Patent Publication Number: US-2021172470-A1

Title: Crankshaft and method of manufacturing the same

Description:
TECHNICAL FIELD 
     The present invention relates to a crankshaft and a method of manufacturing such a crankshaft. 
     BACKGROUND ART 
     Crankshafts are required to have fatigue strength, wear resistance and, in addition, seizure resistance. 
     Proposals have been made to improve seizure resistance by controlling the surface geometry of a sliding part. For example, JP 2017-218951 A describes a crankshaft for a freezer compressor having a surface roughness Ra of 0.05 μm or lower. WO 2016/072305 describes a rotating slide bearing composed of a bearing and a shaft, the shaft having a surface roughness Ra of 0.10 μm or lower. 
     Japanese Patent No. 5503417 describes a case hardening steel part having a surface roughness Ra of 0.16 μm or lower to improve sliding properties. Japanese Patent No. 4352261 describes a gear with a surface roughness as measured along the direction of load movement of 0.2 μm≤Rpk+0.5 Rk≤0.8 μm to improve pitting resistance. 
     JP 2004-276121 describes a method of roller burnishing that involves preparing a workpiece having a surface to be treated with an arc-shaped cross section and pressing burnishing rollers against the workpiece for finishing, where the workpiece surface to be treated is lapped so as to be recessed at its center and, thereafter, the protrusions at both ends are burnished by the burnishing rollers. 
     DISCLOSURE OF THE INVENTION 
     In recent years, there has been a growing trend to use lubricants with lower and lower viscosities and crankshaft sliding parts with thinner and thinner shafts in order to improve fuel efficiency, and crankshafts are required to have even better seizure resistance. 
     An object of the present invention is to provide a crankshaft with improved seizure resistance and a method of manufacturing such a crankshaft. 
     A crankshaft according to an embodiment of the present invention includes a journal and a pin, each of the journal and pin having such a surface geometry that an arithmetical mean height of a primary profile, Pa, is 0.090 μm or smaller and a reduced peak height Rpk is 0.070 μm or smaller. 
     A method of manufacturing a crankshaft according to an embodiment of the present invention is a method of manufacturing such a crankshaft as described above, including: a grinding step in which the journal and the pin are ground; a rough lapping step in which the journal and pin that have been ground are lapped using a film coated with alumina abrasive grains; and a finish lapping step in which the journal and pin that have been roughly lapped are lapped using a film coated with diamond abrasive grains. 
     The present invention provides a crankshaft with improved seizure resistance. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a schematic view of a crankshaft according to an embodiment of the present invention. 
         FIG. 2  is an exemplary primary profile. 
         FIG. 3  is an exemplary roughness profile. 
         FIG. 4  shows the relationship between a roughness profile and a material ratio curve. 
         FIG. 5  illustrates reduced peaks. 
         FIG. 6  is a flow chart illustrating an exemplary method of manufacturing the crankshaft of  FIG. 1 . 
         FIG. 7  is a heat pattern for test shafts fabricated for the examples. 
         FIG. 8  shows the primary profiles of the test shafts fabricated for the examples. 
         FIG. 9  is a schematic view of evaluation equipment used for the seizure tests. 
         FIG. 10  is a schematic diagram showing how the surface pressure applied to the test shafts was changed over time. 
         FIG. 11  shows the relationship between the average roughness Ra and the arithmetical mean height of a primary profile Pa. 
         FIG. 12  shows the relationship between the conditions for finishing and the surface geometry (Pa and Rpk). 
         FIG. 13  shows the relationship between Pa and seizure surface pressure. 
         FIG. 14  is the primary profile of a test shaft for a comparative example. 
         FIG. 15  is the primary profile of a test shaft for an inventive example. 
     
