Patent Publication Number: US-10322489-B2

Title: Cam grinding machine and cam grinding method

Description:
INCORPORATION BY REFERENCE 
     The disclosure of Japanese Patent Application No. 2015-227203 filed on Nov. 20, 2015 including the specification, drawings and abstract, is incorporated herein by reference in its entirety. 
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to cam grinding machines and cam grinding methods. More particularly, the present invention relates to a grinding machine and a grinding method for a composite cam in which two cams having different cam lifts and different phase angles are disposed to adjoin each other in the axial direction. 
     2. Description of the Related Art 
     Intake and exhaust processes to and from a cylinder of an internal combustion engine are performed by a valve opening operation. The valve opening operation is performed by operation of a rotary cam. 
     In order to improve output of the internal combustion engine etc., different valve opening control processes are used for the valve opening operation depending on whether the engine speed is high or low. 
     In one of such control methods, a first cam for low speeds and a second cam for high speeds are provided as a cam that operates a valve, and valve opening control is performed by selecting the first cam and the second cam as appropriate according to the engine speed. In this case, selective switching between the first cam and the second cam is carried out as a tappet of the valve moves relative to the first cam and the second cam in the axial direction while in contact with the first cam and the second cam. 
       FIGS. 21 to 23  are schematic views showing the positional relationship between a first cam  112  for low speeds and a second cam  114  for high speeds. As can also be seen from these figures, the first cam  112  for low speeds typically has low maximum lift height, and the maximum lift height of the second cam  114  for high speeds is typically greater than that of the first cam  112 . The phase angles of the first and second cams  112 ,  114  are such that the phase of the second cam  114  for high speeds is ahead of that of the first cam  112  for low speeds with respect to their rotational direction (direction shown by arrow in  FIG. 21 ), namely such that the valve opening operation is performed earlier by the second cam  114  than by the first cam  112 . As shown in  FIG. 21 , the first cam  112  for low speeds and the second cam  114  for high speeds are positioned such that the cam profile in the lift height direction of the second cam  114  and the cam profile in the lift height direction of the first cam  112  are shifted from each other in the angular direction. 
     As shown in  FIGS. 22 and 23 , the first cam  112  for low speeds and the second cam  114  for high speeds are disposed so as to adjoin each other in the axial direction. Namely, the first and second cams  112 ,  114  are provided as a composite cam  110 . In this case, both the first cam  112  for low speeds and the second cam  114  for high speeds are formed such that a base circle portion other than the cam profile that changes in the lift height direction according to the angle has a fixed radius r from the camshaft center. A certain angle range in which the base circle portions of the first and second cams  112 ,  114  overlap each other is a common base circle portion C. In the range of this common base circle portion C, the tappet moves relative to the first and second cams  112 ,  114  while in contact therewith to switch between the first and second cams  112 ,  114  as described above. 
     Grinding of the composite cam  110  comprised of the first cam  112  for low speeds and the second cam  114  for high speeds is usually performed with a cam grinding machine using a grinding wheel T (see  FIGS. 22 and 23 ). Grinding of the composite cam  110  is implemented by performing plunge grinding of one of the first and second cams  112 ,  114  and then performing plunge grinding of the other. 
     For example,  FIGS. 22 and 23  show the case where grinding of the first cam  112  for low speeds is first performed and then grinding of the second cam  114  for high speeds is performed. In this case, grinding of the first cam  112  is performed with the grinding wheel T based on preset cam lift data of the first cam  112  for low speeds. Thereafter, the grinding wheel T is moved to the position corresponding to the second cam  114  for high speeds, and grinding of the second cam  114  is performed with the grinding wheel T based on preset cam lift data of the second cam  114  for high speeds. Grinding of the composite cam  110  is thus performed with the cam grinding machine. See, e.g., German Patent No. DE 10333916 B4 and Japanese Patent Application Publication No. H04-13560 (JP H04-13560 A). 
     As shown in  FIG. 23 , in the above grinding of the composite cam  110  with the cam grinding machine using the grinding wheel T, the composite cam  110  is not completely ground. Namely, the composite cam  110  has an unground part F at the boundary between the first and second cams  112 ,  114  in the range of the common base circle portion C. In  FIGS. 22 and 23 , the unground part F is shown exaggerated in order to facilitate understanding. Specifically, the size of the unground part F is on the order of several micrometers. 
     If the composite cam  110  has the unground part F at the boundary between the first and second cams  112 ,  114  in the range of the common base circle portion C, the tappet gets over the unground part F when relatively moving between the first and second cams  112 ,  114 . The operation of moving the tappet relative to the first and second cams  112 ,  114  is therefore not smoothly performed, which affects valve opening control. The grinding wheel T therefore need be trued frequently. 
     The problem that the composite cam  110  has the unground part F will be described specifically. As shown in  FIGS. 22 and 23 , the grinding wheel T has a greater axial width than the first cam  112  for low speeds and the second cam  114  for high speeds. The grinding wheel T becomes blunt at both ends Ta, Tb of its grinding surface as a workpiece, or a cam, is ground with the grinding wheel T. Namely, the grinding wheel T is worn faster at both ends Ta, Tb of its grinding surface than in the middle thereof, causing blunting of the ends Ta, Tb of the grinding wheel T. 
     As shown in  FIG. 22 , in the case of performing plunge grinding of the first cam  112  for low speeds, the grinding wheel T is positioned such that its right end Ta is aligned with the boundary between the first and second cams  112 ,  114 . The left end Tb of the grinding wheel T therefore projects beyond the left side of the first cam  112 . Blunting of the left end Tb of the grinding wheel T thus does not affect grinding of the first cam  112 . However, blunting of the right end Ta of the grinding wheel T affects grinding of the first cam  112  side of the boundary between the first and second cams  112 ,  114 , leaving an unground part F. The black part in  FIG. 22  shows the unground part F. In  FIGS. 22 and 23 , grinding allowances of the first and second cams  112 ,  114 , which are shown by phantom lines, are also shown exaggerated in order to facilitate understanding. 
