JP7484408B2 - Stability limit analysis device for machine tools - Google Patents

Description

The present invention relates to a stability limit analysis device for machine tools.

In machine tools that use tools to machine workpieces, suppressing the occurrence of chatter is important for improving the machining accuracy of the workpiece. It is known to grasp the frequency response characteristics of the machine tool by performing hammering tests on the tools, etc., and to perform a stability limit analysis of the machine tool. By determining machining conditions that fall within the stable region based on the results of the stability limit analysis, it is possible to suppress the occurrence of chatter.

Hammering tests and the like are performed with the tool spindle of the machine tool stopped, which is a different state from actual machining. Therefore, Patent Document 1 describes placing a sensor that detects vibrations near where the tool is attached, and setting the conditions for stability limit analysis using the detection value of the sensor during actual machining. Patent Document 2 also describes performing a stability limit analysis.

JP 2018-126837 A JP 2007-222981 A

Measures to suppress the occurrence of chatter using the results of stability limit analysis include changing the machining conditions and changing the design of each structure and support element. A hammering test is one of the dynamic characteristic measurement methods for stability limit analysis. The measured values of a hammering test and the vibrations around the tool during actual machining contain various vibration components, such as the tool spindle vibration and other machine tool structures vibrations in addition to the vibration of the tool itself. However, the measured values of a hammering test, etc., do not identify which part of the machine tool is causing each peak in the frequency domain. Therefore, it is not possible to identify the vibration mode that causes chatter, and it is not easy to take appropriate measures. In order to identify the vibration mode that causes chatter, a machine model-based analysis can be considered, but when performing a stability limit analysis, it is necessary to shorten the analysis time and make it easy to set the analysis conditions.

The present invention aims to provide a vibration analysis model that shortens analysis time and makes it easy to set analysis conditions for a machine tool stability limit analysis device that can consider measures to suppress the occurrence of chatter phenomena from the stability limit analysis results.

The stability limit analysis device for a machine tool according to the present invention is a stability limit analysis device for machining a workpiece with a tool in a machine tool composed of multiple structures, and includes a rigid body model storage unit that stores a rigid body model composed of rigid elements that make each of the multiple structures a rigid body and support elements that support the rigid body elements, an elastic body model storage unit that stores an elastic body model that targets a portion of the multiple structures and can express a bending mode, and an analysis unit that performs a stability limit analysis for the machine tool based on the results of a first analysis using the rigid body model regarding changes in position and orientation of a first target structure relative to a first reference and the results of a second analysis using the elastic body model regarding deformation of a second target structure.

In other words, in the present invention, the analysis unit performs a stability limit analysis based on the results of a first analysis using a rigid body model and the results of a second analysis using an elastic body model. Generally, the displacement analysis of the entire machine tool can be performed by an analysis using a rigid body model. The displacement analysis of the entire machine tool can also be performed by an analysis using an elastic body model.

However, a displacement analysis of the entire machine tool using only a rigid body model is an analysis in which all structures are represented as rigid elements. Therefore, if there is a structure that is significantly affected by the bending mode, a displacement analysis of the entire machine tool using only a rigid body model cannot obtain highly accurate analysis results.

On the other hand, a displacement analysis of the entire machine tool using only an elastic body model can obtain highly accurate analysis results because the analysis includes bending modes for all structures. However, a displacement analysis of the entire machine tool using only an elastic body model requires a significant amount of analysis time. Furthermore, since it is not easy to set analysis conditions for an elastic body model, it is not easy to represent the entire machine tool with an elastic body model, even in terms of setting analysis conditions.

Therefore, in the present invention, a second analysis is performed using an elastic body model by using only a portion of the structure as an elastic body model. In the stability limit analysis, the results of the first analysis using a rigid body model and the results of the second analysis using an elastic body model are used together.

Therefore, in the present invention, the stability limit analysis by the analysis unit can obtain more accurate analysis results than when only a rigid body model is used. On the other hand, in the present invention, the stability limit analysis by the analysis unit can shorten the analysis time and make it easier to set the analysis conditions than when only an elastic body model is used.

FIG. 1 illustrates an example of a machine tool. FIG. 2 is a functional block diagram showing a stability limit analysis device. FIG. 4 is a stability limit diagram showing the relationship between the rotation speed of the tool spindle and the limit cutting amount. FIG. 2 is a diagram illustrating an example of a rigid body model. FIG. 13 is a diagram illustrating an example of an elastic body model. FIG. 4 is a processing block diagram of a stability limit analysis performed by an analysis unit. FIG. 2 is a processing block diagram of a frequency response analysis performed by an analysis unit. 1 is a graph showing the results of frequency response analysis (frequency response characteristics) when a first analysis using a rigid body model and a second analysis using an elastic body model are applied, showing the relationship between the frequency of relative vibration between a tool and a workpiece and mechanical compliance. 13 is a graph showing the results of a frequency response analysis when only a rigid body model is used. 13 is a graph showing the results of a frequency response analysis when only an elastic body model is used.

