Profile measuring method and profile measuring instrument

The entire disclosure of Japanese Patent Applications No. 2012-101715 filed Apr. 26, 2012 is expressly incorporated by reference herein.

1. Field of the Invention

The present invention relates to a profile measuring method and a profile measuring instrument.

2. Description of Related Art

Some of known profile measuring instruments include a probe that has a stylus tip to be in contact with a workpiece, a movement mechanism for moving the probe, and a controller for controlling the movement mechanism has been conventionally known, where the stylus tip is moved along a target surface of the workpiece while the stylus tip is pressed against the workpiece to measure a profile of the workpiece (see, for instance, Literature 1: JP-A-2005-345123).

A coordinate measuring machine (profile measuring instrument) disclosed in the Literature 1 includes a motion controller that has an autonomous scanning vector generator that generates a velocity vector (probe command value) for moving the stylus tip along a target surface of the workpiece while the stylus tip is pressed against the workpiece.

FIG. 18 shows a stylus tip 100 that is moved along a target surface (lateral face of a truncated cone) of a truncated-cone-shaped workpiece W.

As shown in FIG. 18 , the autonomous scanning vector generator defines a workpiece coordinate system for measuring the profile of the workpiece W, in which a central axis of the workpiece W is defined as a Z W -axis, and two axes orthogonal to the Z W -axis are defined as a X W -axis and Y W -axis. An instance in which the stylus tip 100 is moved along the measurement target face of the workpiece W within a restraining section S (shown in two-dot chain lines in FIG. 18 ) of which coordinate value in the Z W -axis direction (i.e. in a height direction of the workpiece W) is set at a constant Z h to measure the profile of the workpiece W at the Z W -axis coordinate value Z h (referred to as a “constant-height scanning measurement” hereinafter) will be described below. It should be noted that a locus LS of a point to be measured (referred to as a measurement target point hereinafter) is represented by a two-dot chain line in FIG. 18 . Further, in order to simplify the drawing, a part of reference signs to be used in a later-described formula including the above-mentioned Z W -axis coordinate value Z h is omitted in FIG. 18 .

The autonomous scanning vector generator generates a velocity vector V P in an advancement direction of a scanning probe as shown in the following formula (1) supposing that a direction in which the stylus tip 100 is pressed (i.e. a deflection direction of the stylus tip 100 ) is normal to the measurement target face of the workpiece W at a contact point between the stylus tip 100 and the measurement target face.

{right arrow over (V)} P =V S ·{right arrow over (P)} u   (1)

In the formula (1), V S is a parameter for controlling velocity in the advancement direction. For instance, the parameter V S is set to be small when a deviation from the target value in the deflection direction or the height direction becomes large.

The vector P u is a unit vector of a vector P calculated according to the following formula (2).

{right arrow over (P)}={right arrow over (E)}×{right arrow over (Z)} u   (2)

In the formula (2), the operator× represents an outer product of the vector, which also applies in the later formulae.

Thus, the vector P is an outer product of a vector E based on a deflection value of the stylus tip 100 and the unit vector Z u in the Z W -axis direction.

The autonomous scanning vector generator also generates a velocity vector V E in the deflection direction as shown in the following formula (3).

{right arrow over (V)} E =V e ·(| {right arrow over (E)}|−E O )· {right arrow over (E)} u   (3)

In the formula (3), V e is a parameter for controlling the velocity in the deflection direction. E 0 is a reference deflection value of the scanning probe (i.e. a target value in the deflection direction). The vector E u is a unit vector of the vector E.

The autonomous scanning vector generator also generates a velocity vector V H in the height direction of the scanning probe as shown in the following formula (4).

{right arrow over (V)} H =V h ·( C h −Z h )· {right arrow over (H)} h   (4)

In the formula (4), V h is a parameter for controlling the velocity in the height direction. C h is a Z W -axis coordinate value at a center of the stylus tip 100 . Z h is a Z W -axis coordinate value of the restraining section S (a target value in the height direction).

Further, a vector H h is a vector parallel to the measurement target face of the workpiece W of which magnitude in the Z W -axis direction is 1. The vector H h is calculated according to the following formulae (5) and (6).

In the formula (5), the operator (,) represents an inner product of the vector, which also applies in the later formulae.

Thus, the vector H h is equal to the vector H u divided by the inner product of the vector H u and the unit vector Z u in the Z W -axis direction. The vector H u is an outer product of the vector P u and the vector E u .

Then, the autonomous scanning vector generator synthesizes each of the velocity vectors V P , V E and V H as shown in the following formula (7) to generate a velocity vector V C (probe command value) in the scanning direction in which the stylus tip 100 is moved along the measurement target face of the workpiece W.

{right arrow over (V)} C ={right arrow over (V)} F +{right arrow over (V)} E +{right arrow over (V)} H   (7)

FIGS. 19A and 19B illustrate a problem associated with the typical arrangement. Specifically, FIG. 19A is a perspective view of a straight bevel gear W 1 (the workpiece). FIG. 19B is a perspective view in which an area Ar 1 in FIG. 19A is enlarged to show a tooth flank WF 1 (measurement target face).

Incidentally, in order to simplify the drawing, only a part of teeth of the straight bevel gear W 1 is shown in solid lines and the rest of the teeth are imaginarily shown in two-dot chain lines in FIG. 19A .

The tooth flank WF 1 of the straight bevel gear W 1 shown in FIGS. 19A and 19B does not conform to a plane (the above-described restraining section) orthogonal to the Z W -axis (i.e. the central axis of the straight bevel gear W 1 ).

Thus, it is difficult to move the stylus tip along the tooth flank WF 1 according to the above-described constant-height scanning measurement and, consequently, it is difficult to measure the tooth flank WF 1 .

In order to measure the tooth flank WF 1 of the straight bevel gear W 1 as shown in FIGS. 19A and 19B , a point measurement in which the stylus tip is brought into contact with a plurality of points on the tooth flank WF 1 may be employed instead of the autonomous scanning measurement.

