterize structureborne and airborne loads of an Electric Drive Unit (EDU) that is softly mounted to a vehicle body. This is shown in Figure 9.
 

5.1    Estimated blocked forces at active-side EDU mounts

An ideal location to define the connection interface is at the active-side mounts. This completely separates the EDU characterization from the mounts and vehicle body, allowing each component to be modified independently in future assemblies. This is shown in Figure 10.

In-situ TPA is often the preferred invariant load identification method for general structureborne applications. However, in this case the soft mounts limit the energy transfer towards the vehicle body indicators (4). This can significantly obstruct the measurements of the coupled transfer functions (H_24,AB) depending on how soft the mounts are in the frequency range of interest.

In summary:

5.2    Estimated blocked forces at passive-side EDU mounts

The results obtainable with in-situ TPA can be improved by defining the connection interface at the passive-side mounts. This side of the mounts is strongly coupled to the vehicle body, which allows the coupled transfer functions (H_24,AB) to be measured much more accurately than before. This is shown in Figure 11.
 

The downside to this approach is that the mount influence will be inseparable from the EDU characterization. It will not be possible to modify the EDU and mounts independently in future assemblies. However, this limitation may be irrelevant if no future modifications to the mounts are expected.

In summary:

5.3    Measured free velocities at active-side EDU mounts

Characterizing the EDU at the active-side mounts is still possible if the mounts are sufficiently soft in the frequency range of interest as illustrated in Figure 12.
 

In that case we can assume weak coupling between the EDU and vehicle body, allowing a direct measurement of free velocities using accelerometers at the connection interfaces.

In summary:

5.4    Estimated volume accelerations

As explained previously, airborne source characterization is often performed by indirectly estimating volume accelerations (m³/s²) using Airborne Source Quantification (ASQ) while assuming weak coupling to the surrounding air. This is illustrated in Figure 13.
 

This approach can be applied on any test bench or assembly with realistic boundary conditions and delivers high-quality invariant loads. Note that sometimes volume velocities (m³/s) can be used, they are just the integral of volume acceleration (m³/s²).

In summary:

More on acoustic quantity Q in this knowledge article: What is the acoustic quantity called Q?

6.    Structureborne road loads

This example explains how to characterize the structureborne road loads travelling through the wheels and suspension system to the vehicle body as shown in Figure 14.

A useful location to characterize road loads is at the connection interface between the wheels and wheel hub of the suspension system. This completely separates the wheels from the suspension system, suspension mounts and vehicle body and allows those components to be modified in future assemblies.

6.1    Measured blocked forces at wheel center

Wheel force transducers provide a convenient way to measure wheel forces at the wheel center. Such sensors measure both translational and rotational degrees of freedom, both of which are relevant for characterizing road loads.

Directly measuring blocked forces with a wheel force transducer requires mounting the wheel to a rigid test bench, as the suspension system is typically too flexible.
 

Even so, this approach will be limited to low frequency investigations as resonances start appearing at higher frequencies in even the stiffest structures. To improve the realism of the results, a pre-load is applied to the wheel (e.g. ¼ vehicle weight) and the measurements are performed at several vehicle speeds.

In summary:

6.2    Estimated blocked forces at wheel center

A second way to characterize road loads at the connection interface between the wheels and wheel hub of the suspension system is using an indirect estimation method. The wheels are typically connected to the wheel hub using four up to eight bolts, resulting in a strong coupling condition that should provide high-quality results using in-situ TPA. This is illustrated in Figure 16.
 

 

However, the geometric density of the four to eight connecting bolts poses a different challenge. Estimating the blocked forces in all three translational directions in each bolt using in-situ TPA would result in numerical conditioning issues in practice. Instead, the connection interface can be simplified to a single virtual point at the wheel center using a technique called Virtual Point Transformation (VPT). This technique recalculates local FRFs to a virtual point based on local geometric relationships, assuming the structure is locally rigid and these relationships are constant.

This assumption will often hold up to higher frequencies than the previous method using a rigid test bench, though this does depend on the construction of the wheels. In addition, the transformation to a virtual point will quantify both the translational and rotational degrees of freedom, resulting in a more complete source characterization for road loads.