(1. Example of machine tool 1)
The machine tool 1 that is the target of the stability limit analysis device is a device that machines a workpiece W with a tool T by moving the tool T relatively to the workpiece W. Furthermore, the target machine tool 1 is composed of a plurality of structures for relatively moving the tool T and the workpiece W. The target machine tool 1 is a machine tool that performs cutting or grinding, such as a machining center, a lathe, a milling machine, a gear processing device, or a grinding machine.

An example of a machine tool 1 will be described with reference to FIG. 1. In this example, the machine tool 1 is a machining center capable of tool replacement. In particular, the machining center as the machine tool 1 can machine a tooth profile on the workpiece W by gear skiving or hobbing. Furthermore, the machining center as the machine tool 1 is basically configured as a horizontal machining center. Note that although the above configuration is given as an example of the machine tool 1, other configurations such as a vertical machining center can also be applied.

As shown in FIG. 1, the machine tool 1 has, for example, three mutually orthogonal linear axes (X-axis, Y-axis, and Z-axis) as drive axes. Here, the direction of the rotation axis of the tool T (equal to the rotation axis of the tool spindle) is defined as the Z-axis direction, and the two axes perpendicular to the Z-axis direction are defined as the X-axis direction and the Y-axis direction. In FIG. 1, the horizontal direction is the X-axis direction, and the vertical direction is the Y-axis direction. Furthermore, the machine tool 1 further has two rotation axes (B-axis and Cw-axis) as drive axes for changing the relative attitude of the tool T and the workpiece W. The machine tool 1 also has a Ct-axis as a rotation axis for rotating the tool T.

In other words, the machine tool 1 is a 5-axis machining center (a 6-axis machining center when the tool spindle (Ct axis) is taken into account) capable of machining free-form surfaces. Here, instead of a configuration having a B-axis (axis of rotation about the Y-axis in the reference state) and a Cw-axis (axis of rotation about the Z-axis in the reference state), the machine tool 1 may be configured to have an A-axis (axis of rotation about the X-axis in the reference state) and a B-axis, or an A-axis and a Cw-axis. Furthermore, the machine tool 1 can be used as a dedicated machine capable of gear skiving machining, with a machine tool having a different number of drive axes from that of a 5-axis machining center.

The tool T is a rotating tool used to machine the workpiece W. The tool T is, for example, an end mill, a gear skiving cutter, a hob cutter, etc. In this example, the tool T will be described using a gear skiving cutter used to create a tooth profile on the workpiece W by gear skiving.

In the machine tool 1, the configuration for moving the tool T and the workpiece W relative to one another can be selected as appropriate. In this example, the machine tool 1 allows the tool T to move linearly in the Y-axis and Z-axis directions, allows the workpiece W to move linearly in the X-axis direction, and further allows the workpiece W to rotate about the B-axis and Cw-axis. In addition, the tool T can rotate about the Ct-axis.

The machine tool 1 comprises a bed 10, a workpiece holding device 20, and a tool holding device 30. The bed 10 is formed in any shape, such as a substantially rectangular shape, and is placed on the floor. The workpiece holding device 20 allows the workpiece W to move linearly in the X-axis direction relative to the bed 10, and to rotate about the B-axis and Cw-axis. The workpiece holding device 20 mainly comprises an X-axis moving table 21, a B-axis rotating table 22, and a workpiece spindle device 23.

The X-axis moving table 21 is provided so as to be movable in the X-axis direction relative to the bed 10. Specifically, the bed 10 is provided with a pair of X-axis guide rails extending in the X-axis direction (front-to-back direction in FIG. 1), and the X-axis moving table 21 is driven by a linear motor or a ball screw mechanism (not shown) to move back and forth in the X-axis direction while being guided by the pair of X-axis guide rails.

The B-axis rotating table 22 is placed on the top surface of the X-axis moving table 21, and moves back and forth in the X-axis direction together with the X-axis moving table 21. The B-axis rotating table 22 is also arranged to be rotatable about the B-axis relative to the X-axis moving table 21. A rotating motor (not shown) is housed in the B-axis rotating table 22, and the B-axis rotating table 22 is driven by the rotating motor to be able to rotate about the B-axis.

The workpiece spindle device 23 is installed on the B-axis rotating table 22 and rotates about the B-axis together with the B-axis rotating table 22. The workpiece spindle device 23 includes a workpiece spindle base 23a, a workpiece spindle housing 23b, and a workpiece spindle 23c. The workpiece spindle base 23a is fixed to the upper surface of the B-axis rotating table 22.

The workpiece spindle housing 23b is fixed to the workpiece spindle base 23a and has a cylindrical inner peripheral surface centered on the Cw-axis centerline that is perpendicular to the B-axis centerline. The workpiece spindle 23c is rotatably supported by the workpiece spindle housing 23b. The workpiece W is removably held by the workpiece spindle 23c. In other words, the workpiece spindle 23c holds the workpiece W in the workpiece spindle housing 23b rotatably about the Cw-axis and rotates integrally with the workpiece W.

Inside the workpiece spindle housing 23b, there is provided a rotary motor (not shown) that rotates the workpiece spindle 23c, and a detector (not shown) such as an encoder that detects the rotation angle of the workpiece spindle 23c. In this way, the workpiece holding device 20 allows the workpiece W to be moved in the X-axis direction relative to the bed 10, and to be rotated about the B-axis and Cw-axis.

