BASICS OF HEAVY DUTY DIESEL NVH November 7, 2006 Ed Green Roush Industries, Inc. 734-779-7421, firstname.lastname@example.org
Course Outline • Introduction (8:00 AM - 8:15 AM) • Roush Industries • Ed Green • Course objectives • Pre-Quiz II. Fundamentals of noise and vibration (N&V) (8:15 AM – 11:30 AM) • Time and frequency domain analysis (8:15 AM – 8:45 AM) • The single degree of freedom system (SDOF) (8:45 AM – 9:30 AM) • Transmissibility and isolation (10:00 AM – 10:45 AM) • The source/path/receiver model (10:45 AM – 11:00 AM) • Summary (11:00 AM – 11:05 AM) • Discussion (11:05 AM – 11:30 AM) III. Vibration (12:30 PM – 3:00 PM) • Sensitivity to vibration (12:30 PM – 12:45 PM) • Forced vs resonant vibration (12:45 PM – 12:50 PM) • Rotating machinery vibration, orders, and critical speed (12:50 PM – 1:00 PM) • Vehicle driveline issues (1:00 PM – 2:00 PM) • Summary (2:30 PM – 2:35 PM) • Discussion (2:35 PM – 3:00 PM) IV. Sound and sound quality (3:00 PM – 3:30 PM) • Decibels and A-weighting (3:00 PM – 3:05 PM) • Beating, fluctuation, roughness, loudness, sharpness, and knock (3:05 PM – 3:20 PM) • Passby noise procedure and stationary noise requirement (3:20 PM – 3:30 PM) V. N&V features of DDC engines (3:30 PM – 3:45 PM) • Engine mounting system • Isolated oil pan • Isolated rocker cover • Crankshaft damper • Lined bellows exhaust manifold VI. N&V sensors (3:45 PM – 4:00 PM) • Accelerometers • Microphones • Rotational speed transducers • Transducer calibration • Quiz and Review (4:00-4:30)
I. Introduction • Roush Industries • Detroit based automotive engineering service company. • Associated with famous Roush NASCAR Racing Teams. • 2200 employees total. • 45 employees dedicated to noise and vibration engineering and products. • www.roushind.com
Station Class Lightning Arrestor I. Introduction • Ed Green • Ph.D. from Purdue University • 1983-1984, earthquake certification of lightning arrestors • 1986-1990, modeling of ultrasonic sound waves for NRC, ultrasonic inspection • 1994-present, automotive N&V at Roush • Vehicle N&V engineering • Noise-control-material engineering • Vibration dampers • Intake and exhaust systems • Passby noise
I. Introduction • Course Objectives • Give tools and training to improve efficiency of N&V issue field response • Provide an introduction to N&V concepts • Teach “language” of N&V • Not to make experts
II. Fundamentals of Noise and Vibration (N&V) • Time and frequency domain analysis • The single degree of freedom system (SDOF) • Transmissibility and isolation • The source/path/receiver model • Summary • Discussion
II.A. Time and Frequency Domain Analysis • Microphones and accelerometers produce time domain signals • The Fast Fourier Transform (FFT) is a technique used for conversion to the frequency domain (for display by spectrum analyzers like the MTS4100)
II.A. Time and Frequency Domain Analysis • With the FFT: • Any time domain signal can be approximated by a summation of sinusoids • A unique set of sinusoids is defined by magnitude, phase, and frequency (MTS4100 displays only magnitude vs frequency) • The magnitude vs frequency is called the “Spectrum” • Based on the frequency range, the MTS automatically filters the data and sets the sample rate.
II.A. Time and Frequency Domain Analysis • Animation of FFT applied to a square wave.
