Off-highway machine mounting systems, especially the cab mounting system, significantly affect the operator comfort in the cab by providing enough damping to the harsh inputs for a good ride, and isolating the structure-borne forces from traveling into the cab, which can cause structure-borne noise (SBN) issues.
A mounting system includes the isolation component and the adjacent mounting structures that work like two springs in series to provide isolation. Both components experience the same load and deflect inversely proportional to their relative stiffness. To properly isolate the vibrations, it is expected that the cab isolators do most of the deflection and isolation; however, the mounting-system isolation performance also relies on the stiffness of the structures to which the mount is attached, and they should be treated as a system when considering isolation performance or capability, according to experts from Caterpillar Inc. If the mounting structure is not optimized or stiff enough, then the mounting system will not perform no matter how well the isolation component is designed.
In the automotive world, it is generally required to have the mounting structure be 10-20 times stiffer than the isolator itself. For off-highway machines, the isolators are much stiffer due to other requirements like loads and durability, and hence require stiffer mounting structures.
Cat engineers set out to identify how the mounting structure’s stiffness affects the mounting-system isolation performance, and why one wants to design the mounting structures to be at least 10 times stiffer than the isolator stiffness.
Mounting system isolation metric: transmissibility
The concept of vibration isolation can be illustrated by considering the one degree of freedom (1-DOF) system; the mounting system will isolate the vibration forces from the engine to the machine frame or from the machine frame to the cab.
In either case, transmissibility can be used as a measure of the reduction of the transmitted force or vibration through the mounts. In the first case, transmissibility is the ratio of the force amplitude of the frame to the force amplitude of the engine; in the second case, it can be defined by the ratio of the vibration amplitude of the cab to the vibration amplitude of the frame.
With the definition of transmissibility, one should do one's best to approach the lowest possible transmissibility for better mounting system isolation performance. The problem is that a mounting system will not isolate force or vibration over the entire frequency range, which is the transmissibility curve with different damping coefficients. The mounting system actually amplifies the force or vibration amplitudes in the lower frequency.
There are a few ways to look at the transmissibility; one is to describe it in terms of mobility, another is to look at it in terms of vibration.
In the mobility approach, the mounting system transmissibility is defined as the force ratio at the interface point with and without mount isolation. In the vibration transfer approach, transmissibility is defined as the ratio of vibration amplitude after and before the mounting system. An example of an off-highway cab support features a mounting system with four rubber mounts.
To look at the effect of the mounting structure stiffness, Cat engineers modeled the cab mounting system in two simplified ways: 1-DOF system and 3-DOF system.
1-DOF mounting system
In a simplified 1-DOF system model of the mounting system, the mass is concentrated on the frame and cab side, the masses of the isolator and mounting brackets are neglected, but the stiffness of the brackets is considered. It was found that the transmissibility is higher when the mounting structure stiffness is low; once the mounting structure stiffness is 10 times higher than that of the isolator, the change of the transmissibility over the change of the structural stiffness is small.
Illustrated in a few transmissibility curves due to different mounting-structure and isolator stiffness ratios, the transmissibility between stiffness ratios above 5 is really small in the isolation range above 100 Hz, but it is considerable around 20 Hz at the resonance peak, which suggests that the structural stiffness’ effect on the mount transmissibility is greater for the first system resonance peak, but not for higher frequencies.
This is due to the simplification of the mounting system to 1-DOF. In the 1-DOF mounting system, the mounting structure stiffness is considered as part of the mounting stiffness, but the mounting structure masses are omitted. To address this problem further, a 3-DOF mount system model with bracket mass was considered.
3-DOF mounting system
The simplified 3-DOF mounting system considers both receiver and source side mounting bracket masses. Based on the equations of motion, the transmissibility of the isolator itself as well as the system including the brackets was calculated in MathWorks’ Matlab.
The system transmissibility trends due to the stiffness change of the frame or cab bracket were examined. Since they are in series with the isolator, the effects are similar. The resonance peak frequency shifts with the bracket stiffness due to its effect on the overall system stiffness, and the transmissibility varies with it as well. Generally speaking, after the brackets are five times stiffer than the mount, the transmissibility change becomes slow; when the brackets are 10 times stiffer, the effect on the transmissibility is stable and does not change much even if the brackets are a lot stiffer.
The second natural frequency zone is due to the source and receiver mounting bracket stiffness. Even though the transmissibility seems low in that region compared with the first natural frequency zone, it could cause machine isolation issues that are hard to deal with.
For slices from the 3D plots, only a few stiffness ratios between the receiver and source brackets to the isolator were selected to show the trends of the transmissibility due to the mounting bracket stiffness change.
To match the analysis closer to realistic cases, the frame and cab brackets were assumed to be the same stiffness as the isolator, five times stiffer than the isolator, as well as 10 times stiffer than the isolator. It is apparent that when both the frame and cab bracket are at the same stiffness level of the isolator, the mounting system will have problems isolating at around 100 Hz, which is close to typical major engine excitation frequencies. When the brackets get stiffer, the resonance frequency is then shifted to a higher frequency. Specifically, when the ratios of the structure stiffness is five times more than that of the isolator, the resonance is shifted to above 200 Hz, which could still be around some major engine orders and cause SBN if the excitation is high. But when this ratio is 10 or more, the resonance frequency is shifted to above 300 Hz where no major structural-borne excitations exist in most cases.
As it is shown, the receiver and the source brackets have the same effect on the first peak of the transmissibility since they are in series in the overall mounting stiffness look, but they have different effects on the secondary natural frequency depending on where they are in the link. The source stiffness apparently affects the system more than the receiver stiffness, which indicates it is important to have rigid enough machine frame mounting brackets.
Note that the transmissibility is calculated based on a set of stiffness and damping values that are not relevant to a specific isolator; they were only used in this model for illustration purposes.
Looking at the mounting system transmissibility, it’s seen how important the mounting brackets are to the mounting system isolation. As the isolator is supposed to be the component deflecting the most when the mounting system is loaded dynamically, the bracket stiffness affects the isolator component’s transmissibility more than the overall system transmissibility. The mounting bracket stiffness has less effect on the isolator performance when it is 10 times stiffer than the isolator.
The isolator is not isolating when the brackets are not stiff enough. From the view of just the isolator component, its isolation effectiveness varies greatly with the mounting bracket stiffness. When the bracket is five times stiffer than the isolator, the resonance is driven to above 200 Hz where there could still be some major engine order excitations, but when the bracket is 10 times stiffer than the mount, the resonance is shifted above 300 Hz, which is well above the major structure-borne excitations for off-highway machines.
A real mounting system case study confirmed these results.
This article is based on SAE International technical paper 2015-01-2350 written by Jiantie Zhen and Scott Fredrickson of Caterpillar Inc., in conjunction with the SAE 2015 Noise and Vibration Conference & Exhibition.Continue reading »