Abstract:
Vibrations of rotary shafts, such as shafts of cutting tools used in high speed machining, are reduced by damping structures in holes in the shafts. The damping structures comprise fingers that are urged outwardly by centrifugal force due to rotation of the shafts and that slide relative to adjacent shaft surfaces due to shaft vibrations, so that vibrational energy is absorbed frictionally. Chatter, a self-excited vibration of a cutting tool, can be substantially reduced in this manner.

Description:
CROSS REFERENCE TO CO-PENDING APPLICATION  
       [0001]    This application claims the benefit of provisional Application No. 60/205,547 filed May 22, 2000, incorporated herein by reference. 
     
    
     
       BACKGROUND OF THE INVENTION  
         [0002]    This invention is concerned with damping vibrations of rotary shafts. The invention has particular utility in damping vibrations known as chatter, generated when a rotary cutting tool is applied to a workpiece, but is useful more generally in the damping of vibrations of rotary shafts in other environments, such as the shafts of turbines, for example.  
           [0003]    Chatter, a self-excited vibration of a cutter, such as a milling tool applied to a workpiece, is a well known phenomenon. Milling is characterized by a pattern of intermittent cutting forces as each tooth of a cutter enters and leaves a workpiece. The periodic nature of the cutting force gives rise to vibrations of the tool relative to the workpiece. Each tooth of the tool leaves a cut surface behind it. The exact location of each point on that surface relative to the nominal tooth position is dependent on the magnitude and phase of the tool in its vibration as it passes through the workpiece.  
           [0004]    In general, the tool&#39;s vibration will cause the surface left by the tool to have some “waviness”. If the following tooth is not in the same phase of its vibration as the previous tooth at the time it enters the workpiece, then the chip thickness it encounters will change as it passes through the cut and the wavy surface left by the previous tooth. This leads to a variation in the magnitude and direction of the cutting force, which changes the amplitude of vibration slightly. For some cutting conditions, this changing pattern of cutting force, and therefore chip thickness, magnifies in each cycle, leading to excessive vibration known as chatter. Chatter leads to poor surface finish and shortened tool life, and may even lead to damage of the machine employing the cutting tool.  
           [0005]    Avoidance of chatter is of particular concern in High Speed Machining (HSM), a process which is revolutionizing the manufacture of a number of products in the discrete part industry. Perhaps the easiest, and most common method for chatter avoidance is proper selection of spindle speed in HSM, to ensure desired phasing and stable cuts. This technique is known as “spindle speed regulation”. However, for most end milling operations, these stable spindle speeds occur at very high rpm. For example, if the most flexible natural frequency of an end mill is 1000 Hz, and the cutting tool has four cutting edges, then the most desirable spindle speed for chatter-free machining will be in the neighborhood of 15,000 rpm, depending on the amount of damping in the system. This speed is attainable with current generation spindles and will provide satisfactory results, provided the tool material gives adequate life at this speed. In general, for aluminum and other easy to machine materials, adequate tool life can be obtained at even much higher speeds.  
           [0006]    Methods other than spindle speed regulation can be used to increase stable cut depth, to maximize Material Removal Rate (MMR), and thus to maximize productivity in milling operations. One such method relies on changing the dynamic stiffness of the tool. Dynamic stiffness is defined as the product of stiffness and damping ratio. Increased dynamic stiffness, whether achieved through increased stiffness or increased damping, will allow for much deeper stable cuts at all spindle speeds.  
           [0007]    In general, if the dynamic stiffness of the most flexible mode of vibration of a tool can be increased by some multiple, the chatter-free depth of cut at any speed, and the resulting MMR, will increase by the same multiple. The stiffness is generally determined by the overall geometry (length, diameter, etc.) of a cutter body and by its material properties. To maximize stiffness of a cutting tool, machinists and tooling engineers tend to make use of the largest diameter and shortest tools which can create the necessary part features. However, for many machining operations, the need to produce deep pockets with small radii in the corners of a workpiece dictates the use of long, slender, and relatively flexible tools. It may not be possible to rely upon tool stiffness for chatter avoidance in these circumstances, but increasing damping will have the same effect as increasing the stiffness. In long, slender, and relatively flexible tools damping is typically very low, usually 1% or less.  
