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INTERNATIONAL JOURNAL OF PRECISION ENGINEERING AND MANUFACTURING Vol. 11, No. 3, pp. 419-427 JUNE 2010 / 419 DOI: 10.1007/s12541-010-0048-6 1. Introduction Plate cam mechanism is a widely used machine component with the continuous contact motion of cam and follower, and can easily produce any functional motion of follower due to the rotation of cam. Cam mechanism has the diverse types by the combination of different shape of cam and motion of follower; plate or cylindrical cam, roller or flat-faced follower, and reciprocating or oscillating motion. In spite of the advantages of a few number of links, simple structure, positive motion, and compact size, cam mechanisms require the accurate shape design and precise machining procedures for satisfying the mechanical requirements. Under the low leveled design and manufacturing, cam mechanisms give the heavy effects on vibration, noise, separation, and overloading to an overall system. To avoid these effects, cam mechanism must be well designed accurately and machined precisely. Actually, a hybrid CAD/CAM approach may be the best solution that the shape data from the design process are directly combined to the machining data for the manufacturing process. Line interpolation and circular interpolation are commonly used in construction of the machining data from the profile data of cam. Line interpolation has the low accuracy and circular interpolation can not keep the accuracy because of the disconnective radii of curvatures or the discontinuous slopes at the connected point by two circular arcs as presented in Shin et al.1-3 Recently, parameteric interpolation using B-spline and NURBS curve are suggested in Jung et al.5 and Yang et al.6 Also biarc interpolation is widely used and deeply dependent on the direction angle toward centers of biarc curves. Bolton7 described a biarc curve based on the tangential angles at two points, Parkinson and Moreton8 made a biarc curve based on a quadratic equation at three points, Meek and Walton9 used spline types for constuction of biarc curve. Schonherr10 introduced an approach to minimize the radii of biarc curves. Commonly these interpolation methods make the machining points increasing and then the excessive data for machining a curved shape make the machining errors increased. Thus, the precise machining process requires minimization of the machining points to keep the accuracy under a given machining tolerance. This paper introduces 3 steps of a hybrid CAD/CAM A Hybrid Approach for Cam Shape Design and Profile Machining of General Plate Cam Mechanisms Joong-Ho Shin1, Soon-Man Kwon1 and Hyoungchul Nam1,# 1 Department of Mechanical Design RR RR = (30) () 2 11 1 coscosLAAB R B + = (31) where 1 2 2 cos,A = 1 2 2 2BZ = 5.3 Reduction of machining points Because the excessive machining points on cam profile can go down the accuracy and efficiency in the machining procedures, the reduction of machining points optimally is required. The concept of reduction process is defined as the elimination of cam profile points where the points have the allowable radii within a given machining tolerance. As shown in Fig. 15 the profile points 1 ( ,P 2 P and 3) P are located inside a biarc span. The points (1, 1, P 2, P 3, P 2) correspond to the cam profile designed by the contact points between cam and follower. R2 O2 R1 O1 1 2 P1 P2 P3 Fig. 15 Profile points on biarc fitted curve The biarc curve fitted by the designed radial direction angle at span points (1 and 2) has two regions: The points 1 (P and 2) P are located in an arc consisted by radius 1 R at center 1 O and the point 3 ()P is in the other arc by radius 2 R at center 2. O Radius of each point inside of biarc span can be defined as a distance from center of the corresponding region. Thus, the reduction process can be built by the expansion or contraction of the biarc span, whether all of the radial differences at the inside points are within the range of a given machining tolerance as shown in Fig. 15. All points on cam profile are located between two lines built by a tolerance shown in Fig. 16(a). Thus, end point for biarc span will be expanded as in Fig. 16(b) and vice versa. Generally profile of plate cam has a smooth shape and machining profile point can be reduced if biarc curves for cam shape are defined accurately. 1 2 i j i+1 i+2 j-1 . . S* (a) 1 2 i j i+1 i+2 j-1 j+1 . . S* (b) Fig. 16 Diagram for data reduction procedure 5.4 Tool path and center direction angle NC data consists of radius of tool path, coordinates and direction angle of tool center at each machining point. Fig. 17 shows a machining point on cam profile and a tool center located on the normal line. Here, t R is a radius of tool and n R is a radius of biarc span. The tool center direction angle cut corresponds to the internal radial angle( ) defined in the shape design process of plate cam. Thus, tool center direction angle and radius of tool path are given in Eq.(32) and Eq.(33) respectively. The coordinates of tool center are defined by the geometric condition as in Eq.