Consideration of Natural Frequency Excitation in Water Pump and Fan Bracket Applications

Rich Oblizajek, P.E.
C&U Americas, LLC
Senior Manager
Engineering & Business Development


Water pump applications have been in existence for many years.  The predominant failure mode in many water pump applications is mechanical seal failure leading to coolant leakage.  In many instances, this can lead to coolant contamination of the bearing, causing lubrication failure of the bearing.  Because of this common failure mode, it is likely that other types of water pump bearing failures were not studied as much or understood in as much detail as they should have been.  Conventional wisdom seemed to be that water pump bearings often failed due to coolant intrusion, excessive loads, improper assembly, or even ‘bad’ bearings.

Even the historical testing of water pump bearings would not necessarily find the true root cause of some problems in application, because testing did not always duplicate the entire system with fan and clutch.  Full system testing is needed in order to identify that the systems might be experiencing extremely high unbalanced loads or natural frequency excitation.

Broken shafts are common evidence of these types of water pump (and fan bracket) system issues. Their primary cause is typically the result of excessive vibration and loading created by natural frequency excitations.

However, not all natural frequency excitations will result in shaft breakage. It is also possible that natural frequency excitations might result in significantly higher loads on the bearing that are not high enough to cause shaft breakage, but may result in other issues such as significant damage to the bearing raceways, cracking of the bearing housings, and hubs moving from their original position on the shaft.

More recently, an improved understanding of natural frequency excitations as an important factor in bearing and system failure in some water pump and fan bracket applications has lead to systems that are designed to avoid this situation and these types of failures.

The additional information that follows discusses the background behind this issue, how the loading conditions in a water pump or fan bracket application can be better understood, and what can be done to reduce exposure to or avoid this failure mode.

Why do Natural Frequency Excitation failures occur?

A typical water pump bearing is designed into an application using loading information based on hub loads from the belt and calculable loads from the fan and clutch based on typical or provided misalignments and eccentricities for the mounting of the fan and clutch to the hub.  Theses inputs also are used to support life calculations that indicate how the bearing should work in the application.

However, in applications where a fan and clutch are supported by the bearing, issues such as natural frequency excitation can occur and significantly increase the loads that might be experienced by the bearing beyond the original calculations. This can significantly reduce bearing life and in some cases even cause shaft breakage to occur.  In many new applications, major car manufacturers now take steps to confirm (or, if necessary, modify) the stiffness of the system before a new design is released, to ensure that the natural frequency of the system cannot be excited within the range of operating speeds seen in normal operation.

Excitation of the natural frequency (resonance) is only related to the pump or fan support system itself, not the engine.  The pump/fan support can be considered a system whose main structural component is the bearing shaft.  If the components are too far apart and/or too heavy, and the shaft diameter is too small, then the system natural frequency might be within the typical operating speed range of the system.  Therefore, when the system operates at that speed, the system can go into resonance.

Natural frequency excitation can also occur when a clutch or fan design is changed. Even if the weight and distance from the bearing remains the same, some difference in the system’s design characteristics can change the system’s natural frequency and cause significant reduction in bearing life and possibly shaft fractures.

What are the ‘normal’ loads on a water pump or fan bracket bearing? 

Mechanical water pumps are designed with a belt-driven impeller and a bearing to support the load from the belt.  However, some water pump bearings can also be used to support a fan/clutch assembly. The loads on the bearing from these assemblies are a result of the effects of:

  • mass, axial location and intrinsic imbalance of the clutch
  • mass, axial location and intrinsic imbalance of the fan
  • eccentricity between centerline of fan/clutch and centerline of bearing shaft, which would be a result of such things as offsets of centerline of mounting threads pulley from centerline of shaft or offset of centerline of mounting threads of clutch relative to CG of clutch
  • angular misalignment of centerline of fan/clutch and centerline of bearing shaft

Using the above information, expected life can be calculated using the equation F=mrɰ^2, where m is the mass, r is the offset of the mass from the centerline of the bearing (as a result of the eccentricities and angular misalignments) and ɰ is the speed of the shaft.  An increase of any eccentricity or angular misalignment could significantly increase the loads on the bearing from the fan and clutch.  Increases in any of these inputs would result in increased loads on the bearing, but they can all be calculated when the inputs are known.  These are the “normal” loads that are typically used to design a bearing into a new system.

What are the key contributing factors to Natural Frequency Excitation?

As described above with the equation F=mrɰ^2, as the rotating speed of the system is increased, the loads due to imbalances and misalignments of the fan and clutch should increase at a rate of the speed squared.  As long as these loads are within typical ranges for most such systems, these loads should not be high enough to cause shaft breakage (although could be high enough to cause significant reduction in bearing life).

However, if the natural frequency of the system is within the operating speed range of the system, the loads will increase dramatically when the system approaches this speed.  The key-contributing factor for natural frequency excitation is the stiffness of the system, which determines the natural frequency itself.  To avoid natural frequency excitation, the system natural frequency should be shifted higher so that the operating speed of the system will not reach this frequency.  To do this, the stiffness of the system must be increased.   This is typically achieved by increasing the primary component affecting system stiffness, the bearing shaft, or by reducing fan/clutch mass or moving the bearing closer to the fan/clutch assembly.

