Vibration & Modal Analysis of Extruder

A manufacturer of industrial extruders was losing confidence in one of their units. At higher operating speeds, excessive vibration was shaking the 30-foot assembly — motor, gearbox, barrel assembly, vacuum stuffers, and all the support structure beneath them. They hired an inspection company to take vibration measurements and run spectral analysis. The inspection company found a resonance frequency at approximately 75 Hz driving the excessive response. They also showed that reducing screw speed brought the vibrations down significantly. What they couldn’t do was identify the structural source of the resonance — or tell the manufacturer what to change. The manufacturer subsequently tasked O’Donnell Consulting Engineers, Inc. (OCEI) to perform a vibration analysis of the extruder assembly and make design recommendations. To investigate, OCEI performed the following tasks:

• Created a finite element model of the extruder and support structure
• Performed a modal analysis to determine the natural frequencies and identify the mode shape describing the experimentally determined motion associated with 75 Hertz response
• Provided recommendations on modifying the extruder/support structure to shift the natural frequency of interest
• Performed a subsequent modal analysis to confirm the viability of the recommendations

The majority of the components were assumed to be carbon steel. Since the purpose of the vibration analysis was to determine the structure’s natural frequencies, the pertinent material properties are Modulus of Elasticity and density. The Modulus of Elasticity was assumed as 29 x 10⁶ psi. The density of the components was initially set at 0.283 lb/in³ and adjusted for each component to account for the weight of items that were not explicitly modeled. The extruder assembly consists of a motor, gearbox, barrel assembly, and two vacuum stuffers. These components are bolted to a frame that is approximately 4 feet wide by 2-1/2 feet tall and 30 feet long. The frame is fabricated from predominantly 1-inch thick carbon steel. The base of the frame supports a lube oil piping system and a cooling water system. There are also multiple cabinets under the extruder motor and an electrical cabinet on top of the frame near the extruder motor.

FEA Model

The finite element model of the extruder assembly consisted of approximately 55,000 nodes and 50,000 elements. The model was constructed using the following assumptions:

• Several components were assumed to act as rigid objects and therefore modeled as lumped masses. These include: the motor, gearbox, vacuum stuffers, lube system heat exchanger, lube system motor and cooling water heat exchanger
• The weight and stiffness of the lube oil and cooling water piping are considered insignificant compared to the overall weight and stiffness of the structure. As such, these piping systems were not modeled.
• The lube oil tank, water tank, and various cabinets were modeled with shell elements. Their contents were not modeled. The densities of these items were, however, adjusted to account for the weight of their contents.
• The support frame and barrel assembly supports were modeled with shell elements.
• Solid elements were used in modeling the barrel assembly.

Modal Analysis

A modal analysis of the extruder assembly and support structure was performed. Natural frequencies in the range of 0 to 100 Hz were sought with particular interest at 75 Hz. There were over 200 natural modes of vibration identified in the 0 to 100 Hertz frequency range. The majority of these modes were associated with vibration of the sheet metal cabinet and tank walls. Of the natural frequencies pertaining to the motion of the frame support structure, two were identified near the frequency of interest, 75 Hz. The first of the two closely spaced modes occurs at 75.7 Hz and corresponds to a vertical bending motion of the barrel assembly and portion of the frame. The second mode occurs at 75.9 Hz and corresponds to a torsional motion of the barrel assembly and twisting of the frame. These two modes correlate reasonably well with the sensor data from the inspection company with respect to the location of the sensors and the corresponding direction of significant vibration.

Design Recommendations

Subsequently, several recommendations were made to stiffen the extruder frame to shift the natural frequencies of the system away from the problematic operating speeds. These modifications included:

• The addition of two leveling supports under the frame
• Adding two barrel assembly supports
• Adding ¼” x 2” x 2” angles as cross-bracing at the end of the extruder frame

A modal analysis of the extruder and frame was conducted for the recommended modifications. The results determined:

• One of the two significant modes identified near 75 Hertz was a mode corresponding to the bending of the extruder frame at 75.7 Hz. This bending mode did not show up in the frequency range of 0 to 100 Hertz for the modified extruder frame. Thus, the modifications of the frame have caused this mode to occur above 100 Hertz. Therefore, this mode of vibration should no longer exist at the excitation frequency of 75 Hertz.
• The predicted natural frequency of the second mode, the torsional or twisting mode, was shown to move from 75.9 Hertz to 80.7 Hertz.

---

O’Donnell Consulting Engineers Performs Vibration & Modal Analysis – and Develops Solutions for Clients in Industries including Manufacturing, Petrochemical and Energy