         BRIEF DESCRIPTION OF THE INVENTION  
         [0008]    The present invention achieves significantly increased damping of vibrations of rotary shafts, such as the shafts of milling cutters, by utilizing centrifugal force to create large frictional forces at an interface between sliding damping elements and adjacent surfaces.  
           [0009]    In one embodiment, an elongated damping structure is press fit into a hollow cylindrical rotary shaft. The damping structure comprises a cylindrical rod having a plurality of fingers formed by partially splitting the rod longitudinally from one end, so that the fingers are joined to each other at the opposite end of the rod. The free ends of the fingers enter the hollow shaft first. The damping structure rotates with the hollow shaft, and centrifugal force urges the fingers outwardly to increase the pressure between the fingers and inner surface portions of the hollow shaft. Bending vibrations of the hollow shaft cause longitudinal sliding movement of the fingers relative to adjacent inner surface portions of the shaft, dissipating energy frictionally and resulting in substantial damping of shaft vibrations. 
       
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0010]    The invention will be further described in conjunction with the accompanying drawings, which illustrate preferred and exemplary (best mode) embodiments, and wherein:  
         [0011]    [0011]FIG. 1 is a perspective view showing a hollow cylinder, vibrations of which are to be damped, along with a damper to be inserted in the cylinder;  
         [0012]    [0012]FIG. 2 is an end view showing the damper inserted in the cylinder;  
         [0013]    [0013]FIG. 3 is a perspective view of a milling machine;  
         [0014]    [0014]FIG. 4 is a perspective view of another embodiment of a damper in accordance with the invention;  
         [0015]    [0015]FIG. 5 is an end view of a hollow shaft with an inner surface configuration different from that shown in FIG. 1;  
         [0016]    [0016]FIG. 6 is an end view of a damper designed for use with the shaft shown in FIG. 5;  
         [0017]    [0017]FIG. 7 is a fragmentary sectional view showing a relationship of a finger of the damper of FIG. 6 and an internal recess in the shaft of FIG. 5;  
         [0018]    [0018]FIG. 8 is a diagrammatic view to explain the operation of the embodiment shown in FIGS.  5 - 7 ;  
         [0019]    [0019]FIG. 9 is a perspective view of another embodiment, in which a pair of dampers are inserted in a hollow shaft;  
         [0020]    [0020]FIG. 10 is a longitudinal cross-section of the same embodiment, with the dampers inserted in the shaft;  
         [0021]    [0021]FIG. 11 is a longitudinal sectional view showing a modification of the embodiment of FIGS. 9 and 10;  
         [0022]    [0022]FIG. 12 is a perspective view of another embodiment, employing concentric dampers; and  
         [0023]    [0023]FIGS. 13 and 14 are end views of further embodiments. 
     
    
     DETAILED DESCRIPTION OF THE INVENTION  
       [0024]    [0024]FIGS. 1 and 2 show an embodiment of the invention described earlier, in which it is desired to damp vibrations of a rotary shaft, such as a cylindrical shaft  10  of a cutting tool. Cutting flutes (not shown) can be ground into the outer surface of the shaft. A damper, or damping structure  12  comprises a cylindrical rod that is press fit into a cylindrical center hole  14  provided in the shaft. The rod is slit longitudinally along most of its length from one end  16  to provide a plurality of fingers  18  that are joined at the opposite end  20  of the rod. In the form shown in FIGS. 1 and 2, four fingers are provided by slitting along orthogonal axial planes, so that each finger has an arcuate outer surface that engages an opposing arcuate inner surface portion of the hollow shaft.  