In summary:

6.3    Estimated blocked forces at passive-side suspension mounts

It may be advantageous to define the connection interface further down the assembly when structureborne road loads at higher frequencies than those achievable at the wheel center are desired. There is a strong coupling between the suspension system and vehicle body at the passive-side mounts, which should allow high-quality loads to be estimated using in-situ TPA.
 

The downside to this approach is that the wheels, suspension system and suspension mounts will be inseparable from the road load characterization. It will not be possible to modify these components independently in future assemblies. However, this limitation may be irrelevant for engineers who focus only on tuning the design of the vehicle body.

In summary:
•    Higher achievable frequency ranges compared to wheel center
•    Wheels, suspension system and suspension mounts inseparable from road load characterization

7.    HVAC compressor loads

Another application is the structureborne loads of an Heating Ventilation Air Conditioning  (HVAC) compressor rigidly mounted as shown in Figure 18.
 

Figure 18: HVAC compressor rigidly mounted to the engine
 

The same principles can also be applied to other small auxiliary components like hydraulic pumps, etc.

7.1    Estimated pseudo forces at center of gravity

An HVAC compressor is typically connected to the engine using two or three bolts, resulting in a strong coupling condition that should provide high-quality results using in-situ TPA (Figure 19).
 

Due to their small size, HVAC compressors suffer from a high geometric density of connection points that may complicate the estimation of blocked forces using in-situ TPA in practice.

Small components such as an HVAC compressor can be simplified as virtual point sources at their center of gravity using VPT. This results in a single connection point with both translational and rotational degrees of freedom. In this case the blocked forces estimated at the center of gravity using in-situ TPA are called “pseudo” forces. As with all applications using VPT, the frequency range may be limited by the local rigidity of the structure.

In summary:

7.2    Measured free velocities at HVAC compressor mounts

Due to their small size and weight, it is relatively easy to approximate freely suspended conditions for small auxiliary components such as the HVAC compressor by suspending them with soft bungees (Figure 20).
 

This weak coupling allows the free velocities at the connection interfaces to be directly measured using accelerometers.

In summary:

8.    Wiper motor assembly loads

This section shows how to characterize the structureborne loads of a wiper motor assembly softly mounted to the vehicle body.
 

8.1    Estimated contact forces of vehicle assembly

Although several of the previously discussed invariant load characterization methods could be applied here, a particularly interesting case is where the test bench consists of the front half of the target vehicle body. In this case, it may not be strictly necessary to identify invariant loads at the connection interface since the receiver-dependent contact forces of the test bench will be very similar to those of the final vehicle due to their similar impedances.

Like blocked forces, contact forces can be estimated using Matrix Inversion except that the receiver indicator transfer functions (H_34,B) should be measured without the source component. This has the advantage that these transfer functions can be measured in advance, so estimating contact forces only requires a quick measurement of the receiver indicator responses (a_4,AB) in coupled conditions.

The downside to this approach is that the obtained contact forces are only valid for the specific test bench or vehicle body used. There is no flexibility for studying the effect of modifications to the vehicle body design, since any change to the receiver impedance would influence the contact forces of the assembly. However, this limitation may be irrelevant if the vehicle body design is already considered final.

In summary:

9.    Conclusion

As you have seen, each application has multiple ways to approach the characterization of source components for Component-based Transfer Path Analysis. Our goal with these case studies is not to provide an exhaustive overview, but rather to illustrate the workflow for choosing the optimal method for your application. Remember to think carefully about the two following points for your application:

Curious about the next steps? Read on about how to create source and receiver components for predicting virtual assembly NVH performance using Virtual Prototype Assembly.

Questions? Email eric.sorber@siemens.com
 

Related Links:

• Index of Testing Knowledge Articles
• An Introduction to Transfer Path Analysis
• Simcenter Testlab Transfer Path Analysis: Groupsets
• Simcenter Testlab Transfer Path Analysis: Component Editing
• Time Domain Transfer Path Analysis: Listening to Paths
• Blocked Forces versus Contact Forces in Transfer Path Analysis (TPA)
• FRF Based Substructuring
• What is Frequency Response Function (FRF)?
• Dynamic Stiffness, Compliance, Mobility, and more...
• Transfer Path Analysis Data Naming
• Simcenter Testlab: Matrix-Heatmap Display
• What is the Acoustic Quantity called Q?
• Simcenter Testlab Virtual Prototype Assembly
• Simcenter Testlab Virtual Prototype Assembly
• Transfer Path Analysis Seminar