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Research on a Car Engine Sound Synthesis System Based on Physical Modeling#

Demo Presentation#

1. Analysis of the Limitations of Traditional Engine Sound Effect Systems#

In current automotive simulation and gaming applications, the implementation of engine sound effects primarily relies on sampling playback technology. This method works by pre-recording the sounds of a real engine under various operating conditions and then selecting and controlling the playback of samples based on real-time engine state parameters (RPM, load, throttle position, etc.).

However, this traditional method has several fundamental technical bottlenecks:

Exponential Growth of Storage Resources: To achieve sound coverage for all engine operating conditions, the system needs to record a large number of audio samples. For a typical gasoline engine, from 800RPM idle to 6000RPM redline, with a sampling point every 500RPM, 12 RPM points are required. If different load states (light, medium, heavy) and throttle positions are also considered, the required sample quantity increases dramatically. Each sample typically requires 3-5 seconds of high-quality audio data, and the final resource package often exceeds several GB.

Intrinsic Defects of Interpolation Algorithms: When the engine operating conditions change between preset sampling points, the system can only generate the sound of intermediate states through interpolation algorithms. Whether linear interpolation, cubic spline interpolation, or more complex algorithms, none can accurately reproduce the nonlinear response characteristics of a real engine. Particularly during transient processes such as rapid acceleration, shifting, or sudden changes in engine load, interpolation results often appear stiff and unnatural.

Loss of Dynamic Characteristics: The sound of a real engine contains a wealth of subtle variations and randomness. Even at the same RPM and load, the sound produced by each combustion cycle is slightly different, stemming from the randomness of the combustion process, mechanical system vibrations, and environmental factors. The sampling playback method is essentially deterministic and cannot reproduce these dynamic features.

Poor Configuration Adaptability: When simulating different types of engines, corresponding samples must be re-recorded. This not only increases development costs but also limits the system's flexibility. More importantly, for some special engine configurations (such as variable compression ratio engines, electric superchargers, etc.), it is difficult to obtain sufficient recording samples.

2. Physical Mechanisms of Car Engine Sound Generation#

To build an effective physical modeling system, it is essential to deeply understand the mechanisms behind engine sound generation. Engine sound is a complex multi-source acoustic phenomenon, primarily involving the following aspects:

2.1 Acoustic Contribution of Combustion Explosions#

The core of a four-stroke internal combustion engine is the periodic explosion process within the combustion chamber. In each working cycle, the piston completes four strokes: intake, compression, power, and exhaust. The combustion explosion during the power stroke is the main source of sound.

As the piston approaches the top dead center of the compression stroke, the spark plug ignites the rapid combustion of the air-fuel mixture. This process is completed in a few milliseconds, causing a sharp rise in pressure within the combustion chamber. For naturally aspirated engines, the pressure can instantaneously jump from 10-15 bar after compression to 50-80 bar. Turbocharged engines may have even higher peak pressures.

This rapid change in pressure generates the high-frequency components in engine sound, which is also the source of the "sharp" characteristic of engine sound.

2.2 Mechanical System Vibration Contribution#

In addition to combustion noise, the mechanical motion system of the engine is also an important sound source:

Crank-Rocker Mechanism: The reciprocating motion of the piston is transmitted to the crankshaft through the connecting rod, and the mechanical vibrations generated during this process are transmitted throughout the engine structure. The direction change of the piston at the top and bottom dead centers is particularly important, as the sudden change in acceleration generates impact vibrations.

Valve Mechanism: The opening and closing process of the valves generates mechanical noise, especially at high RPMs. The camshaft pushes the valves to overcome spring force to open, and then relies on spring force to close. The impacts and vibrations during this process affect the acoustic characteristics of the engine. Modern engines' variable valve timing systems change these characteristics during operation, producing audible sound variations.

Transmission System Vibrations: The vibrations of transmission components such as the crankshaft, flywheel, and timing chain (or timing belt) also contribute to the overall engine sound. Different transmission system designs produce different acoustic characteristics.

2.3 Acoustic Shaping of Intake and Exhaust Systems#

The intake and exhaust systems are not only functional components of the engine but also important acoustic components:

Intake System Acoustics: As air passes through the air filter, throttle body, and intake manifold into the cylinder, complex airflow noise is generated. Particularly under high RPM and heavy load conditions, intake sound becomes an important component of engine sound. Some high-performance vehicles deliberately design their intake systems to enhance this sound effect.

Acoustic Treatment of Exhaust Systems: The design of the exhaust system has a decisive impact on engine sound. After exhaust gases exit the cylinder, they pass through components such as the exhaust manifold, catalytic converter, and muffler, each of which modifies the sound. The length and shape of the exhaust manifold affect the propagation and reflection of pressure waves, while the design of the muffler determines which frequency components are retained or suppressed.