         [0025]    The damping structure is anchored to the hollow shaft at the end  20  and rotates with the shaft. Centrifugal force causes the outer surface of the fingers  18  of the damping structure to press against adjacent inner surface portions of the hollow shaft with a force that can be a very large multiple of the weight of the fingers, creating large interface pressures. The neutral bending surfaces of the fingers are displaced outwardly from the neutral bending surface of the hollow shaft (which contains the axis of shaft rotation), and when the shaft bends, the axial strain experienced on the outer surfaces of the fingers is different from the axial strain experienced on the inner surface portions of the shaft, causing relative longitudinal sliding between the opposing surfaces. This relative sliding dissipates energy frictionally. The amount of energy dissipated depends on the frictional force between the opposing surfaces, which is dependent on the normal force between them and the amount of sliding. In the absence of rotation, there will be little, if any, normal force, and therefore little energy dissipation. However, during rotation, particularly at high speeds, the aforementioned large interface pressures result in very large frictional forces and substantial damping.  
         [0026]    Providing a central hole in a rotary shaft, will, of course, decrease stiffness of the shaft. However, the area moment of inertia for circular cross-sections, and thus the bending stiffness, is proportional to the 4 th  power of the diameter, so that the center portion of a cylindrical shaft contributes little to the overall stiffness, and the stiffness loss is minimal for holes of reasonable size. For example, if the diameter of the central hole is one-half the outer diameter of the shaft, the bending stiffness drops by only 7%. This stiffness loss can be easily compensated by the damping achieved in accordance with the invention, providing an overall increase in dynamic stiffness.  
         [0027]    The damping achieved by the invention may be termed “centrifugal damping”, because it uses centrifugal force to achieve the desired frictional damping. If one computes the centripetal acceleration experienced by a point on the surface of a tool rotating at typical HSM speeds, the result is quite surprising. For example, consider a 25 mm diameter tool rotating at 40,000 rpm, a typical top speed of commercial HS spindles. The centripetal acceleration experienced by a point on the surface of the tool amounts to over 22,000 g. Therefore, if a point mass were placed on the surface of this tool, it would need a centrifugal force in excess of 22,000 times its own weight to remain in place. Centrifugal damping utilizes such high centrifugal forces to achieve desired damping.  
         [0028]    An experiment to verify the centrifugal damping effect used the hollow shaft  10  and the damping structure  12  shown in FIGS. 1 and 2. The shaft  10  consisted of a mild steel cylinder, 125 mm long, with 25 mm outer diameter and 15 mm inner diameter. The damping structure  12  was a mild steel rod machined to have a press fit into the hollow shaft, prior to slitting the shaft from one end for 100 mm of the total Length, thereby forming four fingers  18 , with very little bending stiffness, that slid easily into the hollow shaft., The final solid 25 mm of the damping structure insert was then pressed into the shaft, and the assembly was inserted into a shrink-fit tool holder with the solid end of the damping structure inside the holder body. The holder was then mounted into the high-speed spindle on a five-axis machine.  
         [0029]    [0029]FIG. 3 shows a typical machine  22  with a cutting tool  10 ′ attached to a spindle  23  of the machine tool head  25 . The cutting tool shown has flutes on its outer surface, but in the aforesaid experiment flutes were unnecessary. In practice, various types of cutters or drills, for example, can be provided with a central through-hole or a blind hole as may be appropriate to receive a damping structure insert in accordance with the invention. It should be noted that a hollow shaft of a spindle itself may be provided with a damper in accordance with the invention.  
         [0030]    In the aforesaid experiment, transfer functions were measured at various spindle speeds, both with and without the centrifugal damper inserted. The shaft was excited with a hammer and the vibrational displacements were measured with a capacitance probe. In this manner, it is possible to measure the dynamic response of the shaft when it is rotating.  
         [0031]    With no damping structure, and the spindle not rotating, the hollow shaft exhibited a primary bending mode with a natural frequency of approximately 1827 Hz and a damping ratio of approximately 0.018. These parameters remained essentially constant during the experiment. When the damping structure was press-fit into the hollow shaft and the spindle was stationary, the primary bending mode had a frequency of 1707 Hz, and a damping ratio of approximately 0.027. The natural frequency of the assembly decreased due to the added mass of the insert. The slightly higher damping ratio is believed to be due to some friction between the fingers and the inner surface of the hollow shaft, since the outer diameter of the damping structure was slightly larger than the inner diameter of the shaft.  