(34). cut = (32) tpnt RRR=+ (33) () () cos sin xxtscut yytscut TSR TSR =+ =+ (34) s cut X Y T S Center of tool Rt Rn Fig. 17 Direction angle at tool center 6. Example for Shape Design and Profile Machining of Plate Cams11 The displacement conditions for a reciprocating roller follower are defined in Table 1 and Fig. 18. The design parameters for a cam mechanism are follows: Radius of base circle is 80mm, radius of roller is 10mm, and it has no eccentricity between cam and follower. The cam shape designed by the instant velocity center approach is shown in Fig. 19. 426 / JUNE 2010 INTERNATIONAL JOURNAL OF PRECISION ENGINEERING AND MANUFACTURING Vol. 11, No. 3 Table 1 Displacement conditions for plate cam with reciprocating roller follower section cam angle(o) motion curve type 1 0 60 dwell - 2 60 180 30mm rise Modified sinusoidal 3 180 240 dwell - 4 240 360 30mm return Cycloid 090180270360 Cam Rotating angle (deg.) 0 10 20 30 d i s p l a c e m e n t ( mm ) Fig. 18 Displacement curve of plate cam with reciprocating roller follower Fig. 19 Shape of cam with reciprocating roller follower In this case of example, 360 points are generated for profile of the designed cam shown in Fig. 20(a). Generally, linear interpolation method required the 25 times of the points for precise shape machining and circular interpolation method makes the additional machining points as the 1/2 of the design points because of a middle points inside of a fitted span. But, the proposed method reduces the machining points as 121 points under the condition of machining tolerance 0.001mm from 360 points for the designed profile of cam as shown in Fig. 20(b). The each span given in Fig. 20(b) has the unique radius by biarc curve interpolation. The accurate shapes of the design cam and the machining cam shown in Fig. 20 can give the verification of the proposed approach in accuracy and efficiency. In addition, the 3 cases of cam shapes for different cam mechanisms are shown in Figs. 19-20 for reciprocating roller follower, Fig. 21 for reciprocating flat-faced follower, Fig. 22 for oscillating roller follower, Fig. 23 for oscillating flat-faced follower. (a) Designed cam shape (b) Biarc curved cam shape Fig. 20 Profile of plate cam with reciprocating roller follower Table 2 Reduction for plate cam profile11 Number of initial design profile : 360 Machining tolerarce : 0.001 mm Follower type Number of initial design profile Reduction (%) Reciprocating roller 121(33.6%) 66.4 Reciprocating flat-faced 73(20.3%) 79.7 Oscillating roller 105(29.2%) 70.8 Oscillating flat-faced 133(36.9%) 63.1 (a) Designed cam shape (b) Biarc curved cam shape Fig. 21 Profile of plate cam with reciprocating flat-faced (a) Designed cam shape (b) Biarc curved cam shape Fig. 22 Profile of plate cam with oscillating roller follower INTERNATIONAL JOURNAL OF PRECISION ENGINEERING AND MANUFACTURING Vol. 11, No. 3 JUNE 2010 / 427 (a) Designed cam shape (b) Biarc curved cam shape Fig. 23 Profile of plate cam with oscillating flat-faced Application for 4 different types of plate cam mechanisms shows the results in Table 2. The proposed approach gives generally the well defined shapes of the design profile and machining profile with 6380% reduction of the profile data. 7. Conclusions This paper proposes a hybrid method for shape design and profile machining for general plate cam mechanisms. An instant velocity center method is used for shape design of plate cam and a biarc interpolation method is used for profile machining data processing. The main concept is that the design data generated in the design process transfer directly to the machining data and then the accuracy in design and machining process is guaranteed. In this paper, the radius direction angle, which is a most important parameter in accuracy for biarc interpolation, is directly defined by contact angle of cam and follower in designing the profile of plate cam. Also this paper proposes a machining data reduction method by the concept of a machining tolerance. An application for examples shows the verification of the proposed method by the accurate shapes of the designed cam and the machining cam with the minimum NC data within a given tolerance. ACKNOWLEDGEMENT This work was partly supported by the Second Stage of Brain Korea 21 Projects. REFERENCES 1. Cho, I. Y., Kim, B. J., Kim, J. C., Shin, J. H., Kwon, S. M. and Woo, J. Y., “A Study on Machining Information Analysis of Disk Cam using Circular Interpolation,” Proc. of Korean Society for Precision Engineering Spring Conference, pp. 1678- 1681, 2005. 2. Cho, I. Y., Kang, H. S., Shin, J. H. and Kwon, S. M., “A Study on Machining Information Analysis of Disk Cam,” Proc. of Korean Society for Machine Tool Engineering Autumn Conference, pp. 151-156, 2006. 3. Cho, I. Y., Sim, M. Y., Shin, J. H. and Kwon, S. M., “A Study on Machining Information Analysis of Plate Cam,” Proc. of Korean Society for Precision Engineering Spring Conference, pp. 289-290, 2007. 4. Kim, J. S., “Study on Shape Design and Motion Analysis of Disk