    
    
     EMBODIMENTS FOR CARRYING OUT THE INVENTION 
     JP 2017-218951 A, WO 2016/072305 and Japanese Patent No. 5503417, discussed above, specify surface geometries using the arithmetical mean height of a roughness profile, Ra (hereinafter referred to as “average roughness Ra”). However, specifying a geometry using average roughness Ra has the following problems. 
     The surface geometry of an industrial product, such as a crankshaft, includes not only short-period components (i.e., roughness), but also non-negligible levels of long-period components (i.e., undulations) caused by, for example, vibrations of the grinding machine. The average roughness Ra is based on a roughness profile obtained after removal of undulating components through a high-pass filter, and thus it cannot be said, without reserve, that the value exactly reflects the actual surface geometry. Further, the value of the average roughness Ra significantly varies depending on the cut-off value λc of the high-pass filter used to obtain the roughness profile. 
     Actually, even for about the same level of average roughness Ra, seizure resistance significantly varies depending on the magnitude of undulations. Thus, an evaluation parameter using a primary profile as the assessed profile would be a more suitable indication used to control seizure resistance. 
     Further, even for about the same level of average roughness Ra, seizure resistance varies depending on the geometries of protrusions and valleys. Specifically, even for about the same level of average roughness Ra, larger heights of protrusions lead to increased frequency of contact with the other part, decreasing seizure resistance. 
     The present inventors fabricated test shafts with various surface geometries and evaluated their seizure resistance to investigate the relationship between surface geometry and seizure resistance, and found out that seizure resistance can be significantly improved over conventional shafts if the arithmetical mean height of a primary profile, Pa, is 0.090 μm or smaller and the reduced peak height Rpk is 0.070 μm or smaller. 
     The present invention was made based on the above-described findings. An embodiment of the present invention will now be described in detail with reference to the drawings. The same or corresponding portions in the drawings are labeled with the same reference characters, and their description will not be repeated. The size ratios between the components shown in the drawings do not necessarily indicate the actual size ratios. 
     [Crankshaft] 
       FIG. 1  is a schematic view of a crankshaft  10  according to an embodiment of the present invention. The crankshaft  10  includes journals  11 , pins  12 , and arms  13 . 
     The crankshaft  10  may be made from a steel material for mechanical structures, for example. Although not limiting, the crankshaft  10  may be made from a carbon steel material for mechanical structures in accordance with JIS G 4051:2009; a steel material for mechanical structures in accordance with JIS G 4052:2008 which provides sufficient hardenability (H steel); or an alloyed steel material for mechanical structures in accordance with JIS G 4053:2008, for example. Among them, S45C and S50C in accordance with JIS G 4051:2009 and SMn438 in accordance with JIS G 4053:2008 are suitable, and such steel materials to which S has been added to improve machinability are particularly suitable. 
     The crankshaft  10  may have a chemical composition, including, for example, in mass %: 0.30 to 0.60% C; 0.01 to 2.0% Si; 0.1 to 2.0% Mn; 0.01 to 0.50% Cr; 0.001 to 0.06% Al; 0.001 to 0.02% N; up to 0.03% P; and up to 0.20% S. The chemical composition of the crankshaft  10  may include other elements (for example, V and/or Nb). 
     The journals  11  are concentric with the central axis of the crankshaft  10  and are connected to cylinder blocks (not shown). The pins  12  are displaced in position from the central axis of the crankshaft  10 , and connected to connecting rods (not shown). The arms  13  connect the journals  11  with the pins  12 . 
     Each of the journals  11  and pins  12  has such a surface geometry that the arithmetical mean height of the primary profile, Pa, is 0.090 μm or smaller and the reduced peak height Rpk is 0.070 μm or smaller. As used herein, arithmetical mean height of a primary profile Pa is defined in JIS B 0601 (2001), and reduced peak height Rpk is defined in JIS B 0671 (2002). 