         [0032]    When the assembly was rotating at 5000 rpm, the measured damping ratio of this mode appeared to increase to approximately 0.056, an increase of 107%. Thus, the dynamic stiffness was increased by an equal amount, meaning that a stable cut depth would also be increased by this amount if the shaft  10  were used to provide a cutting tool such as an end mill. Further tests have shown that as the spindle speed increased from 5000 rpm to 30,000 rpm, the damping approximately doubled.  
         [0033]    The invention is not limited to damping structures with four fingers. The principles of the invention can be applied, for example, to embodiments with more or fewer fingers, to embodiments with multiple damping structure inserts, to embodiments with hollow damping structures, and to embodiments with individual shaft openings that receive individual fingers.  
         [0034]    [0034]FIG. 4 shows an embodiment with a multi-fingered hollow damping structure  24 , in this case with eight fingers  26 , constructed as an insert in a hollow shaft, such as the shaft  10  of FIG. 1.  
         [0035]    [0035]FIG. 5 is an end view of a hollow shaft  28  in an embodiment in which a central hole has a plurality of circumferentially spaced peripheral recesses  30  that are wedge-shaped in cross-section for receiving mating wedge-shaped fingers  32  of a damping structure  34  shown in the end view of FIG. 6. The recesses become narrower radially outward from the rotational axis of the shaft. Wedging action increases the pressure at the interfaces of the fingers and their recesses. FIG. 7 is a close-up view of a single damping finger  32  inserted in a single recess  30 . FIG. 8 is a diagram illustrating that the interface pressure increases as the wedge angle decreases.  
         [0036]    [0036]FIGS. 9 and 10 show an embodiment in which two damping structures  24  are inserted into a hollow cylindrical rotary shaft  36  from opposite ends. The shaft, which may be part of a turbine, for example, is supported on bearings  38  adjacent to the respective ends. As shown in FIG. 10, with the damping structures fully inserted, the free ends of the fingers  26  of the respective damping structures face each other. FIG. 11 illustrates a modification in which fingers  27  of respective damping structures  29  are interleaved.  
         [0037]    [0037]FIG. 12 shows an embodiment employing a pair of concentric damping structures  24 ,  24 ′ which are inserted in a hollow, cylindrical rotary shaft  10 . The fingers of the inner damping structure  24 ′ slide on the fingers of the outer damping structure  24  in response to bending vibrations of the shaft. More than two concentric dampers can be employed, and the dampers can be inserted in opposite ends of a shaft, like FIG. 9, and still fit inside each other.  
         [0038]    In some circumstances, it may be appropriate to provide a damping structure that is integral with a hollow shaft. FIGS. 13 and 14 show possible internal configurations of shafts  40  and  42 , in which fingers  44  and  46  are supported by thin flexures  48  and  50 . Wire EDM may be used to cut thin axial slots along the length of a shaft from an initial central hole, to form the fingers and flexures. Centrifugal force will push the fingers outwardly into contact with adjacent internal surface portions of the shaft.  
         [0039]    The dampers employed in the invention are preferably formed of a high density material, such as steel or carbide, in particular a material having good friction characteristics, since it is desired to provide a large coefficient of friction at the interface where damping fingers slide on adjacent inner surface portions of a shaft. Interfaces at which relative sliding movement occurs can be treated appropriately to increase the coefficient of friction. For example, a high friction material can be coated, plated, or otherwise applied to the outer surfaces of sliding fingers and/or the adjacent inner surface portions of a shaft.  
         [0040]    While preferred embodiments of the invention have been shown and described, it will be apparent to those skilled in the art that modifications can be made without departing from the principles and spirit of the invention, the scope of which is set forth in the accompanying claims.