     As shown in  FIG. 23 , after grinding of the first cam  112  is finished, the grinding wheel T is relatively moved to the position of the second cam  114  to perform plunge grinding of the second cam  114 . In this plunge grinding, the grinding wheel T is positioned such that its left end Tb is aligned with the boundary between the first and second cams  112 ,  114 . The right end Ta of the grinding wheel T therefore projects beyond the right side of the second cam  114 . Blunting of the right end Ta of the grinding wheel T thus does not affect grinding of the second cam  114 . However, blunting of the left end Tb of the grinding wheel T affects grinding of the second cam  114  side of the boundary between the first and second cams  112 ,  114 , leaving an unground part F. This unground part F together with the unground part F of the first cam  112  in  FIG. 22 , both shown black in  FIG. 23 , remains at the boundary between the first and second cams  112 ,  114 . 
     SUMMARY OF THE INVENTION 
     It is one object of the present invention to provide a cam grinding machine that can remove an unground part that is produced at the boundary in a common base circle portion between a first cam and a second cam of a composite cam which have different lift heights. 
     A cam grinding machine according to one aspect of the present invention grinds a composite cam. 
     The composite cam includes: a first cam that has a first base circle portion having a first radius and a fixed lift height from a central axis to its outer peripheral surface, and a first cam portion having a varying lift height from the central axis to its outer peripheral surface; and a second cam that has a second base circle portion having the first radius and a fixed lift height from the central axis to its outer peripheral surface, and a second cam portion having a varying lift height from the central axis to its outer peripheral surface. The first cam and the second cam are coaxially disposed so as to adjoin each other in an axial direction. The first cam and the second cam have different shapes from each other, the shape of the first cam corresponding to first cam lift data and the shape of the second cam corresponding to second cam lift data. At least a part of the outer peripheral surface of the first base circle portion and at least a part of the outer peripheral surface of the second base circle portion are flush with each other to form a common base circle portion. 
     The cam grinding machine includes: a base unit that serves as a base; a spindle device placed over the base unit and including a workpiece rotating device that supports the composite cam about the central axis so that the composite cam is rotatable; a grinding wheel device placed over the base unit and including a rotary grinding wheel; a traverse moving device that can reciprocate the grinding wheel relative to the composite cam in the axial direction; a plunge moving device that can move the grinding wheel relative to the composite cam in a direction crossing the axial direction; and a control device that controls the workpiece rotating device, the traverse moving device, and the plunge moving device. 
     The control device includes: a common base circle portion setting unit that obtains an angular range of the common base circle portion formed by at least the part of the outer peripheral surface of the first base circle portion and at least the part of the outer peripheral surface of the second base circle portion being flush with each other, based on the first cam lift data in which a lift with respect to a rotation angle of the first cam is set and the second cam lift data in which a lift with respect to a rotation angle of the second cam is set; a first cam grinding unit that controls the plunge moving device and the traverse moving device to move the grinding wheel to a position facing the outer peripheral surface of the first cam, and controls the workpiece rotating device and the plunge moving device to grind the first cam; a second cam grinding unit that, after the grinding of the first cam, controls the plunge moving device and the traverse moving device to move the grinding wheel to a position facing the outer peripheral surface of the second cam, and controls the workpiece rotating device and the plunge moving device to grind the second cam; and a common base circle portion traverse grinding unit that, after the grinding of the second cam, controls the traverse moving device to move the grinding wheel from a position of the second cam to a position beyond a boundary between the first and second cams in a traverse direction, and controls the workpiece rotating device to rotate the composite cam within the angular range of the common base circle portion with respect to the grinding wheel to perform traverse grinding of the common base circle portion. 
     According to the cam grinding machine of the above aspect, if the grinding of the first and second cams of the composite cam with the grinding wheel is performed by using the first cam grinding unit and the second cam grinding unit, an unground part remains at the boundary between the cams in the common base circle portion. This unground part is removed as follows. 
     First, the angular range of the common base circle portion of the first and second cams where the unground part remains is obtained by the common base circle portion setting unit of the control unit. This angular range is obtained based on the first cam lift data of the first cam and the second cam lift data of the second cam. 
     After the grinding of the first cam and the second cam is finished, the grinding wheel is moved in the traverse direction from the position of the second cam ground by using the second cam grinding unit to a position on the outer peripheral surface of the boundary between the first and second cams in the common base circle portion where the unground part remains. Traverse grinding of this angular range of the common base circle portion is performed to remove the unground part at the boundary. 
     After the grinding of the second cam using the second cam grinding unit is finished, the grinding wheel is moved as it is in the traverse direction without being withdrawn or advanced. Accordingly, the unground part can be reliably removed. In the case where the grinding wheel is withdrawn, moved in the traverse direction to the position of the boundary, and advanced to perform plunge grinding after the grinding of the second cam using the second cam grinding unit is finished, there may be a deviation in the advanced position of the grinding wheel, and the unground part may not be completely removed. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The foregoing and further features and advantages of the invention will become apparent from the following description of example embodiments with reference to the accompanying drawings, wherein like numerals are used to represent like elements and wherein: 
         FIG. 1  is a schematic view of a composite cam of an embodiment of the present invention as viewed in the direction of a cam axis; 
         FIG. 2  is a side view of a first cam and a second cam of the composite cam as viewed in a direction perpendicular to the cam axis; 
         FIG. 3  is a perspective view of an embodiment showing an example of a cam control mechanism that selectively controls composite cams  14 ; 
         FIG. 4  is a plan view of a cam grinding machine; 
         FIG. 5  is a right side view of the cam grinding machine; 
         FIG. 6  is a block diagram showing control functions of a control device; 
         FIG. 7  shows a process flow of a first embodiment which is performed by the control device; 
         FIG. 8  shows a process flow of a second embodiment which is performed by the control device; 
         FIG. 9  shows a detailed process flow of a first cam grinding step; 
         FIG. 10  shows a detailed process flow of a second cam grinding step; 
         FIG. 11  shows a detailed process flow of a common base circle portion oscillation grinding step; 
         FIG. 12  shows a detailed process flow of a common base circle portion leftward traverse grinding step; 
         FIG. 13  shows a detailed process flow of a first cam air grinding step; 
         FIG. 14  shows a detailed process flow of a common base circle portion rightward traverse grinding step; 
         FIG. 15  shows a detailed process flow of a second cam air grinding step; 
         FIG. 16  is an illustration of grinding of the first cam; 
         FIG. 17  is an illustration of grinding of the second cam; 
         FIG. 18  is an illustration of the first embodiment, illustrating traverse grinding of a common base circle portion; 
         FIG. 19  is an illustration of the second embodiment, illustrating traverse grinding of the common base circle portion; 
         FIG. 20  is a developed diagram conceptually sowing tracks of a grinding wheel with respect to the first and second cams in a third embodiment; 
         FIG. 21  is a schematic view of a composite cam as viewed in the direction of a cam axis, illustrating a prior art; 
         FIG. 22  is a side view of a first cam and a second cam of the composite cam as viewed in a direction perpendicular to the cam axis, illustrating grinding of the first cam; and 
         FIG. 23  is a diagram illustrating grinding of the second cam. 