       FIGS. 2 and 3  show an exemplary primary profile and an exemplary roughness profile, respectively.  FIG. 4  shows the relationship between a roughness profile and a material ratio curve, and  FIG. 5  illustrates reduced peaks. A method of measuring the arithmetical mean height of a primary profile Pa and a reduced peak height Rpk will be described with reference to these graphs. 
     Test specimens are taken from the crankshaft  10  at locations for measurement (i.e., on the journals  11  and pins  12 ), and a contact-type roughness tester is used to obtain a measured primary profile. The contact roughness tester is to have a stylus with a tip radius of 2 μm and a cone with a taper angle of 60°. The scan rate is to be 0.5 mm/s or lower, and the length for measurement is to be 5 mm or larger. 
     A low-pass filter with a cut-off value λs is applied to the measured primary profile to obtain a primary profile (see  FIG. 2 ). Using the primary profile as the assessed profile, the average of the absolute values of Z(x) in the evaluation length l is calculated, which is treated as the arithmetical mean height of the primary profile Pa. Here, Z(x) is the vertical coordinate at a location X; the cut-off value λs is 2.5 μm, and the evaluation length is 5 mm. 
     A high-pass filter with a cut-off value λc is applied to the primary profile to obtain a roughness profile (see  FIG. 3 ). The cut-off value λc used to obtain the roughness profile is 0.25 mm. 
     A material ratio curve is calculated from the roughness profile. A material ratio curve is a curve representing the material ratio Rmr of a roughness profile as a function of the cut level c (see  FIG. 4 ). The evaluation length l used to calculate the material ratio curve is 5 mm. 
     In a central section of the material ratio curve that includes 40% of measurement points of the roughness profile, secants of the material ratio curve are drawn such that the difference in the material ratio ΔMr is 40%, and the straight line where the inclination of the secant becomes the lowest is treated as the equivalent straight line; the section between the two positions in height at which the equivalent straight line crosses the vertical axes at the material ratios of 0% and 100% will be referred to as core section. The average height of the reduced peaks above the core section will be referred to as reduced peak height Rpk (see  FIG. 5 ). 
     If the arithmetical mean height of the primary profile Pa is 0.090 μm or smaller and the reduced peak height Rpk is 0.070 μm or smaller, this will significantly improve seizure resistance over conventional shafts. The arithmetical mean height of the primary profile Pa is preferably 0.080 μm or smaller. The reduced peak height Rpk is preferably 0.060 μm or smaller. 
     [Method of Manufacturing Crankshaft] 
     An exemplary method of manufacturing the crankshaft  10  will now be described. The method described below is merely an example and is not intended to limit the method of manufacturing the crankshaft  10 . 
       FIG. 6  is a flow chart showing an exemplary method of manufacturing the crankshaft  10 . The method includes: the step of preparing raw material (step S 1 ); a hot-forging step (step S 2 ); a heat treatment step (step S 3 ); a machining step (step S 4 ); a surface-hardening step (step S 5 ); and a finishing step (step S 6 ). These steps will be described in detail below. 
     Raw material for the crankshaft  10  is prepared (step S 1 ). Although not limiting, the raw material for the crankshaft  10  may have a chemical composition including, for example, in mass %: 0.30 to 0.60% C; 0.01 to 2.0% Si; 0.1 to 2.0% Mn; 0.01 to 0.50% Cr; 0.001 to 0.06% Al; 0.001 to 0.02% N; up to 0.3% P; and up to 0.20% S. The raw material for the crankshaft  10  may be material containing other elements (e.g., V and/or Nb). 
     The raw material may be a steel bar, for example. The raw material may be produced by, for example, subjecting steel melt having the above-specified chemical composition to continuous casting or blooming. 
     The raw material is hot forged to produce a roughly shaped product for the crankshaft (step S 2 ). The hot forging may be divided into the substeps of rough forging and finish forging. 
     The roughly shaped product for the crankshaft produced by the hot forging is subjected to a heat treatment, such as normalizing, as necessary (step S 3 ). The heat treatment step (step S 3 ) is optional, and may be omitted depending on the property required of the crankshaft, for example. 
     The roughly shaped product for the crankshaft is machined (step S 4 ). The machining includes cutting, grinding and/or drilling. This step results in an intermediate product that has a shape close to that of the final product. 