What if the system’s natural frequency cannot be changed? 

If the system stiffness can not be increased enough to shift the natural frequency above the operating speed range of the system, then other options to reduce the magnitude of the loads caused during natural frequency excitation must be taken.  Minimization of the angular and eccentric misalignments of the mating components can reduce the amplitude of the loads on the bearing.

What are other indications of a Natural Frequency Excitation issue?

A water pump designed with a mechanical fan can create imbalance and dramatically increase the load and cause the bearing to walk out of the housing. This is not a sure sign of a natural frequency excitation problem, but is an indication of that possibility and should be investigated further. When the system is in resonance, several problems can occur, including cracking of the housing, enlargement of the housing bore on the fan/clutch end, axial movement of the bearing outer ring out of the housing, axial movement of the pulley along the shaft, and breaking of the bearing shaft.  If you see any of these issues in your application, it is likely that you have a natural frequency excitation issue.   There are other possibilities for these issues.

For instance, extremely high unbalanced loads caused by very large misalignments (much higher than typically seen in OEM assemblies) could cause similar problems without a natural frequency excitation.   Also, shaft fracture could occur if an improper shaft heat treatment is used (such as using a through-hardened shaft instead of a case-hardened shaft).  A case-hardened shaft is required for any application supporting significant rotating loads from a fan and clutch, due to the higher bending stresses in this type of application.

In the history of Natural Frequency Excitation, are the issues recent or more frequent? 

Typically, but not always, in order to have enough load/stress to cause shaft fracture, a natural frequency has to be excited enough to cause the loads to be significantly higher than calculated.  Shaft fracture was a much more common failure mode in the aftermarket during the 1980s and 1990s and was likely due to various factors such as the higher number of mechanical fan applications, higher number of home-based repairs (resulting in potentially improper or poor mounting misalignments), more frequent use of extensions to move the fan further from the bearing, and the lack of understanding about this condition and the design options to avoid it.

In recent years, car manufacturers have become more aware of natural frequency excitation issues, and the incidence of these issues has actually reduced.  However, because of many new designs with mechanically driven fans and clutches, and larger clutches being introduced, the potential for these issues has actually increased recently and is a prominent consideration in many new designs.

How can Natural Frequency Excitation failure be distinguished from other failure types?

Natural frequency excitation can be characterized as a ‘low-cycle fatigue.’  Usually, when shaft breakage occurs, the clear indication of a fracture initiation site, as evidenced by the nearly parallel lines emanating from that location, suggest low-cycle fatigue as opposed to a pure brittle fracture. The natural frequency excitation significantly overloads the shaft and causes the bending fatigue to occur relatively quickly.

How can Natural Frequency Excitation be detected?  How do you determine the loads on the bearing, considering the amount of imbalance in the system?

The loads on each raceway that are caused by imbalance rotate with the shaft, so they add vectorially with the belt loads as the shaft rotates.  So, in other words, when the direction of the unbalanced load is in line with the belt load, they directly add together; when they are in opposite direction (180 degrees of rotation from when they were in line) they subtract from each other. All the other 358 degrees out of 360 degrees of rotation they add/subtract vectorially. The total load on each of the raceways, as a function of time, will look like a sinusoidal wave.

However, the loads cannot just be added vectorially to determine a ‘mean force’ because the belt load and imbalance loads act at different locations from the bearing.  The best way to calculate the loads/life for the bearing is to calculate the loads on each raceway resulting from each of the inputs (fan, belt, etc.), and then add the raceway loads, vectorially, to get the equivalent loads on each raceway from the various inputs.  Each raceway of the bearing must be treated as separate bearings.  The load on each raceway would be calculated from the belt and the raceway from the imbalance forces.  Then, both loads would be added vectorially to determine the ‘mean force’ for each raceway.

To determine if a natural frequency excitation exists, the complete water pump with fan and clutch could be tested to determine if the loads that will be seen at each speed within the operating speed range of the system would be higher or similar to what has been calculated. If you use a strain gage or accelerometer to measure the loads as a function of a gradual increase in operating speed throughout its operating range, you will observe a “hump” in the load versus speed curve if there is a natural frequency excitation within the operating speed range of the system.

A test can be conducted which not only identifies a natural frequency excitation issue, but also confirms the magnitudes of loads on the bearing as a result of other inputs in the system, as follows:

  • Assemble a complete water pump assembly with fan and clutch, using a strain-gaged housing or an accelerometer attached to the housing.
  • Determine the intrinsic imbalances of the actual fan and clutch used and align the offsets of their center of gravities in line with each other so that the imbalances are directly additive or that the angle difference between their centers of gravities is known so that the combined imbalance can be calculated.
  • Measure and/or apply a known angular and eccentric misalignment of fan and clutch relative to centerline of the shaft.
  • Apply known loads to the shaft in a static condition, to calibrate the results of the strain gage relative to different loads.
  • Apply a known belt load.
  • Calculate the loads expected for the above conditions as a function of speed.
  • Operate the pump through the full speed range of the engine and plot the strain gage or accelerometer results versus speed.
  • Compare the strain gage results to the calculated loads to confirm the accuracy of the expected/calculated loads as a function of speed.