The tool holding device 30 mainly comprises a column 31, a saddle 32, and a tool spindle device 33. The column 31 is provided so as to be movable in the Z-axis direction relative to the bed 10. Specifically, the bed 10 is provided with a pair of Z-axis guide rails extending in the Z-axis direction (left-right direction in FIG. 1), and the column 31 is driven by a linear motor or a ball screw mechanism (not shown) to reciprocate in the Z-axis direction while being guided by the pair of Z-axis guide rails.

The saddle 32 is disposed on the side of the column 31 facing the workpiece W (the left side in FIG. 1), which is parallel to a plane perpendicular to the Z-axis direction. A pair of Y-axis guide rails extending in the Y-axis direction (the up-down direction in FIG. 1) are provided on the side of the column 31, and the saddle 32 reciprocates in the Y-axis direction by being driven by a linear motor or ball screw mechanism (not shown).

The tool spindle device 33 is mounted on the saddle 32 and moves in the Y-axis direction integrally with the saddle 32. The tool spindle device 33 includes a tool spindle housing 33a and a tool spindle 33b. The tool spindle housing 33a is fixed to the saddle 32 and has a cylindrical inner circumferential surface centered on the Ct-axis center line parallel to the Z-axis. The tool spindle 33b is rotatably supported by the tool spindle housing 33a. A tool T is removably held by the tool spindle 33b. In other words, the tool spindle 33b holds the tool T in the tool spindle housing 33a rotatably about the Ct-axis and rotates integrally with the tool T.

Inside the tool spindle housing 33a, there is provided a tool rotation motor (not shown) that rotates the tool spindle 33b, and a detector (not shown) such as an encoder that detects the rotation angle of the tool spindle 33b. In this way, the tool holding device 30 holds the tool T so that it can move in the Y-axis and Z-axis directions relative to the bed 10 and can rotate about the Ct axis.

(2. Configuration of Stability Limit Analysis Device 50)
The configuration of the stability limit analysis device 50 will be described with reference to Fig. 2. The stability limit analysis device 50 analyzes the stability limit when machining the workpiece W with the tool T in the above-mentioned machine tool 1. The stability limit analysis device 50 generates a stability limit diagram as shown in Fig. 3.

The stability limit diagram is, for example, a diagram showing the relationship between the rotational speed of the tool spindle 33b (equal to the rotational speed of the tool T) and the limit cutting depth, or a diagram showing the relationship between the rotational speed of the workpiece spindle 23c (equal to the rotational speed of the workpiece W) and the limit cutting depth. In this example, as shown in FIG. 3, since the tool spindle 33b has a lower bending rigidity than the workpiece spindle 23c, the stability limit analysis device 50 generates a stability limit diagram showing the relationship between the rotational speed of the tool spindle 33b and the limit cutting depth. In the stability limit diagram, the upper side of the limit cutting depth is an unstable region, and the lower side is a stable region.

The stability limit analysis device 50 includes a rigid body model storage unit 51, an elastic body model storage unit 52, and an analysis unit 53. The rigid body model storage unit 51 stores a rigid body model M1 representing the entire machine tool 1 as one of the analysis models. The rigid body model M1 is composed of rigid body elements, each of which is a rigid body of a plurality of structures constituting the machine tool 1, and support elements that support the rigid body elements.

The elastic body model storage unit 52 stores an elastic body model M2, which is targeted at a portion of the multiple structures that make up the machine tool 1, as another analysis model. Unlike the rigid body model M1, the elastic body model M2 is a model that can represent bending modes. For example, the elastic body model M2 is a model for performing deformation analysis using the finite element method (FEM analysis).

In this example, the elastic body model M2 targets a tool unit including the tool spindle 33b and tool T, which are part of the structure of the machine tool 1. The elastic body model M2 may also target only the tool spindle 33b. The elastic body model M2 may also target a workpiece unit including the workpiece spindle 23c and workpiece W, in addition to the above. The elastic body model M2 may also target only the workpiece spindle 23c. The elastic body model M2 can also target other structures in addition to the tool spindle 33b and workpiece spindle 23c.

The analysis unit 53 performs a stability limit analysis of the machine tool 1 using the rigid body model M1 and the elastic body model M2. Here, the analysis unit 53 does not perform an analysis using only the rigid body model M1, nor does it perform an analysis using only the elastic body model M2. In other words, the analysis unit 53 uses both the analysis results using the rigid body model M1 and the analysis results using the elastic body model M2.

The analysis unit 53 performs a first analysis using the rigid body model M1 and a second analysis using the elastic body model M2. The first analysis is an analysis of changes in the position and orientation of the first target structure relative to a first reference in the machine tool 1. The second analysis is an analysis of deformation of a predetermined position of the second target structure relative to a second reference in the machine tool 1. The second analysis is, for example, a deformation analysis using the finite element method.

The analysis unit 53 then performs a first analysis using some of the multiple structures that make up the machine tool 1 as a rigid body model M1, and performs a second analysis using the remaining part as an elastic body model M2. In other words, by performing the first and second analyses, the analysis unit 53 can obtain the results of an analysis that uses the rigid body model M1 and the elastic body model M2.