     The intermediate product for the crankshaft that has been machined is subjected to surface hardening as necessary (step S 5 ). The surface hardening may be, for example, fillet rolling, induction hardening and/or soft nitriding. The surface hardening step (step S 5 ) is optional and may be omitted depending on the property required of the crankshaft, for example. 
     The surface hardening may be performed on the entire intermediate product for the crankshaft, or may only be performed on the slidable portions, i.e., journals and pins. 
     If the surface hardening step (step S 5 ) is performed, the microstructure in the surface region should be made uniform; otherwise, in the finishing step discussed later (step S 6 ), removing undulations on the surface would be difficult. Conceivable methods for making the microstructure in the surface region uniform include, for example for induction hardening, raising the temperature to or above the Ac 3  point to completely transform the microstructure in the surface region to austenite before quenching. 
     The intermediate product for the crankshaft is subjected to the finishing (step S 6 ). The finishing step (step S 6 ) includes the substeps of grinding (step S 6 - 1 ), rough lapping (step S 6 - 2 ) and finish lapping (step S 6 - 3 ). 
     First, the journals  11  and pins  12  are ground (step S 6 - 1 ). To reduce the average height Pa of the primary profile, both the roughness and undulations must be reduced. The roughness depends on the size of the abrasive grains used for grinding. Accordingly, the finer the abrasive grains used for grinding, the better. 
     The journals  11  and pins  12  have undulations with periods of several hundreds of micrometers to several millimeters caused by the forwarding and/or vibration of the tool during the machining (step S 4 ). Even if the roughness has been sufficiently reduced (i.e., the arithmetical mean height of the roughness profile Ra has been sufficiently reduced), the arithmetical mean height of the primary profile Pa does not decrease if undulations remain. Accordingly, during the grinding substep (step S 6 - 1 ), grinding must be continued even after Ra has been reduced, so as to sufficiently remove undulations. 
     Subsequently, the journals  11  and pins  12  are lapped. Specifically, a film coated with fine abrasive grains are used to polish the journals  11  and pins  12 . The lapping is divided into the substeps of rough lapping (step S 6 - 2 ) and finish lapping (step S 6 - 3 ), where the rough lapping (step S 6 - 2 ) uses a film coated with alumina abrasive grains and the finish lapping (step S 6 - 3 ) uses one with diamond abrasive grains. 
     The lapping substeps (steps S 6 - 2  and S 6 - 3 ) grind off sharp protrusions on the surfaces of the journals  11  and pins  12  to provide plateau surfaces. This reduces the reduced peak height Rpk. 
     During the lapping substeps (steps S 6 - 2  and  6 - 3 ), it is preferable to perform the following processes, (1) to (4), to prevent the product from being recessed at the center as shown in JP 2004-276121: (1) a polishing film with a small width is used, which is forwarded in the axial direction for polishing; this makes it easier for lubricant to reach central regions of the film; (2) the size of the abrasive grains is minimized; this leads to smaller cut depths, which mitigates grinding, preventing excesses; (3) the rate at which the workpiece is rotated is increased, and the pressing force is reduced; this will increase the thickness of the oil (or water) film between the polishing film and workpiece; and (4) the amount of the lubricant oil (or water) is increased; this will increase the thickness of the oil (or water) film between the polishing film and workpiece. 
     For each of the substeps of rough lapping (step S 6 - 2 ) and finish lapping (step S 6 - 3 ), the speed at which the film is forwarded in the axial direction of the crankshaft is minimized. This will remove small undulations, further reducing the arithmetical mean height of the primary profile Pa. 
     The construction of the crankshaft  10  according to an embodiment of the present invention and one exemplary method of manufacturing the same have been described. This present embodiment provides a crankshaft with improved seizure resistance. 
     EXAMPLES 
     Now, the present invention will be described more specifically by means of examples. The present invention is not limited to these examples. 
     A steel having the chemical composition shown in Table 1 was used as raw material to fabricate test shafts for seizure tests.  FIG. 7  shows a heat pattern during the fabrication of the test shafts. 
     