     
    
    
     DETAILED DESCRIPTION OF EMBODIMENTS 
     Embodiments of the present invention will be described below with reference to the accompanying drawings. 
     First, a composite cam  10  according to an embodiment will be described.  FIG. 1  is a schematic view of the composite cam  10  as viewed in the direction of a cam axis x.  FIG. 2  is a side view showing the maximum lift height positions of a first cam  12  and a second cam  14  of the composite cam  10  as viewed in a direction perpendicular to the cam axis x. 
     As shown in  FIG. 2 , the composite cam  10  of the present embodiment is formed by the first cam  12  and the second cam  14  which are disposed so as to adjoin each other in the axial direction. In the present embodiment, the first cam  12  serves as a cam for low speeds and the second cam  14  serves as a cam for high speeds. The maximum lift height of the first cam  12  for low speeds is lower than that of the second cam  14  for high speeds. As shown in  FIG. 2 , the first cam  12  for low speeds and the second cam  14  for high speeds are formed with the same width in the axial direction x. That is, the width E 1  of the first cam  12  is the same as the width E 2  of the second cam  14 . 
     As shown in  FIG. 1 , the first cam  12  for low speeds and the second cam  14  for high speeds have different phase angles. The phase of the second cam  14  for high speeds is ahead of that of the first cam  12  for low speeds with respect to the rotational direction (direction shown by arrow in  FIG. 1 ) of an internal combustion engine. A valve opening operation for the internal combustion engine is therefore performed earlier by the second cam  14  than by the first cam  12 . In the present embodiment, the first cam  12  for low speeds and the second cam  14  for high speeds are positioned such that the cam profile in the lift height direction of the second cam  14  and the cam profile in the lift height direction of the first cam  12  are shifted from each other in the angular direction and also protrude from each other as viewed in the direction of the cam axis. The maximum cam height position of one cam may be out of phase with that of the other cam even if their cam profiles do not protrude from each other and the other cam profile is located within one cam profile. 
     As shown in  FIG. 1 , each of the contour of the first cam  12  and the contour of the second cam  14  consists of a base circle portion having a fixed first radius r from the central axis x of the cam and a cam height varying profile portion other than the base circle portion. In  FIG. 1 , C 1  represents a first base circle portion of the first cam  12 , and D 1  represents a cam height varying profile portion of the first cam  12 . Similarly, C 2  represents a second base circle portion of the second cam  14 , and D 2  represents a cam height varying profile portion of the second cam  14 . Since the first cam  12  and the second cam  14  have different cam heights and different phase angles, the range of the first base circle portion C 1  is different from that of the second base circle portion C 2 . In  FIG. 1 , the common base circle portion C shows the surface portions of the first and second cams  12 ,  14  which are flush with each other, namely the surface portions of the first and second cams  12 ,  14  in which the first base circle portion C 1  of the first cam  12  and the second base circle portion C 2  of the second cam  14  overlap each other. 
       FIG. 3  shows an embodiment illustrating an example of a cam control mechanism  16  that selectively controls the first cam  12  and the second cam  14  of the composite cam  10  mounted on a camshaft  18 . The first cam  12  and the second cam  14  are disposed on the camshaft  18 . The first cam  12  and the second cam  14  are provided for each valve  20  and together form the composite cam  10 . In the present embodiment, two of the composite cams  10  are mounted on the camshaft  18  so that the composite cams  10  can rotate integrally with respect to the camshaft  18  and can move in the axial direction. 
     Each valve  20  is moved up and down by a swinging motion of a corresponding one of tappets  22 . The tappet  22  selectively contacts the first cam  12  or the second cam  14  and is thus swung by the cam  12 ,  14 . Specifically, the tappet  22  is provided with a tappet roller  23 , and the tappet  22  selectively contacts the first cam  12  or the second cam  14  by contact between the tappet roller  23  and the cam  12 ,  14 . This selective contact between the tappet  22  and the cam  12 ,  14  is achieved by engagement between a pin  26  of an actuator  24  such as an electromagnetic solenoid and a helically grooved element  28  provided integrally with the composite cam  10  on a side of the composite cam  10 . The helically grooved element  28  has an axial helical groove in its outer peripheral surface. The pin  26  of each actuator  24  engages with the helical groove of each helically grooved element  28 , whereby the two composite cams  10  are moved in the axial direction by rotation of the camshaft  18  and the composite cams  10 . The helical grooves of the helically grooved elements  28  disposed on the right and left sides are formed in the same direction. For example, the composite cams  10  move to the right when the pin  26  engages with the helical groove of one helically grooved element  28 . The composite cams  10  move to the left when the pin  26  engages with the helical groove of the other helically grooved element  28 . The position of the cam that contacts the tappet  22  is switched in this manner. The switching operation using the actuator  24  is performed when the tappet  22  is in contact with the common base circle portion C of the first cam  12  or the second cam  14 . 
     A cam grinding machine  30  will be described below with reference to  FIGS. 4 and 5 .  FIG. 4  is a plan view and  FIG. 5  is a right side view. A tailstock device  58  in  FIG. 4  is not shown in  FIG. 5 . The X-, Y-, and Z-axes in the figures are perpendicular to each other. The Y-axis direction is the upward vertical direction and the X- and the Z-axis directions are horizontal directions perpendicular to each other. 
