Critical Speed Equation (Nc)
There are two main methods used to calculate critical speed—the Rayleigh–Ritz method and Dunkerley's method. Both calculate an approximation of the first natural frequency of vibration, which is assumed to be nearly equal to the critical speed of rotation. In general, the Rayleigh–Ritz equation overestimates and the Dunkerley equation underestimates the natural frequency. The equation illustrated below is the Rayleigh–Ritz method applied to a shaft. The static deflection expresses the relationship between rigidity of the shaft and inertial forces; it includes all the loads applied to the shaft when placed horizontally. However, the relationship is valid no matter what the orientation of the shaft is.
- Critical speed,
where:
- g = gravitational acceleration (≈ 9.81 m⁄s²)
- δst = vertical static deflection of the shaft when placed horizontally
- Nc is in rpm
Critical speed depends upon the magnitude and location of the shaft unbalance, the length of the shaft, its diameter, and the kind of bearing support. Good practice suggests that the maximum operating speed should not exceed 75% of the critical speed.
Read more about this topic: Critical Speed
Famous quotes containing the words critical, speed and/or equation:
“If our entertainment culture seems debased and unsatisfying, the hope is that our children will create something of greater worth. But it is as if we expect them to create out of nothing, like God, for the encouragement of creativity is in the popular mind, opposed to instruction. There is little sense that creativity must grow out of tradition, even when it is critical of that tradition, and children are scarcely being given the materials on which their creativity could work”
—C. John Sommerville (20th century)
“Spig Wead: I’ve been thinking what a heel I’ve been about you and about my own kids. I don’t know, when I do something, I go all the way. Living. Gambling. Flying. I tap myself out. I guess that’s the way I want it to be. Maybe even the way I am.
Minne Wead: Star-spangled Spig. Damn the martinis, full speed ahead and don’t give up the ship.”
—Frank Fenton, William Wister Haines, co-scenarist, and John Ford. Spig Wead (John Wayne)
“Jail sentences have many functions, but one is surely to send a message about what our society abhors and what it values. This week, the equation was twofold: female infidelity twice as bad as male abuse, the life of a woman half as valuable as that of a man. The killing of the woman taken in adultery has a long history and survives today in many cultures. One of those is our own.”
—Anna Quindlen (b. 1952)