       
         
           
               
             
               
                 TABLE 1 
               
             
            
               
                   
               
               
                 Chemical composition (in mass %, balance Fe and impurities) 
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 C 
                 Si 
                 Mn 
                 P 
                 S 
                 Cr 
                 Al 
                 N 
               
               
                   
               
               
                 0.38 
                 0.50 
                 1.50 
                 0.015 
                 0.060 
                 0.15 
                 0.002 
                 0.0175 
               
               
                   
               
            
           
         
       
     
     Specifically, the raw material was heated at 1250° C. for one hour and then hot forged at 1100° C. to 850° C.; upon completion of forging, the material was air cooled to room temperature. Thereafter, a normalizing process was performed in which the material was heated at 1250° C. for 20 minutes and then air cooled, before being machined (i.e., ground) until the outer diameter was about 48 mm. Then, induction hardening was performed to adjust the surface hardness to HV650. 
     Different pieces of the material were finished by one of the following three processes: (1) grinding only; (2) a combination of grinding and rough lapping; and (3) a combination of grinding, rough lapping and finish lapping, thus producing test shafts having various surface geometries. The rough lapping was performed using a film coated with alumina abrasive grains with grain diameters of 9 to 15 μm, whereas the finish lapping was performed using a film coated with diamond abrasive grains of grain diameters of 1 to 3 μm (#8000 to #4000). The outer diameter of each of the test shafts was adjusted such that the clearance between the shaft and the bearing used for seizure testing, discussed below, was about 0.090 mm. 
     The surface geometries of the fabricated test shafts were measured using a contact roughness tester (SJ-412 from Mitutoyo Corporation) in accordance with the method described in connection with the embodiment. 
       FIG. 8  shows exemplary primary profiles of the fabricated test shafts. The primary profiles on the left represent test shafts on which only grinding was performed, while the primary profiles on the right represent test shafts on which lapping was performed in addition to grinding. As shown in  FIG. 8 , the test shafts on which only grinding had been performed had sharp reduced peaks, where the peaks were triangular in shape, whereas the test shafts on which lapping had been performed in addition to grinding had its reduced peaks ground off such that the peaks were trapezoidal in shape. 
     Next, the fabricated test shafts were used to conduct seizure tests. The seizure tests were conducted using a crank-metal wear/seizure-resistance evaluator from Shinko Engineering Co., Ltd.  FIG. 9  shows a schematic view of the evaluator, indicated by  20 . A test shaft TP was inserted into a plurality of bearings  21 , and the test shaft TP was rotated by a motor (not shown) at 8000 rpm while the bearings  21  were being supplied with oil. The metal of the bearings used was an Al alloy in the range of HV40 to HV50. The lubricant was OW-20, the temperature of oil being supplied was 140° C., and the oil pressure was 0.8 MPa. 
     With these conditions kept, the bearings  21  were moved downward, one at a time, to cause a stepwise increase in the surface pressure applied to the test shaft TP, and the evaluator was operated until seizure occurred.  FIG. 10  schematically shows how the surface pressure applied to the test shaft TP was changed over time. For each step, the surface pressure was held at the same level for three minutes; from one step to the next, the surface pressure was increased by 4.35 MPa; and the time required by each increase in surface pressure was 15 seconds. It was determined that seizure occurred when the surface temperature of the test shaft TP increased to or above 280° C., or when the torque applied to the test shaft increased to or above 25 Nm. 
     The conditions for the finishing of each test shaft, as well as its surface geometry and seizure surface pressure, are shown in Table 2. 
     
       
         
           
               
               
               
               
               
               
               
             
               
                 TABLE 2 
               
               
                   
               
               
                   
                   
                   
                   
                   
                 Seizure 
                   
               
               
                   
                   
                   
                   
                   
                 surface 
               
               
                   
                   
                   
                   
                   
                 pressure 
               
               
                 Test No. 
                 Finishing 
                 Ra (μm) 
                 Pa (μm) 
                 Rpk (μm) 
                 (MPa) 
                 Other info. 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                 1 
                 grinding + rough 
                 0.058 
                 0.068 
                 0.056 
                 134.8 
                 inv. ex. 
               