     The cam grinding machine  30  of the present embodiment rotates and supports the camshaft  18 , or a workpiece W, having the composite cams  10  and grinds the camshaft  18  with a cylindrical grinding wheel T. As shown in  FIG. 4 , the cam grinding machine  30  includes an input device  32  such as a keyboard, a display device  34  such as a monitor, a data read device  36  such as a tape reader, an automatic programming device  38 , a numerical control device  40 , drive units  42 ,  44 ,  46 ,  48 , a grinding wheel device  50 , and a workpiece support device  52 . 
     The data read device  36  reads various data according to an operation that is performed by the operator using the input device  32  and the display device  34 . In this case, the data read device  36  reads cam lift data that specifies the shape of the composite cam  10  to be ground and the radius of the grinding wheel T. In the present embodiment, the data read device  36  reads two pieces of cam lift data, namely cam lift data of the cams  12 ,  14  having different phase angles and different lift heights shown in  FIG. 1 . Namely, the data read device  36  reads first cam lift data showing the shape of the first cam  12 , second cam lift data showing the shape of the second cam  14 , the angle from a reference phase to the phase corresponding to the maximum lift of the first cam  12 , and the angle from a reference phase to the phase corresponding to the maximum lift of the second cam  14 . The reference phase of the first cam  12  is the same as that of the second cam  14 . 
     The operator inputs the following data to the input device  32  while looking at the display device  34 .
         (a) the width E 1  of the first cam  12     (b) the width E 2  of the second cam  14     (c) the width G and diameter H of the grinding wheel T   (d) the rotational speed m 1  of the grinding wheel T, the rotational speed n 1  of a spindle  74 , and the infeed J of the grinding wheel T for air grinding   (e) the rotational speed m 2  of the grinding wheel T, the rotational speed n 2  of the spindle  74 , and the infeed K of the grinding wheel T for rough grinding   (f) the rotational speed m 3  of the grinding wheel T, the rotational speed n 3  of the spindle  74 , and the infeed M of the grinding wheel T for fine grinding   (g) the rotational speed m 4  of the grinding wheel T, the rotational speed n 4  of the spindle  74 , and the amount of rotation of the spindle  74  for spark-out   (h) the rotational speed m 5  of the grinding wheel T, the rotational speed n 5  of the spindle  74 , and the amount of rotation of the spindle  74  at the time of removing an unground part       

     The data (d) to (g) is input for each of a first cam grinding step and a second cam grinding step, and a program for the first cam grinding step and a program for the second cam grinding step are automatically created by the automatic programming device  38 . 
     The cam grinding machine  30  includes a base unit  54  serving as a base on which various devices are placed. The cam grinding machine  30  has a worktable  65  and a wheel head  70  on the base unit  54 . The worktable  65  can be reciprocated in the Z-axis direction by a worktable drive device  66 . The wheel head  70  can be reciprocated in the X-axis direction by a wheel head drive device  68 . The worktable drive device  66  of the present embodiment corresponds to the traverse moving device of the present invention, and the wheel head drive device  68  corresponds to the plunge moving device. 
     The cam grinding machine  30  has a spindle device  56  and the tailstock device  58  on the worktable  65 . The spindle device  56  includes the spindle  74 . The spindle  74  rotates about a spindle rotation axis being parallel to the Z-axis and passing through the center of a center  72 . The tailstock device  58  includes a center  73  disposed on the spindle rotation axis. The spindle  74  can be rotated by a spindle drive device  76 . The spindle drive device  76  corresponds to the workpiece rotating device of the present invention. The centers  72 ,  73  hold the camshaft  18  having the composite cams  10 , or the workpiece W, therebetween. The spindle  74  is provided with a positioning pin  78  that causes the camshaft  18 , or the workpiece W, and the spindle  74  to rotate in phase with each other. The camshaft  18 , or the workpiece W, has a fitting portion (not shown) in which the positioning pin  78  is fitted. The camshaft  18  is thus positioned such that the positioning pin  78  is fitted in the fitting portion, and is held between the centers  72 ,  73 . 
     The wheel head  70  has the grinding wheel T placed thereon. The grinding wheel T is rotated by a grinding wheel drive device  80  such as a motor. In the present embodiment, the wheel head  70 , the grinding wheel T, and the grinding wheel drive device  80  form the grinding wheel device  50  of the present invention. 
     The numerical control device  40  controls various devices by outputting control signals to the drive units  42 ,  44 ,  46 ,  48  to drivingly control the various drive devices  68 ,  76 ,  66 ,  80 . In the present embodiment, the numerical control device  40  controls the position in the X-axis direction of the wheel head  70 , or the position to which the grinding wheel T is advanced or withdrawn, by outputting a control signal to the drive unit  42  to drivingly control the wheel head drive device  68 . The numerical control device  40  also controls the rotation angle of the spindle  74  by outputting a control signal to the drive unit  44  to drivingly control the spindle drive device  76 . The numerical control device  40  also controls the position in the Z-axis direction of the worktable  65  by outputting a control signal to the drive unit  46  to drivingly control the worktable drive device  66 . The numerical control device  40  also controls the rotational speed of the grinding wheel T by outputting a control signal to the drive unit  48  to drivingly control the grinding wheel drive device  80 . 
     The drive unit  44  obtains an actual rotation angle of the spindle  74  from a detection signal of an encoder  76 E of the spindle drive device  76  to perform feedback control. The drive unit  42  obtains an actual position in the X-axis direction of the wheel head  70  from a detection signal of an encoder  68 E of the wheel head drive device  68  to perform feedback. The drive unit  46  obtains an actual position in the Z-axis direction of the worktable  65  from a detection signal of an encoder  66 E of the worktable drive device  66  to perform feedback control. 
     Specifically, the encoder  66 E and the drive unit  46  detect the amount by which the worktable  65  has been moved. The encoder  68 E and the drive unit  42  detect the amount by which the wheel head  70  has been moved toward the worktable  65 . If the amount by which the intended element is to be moved, namely the amount indicated by a command signal or a control signal, matches the amount by which the intended element has actually been moved, namely the amount detected by the encoder and the drive unit, a completion signal is sent to the numerical control device  40 . 
