Vibration and Forces - Torsional vibration
Page 6
1. Engine vibration and critical speed
2. Force and Moments in slow speed diesel engine
3. Vibration damper and detuner
4. Static and dynamic loading and balancing in engine
5. Primary and secondary forces and couple
6. Torsional vibration
7. Axial vibration details
8. Purifier vibration reasons
9. Important element in ship vibration
2. Force and Moments in slow speed diesel engine
3. Vibration damper and detuner
4. Static and dynamic loading and balancing in engine
5. Primary and secondary forces and couple
6. Torsional vibration
7. Axial vibration details
8. Purifier vibration reasons
9. Important element in ship vibration
Torsional vibration
Phenomena of torsional vibration:
Torsional stressing being a result of the forces applied by the connecting rod to the bottom end, varies in magnitude with both the changes in cylinder pressure and the angle of thrust applied by the connecting rod during the power stroke.
The compression stroke, which acts as a resistance to turning, further compounds this variation torque. If the shaft is not adequately dimensioned, then fatigue failure through cyclic torsional stressing could occur.
Torsional vibration indicates a situation where an applied turning moment causes the shaft to 'wind up' (twisting along its length) and then unwind again as the stiffness of the shaft re-asserts itself over the applied torque. There is a limit beyond which any shaft (and indeed any component) subject to a cyclic stress will fatigue and fail. For this reason, torsional stressing beyond the designed value should be avoided.
Torsional Vibration and Critical Speeds:
Vibration in the shafting is due, primarily, to periodic variations in the torque of the engine. In the Diesel engine, these variations are of considerable magnitude. For instance, in a six-cylinder, four-cycle engine the torque will vary, three times per revolution, from approximately —20% to +220% of its mean value. This negative torque means that, three times per revolution, the flywheel and other driven machinery must actually drive the engine. With a greater number of cylinders, or in two-cycle engines, the torque variation is less, but this does not help us appreciably so far as critical speeds are concerned.
If the engine shaft and all attached shafting were absolutely rigid in torsion, the only effect of this torque variation would be to cause a slight periodic speed variation in engine and shafting. One of the purposes of a flywheel is to reduce this speed variation to a minimum value.
Actually, the shafting is not a rigid body, and under the influence of the torque variation, the shafting does not accelerate as a whole, but is thrown into a state of vibration. The entire shafting system, which comprises the engine shaft and pistons, flywheel, and all driven shafting and attached masses, can be considered as a torsionally elastic system.
This elastic system has one or more modes of normal free vibration. These modes of normal vibration are distinguished by the number of nodes associated with each, nodes being points which, with respect to any particular vibration, have no motion. We may have 1 noded normal vibration, 2 noded, 3 noded, etc. In general, only the first two or three forms are of practical importance. Associated with each of these normal modes of vibration is a natural frequency; the greater the number of nodes the higher the natural frequency.
Associated with each of these normal modes of vibration is a normal elastic curve, which is a curve whose ordinates for various points of the shaft line represent the relative amplitude of vibration of those points.
It should be noted that this vibration is an angular, twisting vibration of the shaft and altogether different from the transverse vibration between bearings sometimes known as "Whirling." Also that the torsional vibration problem is not related in any way to the balance of the engine.
When the shaft is turning at such a speed that the frequency of the impulses due to the torque variation coincides with the natural frequency of the shaft system, it is at a critical speed. Under these conditions the amplitude of vibration will build up to an extent determined by certain damping factors. The stresses due to this vibration may or may not be sufficiently great to fracture the shaft. But, any elastic system may thus be set into violent vibration by applying a series of impulses at properly timed intervals.
A critical speed is distinguished by two quantities:
(1) the number of nodes of its normal mode of vibration;
(2) its order number. We may speak thus of a one-nodded critical speed of 6th order, 2-noded critical of order, etc.
And, since there are several modes of vibration and each of these has critical speeds of various orders, there may be, a large number of critical speeds.
Fortunately, often many of these will be of such small amplitude that they can be disregarded.
Also, the critical speeds depend, not on the engine alone, but on the engine and all machinery driven by it. For that reason, it is quite impossible to speak of an engine as having certain critical speeds unless full details of all machinery driven by it are known. Whether an engine does or does not develop serious torsional vibration on the test-bed is no criterion of what its performance will be when driving its actual application on ships.
The probability of a critical speed existing in any given installation may be said to be proportional to the range of speeds over which the engine is to be operated. If the engine is to be operated at a single speed or over a very narrow range of speeds, it is probable that there will be no critical speeds in the range. If the engine is to operate over a wide range of speeds, it is probable that there will be one or more critical speeds within that range.
The critical speeds of any given installation can be calculated, before construction, within a few revolutions of accuracy.
An elastic shaft system of a multi-cylinder diesel engine is acted upon by a periodically varying torque which causes a harmonic displacement of masses in the plane of rotation. This is termed as torsional vibration. Let us consider a cylindrical resilient shaft of length "C, rigidly held at one end and carries a mass M at its free end. If now a torque is applied and released the shaft will be set to vibration. This is free or natural vibration. The elastic shaft is twisted, on releasing the torque the shaft tends to return to its original position of rest. Thus a vibration is set up twisting and untwisting the shaft.