However, the measurement of the tooth flank WF 1 by way of the point measurement requires much measurement time.

An object of the invention is to provide a profile measuring method and a profile measuring instrument capable of reducing a measurement time.

A profile measuring method according to an aspect of the invention uses a profile measuring instrument, the profile measuring instrument including: a probe having a stylus tip to be in contact with a workpiece; a movement mechanism that is adapted to move the probe; and a controller that is adapted to control the movement mechanism, the stylus tip being moved along a measurement target face of the workpiece while the stylus tip is pressed against the measurement target face of the workpiece to measure a profile of the measurement target face, the method including: acquiring profile information on the profile of the workpiece; and calculating a probe command value for moving the probe by the movement mechanism based on the profile information acquired in the acquiring of the information, the acquiring of the information and the calculating of the probe command value being performed by the controller, in which the probe command value is a value for causing a movement of the stylus tip along a lateral face of an imaginary cone that is imaginarily defined in accordance with the profile of the workpiece based on the profile information, the movement of the stylus tip being performed while a distance between a center of the stylus tip and a reference axis passing through a center of a bottom face of the imaginary cone and parallel to the lateral face of the imaginary cone is kept constant.

The outer profile of the straight bevel gear is in a form of a substantially truncated cone that defines a part of a cone. The tooth flank of the straight bevel gear extends along a lateral face of a cone imaginarily defined in accordance with the outer profile of the straight bevel gear (referred to as an imaginary cone) and substantially conforms to a vertical cross section of the imaginary cone.

In the above aspect of the invention, based on the finding that the tooth flank (measurement target face) of the straight bevel gear extends along the lateral face of the imaginary cone and substantially conforms to the vertical cross section of the imaginary cone, the profile measuring method employs the above-described acquiring of the information (information acquisition step) and the calculating of the probe command value (probe-command-value calculating step).

Specifically, in the information acquisition step, the controller of the profile measuring instrument acquires profile information related to the profile of the workpiece (straight bevel gear) (information including an apex angle of the imaginary cone imaginarily defined in accordance with the outer profile of the straight bevel gear, a radius of a bottom surface of the imaginary cone and a center of the bottom surface of the imaginary cone).

In the probe-command-value calculating step, the controller calculates the probe command value for causing the movement of the stylus tip along the lateral face of the imaginary cone, the movement of the stylus tip being performed while a distance between a center of the stylus tip and a reference axis passing through the center of the bottom face of the imaginary cone and parallel to the lateral face of the imaginary cone is kept constant.

Thus, by operating the movement mechanism in accordance with the probe command value, the stylus tip can be moved along the tooth flank of the straight bevel gear. In other words, the tooth flank of the straight bevel gear can be measured by an autonomous scanning measurement.

Thus, as compared to an instance in which the tooth flank of the straight bevel gear is measured by a point measurement, the measurement time can be significantly reduced.

In the profile measuring method according to the above aspect of the invention, it is preferable that the profile measuring instrument comprises a rotary table on which the workpiece is adapted to be fixed, the rotary table being adapted to be rotated to rotate the workpiece relative to the probe, and the profile measuring method further includes calculating a table command value for rotating the rotary table based on the probe command value calculated in the calculating of the probe command value, the calculating of the table command value being performed by the controller.

In the above aspect of the invention, the above-described calculating of the table command value (table-command-value calculating step) is performed.

Thus, the autonomous scanning measurement can be performed on a tooth flank of a helical bevel gear etc. having a curved tooth trace as well as the above-described straight bevel gear having a straight tooth trace.

Specifically, in the table-command-value calculating step, the table command value for rotating the rotary table is calculated based on the probe command value. Thus, by rotating the rotary table in synchronization with the table command value, the rotary table (workpiece) can be rotated in synchronization with the movement of the stylus tip based on the probe command value, whereby the stylus tip can be moved along the curved tooth trace of the helical bevel gear and the like.

In addition, since the rotary table can be rotated in synchronization with the movement of the stylus tip in accordance with the probe command value, it is not necessary to alter the attitude of the probe considering the mechanical interference between the helical bevel gear and the probe when the autonomous scanning measurement is performed on the tooth flank of the helical bevel gear and the like. In other words, since it is not necessary to alter the attitude of the probe, the measurement time can be further reduced.

A profile measuring instrument according to another aspect of the invention includes: a probe having a stylus tip to be in contact with a workpiece; a movement mechanism that is adapted to move the probe; and a controller that is adapted to control the movement mechanism, the stylus tip being moved along a measurement target face of the workpiece while the stylus tip is pressed against the measurement target face of the workpiece to measure a profile of the measurement target face, in which the controller includes: an information acquirer that acquires profile information on the profile of the workpiece; and a probe command unit that calculates a probe command value for moving the probe by the movement mechanism based on the profile information acquired by the information acquirer, and the probe command value is a value for causing a movement of the stylus tip along a lateral face of an imaginary cone that is imaginarily defined in accordance with an outer profile of the workpiece based on the profile information, the movement of the stylus tip being performed while a distance between a center of the stylus tip and a reference axis passing through a center of a bottom face of the imaginary cone and parallel to the lateral face of the imaginary cone is kept constant.

Since the profile measuring instrument of the above aspect of the invention is adapted to implement the above-described profile measuring method, advantages and effects similar to those of the above-described profile measuring method can be obtained.

FIG. 1 schematically illustrates an overview of a coordinate measuring machine according to a first exemplary embodiment of the invention.

FIG. 2 is a block diagram showing an overall structure of the coordinate measuring machine according to the first exemplary embodiment.

FIG. 3 is an illustration schematically showing a probe command value according to the first exemplary embodiment.

FIG. 4 is another illustration schematically showing the probe command value according to the first exemplary embodiment.

FIG. 5 is a flowchart showing a profile measuring method according to the first exemplary embodiment.

FIG. 6A is an illustration showing the profile measuring method according to the first exemplary embodiment.