     As shown in  FIG. 5 , the camshaft  18 , or the workpiece W, is held between the centers  72 ,  73  such that the workpiece rotation axis PW, which is the central axis of the camshaft  18  having the composite cams  10 , matches the spindle rotation axis, which is the rotation axis of the spindle  74 . 
     In the cam grinding machine  30  described in the present embodiment, the spindle rotation axis (which matches the workpiece rotation axis PW in the example of  FIG. 5 ) and the grinding wheel rotation axis PT, or the rotation axis of the grinding wheel T, are located on the same horizontal plane STM. 
     The control that is performed by a control device  64  will be described. The control device  64  is formed by components located in the range surrounded by phantom line in  FIG. 4 . The control device  64  controls each drive device that performs grinding of the first cam  12  and the second cam  14 . That is, the control device  64  controls the spindle drive device  76  serving as the workpiece rotating device, the worktable drive device  66  serving as the traverse moving device, and the wheel head drive device  68  serving as the plunge moving device. 
     As shown in  FIG. 6 , the control device  64  includes control function units that control these drive devices. That is, the control device  64  includes a common base circle portion setting unit  82 , a first cam grinding unit  84 , a second cam grinding unit  86 , a common base circle portion traverse grinding unit  88 , and a first cam spark-out unit  90 . 
     The common base circle portion setting unit  82  is a function unit that sets the common base circle portion C of the first and second cams  12 ,  14  by a program for the common base circle setting step in a control process flow described below. 
     The first cam grinding unit  84  is a function unit that performs grinding of the first cam  12  by a program for the first cam grinding step described below. The second cam grinding unit  86  is a function unit that performs grinding of the second cam  14  by a program for the second cam grinding step described below. 
     The common base circle portion traverse grinding unit  88  is a function unit that performs removal of the unground part produced by the first cam grinding step and the second cam grinding step by a program for the common base circle portion traverse grinding step described below. 
     The first cam spark-out unit  90  is a function unit that performs spark-out of the first cam  12  after the common base circle portion traverse grinding step in a second embodiment described below by a program for the first cam spark-out grinding step described below. 
     The control process flow that controls operation of the drive devices by using the function units include a control process flow of the first embodiment shown in  FIG. 7  and a control process flow of the second embodiment shown in  FIG. 8 . Each of the embodiments will be described below. 
     First, the first embodiment shown in  FIG. 7  will be described. As shown in the control process flow of  FIG. 7 , the first cam lift data on the outer profile of the first cam  12  shown in  FIG. 1  and the second cam lift data on the outer profile of the second cam  14  shown in  FIG. 1  are first read in step S 10  as described above. 
     Next, the common base circle portion C of the first and second cams  12 ,  14  is obtained in the common base circle portion setting step S 11 . The common base circle portion C is obtained from the first cam lift data, or data on setting of the lift with respect to the rotation angle of the first cam  12  shown in  FIG. 1 , and the second cam lift data, or data on setting of the lift with respect to the rotation angle of the second cam  14  shown in  FIG. 1 . The angular range in which the outer peripheral surface of the first base circle portion C 1  of the first cam  12  and the outer peripheral surface of the second base circle portion C 2  of the second cam  14  shown in  FIG. 1  have a common surface with a radius r is obtained as the common base circle portion C. The common base circle portion setting step S 11  need only be performed by the time the second cam grinding step described below is completed. 
     Then, grinding of the first cam  12  is performed in the first cam grinding step S 12 .  FIG. 16  is a schematic view illustrating grinding that is performed in the first cam grinding step. The control device  64  controls the worktable drive device  66  and the wheel head drive device  68  to move the grinding wheel T to the position facing the outer peripheral surface of the first cam  12 . The control device  64  controls the spindle drive device  76  and the wheel head drive device  68  to perform plunge grinding of the first cam  12 . 
       FIG. 9  shows a detailed process flow of the first cam grinding step S 12 . As shown in  FIG. 9 , grinding of the first cam  12  is performed in order of positioning S 31 , air grinding S 32 , rough grinding S 33 , fine grinding S 34 , spark-out S 35 , and wheel head withdrawal S 36 . In the positioning S 31 , the worktable  65  is moved to the right so that the right end of the first cam  12  is located at the position corresponding to the right end of the grinding wheel T in the traverse direction in  FIG. 16  (lateral direction in  FIG. 16 ). The wheel head  70  is advanced so that the grinding wheel T is located at a position away from the axis x of the composite cam  10  toward the wheel head  70  by an amount corresponding to the sum of the radius r, the infeed J for the air grinding, the infeed K for the rough grinding, and the infeed M for the fine grinding in the plunge direction (vertical direction in  FIG. 16 ). 
     In the positioning S 31 , the right end of the grinding wheel T is positioned at the right end of the first cam  12  in the traverse direction (lateral direction) in  FIG. 16 , and the grinding wheel T is positioned at the position away from the first cam  12  by an amount corresponding to the infeed J for the air grinding in the plunge direction (vertical direction). In the air grinding S 32 , the grinding wheel T is moved in the plunge direction by the amount corresponding to the infeed J for the air grinding, so that the grinding wheel T comes into contact with the outer peripheral surface of the first cam  12 . In the rough grinding S 33 , the grinding wheel T contacting the outer peripheral surface of the first cam  12  is advanced in the plunge direction by an amount corresponding to the infeed K for the rough grinding and the rough grinding is performed. In the fine grinding S 34 , the grinding wheel T is advanced in the plunge direction by an amount corresponding to the infeed M for the fine grinding and the fine grinding is performed. Subsequently, in the spark-out S 35 , spark-out is performed until the amount of rotation of the spindle  74  reaches a predetermined value. After these steps are finished, in the wheel head withdrawal S 36 , the wheel head  70  is withdrawn in the plunge direction by an amount corresponding to the sum of the infeed J, the infeed K, and the infeed M to prepare for the subsequent second cam grinding step S 14 . 