Now consider a two-rotor system mounted at the end of an elastic shaft and supported on two friction-less bearings which are to take no part in the vibration of the shaft. If the shafts are twisted in opposite directions and then released, the masses at two ends will be set to vibrations but in opposite directions. The masses will be twisted and untwisted alternately in opposite directions. The mode of vibration is such that there exists a section which has no vibration. It is called a node. The instantaneous direction of oscillation at one side of the node must be opposite to that of other. At the nodal point the vibration changes phase. It is the section of maximum stress and not disturbed by vibration. A multi-mass rotor may have two, three or more nodes. The greater the number of nodes, shorter is the period of vibration. The elastic line shows the angular deflection of the rotor along the shaft.
The torsional vibration arises in the shaft system of a multi-cylinder diesel engine, extended to intermediate shaft and line of shafting up to propeller is due to engine firing impulses which twists the shaft with a varying torque on each crank throw exciting torsional vibration in the system with different frequencies.
If the shaft rotates at such a speed that the power stroke of a cylinder synchronizes with one of its natural frequencies, it is said to be at a critical state of vibration. At the critical speed the torsional vibration twists the shaft more and that causes extra stresses which may be dangerous for the shaft if such state of vibration continues.
From practical point of view torsional vibration of a multi-cylinder engines can be analyzed by substituting an equivalent rotor whose inertia is represented by inertia effects of reciprocating and rotating masses of each cylinder and similar equivalent rotor takes place for flywheel and propeller. Usually the journals and cranks between two cylinder are also included in equivalent shaft for sufficient stiffness. A system with large number of rotors will have as many modes of vibration as the number of rotors. Vibrations with large number of nodes are of no importance in so far as torsional stresses are concerned and it is usually sufficient to examine I and 2, may be extended to 3 nodes. Elastic lines are conceived with the rotor swinging to its extremity by a torque exerted on the shaft. When vibrating freely the only torque which act on the system is inertia torque; and at any instant the algebraic sum of all must be zero, hence the elastic curves are made by considering the swing of all rotors in their extreme positions.
The torsional vibration characteristics investigated is an equivalent system of a 5 cylinder diesel engine with line of shafting including flywheel and propeller is shown in an elastic curve with one node in the vibration system (mode I).
The maximum angular displacement of the shaft at the propeller end is large and the stress caused by the angle of twist of the shaft is unacceptable. The system can be modified by changing its natural frequency if the stiffness of the shaft is increased by inducting a larger diameter shaft, adding mass on flywheel or adjusting the firing order. The modified elastic curve shows a vibration system with two nodes (mode - 2 elastic line). The maximum angle of twist in any part of the shaft system is within acceptable limit.
The calculated level of torsional vibration assumes balance of power and peak pressure in cylinders and maintain the designed balance of all masses, rotating and reciprocating.
Torsional stressing being a result of the forces applied by the connecting rod to the bottom end, varies in magnitude with both the changes in cylinder pressure and the angle of thrust applied by the connecting rod during the power stroke.
The compression stroke, which acts as a resistance to turning, further compounds this variation torque. If the shaft is not adequately dimensioned, then fatigue failure through cyclic torsional stressing could occur.
Torsional vibration indicates a situation where an applied turning moment causes the shaft to 'wind up' (twisting along its length) and then unwind again as the stiffness of the shaft re-asserts itself over the applied torque. There is a limit beyond which any shaft (and indeed any component) subject to a cyclic stress will fatigue and fail. For this reason, torsional stressing beyond the designed value should be avoided.
Torsional Vibration and Critical Speeds:
Vibration in the shafting is due, primarily, to periodic variations in the torque of the engine. In the Diesel engine, these variations are of considerable magnitude. For instance, in a six-cylinder, four-cycle engine the torque will vary, three times per revolution, from approximately —20% to +220% of its mean value. This negative torque means that, three times per revolution, the flywheel and other driven machinery must actually drive the engine. With a greater number of cylinders, or in two-cycle engines, the torque variation is less, but this does not help us appreciably so far as critical speeds are concerned.
If the engine shaft and all attached shafting were absolutely rigid in torsion, the only effect of this torque variation would be to cause a slight periodic speed variation in engine and shafting. One of the purposes of a flywheel is to reduce this speed variation to a minimum value.
Actually, the shafting is not a rigid body, and under the influence of the torque variation, the shafting does not accelerate as a whole, but is thrown into a state of vibration. The entire shafting system, which comprises the engine shaft and pistons, flywheel, and all driven shafting and attached masses, can be considered as a torsionally elastic system.
This elastic system has one or more modes of normal free vibration. These modes of normal vibration are distinguished by the number of nodes associated with each, nodes being points which, with respect to any particular vibration, have no motion. We may have 1 noded normal vibration, 2 noded, 3 noded, etc. In general, only the first two or three forms are of practical importance. Associated with each of these normal modes of vibration is a natural frequency; the greater the number of nodes the higher the natural frequency.