FIG. 6B is another illustration showing the profile measuring method according to the first exemplary embodiment.

FIG. 6C is still another illustration showing the profile measuring method according to the first exemplary embodiment.

FIG. 6D is a further illustration showing the profile measuring method according to the first exemplary embodiment.

FIG. 6E is a still further illustration showing the profile measuring method according to the first exemplary embodiment.

FIG. 7A is an illustration showing a Step S 6 according to the first exemplary embodiment.

FIG. 7B is another illustration showing the Step S 6 according to the first exemplary embodiment.

FIG. 8 is a flowchart showing a Step S 7 according to the first exemplary embodiment.

FIG. 9A is an illustration showing the Step S 7 according to the first exemplary embodiment.

FIG. 9B is another illustration showing the Step S 7 according to the first exemplary embodiment.

FIG. 10 schematically illustrates an overview of a coordinate measuring machine according to a second exemplary embodiment of the invention.

FIG. 11 is a block diagram showing an overall structure of the coordinate measuring machine according to the second exemplary embodiment.

FIG. 12A illustrates a workpiece in the second exemplary embodiment.

FIG. 12B illustrates the workpiece in the second exemplary embodiment.

FIG. 13 is a flowchart showing a profile measuring method according to the second exemplary embodiment.

FIG. 14 is a flowchart showing a Step S 8 according to the second exemplary embodiment.

FIG. 15 is an illustration showing the Step S 8 according to the second exemplary embodiment.

FIG. 16A is another illustration showing the Step S 8 according to the second exemplary embodiment.

FIG. 16B is still another illustration showing the Step S 8 according to the second exemplary embodiment.

FIG. 17A is a further illustration showing the Step S 8 according to the second exemplary embodiment.

FIG. 17B is a still further illustration showing the Step S 8 according to the second exemplary embodiment.

FIG. 17C is a still further illustration showing the Step S 8 according to the second exemplary embodiment.

FIG. 17D is a still further illustration showing the Step S 8 according to the second exemplary embodiment.

FIG. 18 shows a stylus tip moved along a measurement target face of a truncated-cone-shaped workpiece W.

FIG. 19A illustrates a problem associated with a typical arrangement.

FIG. 19B illustrates the problem associated with the typical arrangement.

First Exemplary Embodiment

A first exemplary embodiment of the invention will be described below with reference to the attached drawings.

Overall Structure of Coordinate Measuring Machine

FIG. 1 schematically illustrates an overview of a coordinate measuring machine 1 according to the first exemplary embodiment.

FIG. 2 is a block diagram showing an overall structure of the coordinate measuring machine 1 .

It should be noted that an upper direction in FIG. 1 will be referred to as +Z-axis direction and two axes orthogonal to the Z-axis will be respectively referred to as X-axis and Y-axis. The X-axis direction, Y-axis direction and Z-axis direction define a machine coordinate system. This also applies in the rest of drawings.

In this exemplary embodiment, for the convenience of description, a straight bevel gear W 1 (with a tooth flank WF 1 (measurement target face)) shown in FIGS. 19A and 19B will be used as a workpiece.

As shown in FIG. 1 or 2 , the coordinate measuring machine 1 (profile measuring instrument) includes: a coordinate measuring machine body 2 ; a motion controller 3 for controlling a drive of the coordinate measuring machine body 2 ; an operating unit 4 that provides a command to the motion controller 3 via a control lever and the like to manually operate the coordinate measuring machine body 2 ; a host computer 5 that provides a predetermined command to the motion controller 3 and performs an arithmetic processing; and an input unit 61 ( FIG. 1 ) and an output unit 62 ( FIG. 1 ) that are connected with the host computer 5 .

The input unit 61 inputs measurement conditions and the like of the coordinate measuring machine 1 to the host computer 5 . The output unit 62 outputs the measurements of the coordinate measuring machine 1 .

Structure of Coordinate Measuring Machine Body

As shown in FIG. 1 , the coordinate measuring machine body 2 includes a probe 21 having a spherical stylus tip 211 A for measuring a workpiece, a movement mechanism 22 that holds and moves the probe 21 and a base 23 on which the movement mechanism 22 is vertically provided.

As shown in FIG. 1 , the probe 21 includes a stylus 211 having a stylus tip 211 A at an end thereof (in −Z-axis direction) and a support mechanism 212 that supports a base end (in +Z-axis direction) of the stylus 211 .

The support mechanism 212 supports the stylus 211 while biasing the stylus 211 in each of the X, Y and Z-axis directions so that the stylus 211 is located at a predetermined position. The support mechanism 212 also allows the movement of the stylus 211 in each of the X, Y and Z-axis directions within a predetermined range when an external force is applied (i.e. when the stylus tip 211 A is in contact with the workpiece).

Though not specifically shown, probe sensors for detecting the position of the stylus 211 in the respective axis directions are provided to the support mechanism 212 .

Incidentally, each of the probe sensors are provided by a position sensor that outputs pulse signals in accordance with the displacement of the stylus 211 in the respective axis directions.

As shown in FIGS. 1 and 2 , the movement mechanism 22 includes a slide mechanism 24 that holds the probe 21 and allows a slide movement of the probe 21 and a drive mechanism 25 that drives the slide mechanism 24 to move the probe 21 .

As shown in FIG. 1 , the slide mechanism 24 includes: two columns 241 that extend in +Z-axis direction from both ends of the base 23 in the X-axis direction and are capable of slide movement in the Y-axis direction; a beam 242 that is supported by the columns 241 and extend in the X-axis direction; a cylindrical slider 243 that extends in the Z-axis direction and is capable of slide movement in the X-axis direction on the beam 242 ; and a ram 244 inserted into the slider 243 in a manner capable of slide movement in the Z-axis direction inside the slider 243 .