The analysis unit 53 further performs a stability limit analysis for the entire machine tool 1 based on the results of the first analysis and the second analysis. In this way, in the stability limit analysis for the entire machine tool 1, the results of the first analysis using the rigid body model M1 and the results of the second analysis using the elastic body model M2 are used in combination.

The analysis unit 53 may perform a stability limit analysis of the entire machine tool 1 for all of the multiple axial directions of the relative movement between the workpiece W and the tool T, based on the results of the first analysis and the results of the second analysis. In addition, the analysis unit 53 may perform a stability limit analysis of the entire machine tool 1 by using the results of the first analysis and the results of the second analysis for some of the multiple axial directions, and using only the results of the first analysis or only the results of the second analysis for the remaining axial directions.

Here, generally, displacement analysis of the entire machine tool 1 can be performed by analysis using a rigid body model M1. Displacement analysis of the entire machine tool 1 can also be performed by analysis using an elastic body model M2.

However, a displacement analysis of the entire machine tool 1 using only the rigid body model M1 is an analysis in which all structures are represented as rigid elements. Therefore, if there is a structure that is significantly affected by the bending mode, a displacement analysis of the entire machine tool 1 using only the rigid body model M1 cannot obtain highly accurate analysis results.

On the other hand, a displacement analysis of the entire machine tool 1 using only the elastic body model M2 is an analysis that includes bending modes for all structures, and therefore it is possible to obtain highly accurate analysis results. However, a displacement analysis of the entire machine tool 1 using only the elastic body model M2 requires a significant amount of analysis time. Furthermore, since it is not easy to set analytical conditions for the elastic body model M2, it is not easy to represent the entire machine tool 1 with the elastic body model M2, even in terms of setting analytical conditions.

In contrast, in the stability limit analysis of the entire machine tool 1 by the above-mentioned analysis unit 53, the results of the first analysis by the rigid body model M1 and the results of the second analysis by the elastic body model M2 are used in combination. Therefore, the stability limit analysis by the analysis unit 53 can obtain analysis results with higher accuracy than when only the rigid body model M1 is used. On the other hand, the stability limit analysis by the analysis unit 53 can shorten the analysis time and make it easier to set the analysis conditions than when only the elastic body model M2 is used.

(3. Example of rigid body model M1)
An example of the rigid body model M1 will be described with reference to Fig. 4. The rigid body model M1 represents a plurality of structural elements of the machine tool 1 as rigid body elements. The rigid body model M1 in Fig. 4 represents all structural elements of the machine tool 1 as rigid body elements. However, as described above, the analysis unit 53 may perform an analysis using only some of the elements of the rigid body model M1.

The rigid body model M1 is a three-dimensional model representing the machine tool 1. The rigid body model M1 is composed of rigid body elements representing multiple structures constituting the machine tool 1, and support elements that support the rigid body elements. In FIG. 4, each rigid body element corresponds to each structure of the machine tool 1 shown in FIG. 1, and each rigid body element is assigned the symbol of the corresponding structure. Here, the shape of each rigid body element is an example, and does not necessarily have to match the shape of the corresponding structure. Furthermore, each rigid body element includes information regarding the mass, moment of inertia, and center of gravity position of the corresponding structure.

The support elements connect the rigid elements to each other. The support elements include spring elements S and damper elements D. In the rigid model M1, the spring elements S and damper elements D are arranged at positions corresponding to, for example, linear guides and bearings provided on the machine tool 1. The spring constant of the spring elements S and the damping coefficient of the damper elements D are set based on vibration characteristic data obtained by a hammering test or the like.

Here, in the machine tool 1 shown in FIG. 1, the saddle 32 and the tool spindle housing 33a are fixed. Therefore, in the rigid body model M1 shown in FIG. 4, the saddle 32 and the tool spindle housing 33a are represented as the same rigid body element. Also, in the machine tool 1 shown in FIG. 1, the B-axis rotating table 22, the workpiece spindle base 23a, and the workpiece spindle housing 23b are fixed. Therefore, in the rigid body model M1 shown in FIG. 4, the B-axis rotating table 22, the workpiece spindle base 23a, and the workpiece spindle housing 23b are represented as the same rigid body element.

In addition, in FIG. 1, the tool spindle 33b holds the tool T integrally. Therefore, in the rigid body model M1 shown in FIG. 4, the tool spindle 33b and the tool T are represented as fixed rigid elements so as not to allow any displacement between them. In addition, in FIG. 1, the workpiece spindle 23c holds the workpiece W integrally. Therefore, in the rigid body model M1 shown in FIG. 4, the workpiece spindle 23c and the workpiece W are represented as fixed rigid elements so as not to allow any displacement between them.

Here, the rigid body model M1 is a model for outputting the relative displacement of the first target structure with respect to the first reference in the first analysis. For example, if the elastic body model M2 is a tool unit including the tool spindle 33b, the first reference in the rigid body model M1 is the workpiece W, and the first target structure is the tool spindle housing 33a. For example, if the elastic body model M2 is a workpiece unit including the workpiece spindle 23c, the first reference in the rigid body model M1 is the workpiece spindle housing 23b, and the first target structure is the tool T.