II.A. Time and Frequency Domain Analysis • Animation of FFT applied to idle noise signal from a Series 60 engine. Click to play sound
II.A. Time and Frequency Domain Analysis About the Fast Fourier Transform – The Fourier Transform is a mathematical function that finds the best least squares fit of a function to a set of basis functions based on the sine and cosine functions. The Fourier Transform is named for the French Mathematician and Physicist, Jean Baptiste Joseph (1768-1830). The Fourier Transform (http://mathworld.wolfram.com/FourierTransform.html) is used to find the spectral terms of a closed form expression (such as, y(t) = cos(at2+bt+c)). The Discrete Fourier Transform (DFT) (http://mathworld.wolfram.com/DiscreteFourierTransform.html) is used to calculate the spectral terms of a digitized signal. The Fast Fourier Transform (FFT) (http://mathworld.wolfram.com/FastFourierTransform.html) is a specialized implementation of the DFT that requires that the set of digitized data have a radix-two length (i.e. 512, 1024, 2048, etc.). The FFT is much faster than the DFT, and the FFT is by far the most common implementation of the Fourier Transform. The FFT was first published by Cooley and Tukey (J.W. Cooley and O.W. Tukey, “An Algorithm for the Machine Calculation of Complex Fourier Series,” Math. Comput. 19, 297-301, 1965).
Digitized Signal Example of Aliasing II.A. Time and Frequency Domain Analysis FFT Signal Processing Issues - For the task at hand (using the MTS 4100 to diagnose N&V field issues), an advanced knowledge of the FFT is not necessary, but some participants may be interested. When signals are digitized, issues arise. These are aliasing, leakage, and quantization error. Aliasing – The first step in calculating the FFT is to digitize the signal as shown in the figure. The signal is sampled at intervals of Dt. The sample frequency is defined as 1/Dt. The signal is digiitized by the A/D (analog to digital) circuit of the MTS 4100. If a signal entered the A/D circuit that had a frequency much faster than the sample frequency as shown in the figure, the digiitzed signal would have a lower frequency than the actual frequency as shown. This is called aliasing because a line appears in the spectrum that is not at the true frequency. To prevent aliasing, the sample frequency must be at least two times faster than the signal frequency. Put another way, the “Nyquist frequency” (equal to half the sample frequency) must be greater than the signal frequency. To prevent aliasing, powerful, analog, low-pass filters called “anti-aliasing filters” or “brick-wall filters,” are applied to the analog signal before the A/D circuit. Anti-aliasing is automatically performed by the MTS 4100. Note that anti-aliasing filters must be analog filters and that aliased data cannot be repaired.
II.A. Time and Frequency Domain Analysis FFT Signal Processing Issues – Cont. When a set of digitized samples of length 2n is used to calculate the FFT, it is implicit in the operation that the pattern represented in the set repeats through out the data (i.e. it is periodic) as shown in the upper group of plots in the figure. However, usually the pattern is not periodic as shown in the lower group of plots in the figure. Thus, the assumed input for the FFT is different from the actual input. The assumed input for the FFT is the sine wave with transients added at the beginning and end of the data “window.” The transients cause artifacts in the spectrum called “leakage.” In the figure, the leakage is spectral content at frequencies other than the signal frequency. Often leakage is in the form of spectral “sidebands.” To prevent leakage, a “window function” is applied to the data so that the windowed input is periodic. This eliminates the sidebands as shown in the figure.. A “Hanning Window” like that shown in the figure is automatically applied to the data by the MTS 4100 to eliminate leakage.
II.A. Time and Frequency Domain Analysis FFT Signal Processing Issues – Cont. When the signal is digitized, the value at a sample time is assigned the closest available digital value as shown in the figure. This digital “rounding off” is called quantization error. The most obvious effect of quantization error is the limitation of the “resolution” or “dynamic range” of the instrument. The “dynamic range” is the difference between the strongest measurable signal (without overload) and the weakest measurable signal. As shown, for a 4-bit A/D values are available from 0 to 15. The “dynamic range” or “resolution” of a 4-bit A/D is 20Log10(15) = 24 dB. Similarly, the dynamic ranges of 8-bit, 12-bit, 16-bit, and 24-bit A/Ds are 48 dB, 72 dB, 96dB, and, 144 dB, respectively. To maximize its dynamic range, the MTS 4100 is set for input signals typical of vehicle acceleration and microphone measurements; however, the MTS 4100 does not allow the inputs to be automatically ranged for getter dynamic range.