Acoustic Effects of Exhaust Pulsations: The exhaust pulsations of multi-cylinder engines produce complex acoustic phenomena. When exhaust pulses from multiple cylinders meet in the exhaust system, interference occurs, and the result of this interference directly affects the engine's sound characteristics.

2.4 Influence of Engine Structure on Acoustic Characteristics#

Different engine structural configurations produce distinctly different acoustic characteristics:

Number and Layout of Cylinders: Inline four-cylinder, V6, V8, and horizontally opposed engines produce different acoustic characteristics due to differences in cylinder count and geometric layout.

Firing Order: The firing order determines the timing distribution of combustion pulses, which directly affects the rhythm and harmonic structure of engine sound.

Displacement and Bore-Stroke Ratio: These parameters influence the energy release of each combustion cycle and the characteristics of piston motion, thereby affecting the "thickness" and "strength" of the sound.

3. Architecture and Implementation of the Physical Modeling System#

Based on an in-depth analysis of engine acoustic mechanisms, we have designed a complete physical modeling system. The core idea of this system is to describe the physical processes of the engine through mathematical models and then synthesize sound signals from these physical processes.

3.1 Overall System Architecture#

The entire physical modeling system adopts a layered architecture design, from the low-level physical simulation to the top-level audio output, which can be divided into the following layers:

Physical Simulation Layer: Responsible for calculating the physical state of the engine, including parameters such as pressure, temperature, piston position, and valve opening for each cylinder. This layer operates at a relatively low frequency (usually 1-2kHz), as the time constants of most physical processes are longer than the sampling period of audio signals.

Signal Processing Layer: Converts the results of physical simulation into acoustic signals. This layer needs to handle the conversion from low-frequency physical signals to high-frequency audio signals, including interpolation, filtering, and nonlinear processing.

Audio Synthesis Layer: Mixes and post-processes the signals from various sound sources to generate the final audio output. This layer operates at audio sampling frequencies (44.1kHz or 48kHz).

Parameter Control Layer: Provides external interfaces that allow real-time adjustment of engine parameters (RPM, load, configuration, etc.) and passes these parameters to the physical simulation layer.

3.2 Detailed Process of Physical Simulation#

Physical simulation is the core of the entire system, and its workflow can be broken down into the following key steps:

Step 1: Engine Geometric Modeling
The system first needs to establish the geometric model of the engine, including:

• Number, layout, and geometric dimensions of cylinders
• Geometric parameters of the crankshaft (stroke, connecting rod length, etc.)
• Geometric parameters of the valve mechanism (cam profile, valve size, etc.)
• Geometric parameters of the intake and exhaust systems

Step 2: Kinematic Calculations
Based on the crankshaft angle, calculate the position, velocity, and acceleration of each moving part:

• Piston position and motion speed
• Connecting rod swing angle and angular velocity
• Valve lift and opening/closing timing

Step 3: Combustion Process Modeling
Modeling the combustion process is the core difficulty of the entire simulation. We use a simplified phenomenological model, mainly considering the following factors:

• Ignition timing and combustion duration
• Combustion rate and pressure rise characteristics
• Combustion efficiency and incomplete combustion

Step 4: Multi-Cylinder Coordinated Simulation
For multi-cylinder engines, it is necessary to simultaneously simulate the states of all cylinders and consider their mutual influences:

• Combustion timing for each cylinder (firing order)
• Dynamic changes in intake manifold pressure
• Pressure wave propagation and interference in the exhaust system
• Torsional vibrations of the crankshaft system

3.3 Optimization Strategies for Real-Time Computation#

To meet the strict timing requirements of real-time audio synthesis, the system employs various optimization strategies:

Multi-Threaded Parallel Computation:

• Physical simulation thread: responsible for complex physical calculations
• Audio synthesis thread: responsible for high-frequency audio processing
• Parameter control thread: responsible for user input and parameter adjustments

Each thread communicates through lock-free data structures to avoid the overhead of thread synchronization.

Numerical Stability Optimization:

• Use numerically stable integration algorithms
• Employ appropriate time step control

4. Design and Implementation of Audio Synthesis Algorithms#

The physical simulation produces signals that describe the physical state of the engine, which need to be converted into final audio output through audio synthesis algorithms. This conversion process is a critical link in the entire system, directly affecting the final audio quality.

4.1 Conversion from Physical Signals to Acoustic Signals#

Acoustic Conversion of Pressure Signals:
According to acoustic theory, sound pressure is related to the rate of change of pressure. We time differentiate the cylinder pressure signals to obtain the pressure change rate, and then convert it to sound pressure signals through a transfer function. The key is to design an appropriate transfer function that retains the characteristic frequencies of the engine while suppressing high-frequency noise generated by numerical differentiation.