As shown in FIG. 1 or 2 , the drive mechanism 25 includes a Y-axis drive unit 251 Y that supports one of the columns 241 located in the +X-axis direction and effects a slide movement of the column 241 in the Y-axis direction; an X-axis drive unit 251 X ( FIG. 2 ) that causes the slide movement of the slider 243 on the beam 242 to move the slider 243 in the X-axis direction; and a Z-axis drive unit 251 Z ( FIG. 2 ) that causes the slide movement of the ram 244 inside the slider 243 to move the ram 244 in the Z-axis direction.

Though not specifically shown, a scale sensor for detecting the positions of the slider 243 , the columns 241 or the ram 244 in the respective axis directions is provided to each of the X-axis drive unit 251 X, the Y-axis drive unit 251 Y and the Z-axis drive unit 251 Z.

Incidentally, each of the scale sensors is provided by a position sensor that outputs pulse signals in accordance with the displacement of the slider 243 , the columns 241 and the ram 244 .

Structure of Motion Controller

As shown in FIG. 2 , the motion controller 3 (controller) includes an information acquirer 31 , a counter unit 32 , an arithmetic processor 33 , storage 34 , a probe command unit 35 and a drive control unit 36 .

The information acquirer 31 acquires from the host computer 5 a profile data of the straight bevel gear W 1 and the measurement condition data of the straight bevel gear W 1 .

The counter unit 32 counts the pulse signals outputted from the respective scale sensors to measure the displacement of the slide mechanism 24 and counts the pulse signals outputted from the respective probe sensors to measure the displacement of the stylus 211 .

The arithmetic processor 33 calculates the position P P of the stylus tip 211 A (referred to as a probe position P P (see FIGS. 9A and 9B )) based on the displacement of the slide mechanism 24 and the displacement of the stylus 211 measured by the counter unit 32 .

The arithmetic processor 33 stores the calculated probe position P P in the storage 34 .

In addition, the arithmetic processor 33 calculates the overtraveling amount (magnitude of the vector E) of the stylus tip 211 A based on the displacement (detection values (x, y, z) of the respective probe sensors) of the stylus 211 measured by the counter unit 32 as shown in the following formula (8).

|{right arrow over ( E )}|=√{square root over ( x 1 +y 2 +z 2 )}  (8)

FIGS. 3 and 4 are illustrations schematically showing a probe command value. Specifically, FIG. 3 is a perspective view of an imaginary cone IC imaginarily defined in accordance with an outer profile of the straight bevel gear W 1 . FIG. 4 is a vertical cross section of FIG. 3 .

Based on the probe position P P and the overtraveling amount calculated by the arithmetic processor 33 and the profile information acquired by the information acquirer 31 , the probe command unit 35 calculates the probe command value for moving the stylus tip 211 A along the tooth flank WF 1 of the straight bevel gear W 1 while the stylus tip 211 A is pressed against the tooth flank WF 1 .

As shown in FIGS. 3 and 4 , the outer profile of the straight bevel gear W 1 is in a form of a substantially truncated cone that defines a part of the cone IC. In other words, the virtual cone IC (imaginary cone IC) can be assumed in accordance with the outer profile of the straight bevel gear W 1 . The tooth flank WF 1 of the straight bevel gear W 1 extends along the lateral face of the imaginary cone IC and substantially conforms to a vertical cross section of the imaginary cone IC.

The probe command value is a command value for moving the stylus tip 211 A along the lateral face of the imaginary cone IC while a distance between the position P P (referred to as probe position P P hereinafter) (see FIGS. 9A and 9B ) of the stylus tip 211 A and a reference axis SAx (see FIG. 9A ) passing through a center P C (see FIGS. 9A and 9B ) of the imaginary cone IC and parallel to the lateral face of the imaginary cone IC stays constant.

The drive control unit 36 controls the drive mechanism 25 to move the probe 21 according to the probe command value calculated by the probe command unit 35 .

Structure of Host Computer

The host computer 5 includes a CPU (Central Processing Unit), memory and the like. The host computer 5 provides a predetermined command to the motion controller 3 to control the coordinate measuring machine body 2 .

As shown in FIG. 2 , the host computer 5 includes a form analyzer 51 and storage 52 .

The form analyzer 51 calculates a surface profile data of the workpiece based on the measurement data (probe position P P stored in the storage 34 ) outputted from the motion controller 3 and performs a profile analysis for calculating an error or distortion of the calculated surface profile data of the workpiece.

The storage 52 stores the data used in the host computer 5 , profile data (profile information) related to the profile of the straight bevel gear W 1 (workpiece), the measurement condition data of the straight bevel gear W 1 and the like.

The profile data includes a radius r of the bottom face of the imaginary cone IC that is imaginarily defined in accordance with the outer profile of the straight bevel gear W 1 , coordinates of the center P C of the imaginary cone IC, a semi-apex angle α of the imaginary cone IC (in which positive (+) is defined in a direction enlarging from the center P C to an apex of the imaginary cone IC) and the like (see FIG. 9A ).

The measurement condition data is a data designated in accordance with the outer profile of the straight bevel gear W 1 . The measurement condition data includes coordinates of the temporarily designated measurement start point, information on an approach direction for pressing the stylus tip 211 A from the measurement start point against the tooth flank WF 1 of the straight bevel gear W 1 and the like.

Profile Measuring Method

Next, a profile measuring method using the above-described coordinate measuring machine 1 will be described below.

FIG. 5 is a flowchart showing the profile measuring method.

FIGS. 6A to 6E are illustrations showing the profile measuring method. Specifically, FIGS. 6A to 6E are illustrations showing Steps S 2 to S 7 .

Initially, the information acquirer 31 acquires from the host computer 5 the profile data and the measurement condition data of the straight bevel gear W 1 (both of the profile data and the measurement condition data being stored in the storage 52 ) (step S 1 : information acquisition step).

After the step S 1 , the probe command unit 35 recognizes the probe position P P calculated by the arithmetic processor 33 . Further, the probe command unit 35 outputs to the drive control unit 36 the probe command value for locating the probe position P P at the measurement start point contained in the measurement condition data based on the measurement condition data of the straight bevel gear W 1 acquired in the Step S 1 (Step S 2 ).

