A MOTOR PRIMER - PART 5 Copyright Material IEEE Paper No. PCIC 2005-9 Bryan Oakes Gary Donner Senior Member, IEEE Fellow, IEEE Rockwell Automation Shell Oil Products US 101 Reliance Road 2101 E Pacific Coast Hwy Kings Mountain, NC 28086 Wilmington, CA 90748 USA USA [email protected] [email protected] Steve Evon Wayne Paschall Senior Member, IEEE Member, IEEE Rockwell Automation Rockwell Automation 6040 Ponders Ct. 101 Reliance Road Greenville, SC 29615 Kings Mountain, NC 28086 USA USA [email protected] [email protected] Abstract - In recent years much has been written II. WHAT PURPOSE DOES PERFORMING A about motors concerning efficiencies, vibration TORSIONAL ANALYSIS SERVE AND WHEN IS and resonance conditions as they relate to the IT REQUIRED? WHAT OCCURS DURING A American Petroleum Institutes (API) Standard TORSIONAL RESONANT CONDITION? 541 and motor diagnostics. Most of these papers and articles assume that the reader has Torsional vibration is an oscillatory twisting of significant knowledge of motor theory and the shaft. A motor by design applies a torsional operation. However, this assumption is overly force to the driven equipment and the driven optimistic, considering that only a few colleges equipment applies an equal and opposite force teach motor theory today and that application back to the motor. The shaft system deflects in experience at motor user locations has been torsion or twists away from the free position. At reduced in recent years. free vibration, and at its natural frequencies, the twist is free to unwind, twisting back to the free Index Terms – AC Induction Motors, position and, if undamped, twist an equal amount Efficiency, Torsional, Lateral Critical Speed, in the opposite direction. A system having a Vibration, Shaft Probes, Unbalance Response, natural frequency equal to a driving frequency is and Residual Unbalance. in a state of resonance. This torsional oscillation loads and unloads the shaft system and at a I. INTRODUCTION resonant condition, the shaft can actually be loaded in each direction. These torsional This paper is the fifth in a series where the vibrations produce shear stresses on the shaft authors discuss “Frequently asked Questions” by leading to crack development at discontinuities working engineers in industry. The authors will with the end result being a shaft failure that present motor theory and application information occurs due to fatigue. Identification of a failure with a reference list that will help working due to torsional resonance exists within the engineers increase their understanding and failure itself. Cracks develop on the shaft surface knowledge of motors. This series also serves as 45° to the shaft axis as shown in Figure 1. a reference for those who apply and specify Unlike lateral vibration that can be detected motors. This paper focuses on torsional and with the use of proximity probes or lateral resonance analysis, motor efficiencies and accelerometers, torsional vibration can exist with the effects of vibration on motor life. The first four considerable amplitudes and be undetectable papers in this series can be found in the IEEE without appropriate detection equipment until a Conference Records and Transactions. failure occurs. The normal torsional excitation frequencies are 1 times mechanical and electrical up to 6 times running speed. 1 natural frequency. That would then provide an opportunity for high alternating torques. Determining the system’s torsional resonance frequency during the motor design stage requires an exchange of information from the manufacturer and driven equipment provider. Motor manufacturers should provide the following information: · Torsional stiffness of the rotating assembly · Shaft detail drawing for fatigue analysis · Rotating assembly weight · Shaft material attributes · Inertia Figure 1. Shaft torsional failure Driven equipment manufacturers should provide the following information to the motor The system’s torsional resonance locations supplier: must avoid the excitation forcing frequencies. Figure 2 shows a torsional natural frequency map · Torque angle effort curve for pulsating loads that identifies natural frequencies in respect to of driven equipment at each load condition the multiples of running speed that are of · Harmonic torque analysis of system concern. These maps identify the locations of · System torsional resonance analysis. First torsional natural frequencies, the corresponding four resonant frequencies and mode shapes. speeds these natural frequencies cross and the · Maximum mean and cyclic motor shaft required block out ranges needed to avoid forces. resonance at these frequencies. An exchange of this information will provide the fundamental elements for determining