     Referring back to  FIG. 7 , after the first cam grinding step S 12  is finished, the traverse movement S 13  is performed. The traverse movement is the movement of the grinding wheel T from the position of  FIG. 16  to the position of  FIG. 17 . This is the operation of moving the worktable  65  to the right by an amount corresponding to the width G of the grinding wheel T in the traverse direction. 
     Subsequently, the second cam grinding step S 14  is performed. Grinding of the second cam  14  is performed in the second cam grinding step S 14 .  FIG. 17  illustrates grinding that is performed in the second cam grinding step S 14 . The control device  64  controls the worktable drive device  66  and the wheel head drive device  68  to move the grinding wheel T to the position facing the outer peripheral surface of the second cam  14  through a path shown by arrow in  FIG. 17 . The control device  64  controls the spindle drive device  76  and the wheel head drive device  68  to perform plunge grinding of the second cam  14 . 
       FIG. 10  shows a detailed process flow of the second cam grinding step S 14 . As shown in  FIG. 10 , grinding of the second cam  14  is performed in order of positioning S 41 , air grinding S 42 , rough grinding S 43 , fine grinding S 44 , and spark-out S 45 . In the positioning S 41 , the grinding wheel T is positioned for the second cam grinding step S 14  by the traverse movement S 13 . By this positioning, the left end of the grinding wheel T is positioned at the left end of the second cam  14  in the traverse direction. The grinding wheel T is located at a position away from the second cam  14  by an amount corresponding to the infeed J for the air grinding in the plunge direction. In the air grinding S 42 , the grinding wheel T is advanced in the plunge direction by an amount corresponding to the infeed J for the air grinding. In the rough grinding S 43 , the grinding wheel T is advanced in the plunge direction by an amount corresponding to the infeed K for the rough grinding. In the fine grinding S 44 , the grinding wheel T is advanced in the plunge direction by an amount corresponding to the infeed M for the fine grinding. Subsequently, in the spark-out S 45 , spark-out is performed until the amount of rotation of the spindle  74  reaches a predetermined value. 
     The infeed J for the air grinding in the first cam grinding step S 12  and the second cam grinding step S 14  is an amount that is larger than the maximum lift of the first cam  12  or the second cam  14  and that does not cause the grinding wheel T to interfere with the first cam  12  or the second cam  14  even if the worktable  65  is moved in the traverse direction with the wheel head  70  being located at the position before the air grinding. That is, the maximum lift is equal to the maximum value of the lift data minus the minimum value of the lift data. The minimum value of the lift data is the radius of the first base circle portion C 1  or the second base circle portion C 2 . 
     In the air grinding, the rough grinding, the fine grinding, and the spark-out of the first cam grinding step S 12  and the second cam grinding step S 14 , the wheel head  70  is advanced or withdrawn based on the first cam lift data or the second cam lift data in connection with the rotation angle of the spindle  74 . This advancement and withdrawal of the wheel head  70  is made together with the operation of advancing the grinding wheel T in the plunge direction by an amount corresponding to the infeed. 
     Cam grinding in the first cam grinding step S 12  and the second cam grinding step S 14  is performed in three stages in order of rough grinding, fine grinding, and spark-out. This can reduce the time required for grinding. The cam grinding can be performed by only the fine grinding. In this case, however, it takes long to perform the cam grinding. The spark-out refers to a grinding process that does not involve feeding like plunge grinding. The workpiece W subjected to the fine grinding has deflection due to the machining. The spark-out is performed in order to perform grinding without involving feeding to eliminate the deflection. Namely, the spark-out is performed for improved grinding accuracy. 
     In the plunge grinding of the first cam  12  and the second cam  14  with the grinding wheel T in the first cam grinding step S 12  and the second cam grinding step S 14 , the unground part F remains at the boundary between the first and second cams  12 ,  14 . The black part in the figures represents the unground part F. The unground part F and the grinding allowances of the first and second cams  12 ,  14  which are shown by phantom lines in the figures are shown exaggerated in order to facilitate understanding. 
     After the second cam grinding step S 14 , the unground part F remaining at the boundary between the first and second cams  12 ,  14  is ground and removed in the common base circle portion traverse grinding step S 15  shown in  FIG. 7 . 
       FIG. 18  is a schematic view illustrating grinding in the common base circle portion traverse grinding step S 15 . In the common base circle portion traverse grinding step S 15 , the worktable  65  is moved to the left in the traverse direction so that the right end Ta of the grinding wheel T is located at the position corresponding to the right end of the second cam  14 . The left end Tb of the grinding wheel T is thus located at a position beyond the unground part F remaining at the boundary between the first and second cams  12 ,  14  to the left. In order to perform this operation of moving the worktable  65  to the left, the control device  64  controls the worktable drive device  66  to make the traverse movement of the grinding wheel T as shown by arrow in  FIG. 19 . 
     In the common base circle portion traverse grinding step S 15 , since the angle of the common base circle portion C is 180 degrees or less, the rotational speed n 5  of the spindle  74  in this step S 15  is lower than the rotational speed n 3  of the spindle  74  in the fine grinding, and the speed of the traverse movement in this step S 15  is higher than that of the traverse movement that is made after the first cam grinding step and before the second cam grinding step. 
     The traverse movement is made so that the left end Tb of the grinding wheel T is located at a position beyond the unground part F remaining at the boundary between the first and second cams  12 ,  14  to the left. At the same time, the spindle drive device  76  is controlled to rotate the first and second cams  12 ,  14  in the angular range of the common base circle portion C, thereby removing the unground part F at the boundary and performing spark-out of the common base circle portion C. The unground part F is removed in this manner. 
     In the traverse movement of the grinding wheel T described above, with the grinding wheel T being located at a counterclockwise end CA of the common base circle portion C in  FIG. 1 , the first and second cams  12 ,  14  are rotated in the counterclockwise direction and moved to the right in the traverse direction with respect to the grinding wheel T. With the grinding wheel T being located at a counterclockwise end CB of the common base circle portion C and having been moved by an amount corresponding to the width G of the grinding wheel T minus the width of the unground part F by the traverse movement, the wheel head  70  is quickly withdrawn in order to prevent the cam height varying profile portion D 1  of the first cam  12  from being ground by the grinding wheel T. 