Then, the drive control unit 36 controls the drive mechanism 25 to move the probe 21 to the measurement start point P s as shown in FIG. 6A .

After the Step S 2 , the probe command unit 35 outputs to the drive control unit 36 the probe command value for moving the stylus tip 211 A in the approach direction contained in the measurement condition data (Step S 3 ).

The drive control unit 36 controls the drive mechanism 25 to press the stylus tip 211 A against the tooth flank WF 1 as shown in FIG. 6B .

After the Step S 3 , the probe command unit 35 judges whether or not the stylus tip 211 A is brought into contact with the tooth flank WF 1 and a target overtraveling amount is exceeded while checking the overtraveling amount of the stylus tip 211 A calculated by the arithmetic processor 33 (Step S 4 ).

When the probe command unit 35 judges “Y” in the Step S 4 , the probe command unit 35 outputs to the drive control unit 36 the probe command value for stopping the movement of the stylus tip 211 A in the approach direction (Step S 5 ).

Then, the drive control unit 36 controls the drive mechanism 25 to stop the movement of the stylus tip 211 A in the approach direction.

After the Step S 5 , the probe command unit 35 outputs the probe command value for locating the probe position P P on a scanning path to the drive control unit 36 (Step S 6 ).

Then, the drive control unit 36 controls the drive mechanism 25 to move the probe 21 to the scanning path (the lateral face of the imaginary cone IC) as shown in FIG. 6C .

FIGS. 7A and 7B illustrate the Step S 6 . Specifically, FIG. 7A corresponds to FIG. 6C . FIG. 7B is an illustration showing a part of FIG. 7A that is turned so that a Z temp axis is oriented in up-and-down direction in the figure.

In the Step S 6 , the probe command unit 35 calculates the probe command value for locating the probe position P P on the scanning path as described below.

Herein, based on the profile data (the radius r of the bottom face of the imaginary cone IC, the semi-apex angle α of the imaginary cone IC) of the straight bevel gear W 1 acquired in the Step S 1 , a temporary coordinate system defined by the Z temp axis (an axis along the lateral face of the imaginary cone IC) and X temp axis and Y temp axis orthogonal to the Z temp axis can be assumed.

An origin O temp of the temporary coordinate system is defined at a desired point on the Z temp axis.

The probe command unit 35 then recognizes the probe position P P (the probe position P P of the probe 21 shown in dashed lines in FIG. 7A ) calculated by the arithmetic processor 33 , and calculates the probe command value for moving the stylus tip 211 A in a restraining section S′ (two-dot chain line in FIG. 7B ) in which Z temp -axis coordinate value at the probe position P P stays at a constant Z a and to locate the probe position P P on the Z temp -axis (scanning path).

After the Step S 6 , as shown in FIG. 6D , the motion controller 3 moves the probe 21 along the scanning path (the lateral face of the imaginary cone IC) to start an autonomous scanning measurement (Step S 7 ).

FIG. 8 is a flowchart showing the Step S 7 .

FIGS. 9A and 9B illustrate the Step S 7 .

Incidentally, in order to simplify the drawing, a part of reference signs to be used in a later-described formula is omitted in FIGS. 9A and 9B .

Initially, the arithmetic processor 33 acquires the displacements of the slide mechanism 24 and the stylus 211 measured by the counter unit 32 (Step S 7 A).

After the Step S 7 A, the arithmetic processor 33 calculates the probe position P P based on the acquired displacements of the slide mechanism 24 and the stylus 211 and calculates the overtraveling amount of the stylus tip 211 A (Step S 7 B).

After the Step S 7 B, the arithmetic processor 33 judges whether or not the displacement ΔP of the probe position P P exceeds a predetermined pitch (Step S 7 C).

It should be noted that the above-mentioned displacement ΔP refers to a sum of difference values of the respective probe positions P P (i.e. the difference between the probe position P P stored in the storage 34 as the measurement data in the below-described Step S 7 D and the probe position(s) P P calculated in the Step S 7 B based on the displacements of the slide mechanism 24 and the stylus 211 acquired in the Step S 7 A per a predetermined sampling time (e.g. 0.4 msec)).

For instance, supposing that a probe position P P1 , a probe position P P2 and a probe position P P3 are respectively defined as the probe position P P stored as the measurement data in the Step S 7 D, a probe position P P1 ; the probe position P P calculated in the Step S 7 B after elapsing the sampling time, and the probe position P P calculated in the Step S 7 B after elapsing the next sampling time (i.e. the current time), the displacement ΔP is the sum of the difference value between the probe positions P P1 and P P2 and the difference value between the probe positions P P2 and P P3 .

When the arithmetic processor 33 judges “Y” in the Step S 7 C, the arithmetic processor 33 stores the probe position P P calculated in the preceding Step S 7 B (corresponding to the probe position P P3 in the above instance) in the storage 34 as the measurement data (Step S 7 D). Then, the motion controller 3 performs the processing in Step S 7 E.

On the other hand, when the motion controller 3 judges “N” in the Step S 7 C, the motion controller 3 performs the processing in the Step S 7 E without performing the processing in the Step S 7 D.

In the Step S 7 E, the probe command unit 35 calculates the probe command value for moving the stylus tip 211 A along the tooth flank WF 1 while the stylus tip 211 A is pressed against the tooth flank WF 1 based on the probe position P P and the overtraveling amount of the stylus tip 211 A calculated in the Step S 7 B and the profile data of the straight bevel gear W 1 acquired by the information acquirer 31 (probe-command-value calculating step).

Specifically, the probe command unit 35 generates the velocity vector V C (probe command value) different from the above formula (7) in the workpiece coordinate system (the coordinate system defined by the central axis of the straight bevel gear W 1 (Z W -axis) and X W -axis and Y W -axis defined by the Z W -axis) as described below.

