Transfer Path Analysis (TPA)
Transfer Path Analysis (TPA): Theoretical Foundations
What is TPA?
Professor, what is TPA (Transfer Path Analysis)?
A technique to quantitatively analyze through which paths sound and vibration reach a response point. Essential for formulating NVH countermeasures.
Basic TPA Equation
The sound pressure $p$ at a response point (e.g., driver's ear) is the sum of contributions from all paths:
$H_i$: Transfer Function (NTF: Noise Transfer Function) for the $i$-th path, $F_i$: Input force (acting force) for the $i$-th path.
So you can see the contribution of each path.
Correct. This makes it immediately clear "which mount is dominant" and "which frequency band is problematic."
Path Classification
In automotive NVH, structure-borne paths dominate low frequencies (~500Hz), and air-borne paths dominate high frequencies.
Input Force Identification
Methods to determine input force $F_i$:
1. Direct Measurement Method: Install force sensors at input points. Most accurate, but sensor installation can be difficult.
2. Mount Stiffness Method: $F = k \cdot \Delta x$. Displacement difference across mount × stiffness.
3. Inverse Matrix Method: $\{F\} = [H]^{-1}\{a\}$. Calculate input force inversely from response acceleration.
Summary
The Prototype of TPA Theory Originated from Building Vibration and Noise Countermeasures
The mathematical framework of Transfer Path Analysis (TPA) was formed in the architectural acoustics and mechanical vibration fields during the 1950s-60s. In particular, Möser (German Institute for Building Acoustics) and others developed vibration transmission path models for building structures, which were later productized in the 1980s by Müller-BBM and LMS International as TPA methods specialized for automotive NVH. Current Component TPA (CTPA) is based on the formulation by Helut Müller in a 1999 SAE paper.
Computational Methods for Transfer Path Analysis (TPA)
Types of TPA
Are there different types of TPA?
Mainly three.
1. Classical TPA
2. OPA (Operational Path Analysis)
3. CAE-TPA (Virtual TPA)
CAE-TPA Implementation
1. Vehicle Body FEM Model — Define input points (mount locations) and response points (driver's ear).
2. NTF Calculation — Apply unit force at each input point, calculate sound pressure at response point via frequency response.
3. Input Force Setting — MBD analysis results or measured data.
4. Contribution Calculation — Calculate $p_i = H_i \cdot F_i$ for each path, compare with sum.
Summary
Inverse Matrix TPA is Practical Even with Over 100 Excitation Points
Classical TPA (inverse matrix method) estimates operating loads as mount interface forces and calculates contribution sound pressure via product with transfer functions (FRF). As the number of excitation points increases, the inverse matrix becomes unstable, so Siemens (formerly LMS) began recommending in-situ TPA around 2015, which estimates transmission paths using only operational data without exciters. This TPA variant (operational TPA) gained attention after reducing test man-hours by 40% compared to conventional methods in BMW chassis development.
Transfer Path Analysis (TPA) in Practice
TPA in Practice
Main applications: automotive road noise, engine idle vibration, EV motor noise.
Practical Workflow
1. Define the Problem — "Booming at 60km/h" → Identify frequency, speed.
2. List Candidate Paths — Engine mount ×3 directions, suspension bush ×4 locations ×3 directions = dozens of paths.
3. Obtain NTF — FEM or experimental FRF.
4. Obtain Input Forces — Actual vehicle measurement or MBD.
5. Contribution Analysis — Visualize each path's contribution with bar graphs.
6. Formulate Countermeasures — Modify stiffness of dominant path, change mount characteristics, add damping material.
Practical Checklist
Why is phase important?
Cancellation (out-of-phase) can occur between paths. Adding amplitudes alone leads to overestimation. Synthesize as complex numbers is the golden rule.
EV Road Noise is Subjectively "More Noticeable" Than ICE
In electric vehicles (EVs), the absence of engine noise has made road noise transmitted from tire contact patches through the body the main NVH performance challenge. After the Nissan Leaf (2010) market launch, user surveys showed road noise complaints reached 1.8 times that of ICE vehicles. Contribution analysis via TPA revealed the front subframe mount as the maximum contributor. Improvements optimizing the mount rubber's dynamic stiffness to reduce the 500-800Hz band by 5dB were implemented in the 2013 model year.
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