The fundamental reason why the machine tool can realize processing at any angle is that the tool or the probe can approach the workpiece at any directions. And five simultaneous axes is the least quantity of simultaneous axe which can realize processing at any angle.
The fundamental reason why the machine tool can realize processing at any angle is that the tool or the probe can approach the workpiece at any directions. And five simultaneous axes is the least quantity of simultaneous axe which can realize processing at any angle. Normally, five axes are adapt only. That's because the less simultaneous axes are used, the simple and compact the machine tool structure will be, which will be easy to assurance the dynamic stiffness and static stiffness of the machine tool. The dynamic stiffness and static stiffness is vital to the machine tool which require very high precision.
There is a mind might stay in our brain. In the 3D space, an object has 6 degrees of freedom (DF for short ). Like below.
Six DF of 3D Space
This is a right-hand coordinate system. These 6 degrees of freedom(DF) are three linear degrees of freedom along with axis of X, Y, Z; and three degrees of freedom which rotates around the axis of X, Y, Z. The positive direction of rotation meet the right-hand spiral rule. Like below.
Right-hand Coordinate System
Due to affected by the this concept, we might thought that the machine tool need 6 degrees of freedom or 6 axes, if the machining need to be realized at any direction. In reality, the object has 6 degrees of freedom which doesn't mean that the machine tool need consist of 6 axes to realize processing at any angle. It's the key of this problem.
When the traditional 3-axis machine is processing the workpiece which consist of complex surface or holes in many direction. We need use special jig and make many changes on the process , just to make sure the tool can touch the workpiece from any direction.
However, when using 5-axis simultaneous CNC machine tool, one time clamping can realize the high speed and high precision machining for the complex-shape workpiece.
In other words, the tool or probe can approach the workpiece at any direction which is the key point that the machine tool can to realize processing at any direction.
The machine tool realize machining by control the the position and posture of tool or probe. Hence, the key point or premise is how to describe the position and posture of the tool or probe.
Three Axes CNC Machine Tool
During the processing of 3-axis CNC machine, the position of tool or probe is changing, but its posture is fixed. For example, the tool direction of general vertical 3-axis machine is forward the Z axis during the machining. The position and posture of tool or probe can be confirmed according to the coordinate of the linear axis of X, Y, Z.
Five-axis CNC Machine
Normally, the 5-axis machine added 2 rotation axes at the basis of 3-axis machine. Usually, the axis of A, B, C will represent the rotation axis which rotates around the linear axis of X, Y, Z. The 5-axis machine consist of any two axis of A, B, C.
Please be noticed that above drawing is just showing the relationship of rotation axis and linear axis, and it's not the actual configuration of 5-axis machine. In fact, the rotation axis of 5-axis machine consist two axes of A, B, C. Such as, A and B, or A and C, or B and C.
Due to the exist of these two rotation axes, the position and posture of tool or probe will be changed during 5-axis machining. Apparently, the position of tool or probe can be confirmed through the linear axis X, Y, Z after determined the reference point at the main axis. Of course, the distance of rotation center to the tool tips and the effect of rotation angle need be considered during real operating.
But how about the posture of tool or probe?
In order to describe the posture of tool or probe during machining or testing, the concept of tool axis vector is derived. The tool axis vector is a three-dimensional unit vector (i,j,k). Each element corresponds to the projection value of unit vector in the tool axis direction which projected at the linear axis X, Y, Z.
Tool Axis Vector
Due to the tool axis vector is a unit vector, the modulus length is 1. So all possible position of the top point of tool axis vector in the space form a spherical surface which radius is 1.
Any tool axis vector direction can be obtained by rotating a vector in space around two non-collinear axes in space.
It sounds abstract, but there is a good example during our daily life. Longitude and latitude, which is φ and θ in above drawing. We can confirm any position on the earth surface through the longitude and latitude. The longitude and latitude consist two coordinates only, and these two coordinates can be described by the angle of two rotating axes which is perpendicular.
In below picture, when confirming the position of a point on the sphere surface, and every point is corresponding to a tool axis vector, it can be described by two kinds of coordinate system.
1. Using the sphere coordinate system in left side, which is also called the explicit expression of sphere coordinate. That's longitude and latitude, which consists of two coordinates, so it corresponds to two degrees of freedom, as longitude and latitude are mutually independent.
2. Using the XYZ system in right side, which is also called the implicit expression. Three coordinates are consisted in, but it still corresponds to two degrees of freedom. As these three coordinates consist of a implicit constraint.
Sphere Coordinate System (Left) & XYZ System (Right)
Therefore, the rotation angle of two rotation axes can describe a determined position on the sphere surface. And the projection value of the determined sphere position forward X, Y, Z is used to describe the tool axis vector(i,j,k) of the posture of tool or probe.
In this way, the rotation angle of two axes and tool axis vector established a one-to-one correspondence. During the practical 5-axis machining, numerical system will obtain respective rotation angle of two rotation axes
according to the tool axis vector of numerical program, and kinematic relation. Then the system will control these two rotation axes and three linear axes, after combined with the coordinate of linear axis. So as to make the tool or probe move to predetermined position and posture.
In a popular but not very rigorous way, as long as two more rotation axes are added on the 3-axis machine, then it can control tool to approach the workpiece at any direction and realize the processing for any complex curved surface.
If the machine tool added two more rotation axes on the basis of 3-axis machine, and applied with numerical control system, servo system and RTCP (Rotation tool center point), and it could realize the 5-axis simultaneous machining, then it can be called a 5-axis simultaneous CNC machine.
Why 5-axis machine does not apply more simultaneous axes?
In one hand, 5 simultaneous axes is the least simultaneous axes to realize processing at any angel. We explained the reason in previous paragraph. In the other hand, just five axes are applied commonly. Because the less simultaneous axes, the more simple and impact the machine structure will be, and the easier to assurance the dynamic stiffness and the static stiffness of the machine. The dynamic stiffness and the static stiffness is vital to the CNC machine which require high precision.
But this won't affect the born of higher axes simultaneous machine. These kinds of machine tool are produced mainly to meet obstacle avoidance or special optimization target. Such as the minimum motor power. To meet these special requirements, there are too many cases of increasing simultaneous axes by sacrifice dynamic stiffness and static stiffness.
Why does a five-axis machine tool only need five simultaneous axes to achieve any angle processing? The key point is that just two rotational degrees of freedom are needed to express the tool axis vector in any direction.
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Five-Axis Simultaneous Machining