The probe command unit 35 generates the velocity vector V H oriented in a V h direction (i.e. a direction passing through the probe position P P and perpendicular to a reference axis SAx) (see FIG. 9A ) as shown in the following formula (9).

{right arrow over (V)} H =h·{right arrow over (V)}h   (9)

In the formula (9), h represents a deviation of the probe position P P from the lateral face of the imaginary cone IC (a parameter for controlling the velocity in the V h direction).

h is calculated according to the formula (10) below with the use of a unit vector V hu in the V h direction (see formula (11) below), a vector Q from the central axis (Z W -axis) of the imaginary cone IC toward the probe position P P along a direction perpendicular to the central axis (see formula (12) below) and a vector S from the center P C to the probe position P P .

h =( {right arrow over (V)} hu ,{right arrow over (S)} )− r ·cos(α)  (10)

{right arrow over (V)} hu =sin(−α)· {right arrow over (Z)} u +cos(α)· {right arrow over (Q)} u   (11)

{right arrow over (Q)}={right arrow over (S)} −( {right arrow over (Z)} u ,{right arrow over (S)} )· {right arrow over (Z)} u   (12)

In the formula (11), a vector Q u is a unit vector of the vector Q. Further, in the formula (12), a vector Z u is a unit vector in the Z W -axis direction.

In other words, the probe command unit 35 calculates the vector Q according to the formula (12) with the use of the vector S and a vector projecting the vector S in the Z W -axis direction (second term in the right-hand side of the formula (12)). Then, after calculating the V h direction by rotation according to the formula (11) with the use of the vectors Z u and Q u and the semi-apex angle α, the probe command unit 35 calculates the deviation h according to the formula (10).

Further, as shown in the following formula (13), the probe command unit 35 generates the velocity vector V E in an overtraveling direction (deflection direction) E ( FIG. 9B ) of the stylus tip 211 A against the tooth flank WF 1 .

{right arrow over (V)} E =m ·( |{right arrow over (E)}−E O )· {right arrow over (E)} u   (13)

In the formula (13), m is a parameter for controlling the velocity in the overtraveling direction E. E 0 is a reference displacement of the stylus tip 211 A (i.e. a target value in the overtraveling direction E). Specifically, when the overtraveling amount of the stylus tip 211 A calculated in the Step S 7 B is E 0 , the velocity in the overtraveling direction E can be calculated as 0 as shown in the formula (13). Further, the vector E u is a unit vector of the vector E based on the overtraveling amount of the stylus tip 211 A calculated in the Step S 7 B.

Further, as shown in the following formula (14), the probe command unit 35 generates a velocity vector V F in an advancement direction V ( FIGS. 9A and 9B ) of the stylus tip 211 A.

{right arrow over (V)} F =n·{right arrow over (V)} u   (14)

In the formula (14), n is a parameter for controlling the velocity in the advancement direction. The vector V u is a unit vector of a vector V calculated according to the following formula (15).

{right arrow over (V)}={right arrow over (V)} hu ×{right arrow over (E)} u   (15)

Thus, the direction of the outer product of the unit vector V hu in the V h direction and the unit vector E u of the vector E based on the overtraveling amount of the stylus tip 211 A is defined as the advancement direction of the stylus tip 211 A in this exemplary embodiment.

Then, the probe command unit 35 synthesizes each of the velocity vectors V H , V E and V F as shown in the following formula (16) to generate a velocity vector V C (probe command value) in the scanning direction in which the stylus tip 211 A is moved along the tooth flank WF 1 .

In other words, the probe command unit 35 generates the probe command value for moving the stylus tip 211 A in a direction summing the V h direction, the overtraveling direction E and the advancement direction V.

{right arrow over (V)} C ={right arrow over (V)} H +{right arrow over (V)} E +{right arrow over (V)} F   (16)

After the Step S 7 E, the probe command unit 35 outputs the velocity vector V C calculated in the Step S 7 E to the drive control unit 36 (Step S 7 F).

Then, the stylus tip 211 A is moved in accordance with the velocity vector V C shown in the formula (16), whereby the stylus tip 211 A is moved along the lateral face of the imaginary cone IC while keeping a constant distance between the reference axis SAx and the probe position P P (i.e. conforming to the tooth flank WF 1 ).

As described above, the velocity vector V C (probe command value) is calculated for every predetermined sampling time in the Step S 7 E and the velocity vector V C is outputted to the drive control unit 36 in the Step S 7 F in this exemplary embodiment.

After the Step S 7 F, the motion controller 3 recognizes the number of the measurement data (probe position P P ) stored in the storage 34 and judges whether or not the number of the measurement data exceeds a designated point number N (Step S 7 G).

When the motion controller 3 judges “N” in the Step S 7 G, the motion controller 3 again performs the processing of the Step S 7 A.

On the other hand, when the probe command unit 35 judges “Y” in the Step S 7 G, the probe command unit 35 outputs to the drive control unit 36 the probe command value for stopping the movement of the stylus tip 211 A (Step S 7 H).

Then, the stylus tip 211 A stops its movement while being in contact with the tooth flank WF 1 .

After the step S 7 H, the probe command unit 35 outputs to the drive control unit 36 the probe command value for moving the stylus tip 211 A in the normal direction of the tooth flank WF 1 based on the overtraveling amount of the stylus tip 211 A calculated by the arithmetic processor 33 (Step S 7 I).

Then, the probe 21 (stylus tip 211 A) is separated from the tooth flank WF 1 .

After the step S 7 I, the motion controller 3 outputs the N measurement data (probe positions P P ) stored in the storage 34 to the host computer 5 (step S 7 J).

Based on the N measurement data, the profile analysis is performed by the host computer 5 (form analyzer 51 ).

The above-described first exemplary embodiment provides the following advantages.

In the first exemplary embodiment, based on the finding that the tooth flank WF 1 of the straight bevel gear W 1 (workpiece) extends along the lateral face of the virtually defined imaginary cone IC and substantially conforms to the vertical cross section of the imaginary cone IC, the profile measuring method employs the information acquisition step S 1 and the probe-command-value calculating step S 7 E.