For example, if the elastic body model M2 is the tool unit including the tool spindle 33b and the workpiece unit including the workpiece spindle 23c, the first reference in the rigid body model M1 is the workpiece spindle housing 23b, and the first target structure is the tool spindle housing 33a. If the elastic body model M2 is not used, the first reference in the rigid body model M1 is the workpiece W, and the first target structure is the tool unit including the tool spindle 33b and the tool T.

(4. Example of Elastic Body Model M2)
An example of the elastic body model M2 will be described with reference to Fig. 5. The elastic body model M2 targets a second target structure which is a part of the structure of the machine tool 1, and in particular targets a structure having a bending mode. The second target structure which is the target of the elastic body model M2 targets, for example, a tool unit including a tool spindle 33b and a workpiece unit including a workpiece spindle 23c. The tool unit includes the tool spindle 33b and a tool T held by the tool spindle 33b. The workpiece spindle unit includes the workpiece spindle 23c and a workpiece W held by the workpiece spindle 23c.

Here, the elastic body model M2 is a model for outputting the absolute displacement of a predetermined position of the second target structure relative to the second reference in the second analysis. For example, if the second target structure is a tool unit including the tool spindle 33b, the second reference is the tool spindle housing 33a. Also, if the second target structure is a workpiece unit including the workpiece spindle 23c, the second reference is the workpiece spindle housing 23b.

It is effective for the elastic body model M2 to target a structure having a bending mode, so it is advisable to use a long structure as the second target structure. In general, the ratio of axial length to outer diameter (L/D) of the tool spindle 33b is larger than that of other structures. Therefore, it is advisable for the elastic body model M2 to include the tool spindle 33b.

The elastic body model M2 may be a three-dimensional model or a two-dimensional model. In this example, the elastic body model M2 can be a two-dimensional model that represents a cross section passing through the rotation axis of the rotating body element by targeting a rotating body element as the second target structure. As shown in FIG. 5, a two-dimensional model in the X-Z plane and a two-dimensional model in the Y-Z plane are defined. Then, when the second target structure is a rotating body element, the same model can be used for the two-dimensional model in the X-Z plane and the two-dimensional model in the Y-Z plane.

In other words, the elastic body model M2 can be a two-dimensional model whether it is a tool unit including the tool spindle 33b or a workpiece unit including the workpiece spindle 23c. By making the elastic body model a two-dimensional model, it becomes easier to set the analysis conditions for the second analysis, and the time required for the second analysis can be shortened.

(5. Processing of Analysis Unit 53)
(5-1. Stability limit analysis by analysis unit 53)
The stability limit analysis by the analysis unit 53 will be described with reference to Fig. 6. When an average cutting thickness (cut-in amount) is input with the tool spindle 33b rotating, the analysis unit 53 outputs the vibration amplitude of the tool T relative to the workpiece W, thereby performing a stability limit analysis for the entire machine tool 1. That is, the analysis unit 53 generates a stability limit diagram as shown in Fig. 3 based on the vibration amplitude when the rotation speed of the tool spindle 33b and the average cutting thickness (cut-in amount) are changed.

As shown in FIG. 6, the analysis unit 53 that performs the stability limit analysis includes an adder 61, a subtractor 62, a processing force calculation unit 63, a first analysis unit 64 that performs the first analysis, a second analysis unit 65 that performs the second analysis, and a synthesis processing unit 66. The adder 61 receives the average cutting thickness (corresponding to the command cutting thickness and command cutting depth) as input and adds the vibration amplitude of the workpiece W one rotation ago. The subtractor 62 subtracts the current vibration amplitude of the workpiece W from the sum of the average cutting thickness and the vibration amplitude one rotation ago to calculate the current cutting thickness.

The machining force calculation unit 63 performs machining force calculation based on the current cutting thickness to calculate the machining forces acting on the tool T and the workpiece W during machining. The machining force calculation unit 63 calculates the machining forces in the X-axis direction, the Y-axis direction, and the Z-axis direction.

The first analysis unit 64 and the second analysis unit 65 use the processing force to output the relative displacement of the target structure with respect to a reference. The first analysis unit 64 performs a first analysis using a rigid body model M1, and the second analysis unit 65 performs a second analysis using an elastic body model M2.

Here, the X-axis direction and the Y-axis direction are perpendicular to the rotation axis of the tool spindle 33b and the tool T. Therefore, the X-axis direction and the Y-axis direction are directions that are greatly affected by the bending mode of the tool spindle 33b and the tool T. Therefore, in the X-axis direction and the Y-axis direction, the first analysis and the second analysis are used together to take into account the bending mode of the tool spindle 33b and the tool T.

On the other hand, the Z-axis direction is the direction of the rotation axis of the tool spindle 33b and the tool T. Therefore, the influence of the bending mode of the tool spindle 33b and the tool T is smaller in the Z-axis direction than in the X-axis and Y-axis directions. Therefore, in the Z-axis direction, only an analysis that does not consider the bending mode of the tool spindle 33b and the tool T, i.e., the first analysis, is used.