Associated with each of these normal modes of vibration is a normal elastic curve, which is a curve whose ordinates for various points of the shaft line represent the relative amplitude of vibration of those points.
It should be noted that this vibration is an angular, twisting vibration of the shaft and altogether different from the transverse vibration between bearings sometimes known as "Whirling." Also that the torsional vibration problem is not related in any way to the balance of the engine.
When the shaft is turning at such a speed that the frequency of the impulses due to the torque variation coincides with the natural frequency of the shaft system, it is at a critical speed. Under these conditions the amplitude of vibration will build up to an extent determined by certain damping factors. The stresses due to this vibration may or may not be sufficiently great to fracture the shaft. But, any elastic system may thus be set into violent vibration by applying a series of impulses at properly timed intervals.
A critical speed is distinguished by two quantities:
(1) the number of nodes of its normal mode of vibration;
(2) its order number. We may speak thus of a one-nodded critical speed of 6th order, 2-noded critical of order, etc.
And, since there are several modes of vibration and each of these has critical speeds of various orders, there may be, a large number of critical speeds.
Fortunately, often many of these will be of such small amplitude that they can be disregarded.
Also, the critical speeds depend, not on the engine alone, but on the engine and all machinery driven by it. For that reason, it is quite impossible to speak of an engine as having certain critical speeds unless full details of all machinery driven by it are known. Whether an engine does or does not develop serious torsional vibration on the test-bed is no criterion of what its performance will be when driving its actual application on ships.
The probability of a critical speed existing in any given installation may be said to be proportional to the range of speeds over which the engine is to be operated. If the engine is to be operated at a single speed or over a very narrow range of speeds, it is probable that there will be no critical speeds in the range. If the engine is to operate over a wide range of speeds, it is probable that there will be one or more critical speeds within that range.
The critical speeds of any given installation can be calculated, before construction, within a few revolutions of accuracy.
An elastic shaft system of a multi-cylinder diesel engine is acted upon by a periodically varying torque which causes a harmonic displacement of masses in the plane of rotation. This is termed as torsional vibration. Let us consider a cylindrical resilient shaft of length "C, rigidly held at one end and carries a mass M at its free end. If now a torque is applied and released the shaft will be set to vibration. This is free or natural vibration. The elastic shaft is twisted, on releasing the torque the shaft tends to return to its original position of rest. Thus a vibration is set up twisting and untwisting the shaft.
Now consider a two-rotor system mounted at the end of an elastic shaft and supported on two friction-less bearings which are to take no part in the vibration of the shaft. If the shafts are twisted in opposite directions and then released, the masses at two ends will be set to vibrations but in opposite directions. The masses will be twisted and untwisted alternately in opposite directions. The mode of vibration is such that there exists a section which has no vibration. It is called a node. The instantaneous direction of oscillation at one side of the node must be opposite to that of other. At the nodal point the vibration changes phase. It is the section of maximum stress and not disturbed by vibration. A multi-mass rotor may have two, three or more nodes. The greater the number of nodes, shorter is the period of vibration. The elastic line shows the angular deflection of the rotor along the shaft.
The torsional vibration arises in the shaft system of a multi-cylinder diesel engine, extended to intermediate shaft and line of shafting up to propeller is due to engine firing impulses which twists the shaft with a varying torque on each crank throw exciting torsional vibration in the system with different frequencies.
If the shaft rotates at such a speed that the power stroke of a cylinder synchronizes with one of its natural frequencies, it is said to be at a critical state of vibration. At the critical speed the torsional vibration twists the shaft more and that causes extra stresses which may be dangerous for the shaft if such state of vibration continues.
From practical point of view torsional vibration of a multi-cylinder engines can be analyzed by substituting an equivalent rotor whose inertia is represented by inertia effects of reciprocating and rotating masses of each cylinder and similar equivalent rotor takes place for flywheel and propeller. Usually the journals and cranks between two cylinder are also included in equivalent shaft for sufficient stiffness. A system with large number of rotors will have as many modes of vibration as the number of rotors. Vibrations with large number of nodes are of no importance in so far as torsional stresses are concerned and it is usually sufficient to examine I and 2, may be extended to 3 nodes. Elastic lines are conceived with the rotor swinging to its extremity by a torque exerted on the shaft. When vibrating freely the only torque which act on the system is inertia torque; and at any instant the algebraic sum of all must be zero, hence the elastic curves are made by considering the swing of all rotors in their extreme positions.
The torsional vibration characteristics investigated is an equivalent system of a 5 cylinder diesel engine with line of shafting including flywheel and propeller is shown in an elastic curve with one node in the vibration system (mode I).
The maximum angular displacement of the shaft at the propeller end is large and the stress caused by the angle of twist of the shaft is unacceptable. The system can be modified by changing its natural frequency if the stiffness of the shaft is increased by inducting a larger diameter shaft, adding mass on flywheel or adjusting the firing order. The modified elastic curve shows a vibration system with two nodes (mode - 2 elastic line). The maximum angle of twist in any part of the shaft system is within acceptable limit.
The calculated level of torsional vibration assumes balance of power and peak pressure in cylinders and maintain the designed balance of all masses, rotating and reciprocating.
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