     It is desirable that, when the traverse movement of the grinding wheel T in  FIG. 18  is made so that the left end Tb of the grinding wheel T is located at a position beyond the unground part F to the left, the right end Ta of the grinding wheel T not be located at a position beyond the right end of the second cam  14  to the left. The ground surface of the second cam  14  ground in the second cam grinding step is thus not affected. 
     The control process flow of the second embodiment shown in  FIG. 8  will be described below. In the control process flow of the second embodiment, the same steps as those of the control process flow of the first embodiment shown in  FIG. 7  are denoted by the same reference characters and detailed description thereof will be omitted. The step S 10  of inputting the cam lift data of the first and second cams, the common base circle portion setting step S 11 , the first cam grinding step S 12 , the traverse movement S 13 , and the second cam grinding step S 14  are the same as those of the control process flow of the first embodiment. 
     As in the common base circle portion traverse grinding step S 15  of the first embodiment, the unground part F remaining at the boundary between the first and second cams  12 ,  14  is ground and removed in the common base circle portion traverse grinding step S 25  of the second embodiment shown in  FIG. 8 . However, the common base circle portion traverse grinding step S 25  of the second embodiment is different from the common base circle portion traverse grinding step S 15  of the first embodiment in the range of the traverse movement that is made to remove the unground part F. 
       FIG. 19  is a schematic view illustrating grinding of the common base circle portion traverse grinding step S 25 . As in the first embodiment, the control device  64  first controls the spindle drive device  76  to position the grinding wheel T such that the grinding wheel T contacts the common base circle portion C of the second cam  14 . In this state, the control device  64  controls the worktable drive device  66  to make the traverse movement of the grinding wheel T as shown by arrow in  FIG. 19 . 
     In the second embodiment, this traverse movement is made so that the left end Tb of the grinding wheel T is located at a position beyond the unground part F remaining at the boundary between the first and second cams  12 ,  14  to the left and that the right end Ta of the grinding wheel T is located at the position corresponding to the left end of the second cam  14 . In this traverse movement, the control device  64  controls the spindle drive device  76  and the wheel head drive device  68  to rotate the first and second cams  12 ,  14  in the angular range of the common base circle portion C obtained in the common base circle portion setting step S 11 , thereby removing the unground part F at the boundary and performing spark-out of the common base circle portion C. The unground part F is removed in this manner. As used herein, the term “traverse grinding” refers to removal of the unground part F and spark-out in the range of the common base circle portion C by the traverse movement of the grinding wheel T. 
     In the second embodiment, the first cam spark-out step S 26  is performed after the traverse grinding is performed in the common base circle portion traverse grinding step S 25 . 
     In the first cam spark-out step S 26 , the grinding wheel T is located at the counterclockwise end CB of the common base circle portion C and is moved in the traverse direction by an amount corresponding to the width G of the grinding wheel T. In this state, the wheel head  70  is advanced or withdrawn based on the lift data of the first cam  12  according to the rotation angle of the spindle  74  to perform spark-out of the first cam  12 . A tool mark formed on the common base circle portion C in the common base circle portion traverse grinding step S 25  is removed only from the first cam  12  by the spark-out of the first cam  12 . 
     After the spark-out is finished, the wheel head  70  is quickly withdrawn in order to prevent the cam height varying profile portion D 1  of the first cam  12  from being ground by the grinding wheel T. In the first embodiment, the grinding wheel T is moved in the traverse direction by a small amount in the common base circle portion C. In the second embodiment, however, the grinding wheel T is moved in the traverse direction by a large amount in the common base circle portion C. Accordingly, if there is a limit on the speed of the traverse movement, the rotational speed of the spindle  74  is reduced as compared to the first embodiment. 
     A third embodiment shown in  FIG. 11  will be described below. In the third embodiment, steps S 10  to S 14  in the control process flow of  FIG. 7  are performed as in the first embodiment, but the common base circle portion traverse grinding step S 15  is replaced with a common base circle portion oscillation grinding step S 50  shown in  FIG. 11 . In the common base circle portion traverse grinding step S 25  of the second embodiment, the traverse grinding of the common base circle portion C is performed by a single transverse movement to the left. In the common base circle portion oscillation grinding step S 50  of the third embodiment, however, traverse grinding of the common base circle portion C is performed by a plurality of reciprocating transverse movements. 
     The common base circle portion oscillation grinding step S 50  of the third embodiment will be described with reference to  FIG. 11 . The common base circle portion oscillation grinding step S 50  is performed in order of a common base circle portion leftward traverse grinding step S 51 , a first cam air grinding step S 60 , a common base circle portion rightward traverse grinding step S 70 , a second cam air grinding step S 80 , a count-up step S 52  (n=n+1), a count value determining step S 53  (n=a), and a count value reset step S 54  (n=0). If it is determined in the count value determining step S 53  that the count value n has not reached the value a, steps S 51  to S 53  are performed again. If it is determined in the count value determining step S 53  that the count value n is equal to the value a, the common base circle portion oscillation grinding step S 50  is terminated. 
     The common base circle portion leftward traverse grinding step S 51  will be described with reference to  FIG. 12 . The common base circle portion leftward traverse grinding step S 51  is performed in order of steps S 55 , S 56 , and S 57 . In the step S 55 , the phase CA of the common base circle portion C corresponds to the grinding wheel T, and the left end of the grinding wheel T corresponds to the left end of the second cam  14 . In the leftward traverse movement step S 56 , the first and second cams  12 ,  14  are rotated in the counterclockwise direction and are also moved to the left with respect to the grinding wheel T to perform traverse grinding. In the step S 57 , the phase CB of the common base circle portion C corresponds to the grinding wheel T, and the right end of the grinding wheel T corresponds to the right end of the first cam  12 . 