The first analysis unit 64 performs a first analysis using the rigid body model M1 using the combined machining forces in the X-axis, Y-axis, and Z-axis directions. The rigid body model M1 is a three-dimensional model. Therefore, the first analysis unit 64 performs an analysis in a three-dimensional coordinate system. In the first analysis, when the combined machining forces in the X-axis, Y-axis, and Z-axis directions act on the tool T and workpiece W in the rigid body model M1, the first analysis outputs the relative displacement of the first target structure with respect to the workpiece W as the first reference.

Here, in the X-axis and Y-axis directions, the first target structure in the first analysis unit 64 is the tool spindle housing 33a. That is, when a combined machining force in the X-axis, Y-axis, and Z-axis directions acts on the tool T and workpiece W in the rigid body model M1, the first analysis unit 64 outputs the relative displacement of the tool spindle housing 33a as the first target structure with respect to the workpiece W as the first reference. That is, in the X-axis and Y-axis directions, the change in position and attitude of the tool spindle housing 33a with respect to the workpiece W is output as a result of the first analysis.

The elastic body model M2 is a tool spindle unit including the tool spindle 33b and the tool T. That is, in the X-axis direction and the Y-axis direction, the first analysis unit 64 outputs the relative displacement of the structures of the rigid body model M1 excluding the tool spindle unit (33b, T) as the elastic body model M2. In the X-axis direction and the Y-axis direction, the rigid body model M1 is used as a model for outputting the relative displacement of the tool spindle housing 33a as the first target structure with respect to the workpiece W as the first reference.

In the Z-axis direction, the first target structure in the first analysis unit 64 is the tool spindle 33b. In other words, when a combined machining force in the X-axis, Y-axis, and Z-axis directions acts on the tool T and workpiece W in the rigid body model M1, the first analysis unit 64 outputs the relative displacement of the tool spindle 33b as the first target structure with respect to the workpiece W as the first reference. Here, in the rigid body model M1, the displacement of the tool spindle 33b corresponds to the displacement of the tool T.

In the Z-axis direction, the change in position and attitude of the tool spindle 33b relative to the workpiece W (equal to the change in the tool T) is output as a result of the first analysis. In other words, in the Z-axis direction, the rigid body model M1 is used as a model for outputting the relative displacement of the tool spindle unit (33b, T) as the first target structure relative to the workpiece W as the first reference.

The second analysis unit 65 performs a second analysis (FEM analysis) using the elastic body model M2 in parallel with the first analysis performed by the first analysis unit 64. The elastic body model M2 is a two-dimensional model. Therefore, the second analysis unit 65 performs an analysis in a two-dimensional coordinate system. In this example, the elastic body model M2 targets the tool spindle unit including the tool spindle 33b and the tool T. That is, the elastic body model M2 sets the second reference to the tool spindle housing 33a, and sets the tool spindle unit (33b, T) including the tool spindle 33b and the tool T as the second target structure. The elastic body model M2 is used as a model for outputting the absolute displacement of the tip position (machining position) of the tool T as a predetermined position in the tool spindle unit relative to the tool spindle housing 33a.

In detail, in the second analysis in the X-axis direction, when a machining force in the X-axis direction acts on the tool T and the workpiece W in the elastic body model M2, the second analysis unit 65 outputs the deformation state of the tool unit (33b, T) including the tool spindle 33b and the tool T as the second target structure relative to the tool spindle housing 33a as the second reference.

Furthermore, in the second analysis in the Y-axis direction, the second analysis unit 65 outputs the deformation state of the tool unit (33b, T) including the tool spindle 33b and the tool T as the second target structure relative to the tool spindle housing 33a as the second reference when a machining force in the Y-axis direction acts on the tool T and the workpiece W in the elastic body model M2.

In particular, as a result of the second analysis, the second analysis unit 65 outputs the absolute displacement of the tip position (machining position) of the tool T as a predetermined position of the second target structure in a state in which the tool spindle 33b and the tool T are deformed relative to the tool spindle housing 33a in each of the X-axis direction and the Y-axis direction. Note that the second analysis is not performed in the Z-axis direction.

The synthesis processing unit 66 synthesizes the results of the first analysis and the second analysis for each of the X-axis and Y-axis directions. That is, the synthesis processing unit 66 synthesizes the relative displacement of the tool spindle housing 33a with respect to the workpiece W as the result of the first analysis and the absolute displacement of the tool T with respect to the tool spindle housing 33a as the result of the second analysis. That is, in the X-axis and Y-axis directions, the obtained synthetic displacement becomes a vibration amplitude that is the relative displacement of the tool T with respect to the workpiece W.

On the other hand, the synthesis processing unit 66 outputs only the results of the first analysis in the Z-axis direction as is. In other words, in the Z-axis direction, the result of the first analysis becomes the vibration amplitude, which is the relative displacement of the tool T with respect to the workpiece W.

Then, the composite displacements in the X-axis, Y-axis, and Z-axis directions (the relative displacement of the tool T with respect to the workpiece W) are set as the current vibration amplitude, and the time delay processing unit 67 performs time delay processing to calculate the vibration amplitude of the workpiece W one rotation ago and feeds it back.