Modeling of Fluid Noise:
The airflow noise in the intake and exhaust systems needs to be modeled separately. We use empirical formulas based on turbulence theory to calculate the intensity and spectral characteristics of airflow noise, considering the influence of pipe geometry on sound propagation.

4.2 Spectral Shaping and Harmonic Processing#

Fundamental Frequency and Harmonic Structure:
The fundamental frequency of a four-stroke engine is half of the RPM (RPM/120Hz), but the actual engine sound contains rich harmonic components. The distribution and intensity of harmonics are determined by the number of cylinders, firing order, and combustion characteristics.

Nonlinear Harmonic Generation:
The sound of a real engine contains harmonic components generated by nonlinear effects. We use controllable nonlinear processing to simulate these effects, including harmonic distortion and intermodulation distortion.

5. Modeling Adaptation for Special Engine Technologies#

Modern automotive engines employ many advanced technologies to improve performance and efficiency, which significantly impact the acoustic characteristics of the engine. Our modeling system needs to adapt to these technologies.

5.1 Modeling of Turbocharging Systems#

Turbocharging technology significantly alters the acoustic characteristics of the engine, requiring specialized modeling methods:

Turbo Dynamics Modeling:
The core of the turbocharger is a high-speed rotating turbine, which can reach speeds of 100,000 to 200,000 RPM. The rotation of the turbine produces a unique high-frequency "whistle" sound, with the frequency of this sound directly related to the turbine speed. We have established a physical model for the turbine, considering the impact of turbine blade-induced changes in airflow conditions on sound.

Modeling of Blow-Off Valves and Wastegates:
Modern turbocharged engines are typically equipped with blow-off valves (BOV) and wastegates. The blow-off valve releases boost pressure when the throttle is closed, producing a characteristic "hiss" or "puff" sound. The wastegate controls the turbine speed, and its opening and closing also produce audible sound changes.

5.2 Adaptation of Variable Valve Timing Systems#

Variable valve timing technologies (such as Honda's VTEC, BMW's Valvetronic, Toyota's VVT-i, etc.) dynamically adjust valve timing characteristics during operation, significantly affecting engine sound:

Modeling of the VTEC System:
Honda's VTEC system is the most representative variable valve technology. At specific RPMs (usually 5000-6000RPM), the system switches to a high-performance cam profile, significantly altering intake volume and combustion characteristics. This switch manifests in sound as a noticeable "jump," making the engine sound sharper and more aggressive.

Our modeling approach uses piecewise processing: parameters of the low RPM cam are used before the VTEC switch, and parameters of the high RPM cam are used afterward. The transition process itself is handled with a smooth transition function to avoid abrupt changes in sound.

6. Future Development: Game Engine Integration and Industrialization Outlook#

6.1 Development Plan for Unreal Engine Plugin#

Currently, we are developing a professional audio plugin for Unreal Engine 5, aiming to seamlessly integrate the physical modeling engine sound system into modern game development workflows.

Technical Architecture Design:
The plugin is developed in native C++, fully utilizing the audio engine architecture of UE5. The core physical simulation module runs in an independent worker thread, with task scheduling managed through UE5's Task Graph system to ensure it does not impact the performance of the main game thread. The audio synthesis part is directly integrated into UE5's Audio Mixer, leveraging its powerful signal processing capabilities.

Blueprint Integration:
To facilitate use by game developers, the plugin exposes key engine parameters as editable properties in Blueprint. Developers can adjust engine type, displacement, cylinder count, compression ratio, and other parameters through a visual interface, with real-time sound effect previews. It also provides a rich set of preset configurations, covering various types from economical small-displacement engines to high-performance sports car engines.

Performance Optimization Strategies:
Considering the performance requirements of game applications, the plugin implements a multi-level LOD (Level of Detail) system. Based on the distance of the sound source from the player, its importance, and system performance load, the simulation accuracy is dynamically adjusted:

• High importance at close range: full-precision physical simulation
• Medium importance at mid-range: simplified physical model
• Low importance at far range: sample-based fallback mode

Spatial Audio Support:
The plugin supports UE5's spatial audio system, including 3D positioning, Doppler effects, and environmental acoustic processing. Engine sounds can automatically adjust audio characteristics based on the vehicle's position and motion state in 3D space.

Conclusion and Outlook#

Building on existing open-source projects, we have made a series of improvements and extensions to the system, particularly exploring real-time performance optimization, multi-cylinder coordinated modeling, and adaptation to special engine technologies. Although there is still some distance to a perfect solution, the technological development in this direction opens new possibilities for the field of audio synthesis.