     The first cam air grinding step S 60  will be described with reference to  FIG. 13 . The first cam air grinding step S 60  is performed in order of a withdrawing air grinding step S 61  and an advancing air grinding step S 62 . In the withdrawing air grinding step S 61 , the wheel head  70  is withdrawn by an amount corresponding to the infeed J, and the wheel head  70  is advanced or withdrawn based on the first cam lift data with the first and second cams  12 ,  14  being rotated in the counterclockwise direction. In the advancing air grinding step S 62 , the wheel head  70  is advanced by the amount corresponding to the infeed J, and the wheel head  70  is advanced or withdrawn based on the first cam lift data with the first and second cams  12 ,  14  being rotated in the counterclockwise direction. 
     The common base circle portion rightward traverse grinding step S 70  will be described with reference to  FIG. 14 . The common base circle portion rightward traverse grinding step S 70  is performed in order of steps S 71 , S 72 , and S 73 . In the step S 71 , the phase CA of the common base circle portion C corresponds to the grinding wheel T, and the right end of the grinding wheel T corresponds to the right end of the second cam  14 . In the rightward traverse movement step S 72 , the first and second cams  12 ,  14  are rotated in the counterclockwise direction and are also moved to the right with respect to the grinding wheel T to perform traverse grinding. In the step S 73 , the phase CB of the common base circle portion C corresponds to the grinding wheel T, and the left end of the grinding wheel T corresponds to the left end of the second cam  14 . 
     The second cam air grinding step S 80  will be described with reference to  FIG. 15 . The second cam air grinding step S 80  is performed in order of a withdrawing air grinding step S 81  and an advancing air grinding step S 82 . In the withdrawing air grinding step S 81 , the wheel head  70  is withdrawn by an amount corresponding to the infeed J, and the wheel head  70  is advanced or withdrawn based on the second cam lift data with the first and second cams  12 ,  14  being rotated in the counterclockwise direction. In the advancing air grinding step S 82 , the wheel head  70  is advanced by the amount corresponding to the infeed J, and the wheel head  70  is advanced or withdrawn based on the second cam lift data with the first and second cams  12 ,  14  being rotated in the counterclockwise direction. 
     The track of the grinding wheel T with respect to the first cam  12  and the second cam  14  of the third embodiment will be described with reference to  FIG. 20 .  FIG. 20  is a diagram showing the outer peripheries of the first and second cams  12 ,  14  developed in a planar manner. 
     The grinding wheel T moves along a track T 2  in the leftward traverse movement step S 56 . The grinding wheel T moves along a track T 3  in the withdrawing air grinding step S 61  and the advancing air grinding step S 62 . The grinding wheel T moves along a track T 4  in the rightward traverse movement step S 72 . The grinding wheel T moves along a track T 1  in the withdrawing air grinding step S 81  and the advancing air grinding step S 82 . 
     According to the above embodiments, the unground part F produced at the boundary between the first and second cams  12 ,  14  in the first cam grinding step S 12  and the second cam grinding step S 14  is removed by the common base circle portion traverse grinding steps S 15 , S 25 . Accordingly, when the tappet  22  relatively moves between the first and second cams  12 ,  14 , the tappet  22  does not get over the unground part F as in conventional examples, and the operation of the tappet  22  is performed smoothly. This eliminates the need for frequent replacement of the grinding wheel and early dressing of the grinding wheel. 
     According to the above embodiments, in the common base circle portion traverse grinding step S 15 , S 25  that is performed after the second cam grinding step S 14 , the grinding wheel T is moved in the traverse direction from the second cam  14  ground in the second cam grinding step S 14  toward the position of the unground part without being moved in the plunge direction in both of the first and second embodiments. This produces an accurately finished cam surface with the unground part removed therefrom. In the case where the grinding wheel T is withdrawn in the plunge direction, moved in the traverse direction, and advanced in the plunge direction in order to move the grinding wheel T to the position of the unground part after the second cam grinding step S 14 , a positional deviation of several micrometers may be caused in the plunge direction, and the unground part may not be completely removed. 
     In the first embodiment, the amount by which the grinding wheel T is moved in the traverse direction in the common base circle portion traverse grinding step S 15  is as small as the width of the unground part F. The machining time is therefore short. On the other hand, since the grinding wheel T is moved in the traverse direction with the spindle  74  being rotated, a tool mark is formed in a helical pattern in the common base circle portion C. However, since the depth of the tool mark is as shallow as several micrometers, the tool mark affects the tappet less than the unground part F with a size of several micrometers. 
     In the second embodiment, the amount by which the grinding wheel T is moved in the traverse direction in the common base circle portion traverse grinding step S 25  is as large as the width G of the grinding wheel T. The machining time is therefore long. However, spark-out of the first cam  12  is performed after spark-out of the common base circle portion C. This is advantageous in that a tool mark formed on the common base circle portion C of the first cam  12  is removed. 
     In the third embodiment, since the traverse grinding of the common base circle portion C is performed repeatedly, the machining time is long. However, since a plurality of tool marks are formed on the common base circle portion C such that the tool marks are shifted from each other, the tool marks are less noticeable. 
     In the first to third embodiments described above, traverse grinding and oscillation grinding of the common base circle portion C are performed only after spark-out of the second cam. This can reduce the machining time as compared to the case where traverse grinding and oscillation grinding of the common base circle portion C are performed even after rough grinding and fine grinding. 
     Although the present invention is described above with respect to the specific embodiments, the present invention can be carried out in various other forms. 
     For example, in the above embodiments, the first cam and the second cam have the same width in the axial direction. However, the first cam and the second cam may have different widths in the axial direction. It should be noted that, in this case, the first and second cams are subjected to different surface pressures from the grinding wheel T in the plunge grinding. 
     For example, the second embodiment is described with respect to an example in which spark-out of the first cam  12  is performed in the first grinding step S 12  and also after the common base circle portion traverse grinding step S 25 . In other embodiments, spark-out of the first cam  12  may not be performed in the first grinding step S 12  and may be performed after the common base circle portion traverse grinding step S 25 . This is advantageous because the overall machining time can be reduced. 
     The above embodiments are described with respect to the case where the first cam  12  is a cam for low speeds and the second cam  14  is a cam for high speeds. However, the first cam  12  may be a cam for high speeds and the second cam  14  may be a cam for low speeds.