the torsional resonant frequencies and forced responses of the system in the design stages eliminating possible problems in the field. If torsional issues are suspected in an existing application, field-testing will be necessary. One method involves using a strain gage network. This approach evaluates the actual transmitted and dynamic torque in a shaft. Strain levels should be measured at various load conditions and for starting and acceleration conditions. Other methods involve using encoders or a strobe light. Shifting a torsional resonance frequency may Figure 2. Torsional natural frequency map require changes to the coupling mass and stiffness, and special shaft diameters. A complete drive train system analysis must be performed to Sources for this type of vibration exist during assure a torsional resonance will not be excited acceleration in induction motors that exhibit and forced response stresses are within material torque oscillations at line frequency. Another strength limits. source is the driven machine itself. Reciprocating It’s important that system responsibility be compressors, chippers, and crushers generate clearly defined during the bidding process. steady-state torque pulsation at various Typically, the driven equipment manufacturer accepts system responsibility but this becomes frequencies and can reach destructive less clear when packagers are involved or when magnitudes even without resonance. Inverters components are purchased directly by an end also generate oscillating motor torques at user. frequencies dependent upon speed. Some types Synchronous motors also are a potential of inverters give rise to large fifth and seventh source of very significant transient torques. harmonic currents and thereby sixth harmonic Discussion of this subject is very complex and torque. Depending on the operating speed, it exceeds the scope of this paper. Users of large synchronous motors are encouraged to research might be possible to operate close to a torsional this subject before selecting synchronous motors. 2 III. WHAT PURPOSE DOES PERFORMING A requires knowing the mass of the system and the LATERAL CRITICAL SPEED ANALYSIS shaft -spring constant. SERVE AND WHEN IS IT REQUIRED? CAN 1/2 I PERFORM THIS ANALYSIS MYSELF? wc = (k / m) WHAT SOFTWARE IS AVAILABLE? Where: Any body that is free to vibrate has natural k = spring constant (lb/in) frequencies of oscillation. The amplitude of m = mass (lbs-sec2/in) oscillation will depend on its mass, length, and other mechanical properties. Its natural The Rayleigh-Ritz Equation applies to a shaft frequencies depend on its density and stiffness, carrying several concentrated masses. diameter and length. The body stops vibrating j j 2 1/2 because it is performing work and thus losing wc = (g 1 SWn dn / 1 SWn d n) energy. When a body is subjected to a vibrating source of energy that has the same frequency as Where: the natural frequency of the body, it will start to th oscillate in sympathy with the external source. Wn = weight of n mass (lbs) th This phenomenon is called resonance. dn = static deflection at the n mass (in) When the rotating assembly operates at one j = total number of masses of these natural frequencies, it deflects and goes g = gravitational constant (in/sec2) into a state of resonance. This condition is known as a lateral critical speed. All rotating assemblies The Dunkerley Equation is another have lateral critical speeds but they will not pose approximation for the first lateral critical speed of a problem unless a critical speed coincides with a a multimass system. forcing function. 2 2 2 2 1/w c = (1 / w 1) + (1 / w 2) + (1 / w 3) + … Forcing functions, which are to be avoided, include the following: Where: · Running speed and twice running speed · Line frequency and twice line frequency wc = first critical speed of multi-mass system · Driven equipment frequencies w1 = critical speed with only one mass · Drive harmonic frequencies w2 = critical speed with only mass two w3 = critical speed with only mass three, etc When a machine passes through a lateral critical speed, the rotating assembly is known as a These calculation methods approximate flexible shaft design. A rigid shaft design is one lateral critical speed. A more accurate analysis where the lateral critical speed is above the using software requires the following information: operating speed. Knowing the location of a lateral critical speed is essential to successful motor a. Support (base, frame, bearing-housing, and operation. Whether the rotating assembly is rigid bearing) stiffness, mass, and damping or flexible the first lateral critical speed must have characteristics. a separation margin of al least 15% from operating b. Bearing lubricant-film stiffness