The stylus tip 211 A is moved along the velocity vector V C calculated in the probe-command-value calculating step S 7 E, whereby the stylus tip 211 A is movable along the lateral face of the imaginary cone IC while keeping a constant distance between the reference axis SAx and the probe position P P (i.e. conforming to the tooth flank WF 1 ). In other words, the tooth flank WF 1 of the straight bevel gear W 1 can be measured by the autonomous scanning measurement.

Thus, as compared to an instance in which the tooth flank WF 1 of the straight bevel gear W 1 is measured by a point measurement, the measurement time can be significantly reduced.

Second Exemplary Embodiment

Next, a second exemplary embodiment of the invention will be described below.

Incidentally, the same components as those in the first exemplary embodiment will be denoted by the same reference signs and the like and detailed description of the components will be omitted below.

FIG. 10 schematically illustrates an overview of a coordinate measuring machine 1 according to the second exemplary embodiment.

FIG. 11 is a block diagram showing an overall structure of the coordinate measuring machine 1 .

FIGS. 12A and 12B illustrate a helical bevel gear W 2 (workpiece). Specifically, FIG. 12A is a perspective view of the helical bevel gear W 2 . FIG. 12B is a perspective view enlarging an area Ar 2 in FIG. 12A to show a tooth flank WF 2 (measurement target face).

Incidentally, in order to simplify the drawing, only a part of teeth of the helical bevel gear W 2 is shown in solid lines and the rest of the teeth are imaginarily shown in two-dot chain lines in FIG. 12A in a manner similar to FIG. 19A .

The second exemplary embodiment differs from the first exemplary embodiment only in that, as shown in FIGS. 10 to 12B , a different workpiece is used and, in accordance with the difference in the workpiece, a rotary table 26 and a rotation drive unit 27 are added to the coordinate measuring machine body 2 while a table command unit 37 is added to the motion controller 3 . The rest of the components are the same as those in the first exemplary embodiment.

Specifically, as shown in FIGS. 12A and 12B , the helical bevel gear W 2 (with the tooth flank WF 2 as the measurement target face) having a curved tooth trace is used instead of the straight bevel gear W 1 having a linear tooth trace.

The rotary table 26 is a substantially disc-shaped member, which is supported on an upper surface of the base 23 in a manner rotatable around a central axis (Z t -axis (see FIG. 15 )) of the rotary table 26 .

The helical bevel gear W 2 is fixed on the rotary table 26 with a chuck (not shown) provided to the rotary table 26 .

Incidentally, the helical bevel gear W 2 may be fixed on the rotary table 26 at a position where a central axis (Z W -axis) of the helical bevel gear W 2 matches the central axis (Z t -axis) of the rotary table 26 or, alternatively, the helical bevel gear W 2 may be fixed on the rotary table 26 at a position where the Z W -axis does not match the Z t -axis. In the later-described FIG. 15 , the latter instance is illustrated.

The rotation drive unit 27 rotates the rotary table 26 along the upper surface of the base 23 .

Incidentally, though not illustrated, the rotation drive unit 27 is provided with a sensor for detecting a rotation amount of the rotary table 26 . The sensor outputs pulse signals corresponding to the rotation amount of the rotary table 26 . The counter unit 32 counts the pulse signals outputted from the above-described sensor to measure the rotation amount of the rotary table 26 and outputs the rotation amount to the host computer 5 . The form analyzer 51 performs a profile analysis based on the measurement data outputted from the motion controller 3 and the rotation amount of the rotary table 26 .

The table command unit 37 calculates a table command value for rotating the rotary table 26 based on the velocity vector V C calculated by the probe command unit 35 .

Next, a profile measuring method according to the second exemplary embodiment will be described below.

FIG. 13 is a flowchart showing the profile measuring method according to the second exemplary embodiment.

FIG. 14 is a flowchart showing a Step S 8 .

FIGS. 15 to 17D are illustrations showing the Step S 8 .

Incidentally, FIGS. 17A to 17D illustrate a workpiece W different from the helical bevel gear W 2 in order to schematically show a control process for keeping a constant orientation of the stylus tip 211 A.

In the profile measuring method according to the second exemplary embodiment, the Step S 8 as described below is performed as shown in FIG. 13 instead of the Step S 7 in the profile measuring method according to the first exemplary embodiment. Thus, the Step S 8 will be mainly described below.

Incidentally, the data acquired in the Step S 1 in the second exemplary embodiment is a profile data related to the helical bevel gear W 2 (i.e. a data including the radius r of the bottom face of the imaginary cone IC that is imaginarily defined in accordance with the outer profile of the helical bevel gear W 2 (see FIGS. 16A and 16B ) and the like), and the measurement condition data (i.e. a data including coordinates of the temporarily designated measurement start point and the like) that is designated in accordance with the outer profile of the helical bevel gear W 2 .

In the Steps S 2 to S 6 , the processing is performed based on the measurement condition data of the helical bevel gear W 2 . The same applies in the Step S 7 E.

Initially, the motion controller 3 performs the Steps S 7 A to S 7 E in the same manner as in the first exemplary embodiment.

After the Step S 7 E, the table command unit 37 calculates the table command value (an angular velocity ω t for rotating the rotary table 26 ) based on the velocity vector V C (probe command value) calculated in the Step S 7 E as shown below (Step S 7 K: table-command-value calculating step).

It should be noted that the Step S 7 K is substantially the same as a calculation process of an angular velocity ω t disclosed in JP-B-3433710. Thus, the description of the Step S 7 K will be simplified below.

Initially, the table command unit 37 calculates an angular velocity ω w of the rotary table 26 around the central axis (Z W -axis) of the helical bevel gear W 2 with reference to the velocity vector V C of the probe 21 .

Specifically, the table command unit 37 calculates the angular velocity ω w according to the following formula (17).