Setup II.B. The Single Degree of Freedom System (SDOF) • Demo Description – An elastic cord is driven by a sine wave signal at its first four natural frequencies. A strobe is used to show the mode shapes. • This demonstration shows that the motion of an elastic structure is made up of specific shapes (called mode shapes or eigenshapes) associated with specific frequencies (called natural frequencies or eigenvalues). • The demonstration also shows that a strobe can be used to determine the natural frequency and mode shapes of structures undergoing relatively large displacements. • This same behavior could be shown on a truck frame, steering wheel, or seat while the truck is under operation.
Second Mode Setup First Mode Third Mode II.B. The Single Degree of Freedom System (SDOF)
II.B. The Single Degree of Freedom System (SDOF) • Many of the characteristics of a vibrating system can be examined using the SDOF System consisting of a mass, spring, and damper. The model is also known as the mass/spring/damper model. • The SDOF System model can be used to understand the behavior of engine mounts, cab mounts, steering columns, frames, and other important dynamic systems of a truck. • Even though all dynamic systems of trucks have multiple degrees of freedom, the performance of each mode is represented by the SDOF.
II.B. The Single Degree of Freedom System (SDOF) Why study the SDOF? – True SDOF systems are rare. For example, a truck engine on flexible engine mounts will have six different rigid-body natural frequencies. As we saw in the previous demonstration with the elastic cord, the behavior of multiple DOF systems and continuous systems is the sum of an infinite number of modes. The mathematical process of describing the response of a complex dynamic system as the sum of modes is called modal superposition. Modal superposition shows that the behavior of the structure for each natural frequency and mode shape is described by the behavior of the SDOF system. Associated with each mode is a modal mass, modal stiffness, and modal damping; but these properties will be different from the global mass, stiffness, and damping.
II.B. The Single Degree of Freedom System (SDOF) • The frequency domain transfer function (output displacement normalized by input force as a function of frequency) is: • X(w) and F(w) are the complex amplitudes of the response displacement and the input force, respectively. The variable “w” is the frequency in radians/second, and “j” is the square root of minus one. A Note Regarding Equations – Equations are used throughout this presentation to show that the conclusions stated are strongly supported by well established theory and that the conclusions are not opinions. An understanding of the equations is not required to develop a strong understanding of vibratory systems, but some participants may feel more comfortable with the material after examining the equations.
II.B. The Single Degree of Freedom System (SDOF) • The animation below shows the behavior of a SDOF system with m=1000 kg, fn=10 Hz, and 10% damping:
II.B. The Single Degree of Freedom System (SDOF) • At low frequency (stiffness controlled region): • Near the natural frequency (damping controlled region): • At high frequency (mass controlled region):
II.B. The Single Degree of Freedom System (SDOF) • At low frequency, the response of a forced resonant system is a function of stiffness. • Near the natural frequency, the response is very strong and is a function of damping. • At high frequency, the response weakens and is a function of mass. For example, this would be the desirable operating condition of truck engine mounts, etc. The natural frequency would be below the engine firing frequency.
Demonstration Setup Electric Motor with Imbalance Springs Base II.B. The Single Degree of Freedom System (SDOF) • Demo Description – To simulate an engine on mounts an electric motor is suspended from elastic cords. A tap test and the MTS 4100 was previously used to determine the natural frequencies. The motor is operated discrete speeds and the peak-hold spectrum is observed using the MTS 4100. • As the motor speed passes through the natural frequencies of the dynamic system, the response increases significantly as seen on the plot. • This behavior is similar to what would be seen in an operating engine except that the engine excites more frequencies than the rotational speed. These additional engine “orders” are discussed later in the presentation.
II.B. The Single Degree of Freedom System (SDOF) • Demo screen shot from MTS 4100. • Resonances at low speed (frequency). • Response due to centifugal force at high speed proportional to speed squared.