By repeating the above, it is possible to output the change over time in the relative displacement of the tool T with respect to the workpiece W in each of the X-axis, Y-axis, and Z-axis directions, i.e., the relative vibration amplitude of the tool T with respect to the workpiece W.

Furthermore, the analysis unit 53 generates a stability limit diagram for the entire machine tool 1 using the vibration amplitudes in the X-axis, Y-axis, and Z-axis directions output by the synthesis processing unit 66. That is, the analysis unit 53 generates a stability limit diagram for the entire machine tool 1 based on the vibration amplitudes obtained in the X-axis and Y-axis directions by using both the rigid body model M1 and the elastic body model M2, and the vibration amplitude in the Z-axis direction by using only the rigid body model M1. Therefore, by using the highly accurate stability limit analysis results, it becomes possible to consider effective measures to suppress the occurrence of chatter.

Furthermore, the vibration analysis model includes an elastic body model M2. If the entire machine tool 1 were to be represented by an elastic body model, it would not be easy to set the analysis conditions. However, since the elastic body model M2 in the second analysis targets only some of the structures in the machine tool 1, even if the elastic body model M2 is used, it is possible to easily set the analysis conditions and shorten the analysis time.

(5-2. Frequency response analysis by analysis unit 53)
The analysis unit 53 can also perform a frequency response analysis in addition to the above-mentioned stability limit analysis. The frequency response analysis is an analysis performed independently of the stability limit analysis, and outputs the relationship between the frequency of vibration of the tool T with respect to the workpiece W and the mechanical compliance. The target model in the frequency response analysis is a vibration analysis model in which the first analysis and the second analysis applied in the above-mentioned stability limit analysis are used in combination.

The frequency response analysis by the analysis unit 53 will be described with reference to Figs. 7 and 8. As shown in Fig. 7, in the frequency response analysis, a time domain excitation force such as a sweep signal is used as an input signal to the vibration analysis model (the area surrounded by the dashed line in Fig. 7). The excitation forces as input signals have X-axis, Y-axis, and Z-axis directions. The vibration analysis model then outputs the vibration amplitudes in the X-axis, Y-axis, and Z-axis directions as output signals.

The analysis unit 53 that performs the frequency response analysis includes a first analysis unit 71 that performs the first analysis, a second analysis unit 72 that performs the second analysis, a synthesis processing unit 73, an input Fourier transform unit 74, an output Fourier transform unit 75, and a frequency response characteristic calculation unit 76. Here, the first analysis unit 71, the second analysis unit 72, and the synthesis processing unit 73 perform substantially the same processing as the first analysis unit 64, the second analysis unit 65, and the synthesis processing unit 66 in the analysis unit 53 that performs the above-mentioned stability limit analysis.

In other words, the vibration amplitude that is output is the vibration amplitude of the tool T relative to the workpiece W. The vibration amplitude that is output is the vibration amplitude obtained by using both the rigid body model M1 and the elastic body model M2 in the X-axis and Y-axis directions, and is the vibration amplitude obtained by using only the rigid body model M1 in the Z-axis direction.

Since the input signal and the output signal are signals in the time domain, the input Fourier transform unit 74 and the output Fourier transform unit 75 perform a process of converting the input signal and the output signal into the frequency domain. The frequency response characteristic calculation unit 76 calculates the frequency response characteristic of the vibration analysis model (71, 72, 73) based on the converted input signal and output signal. In other words, the frequency response characteristic is the mechanical compliance obtained by dividing the vibration amplitude by the excitation force in the frequency domain. In other words, the frequency response characteristic is the relationship between the vibration frequency (Hz) and the mechanical compliance (m/N). The frequency response characteristic according to the vibration analysis model described above is as shown in Figure 8.

For comparison, Figure 9 shows the frequency response characteristics when the target vibration analysis model is a rigid body model M1. As shown in Figure 9, the mechanical compliance in the low frequency range is high, whereas the mechanical compliance in the high frequency range is low. Figure 10 shows the frequency response characteristics when the target vibration analysis model is an elastic body model M2. As shown in Figure 10, the mechanical compliance in the low frequency range varies little with frequency, whereas the mechanical compliance in the high frequency range varies greatly with frequency.

In other words, the frequency response characteristics of the vibration analysis model shown in FIG. 8 are roughly a combination of the frequency response characteristics of only the rigid body model M1 shown in FIG. 9 and the frequency response characteristics of only the elastic body model M2 shown in FIG. 10.

In other words, the frequency response characteristics shown in Figure 8 are the result of taking into account the characteristics of the machine tool 1 as a whole through a first analysis using the rigid body model M1, and taking into account the characteristics of the structure that is greatly influenced by the bending mode through a second analysis using the elastic body model M2. Therefore, it can be seen that by using the first analysis and the second analysis together, highly accurate frequency response characteristics can be obtained.

The frequency response characteristics shown in Figure 8 were also found to be close to the frequency response characteristics obtained by a hammering test (not shown). This also shows that the vibration analysis model using both the rigid body model M1 and the elastic body model M2 has highly accurate frequency response characteristics. The results of the frequency response analysis also show that the results of the above-mentioned stability limit analysis are highly accurate.