In the formula (17), the vector C r is a perpendicular vector drawn from the probe position P P to the Z W -axis as shown in FIG. 15 . The vector C u is a unit vector in a reference direction C ( FIG. 15 ) relative to the vector C r .

Incidentally, the reference direction C shown in FIG. 15 represents a direction at a position at which a rotary angle θ of the rotary table 26 and the probe position P P are situated as shown in FIG. 15 . In other words, the reference direction C varies in accordance with the rotation of the rotary table 26 .

Next, the table command unit 37 adjusts an advancement or delay relative to a target value of the rotary angle θ due to a control error with reference to the rotary angle θ of the rotary table 26 and the positional relationship of the probe position P P and calculates a corrected angular velocity Δω so that the vector C r always becomes 90 degrees against the reference direction C.

Specifically, the table command unit 37 calculates the corrected angular velocity Δω according to the following formula (18).

Δω= S ·( {right arrow over (C)} u ,{right arrow over (C)} ru )  (18)

In the formula (18), n is a angular velocity compensation coefficient of the rotary table 26 . The vector C ru is a unit vector of the vector C r .

The table command unit 37 calculates the angular velocity ω t for rotating the rotary table 26 according to the following formula (19).

ω t =ω w +Δω  (19)

After the Step S 7 K, the probe command unit 35 and the table command unit 37 outputs the probe command value to the drive control unit 36 and outputs the table command value (angular velocity ω t ) to the rotation drive unit 27 (Step S 7 L).

In the second exemplary embodiment, the probe command unit 35 outputs to the drive control unit 36 the probe command value substantially the same as the probe command value disclosed in JP-B-3433710 in the Step S 7 L.

Specifically, the probe command unit 35 calculates a velocity vector V ωt at a point X (probe position P P ) when the rotary table 26 is rotated at the angular velocity ω t according to the following formula (20).

Then, as shown in the following formula (21), the probe command unit 35 outputs a vector sum V T of the velocity vector V ωt calculated by the formula (20) and the velocity vector V C calculated in the Step S 7 E as the probe command value.

The probe 21 is moved in accordance with the velocity vector V T and the rotary table 26 is moved according to the angular velocity ω t , whereby the stylus tip 211 A moves along the tooth flank WF 2 of the helical bevel gear W 2 as shown in FIGS. 16A and 16B .

According to the components of the velocity vector V ωt in the velocity vector V T , the orientation of the stylus tip 211 A can be kept constant as shown in FIGS. 17A to 17D .

Specifically, even when the rotary table 26 is rotated in an order from FIG. 17A to FIG. 17D as the time passes, a vector B (i.e. a vector defined by projecting the vector extending from an origin C of the workpiece W (corresponding to the center P C (Z W -axis) of the bottom face of the imaginary cone IC) to the probe position P P on the table surface of the rotary table 26 ) can be kept constant with reference to the machine coordinate system.

Incidentally, in the second exemplary embodiment, the probe command value and the table command value are calculated per a predetermined sampling time in the Steps S 7 E and S 7 K and the probe command value and the table command value are outputted to the drive control unit 36 and the rotation drive unit 27 in the Step S 7 L as in the first exemplary embodiment.

After the Step S 7 L, the motion controller 3 performs the Steps S 7 G to 57 J in the same manner as in the first exemplary embodiment.

The above-described second exemplary embodiment provides the following advantages in addition to the same advantages as those in the first exemplary embodiment.

In the second exemplary embodiment, the profile measuring method is provided with the table-command-value calculating step S 7 K.

Since the rotary table 26 , the rotation drive unit 27 and the table command unit 37 are added to the coordinate measuring machine 1 and the table-command-value calculating step S 7 K is added in the profile measuring method as compared to the first exemplary embodiment, the autonomous scanning measurement can be performed on the tooth flank WF 2 of the helical bevel gear W 2 of which tooth trace is curved unlike the straight bevel gear W 1 .

Specifically, in the table-command-value calculating step S 7 K, the table command value for rotating the rotary table 26 is calculated based on the velocity vector V C calculated in the probe-command-value calculating step S 2 . Thus, the rotary table 26 (helical bevel gear W 2 ) can be rotated in synchronization with the movement of the stylus tip 211 A in accordance with the velocity vector V C , whereby the stylus tip 211 A can be moved along the curved tooth trace of the helical bevel gear W 2 .

In addition, since the rotary table 26 can be rotated in synchronization with the movement of the stylus tip 211 A in accordance with the velocity vector V C , it is not necessary to alter the attitude of the probe 21 considering the mechanical interference between the helical bevel gear W 2 and the probe 21 when the autonomous scanning measurement is performed on the tooth flank WF 2 of the helical bevel gear W 2 . In other words, since it is not necessary to alter the attitude of the probe 21 , the measurement time can be further reduced.

It should be appreciated that the scope of the invention is not limited to the above exemplary embodiments but modifications and improvements that are compatible with an object of the invention are included within the scope of the invention.

Though the workpiece is the straight bevel gear W 1 or the helical bevel gear W 2 in the exemplary embodiments, different workpiece is measurable as long as the following conditions (1) and (2) or the conditions (1) and (3) are met.

(1) An imaginary cone can be defined in accordance with the profile of the workpiece.

(2) A measurement target face of the workpiece extends along a lateral face of the imaginary cone and substantially conforms with a vertical cross section of the imaginary cone.

(3) The measurement target face of the workpiece extends along the lateral face of the imaginary cone and is twisted along the lateral face.

Though the motion controller 3 in the above-described exemplary embodiments judges that the autonomous scanning measurement is terminated when the number of measurement data reaches the designated point number N, the termination of the autonomous scanning measurement may be determined in a different manner.

For instance, the termination of the autonomous scanning measurement may be determined when the Z W -axis coordinate value at the probe position P P becomes a predetermined height Z e or less.

Alternatively, the termination of the autonomous scanning measurement may be determined when the probe position P P reaches within a sphere with a radius R C and predetermined central coordinates (X C , Y C , Z C ).