               
                   
                 lapping + finish lapping 
               
               
                 2 
                 grinding + rough 
                 0.059 
                 0.073 
                 0.057 
                 130.5 
                 inv. ex. 
               
               
                   
                 lapping + finish lapping 
               
               
                 3 
                 grinding + rough 
                 0.065 
                 0.076 
                 0.070 
                 139.2 
                 inv. ex. 
               
               
                   
                 lapping + finish lapping 
               
               
                 4 
                 grinding only 
                 0.436 
                 0.501 
                 0.760 
                 4.3 
                 comp. ex. 
               
               
                 5 
                 grinding only 
                 0.338 
                 0.466 
                 0.584 
                 4.3 
                 comp. ex. 
               
               
                 6 
                 grinding only 
                 0.524 
                 0.633 
                 0.715 
                 4.3 
                 comp. ex. 
               
               
                 7 
                 grinding only 
                 0.411 
                 0.427 
                 0.557 
                 8.7 
                 comp. ex. 
               
               
                 8 
                 grinding only 
                 0.369 
                 0.427 
                 0.559 
                 8.7 
                 comp. ex. 
               
               
                 8 
                 grinding only 
                 0.318 
                 0.376 
                 0.399 
                 13.0 
                 comp. ex. 
               
               
                 10 
                 grinding only 
                 0.125 
                 0.137 
                 0.142 
                 91.3 
                 comp. ex. 
               
               
                 11 
                 grinding only 
                 0.133 
                 0.143 
                 0.138 
                 87.0 
                 comp. ex. 
               
               
                 12 
                 grinding only 
                 0.143 
                 0.153 
                 0.141 
                 91.3 
                 comp. ex. 
               
               
                 13 
                 grinding only 
                 0.136 
                 0.146 
                 0.136 
                 95.7 
                 comp. ex. 
               
               
                 14 
                 grinding only 
                 0.125 
                 0.132 
                 0.138 
                 82.5 
                 comp. ex. 
               
               
                 15 
                 grinding only 
                 0.160 
                 0.173 
                 0.190 
                 91.3 
                 comp. ex. 
               
               
                 16 
                 grinding only 
                 0.077 
                 0.091 
                 0.066 
                 87.0 
                 comp. ex. 
               
               
                 17 
                 grinding only 
                 0.079 
                 0.090 
                 0.074 
                 78.3 
                 comp. ex. 
               
               
                 18 
                 grinding only 
                 0.086 
                 0.095 
                 0.105 
                 65.2 
                 comp. ex. 
               
               
                 19 
                 grinding only 
                 0.076 
                 0.081 
                 0.074 
                 100.0 
                 comp. ex. 
               
               
                 20 
                 grinding only 
                 0.079 
                 0.086 
                 0.075 
                 104.4 
                 comp. ex. 
               
               
                 21 
                 grinding only 
                 0.071 
                 0.080 
                 0.080 
                 95.7 
                 comp. ex. 
               
               
                 22 
                 grinding only 
                 0.071 
                 0.104 
                 0.070 
                 82.6 
                 comp. ex. 
               
               
                 23 
                 grinding only 
                 0.070 
                 0.091 
                 0.065 
                 87.0 
                 comp. ex. 
               
               
                 24 
                 grinding only 
                 0.069 
                 0.078 
                 0.074 
                 52.2 
                 comp. ex. 
               
               
                 25 
                 grinding + rough lapping 
                 0.515 
                 0.587 
                 0.266 
                 4.3 
                 comp. ex. 
               
               
                 26 
                 grinding + rough lapping 
                 0.522 
                 0.615 
                 0.399 
                 8.7 
                 comp. ex. 
               