Note: The above test should also be conducted for two or different misalignments in order to see the effect of misalignment on the results.

As a simpler approach, you can also eliminate steps 2 through 6 to look only for the potential existence of a natural frequency excitation.  Use a sensitive strain gage or accelerometer on the housing, as in step 1. Then, run the pump through the full range of operating speed, increasing very slowly, and see if the loads measured through the strain gage or accelerometer increase as expected as a function of speed increase (unbalanced loads are a function of the square of the speed), or whether there is a large increase at some particular speed. A much higher load than expected at some specific speed will indicate the existence of a natural frequency excitation.

It is advisable to stop quickly or pass through that speed to a different speed quickly, since operating too long at the natural frequency can cause significant damage, such as shaft breakage. Make sure to employ a strong safety guard around the equipment during the test for protection.

How to calculate the expected life of a bearing in a water pump system and understand the impact of unbalanced load on the life (assuming no natural frequency excitation)?

Here is a sample life calculation based on the following assumptions:

  • Bearing with 18mm shaft diameter, 35mm OD, and 35mm outer ring length
  • Belt location relative to front of bearing: -14.2mm Fan location relative to front of bearing: 92.85mm
  • Mass of Fan: 3.64 kg
  • Mass of Adapter: 0.42 kg
  • Intrinsic imbalance of Fan and Adapter: 0.45 kg-mm
  • Eccentricity of fan from centerline of bearing shaft: 0.15 mm
  • Duty cycle as provided by the manufacturer
  • Angular misalignment of fan from centerline of bearing shaft: 0.001 mm/mm

Based on the above assumptions, this bearing would have a calculated L10 life of 20,300 hours. To showcase the importance of the eccentricity and angular misalignment in these calculations, here are some additional calculations with different values:

As calculated above:

  • 0.15mm eccentricity, 0.001-mm/mm angular misalignment: 20,300 hours
  • 0.20mm eccentricity, 0.001 mm/mm angular misalignment: 13,300 hours
  • 0.25mm eccentricity, 0.001 mm/mm angular misalignment: 9,100 hours
  • 0.30mm eccentricity, 0.001 mm/mm angular misalignment: 6,500 hours
  • 0.25mm eccentricity, 0.002 mm/mm angular misalignment: 6,600 hours

The biggest potential issue is that loads could occur because of either inaccurate assumptions for eccentric or angular misalignments, or natural frequency excitations.  Confirming and improving the eccentric and angular misalignments will help improve life regardless of whether a natural frequency excitation exists.

What can be done in the WP design to decrease the probability of a Natural Frequency Excitation failure?   What are the possible solutions if Natural Frequency Excitation failures are occurring or suspected?

If natural frequency excitation has been determined as the issue in the application, the following solutions can help address the problem:

  • Ensure minimized angular and eccentric misalignments. The loads from the imbalance of the fan and clutch are calculated by F=mrɯ2, with r being the radial distance of the center of gravity of the fan/clutch relative to the centerline of the shaft. This r is a function of both the angular and eccentric misalignments, particularly at the clutch mounting face.  Reducing this r will reduce the unbalanced loads, and can affect the Natural Frequency Excitation of the system.  Even if there is a natural frequency excitation, minimizing these misalignments may reduce the stresses to levels to avoid significantly reduced bearing life or shaft fracture.
  • Change the natural frequency of the system. One way to do this is to change the mass of the imbalance. A higher mass not only adds to the unbalanced loads calculated above (which could be very significant) but also changes the natural frequency of the system. Reducing mass could shift the natural frequency of the system above the operating speed range of the system.
  • If it is determined that the natural frequency of the system is within the operating speed range of the system, even without instrumentation attached, then increasing the stiffness of the system may be required in order to shift the natural frequency out of this speed range. This can be done by increasing the shaft diameter. Unfortunately, this also typically requires a significant design change, since with a larger shaft, the rest of the bearing is also larger.

When resolving the potential for Natural Frequency Excitation, is it also helpful to increase the dynamic capacity of the bearing?

It is not necessary to increase bearing dynamic capacity to address the natural frequency excitation issue.  The increase in bearing size is typically accomplished only to increase the system stiffness by increasing the shaft diameter (and possibly widening the rolling element raceway locations).  In fact, one important point is to NOT attempt to solve a natural frequency excitation problem by only increasing dynamic capacity of the bearing.  For instance, simply using higher capacity rolling elements while keeping the system stiffness roughly the same, will result in only a marginal improvement in trying to address a major issue.  It is important to address the issue with a system solution.