I m k k c c II.B. The Single Degree of Freedom System (SDOF) • SDOF Systems can represent torsional resonances also. • Mass (kg), stiffness (N/m), and damping (N*s/m) are analogous to moment of inertia (kg*m2), rotational stiffness (N*m), and rotational damping (N*m*s). Linear System Torsional System
II.B. The Single Degree of Freedom System (SDOF) • The animation shows the resonance of a shaft system in a hybrid powerplant as it passes through a torsional resonance.
II.C. Transmissibility and Isolation • Many of the characteristics of an isolated mass (e.g. an engine on rubber mounts) can be examined using a slight variant of the previous SDOF System:
II.C. Transmissibility and Isolation • The transmissibility (mass response normalized by base motion as a function of frequency) is: • Lower transmissibility is better. • Isolation is the reciprocal of transmissibility. • Higher isolation is better. An understanding of the equations is not required to develop a strong understanding of vibratory systems.
II.C. Transmissibility and Isolation • At low frequency: • Near the natural frequency: • At high frequency:
II.C. Transmissibility and Isolation • At low frequency, the mass moves in phase with the base, and there is no isolation. • Near the natural frequency, the transmissibility is greater than one (gain rather than isolation). The gain is controlled by the ratio of the damping squared to the product of the mass and the stiffness (the damping ratio squared). • At high frequency, the transmissibility is less than one, and the gain is controlled by the ratio of damping to mass. • Overall, the goal of an effective isolation system is to have the natural frequency lower than the excitation frequency. Damping is good to have near the natural frequency, but decreases isolation at higher frequencies.
II.C. Transmissibility and Isolation • When motion of the engine mounts causes motion at the frame-side attachments, vibration energy is transmitted into the truck chassis. • To minimize this effect for automobiles, the static stiffness of the frame-side attachments is made relatively large (10 times). • For heavy trucks, this is not possible because the mounts are much stiffer and the frame is not relatively stiff (maybe 2 times). • A secondary isolation system (cab mounts) is necessary to keep vibration at a reasonable level. • Field experience will establish what are good values for engine and cab mount transmissibility.
Sources Paths Receiver II.D. The Source/Path/Receiver Model • Engine • Wind • Tire/Road • Exhaust • Intake • Driveline • Axle • Traffic • HVAC • Airborne Paths • Structure-Borne Paths • SPL at Front/Rear Seat Ear Positions • Vibration at Floor, Pedals, Steering Wheel, and Seat
Sources Paths Receiver II.D. The Source/Path/Receiver Model • All truck vibration issues will be due to engine, driveline, or tire orders. • This indicates that the engine (etc.) is the source of the vibration, but not necessarily the root cause because the path may be inadequate. • Inadequate paths include bad engine mounts, cab mounts, and exhaust mounts. • Inadequate paths can also include strong (or multiple) resonances of the truck structure.
Sources Paths Receiver II.D. The Source/Path/Receiver Model A Case Study – Several years ago Roush worked on a medium duty truck that had unacceptable vibration at a particular frequency. It was found that the truck had four major subsystems with that same natural frequency including: (1) the back panel of the cab, (2) the second acoustical mode of the cab, (3) the exhaust system, and (4) the clutch system. Presumably, the same natural frequency had been used as a minimum design target for the subsystems. The natural frequency of these subsystems was excited by the first strong torsional “order” of the engine. In this case, the unacceptable vibration was excited by the engine, but the engine was not the root cause of the vibration issue. There was nothing wrong with the design of the cab, the exhaust system, or the clutch system. The issue was the NVH design integration. This is an example of the path being the root cause of the issue without any specific part in the path being the cause. When designing vehicles, many-but-not-all vehicle developers check the modal alignment of the vehicle. A chart is made of all the natural frequencies of all the major subsystems of the vehicle. When natural frequencies align, the design is checked and usually changed.
II.D. The Source/Path/Receiver Model • For trucks without N&V issues, low frequency noise is dominated by structural paths and high frequency noise is dominated by airborne paths.
II.E. Summary • The magnitude of sound or vibration vs frequency is called the spectrum and it is calculated using the FFT (Fast Fourier Transform). • For a resonant SDOF (Single Degree of Freedom) system: • Low frequency is stiffness controlled. • Near the natural frequency is damping controlled. • High frequency is mass controlled.