               
                 27 
                 grinding + rough lapping 
                 0.476 
                 0.595 
                 0.205 
                 4.3 
                 comp. ex. 
               
               
                 28 
                 grinding + rough lapping 
                 0.227 
                 0.274 
                 0.146 
                 52.2 
                 comp. ex. 
               
               
                 29 
                 grinding + rough lapping 
                 0.240 
                 0.291 
                 0.132 
                 34.8 
                 comp. ex. 
               
               
                 30 
                 grinding + rough lapping 
                 0.243 
                 0.288 
                 0.105 
                 52.2 
                 comp. ex. 
               
               
                 31 
                 grinding + rough lapping 
                 0.076 
                 0.099 
                 0.057 
                 91.3 
                 comp. ex. 
               
               
                 32 
                 grinding + rough lapping 
                 0.082 
                 0.110 
                 0.062 
                 95.7 
                 comp. ex. 
               
               
                 33 
                 grinding + rough lapping 
                 0.081 
                 0.110 
                 0.073 
                 100 
                 comp. ex. 
               
               
                 34 
                 grinding + rough lapping 
                 0.069 
                 0.094 
                 0.074 
                 104.4 
                 comp. ex. 
               
               
                 35 
                 grinding + rough lapping 
                 0.067 
                 0.107 
                 0.068 
                 104.4 
                 comp. ex. 
               
               
                 36 
                 grinding + rough lapping 
                 0.068 
                 0.109 
                 0.140 
                 104.4 
                 comp. ex. 
               
               
                 37 
                 grinding + rough lapping 
                 0.125 
                 0.145 
                 0.122 
                 95.7 
                 comp. ex. 
               
               
                 38 
                 grinding + rough lapping 
                 0.128 
                 0.148 
                 0.131 
                 95.7 
                 comp. ex. 
               
               
                 39 
                 grinding + rough lapping 
                 0.165 
                 0.184 
                 0.144 
                 65.2 
                 comp. ex. 
               
               
                   
               
            
           
         
       
     
       FIG. 11  shows the relationship between the average roughness Ra and the arithmetical mean height of a primary profile Pa.  FIG. 11  shows that the value of Pa can vary even for about the same value of Ra. 
       FIG. 12  shows the relationship between the conditions for finishing and the surface geometry (Pa and Rpk).  FIG. 12  shows that if lapping, in addition to grinding, was performed for the finishing, the reduced peak height Rpk tended to be small compared with examples with only grinding. The graph also shows that if grinding, rough lapping and finish lapping were performed, surface geometries were obtained in which the arithmetical mean height of the primary profile Pa was not larger than 0.090 μm and the reduced peak height Rpk was not larger than 0.070 μm. 
       FIG. 13  shows the relationship between Pa and seizure surface pressure.  FIG. 13  shows that the smaller the arithmetical mean height of the primary profile Pa, the larger the seizure surface pressure. The graph also shows that if lapping was performed in addition to grinding, the seizure surface pressure was higher than in examples with only grinding. The graph also shows that the test shafts on which grinding, rough lapping and finish lapping had been performed such that Pa was not larger than 0.090 μm and Rpk was not larger than 0.070 μm had significantly improved seizure surface pressures. 
       FIG. 14  shows the primary profile of the test shaft for a comparative example (Test No. 15).  FIG. 15  shows the primary profile of the test shaft for an inventive example (Test No. 1). A comparison between  FIGS. 14 and 15  shows that the test shaft of the inventive example ( FIG. 15 ) had smaller undulations, not just smaller surface roughnesses. 
     These results demonstrate that if the arithmetical mean height of the primary profile Pa is 0.090 μm or smaller and the reduced peak height Rpk is 0.070 μm or smaller, seizure resistance can be significantly improved over conventional shafts. 
     Although an embodiment of the present invention has been described, the above-described embodiment is merely an example that can be used to carry out the present invention. Accordingly, the present invention is not limited to the above-described embodiment, and the above-described embodiment, when carried out, can be modified as appropriate without departing from the spirit of the invention.