Construction and Restoration Blog : Bearing Edges and Their Effects on Drum Head Vibration
Few areas of drum construction effect the overall sound of a drum as much as the bearing edge, i.e. the area of contact between the drum shell and the drum head. If a drum head is imagined as a collection of strings, each running across the diameter of a shell and rotating about the shell so as to eventually cover the entire surface, then the bearing edge is the endpoints of each of those strings. These endpoints have a great deal to contribute to how each string vibrates, how each periodic wave propagates through that string, and what dampening factor can naturally be applied to each periodic wave. In other words, when you strike a drum head, it vibrates. The bearing edges contribute most to how that vibration eventually dampens to the point of stopping and how the energy placed in the head translates to the shell where it is dissipates as sound or resonance. There are three basic bearing edge profiles we will discuss here. We are going to take some liberties and make some generalizations to simplify the discussion, however the underlying theory is sound without loss of generality. For our discussion, we are going to examine a fully rounded edge, a sharp edge, and a flat edge.
Flat Bearing Edges:
Beginning with a flat edge, or a completely squared-off shell, we can see from the diagram below that at rest, a drum head is completely contacting the entire thickness of the shell. This gives us the largest surface area of the head dampened by the drum shell, an area that does not change when the drum head is struck and deflected. Within this group of bearing edge profiles, we can include round-over profiles that are not true radii and feature a flattened "top" of the round over.
Flat Bearing Edges:
Beginning with a flat edge, or a completely squared-off shell, we can see from the diagram below that at rest, a drum head is completely contacting the entire thickness of the shell. This gives us the largest surface area of the head dampened by the drum shell, an area that does not change when the drum head is struck and deflected. Within this group of bearing edge profiles, we can include round-over profiles that are not true radii and feature a flattened "top" of the round over.
With this type of profile, the inward deflection of the head is restricted must begin at the inner edge of the flat bearing edge, however since the initial outward deflection is free to move from the outside edge of the shell, contact area is decreased. This cycle continues between increasing and decreasing contact area until the vibration ceases. This cycle adds significantly to the natural dampening of the head, and as such the vibrations end fairly quickly. Interestingly, this dampening of the head is also periodic, with the maximum dampening occurring while the head is vibrating towards the center of the shell, and the minimum dampening occurring when the head is vibrating away from the center of the shell. This adds short bursts of alternating harmonics to the overall complex sound of the head.
Full Round Over Bearing Edges:
Next, lets consider full round over bearing edges. These edges feature a true radius over the entire thickness of the shell, with no discernable flattened section. For these to function as expected, the radius must be cut to half the thickness of the shell both along the inside and outside edges.
Next, lets consider full round over bearing edges. These edges feature a true radius over the entire thickness of the shell, with no discernable flattened section. For these to function as expected, the radius must be cut to half the thickness of the shell both along the inside and outside edges.
With this profile, minimal contact between the shell and the head occurs while the head is at rest. Once struck, the head deflects towards the center of the shell, and exponentially more contact occurs. This increase in shell to head contact increases the dampening factor and thus muffles the overtones and overall volume of the tone. As the head deflects periodically away from the center of the shell, this dampening is first reduced to its original nominal state, then again maximal as the contact area alternates between the inside and outside of the shell. We can consider this alternating between minimum and maximum dampening as occurring twice as often as with a flat edge.
Sharp Bearing Edges:
Last, we will consider bearing edges with a sharp bevel, or a defined vertex between the inner and outer edges. These include most modern edges no matter the angle - 45 degrees, 30 degrees, 22.5 degrees, etc. Lets examine the motion of the head over these edges before explaining why the angle of the bevel has no effect on the motion or sound.
At rest, the head is making minimal contact with the shell over the sharp vertex of the edge. As the head is struck and deflected towards the center of the shell, there is no increase in contact and the head is allowed to move freely. Similarly, as the head deflects away from the center of the shell, there is no increase in surface area of contact with the shell. Thus, this profile of bearing edge allows for the maximal amount of movement, the least amount of dampening, and results in the largest number of overtones and resonance.
Last, we will consider bearing edges with a sharp bevel, or a defined vertex between the inner and outer edges. These include most modern edges no matter the angle - 45 degrees, 30 degrees, 22.5 degrees, etc. Lets examine the motion of the head over these edges before explaining why the angle of the bevel has no effect on the motion or sound.
At rest, the head is making minimal contact with the shell over the sharp vertex of the edge. As the head is struck and deflected towards the center of the shell, there is no increase in contact and the head is allowed to move freely. Similarly, as the head deflects away from the center of the shell, there is no increase in surface area of contact with the shell. Thus, this profile of bearing edge allows for the maximal amount of movement, the least amount of dampening, and results in the largest number of overtones and resonance.
Now, the angle of the actual bearing edge has absolutely no effect on the motion or sound of the head. To prove this, lets consider a shell thickness of 3/8" and a deflection of 1/8" when the head is stuck in the very center of a drum with a 14" diameter. The resulting angle between the resting position of the head and the fully deflected position would be 1.02 degrees over the 7" radius. Looking at the area of the head directly over the shell wall, this 1/8" deflection at the center of the head at 1.02 degrees translates to 0.0067" of actual maximal deflection only at the inner edge of the shell, tapering evenly to zero deflection at the point of contact of the bearing edge. At less than 1/128", the machining tolerances of the drum shell itself is greater than the deflection of the head at that point. As a result, we can negate any fluid dynamic theory or theory of compressed air pockets effecting the motion of the head, and so the angle between the bearing edge and the head and thus the distance between the shell and the head, being much, much larger that of the deflection over this edge, has no practical affect. All angles of sharp bearing edges work exactly the same way.
Transfer of Energy Between the Shell and the Head:
Slightly outside the scope of this post, however intimately related, is the amount of energy transferred between the vibrating drum head and the drum shell. Ideally, the shell and thus the entire assembled drum should vibrate as one instrument. To achieve this, sufficient energy has to be transferred into the shell from the strike of the head. With increased contact area and time in maximum contact between the head and the shell, greater energy can be transferred, and so a round over bearing edge should lead to the maximum amount of resonance of the drum shell. Next would be a flat bearing edge, with roughly half the time of maximum contact as the round over profile. Finally, a sharp bearing edge profile will allow for some transfer of energy, but their purpose is more for volume and sustain due to the pure movement of the head.
Transfer of Energy Between the Shell and the Head:
Slightly outside the scope of this post, however intimately related, is the amount of energy transferred between the vibrating drum head and the drum shell. Ideally, the shell and thus the entire assembled drum should vibrate as one instrument. To achieve this, sufficient energy has to be transferred into the shell from the strike of the head. With increased contact area and time in maximum contact between the head and the shell, greater energy can be transferred, and so a round over bearing edge should lead to the maximum amount of resonance of the drum shell. Next would be a flat bearing edge, with roughly half the time of maximum contact as the round over profile. Finally, a sharp bearing edge profile will allow for some transfer of energy, but their purpose is more for volume and sustain due to the pure movement of the head.