1: Machine tool, 10: Bed, 20: Workpiece holding device, 21: X-axis moving table, 22: B-axis rotating table, 23: Workpiece spindle device, 23a: Workpiece spindle base, 23b: Workpiece spindle housing, 23c: Workpiece spindle, 30: Tool holding device, 31: Column, 32: Saddle, 33: Tool spindle device, 33a: Tool spindle housing, 33b: Tool spindle, 50: Stability limit analysis device, 51: Rigid body model storage unit, 52: Elastic body model storage unit, 53: Analysis unit, 64, 71: First analysis unit, 65, 72: Second analysis unit, 66, 73: Synthesis processing unit, M1: Rigid body model, M2: Elastic body model, T: Tool, W: Workpiece

Claims (13)

A stability limit analysis device for machining a workpiece with a tool in a machine tool composed of a plurality of structures, comprising:
a rigid body model storage unit that stores a rigid body model including rigid elements each of the plurality of structures as a rigid body and support elements that support the rigid body elements;
an elastic body model storage unit that stores an elastic body model that targets a portion of the plurality of structures and is capable of expressing a bending mode;
an analysis unit that performs a stability limit analysis on the machine tool based on a result of a first analysis on a change in position and orientation of a first target structure relative to a first reference using the rigid body model and a result of a second analysis on a deformation of a second target structure using the elastic body model;
The present invention relates to a machine tool stability limit analysis device. the elastic body model is a model for performing deformation analysis using a finite element method,
2. The stability limit analysis device for a machine tool according to claim 1, wherein the second analysis using the elastic body model is a deformation analysis by the finite element method. the elastic body model is a two-dimensional model that targets a rotor element as the second target structure and expresses a cross section passing through a rotation axis of the rotor element,
3. The stability limit analysis device for a machine tool according to claim 2, wherein the second analysis using the elastic body model is an analysis in a two-dimensional coordinate system. the rigid body model is a three-dimensional model,
4. The stability limit analysis device for a machine tool according to claim 3, wherein the first analysis using the rigid body model is an analysis in a three-dimensional coordinate system. The stability limit analysis device for a machine tool according to any one of claims 1 to 4, wherein the support elements constituting the rigid body model include spring elements and damper elements. The stability limit analysis device for a machine tool according to any one of claims 1 to 5, wherein the elastic body model targets at least one of the multiple structures: a tool unit consisting of the tool and a structure that holds the tool, and a workpiece unit consisting of the workpiece and a structure that holds the workpiece. The stability limit analysis device for a machine tool according to claim 6, wherein the elastic body model is directed to the tool unit including the tool and a tool spindle that holds the tool and rotates integrally with the tool. The stability limit analysis device for a machine tool according to claim 6 or 7, wherein the elastic body model is directed to the workpiece unit including the workpiece and a workpiece spindle that holds the workpiece and rotates integrally with the workpiece. The analysis unit is
A machining force acting on the tool and the workpiece due to machining is input to the first analysis and the second analysis;
outputting, as a result of the first analysis, a relative displacement of the first target structure with respect to the first reference when the machining force acts on the tool and the workpiece in the rigid body model;
outputting, as a result of the second analysis, an absolute displacement of a predetermined position of the second target structure relative to a second reference when the machining force acts on the tool in the elastic body model;
A stability limit analysis device for a machine tool described in any one of claims 1 to 8, which performs a stability limit analysis for the machine tool by calculating a resultant displacement that is a combination of the relative displacement of the first target structure and the absolute displacement of the specified position of the second target structure. The machine tool comprises:
The tool;
a tool spindle that supports the tool and rotates integrally with the tool;
a spindle housing that rotatably supports the tool spindle;
At least
the elastic body model targets a tool unit, among the plurality of structures, that is configured by the tool and the tool spindle,
The analysis unit is
outputting, as a result of the first analysis, a relative displacement of the spindle housing as the first target structure with respect to the workpiece as the first reference;
outputting, as a result of the second analysis, an absolute displacement of the tool as the predetermined position of the second target structure relative to the spindle housing as the second reference;
10. The stability limit analysis device for a machine tool according to claim 9, wherein a stability limit analysis for the machine tool is performed by calculating, as the resultant displacement, a relative displacement of the tool with respect to the workpiece serving as the first reference. A direction of a rotation axis of the tool spindle is defined as a Z-axis direction, and two orthogonal axes perpendicular to the Z-axis direction are defined as an X-axis direction and a Y-axis direction,
The analysis unit is
11. The apparatus for analyzing a stability limit for a machine tool according to claim 10, further comprising: a stability limit analysis for the machine tool being performed by calculating the resultant displacement in the X-axis direction and the Y-axis direction. The analysis unit is
With respect to the Z-axis direction,
outputting, as a result of the first analysis, a relative displacement of the tool spindle as the first target structure with respect to the workpiece as the first reference;
The apparatus for analyzing a stability limit for a machine tool according to claim 11, further comprising: a relative displacement of the tool spindle for performing a stability limit analysis for the machine tool. The stability limit analysis device for a machine tool according to any one of claims 1 to 12, wherein the analysis unit outputs a stability limit diagram relating to the rotational speed and cutting depth limit of the tool.

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