II.E. Summary • Transmissibility is the reciprocal of isolation. • Lower transmissibility is better. • For the modified SDOF model transmissibility: • Low frequency, transmissibility is approximately one. • Near the natural frequency, transmissibility is higher than one and controlled by the damping ratio squared (c2/km). • High frequency, transmissibility is less than one and controlled by damping and mass (c/m). • Frame flexibility reduces the effectiveness of engine mounts.
II.E. Summary • The source/path/receiver model shows that the root cause of a N&V issue may be the path rather than the source. • Paths may be mounts or structural resonances. • Low frequency noise is normally dominated by structural paths, and high frequency noise is normally dominated by airborne paths.
II.F. Discussion • What should the natural frequency of a truck steering column be and why? Typically steering columns (including all attachments and the steering wheel) have relatively little damping (approximately 1 %). Thus, it is important that the natural frequency is not in a frequency range where engine vibration is strong. This would be most easily achieved by making the natural frequency very low (e.g. 10 Hz. This low frequency would require that the steering column be mounted relatively softly, potentially compromising steering feel and control. Also, at low frequency, excitation from the road (bumps, dips, and potholes) is strong. The steering column is usually tuned to have a natural frequency just above idle “firing frequency” because this is a condition where the engine is not typically operated continuously. For example, the firing frequency at idle for a Series 60 engine at 600 rpm is 30 Hz (= 600 revs/min * 3 fires/rev ÷ 60 sec/min). The steering column could be designed to have a natural frequency of 36 Hz which would correspond to the firing frequency at 720 rpm.
II.F. Discussion • Steering wheel vibration in a truck is excessive at the engine firing order. Name two reasons why excessive engine vibration may not be the root cause. Hint – source/path/receiver model. The response of the steering wheel is the product of the input forcing function (vibration from the engine source) and the vibration transfer function. If the engine vibration (source) is within normal limits, the transfer function (path) of the steering wheel is too large at the engine firing frequency. (1) The natural frequency of the steering column might be lower (and closer to a “significant engine-vibration-order”) than intended due to loose fasteners or a poor fit at the attachment points. (2) The steering wheel is mounted to the cab, so deficient cab mounts would contribute to excessive steering wheel vibration. In this case, vibration levels would also be higher than normal in other parts of the cab. Likewise, deficient engine mounts would contribute to excessive steering wheel vibration with higher than normal vibration levels in other parts of the truck.
II.F. Discussion • An off-road truck manufacturer increased the stiffness of the engine mounts to increase durability. Vibration at idle is significantly worse. Name two reasons why. Hint – transmissibility. Normally engine mounts are designed so that the rigid-body natural frequencies of the engine/mount system are lower than the engine firing frequency at idle. This is a fairly low frequency (less than 30 Hz at 600 rpm idle). Thus, the excursion of the mounts under the influence of road inputs can be significant. This negatively impacts the durability of the mounts and can also lead to perceivable “after-shake” of the engine. (1) Vibration at idle is worse because the engine mounts were made stiffer, and this moved the rigid-body natural frequencies closer to the idle frequency. Also, the stiffer mounts would make the ratio of mount stiffness to frame stiffness worse. Engine mounts can be tuned to “decouple” the modes of the engine. This means that the “roll mode” of the engine is not associated with engine bounce, pitch, etc. Likewise, the pitch mode is not associated with engine roll, bounce, and pitch; and so on. (2) Vibration at idle is worse because changing the mount rates increased the coupling of rigid-body modes of the engine/mount system.
III. Vibration • Sensitivity to vibration • Forced versus resonant vibration • Rotating machinery vibration, orders, and critical speed • Vehicle driveline issues • Summary • Discussion
III.A. Sensitivity to Vibration • Human sensitivity to vibration depends on a large number of factors including the part of the body, body position, the nature of the vibration (shock or continuous), and direction of vibration. • A sampling of vibration sensitivity data is presented.