SCIENCE AND TECHNOLOGY ENGLIAH FOR MECHANICAL ENGINEERING LESSON FIVE FOUNDATIONS OF MACHINE DESIGN (PART 2) Action Of a Pair Of Mating Involute Teeth Let a and b be the base circles of a pair of mating involute gears. Line CD is a common tangent to the base circles. while ab is the line of centers. Assume that CD is part of a string being unwound from A and wound upon b, while a and b rotate together in such a manner that string CD remains taut at all times. When A and B start to rotate, point C on the string will leave circle A and move towards circle B, thus describing an involute with respect to circle A
SCIENCE AND TECHNOLOGY ENGLISH FOR MECHANICAL ENGINEERING LESSON FIVE FOUNDATIONS OF MACHINE DESIGN (PART 2) Action Of a Pair Of Mating Involute Teeth Let A and B be the base circles of a pair of mating involute gears. Line CD is a common tangent to the base circles, while AB is the line of centers. Assume that CD is part of a string being unwound from A and wound upon B, while A and B rotate together in such a manner that string CD remains taut at all times. When A and B start to rotate, point C on the string will leave circle A and move towards circle B, thus describing an involute with respect to circle A
SCIENCE AND TECHNOLOGY ENGLIAH FOR MECHANICAL ENGINEERING At the same time, however, one can imagine that, with respect to circle B, point C traces an involute back to its origin B. The involutes form the actual tooth outline in the ideal case. It can be proven that the basic requirement for proper gear action, namely, that no changes in speed ratio occur during the passage of any tooth, is fulfilled when the normal to the mating tooth curves at the point of contact always passes through the pitch point
SCIENCE AND TECHNOLOGY ENGLISH FOR MECHANICAL ENGINEERING At the same time, however, one can imagine that, with respect to circle B, point C traces an involute back to its origin B. The involutes form the actual tooth outline in the ideal case. It can be proven that the basic requirement for proper gear action , namely , that no changes in speed ratio occur during the passage of any tooth, is fulfilled when the normal to the mating tooth curves at the point of contact always passes through the pitch point
SCIENCE AND TECHNOLOGY ENGLIAH FOR MECHANICAL ENGINEERING Let us investigate whether this condition is satisfied b the involute. It is clear that since the string is taut at all times the path of the point of contact between the two involutes is a straight line. This line intersects the line of centers(AB)at P. Also, the involute is by definition normal to its generating line (i.e, the string) at all times, since the involute is a circular arc with everincreasing radius, and a radius is al ways perpendicular to its circular arc. Therefore, if we can prove that point P is the pitch point, we have satisfied all the above mentioned requirements Triangles ACP and BPD are similar since their corresponding angles are equal. Like the friction drive at the beginning of this chapter, A and b have the same circumferential velocity at points C and D. We may therefore state that
SCIENCE AND TECHNOLOGY ENGLISH FOR MECHANICAL ENGINEERING Let us investigate whether this condition is satisfied by the involute. It is clear that since the string is taut at all times, the path of the point of contact between the two involutes is a straight line. This line intersects the line of centers (AB) at P. Also, the involute is by definition normal to its generating line (i.e., the string) at all times, since the involute is a circular arc with everincreasing radius, and a radius is always perpendicular to its circular arc. Therefore, if we can prove that point P is the pitch point, we have satisfied all the above mentioned requirements. Triangles ACP and BPD are similar since their corresponding angles are equal. Like the friction drive at the beginning of this chapter, A and B have the same circumferential velocity at points C and D. We may therefore state that
SCIENCE AND TECHNOLOGY ENGLIAH FOR MECHANICAL ENGINEERING BD/AC=nA/nB 6.17 but BD/AC= BP/AP 6.18 and na/nR is the speed ratio. Therefore, AP and BP must be pitch radii and point P must be the pitch point Path Of Contact And Contact Ratio The path of contact is the line described by the point of contact between two mating teeth during rotation. In involute gearing, the path of contact coincides with the line of action. It begins where the addendum circle of the driven sear intersects the line of action, and ends where the addendum circle of the driving gear intersects the line of action. This definition ignores possible inter ference conditions with pinions of small tooth numbers, which are outside the scope of this text
SCIENCE AND TECHNOLOGY ENGLISH FOR MECHANICAL ENGINEERING BD/AC = nA / nB 6.17 but BD/AC = BP/AP 6.18 and nA /nB is the speed ratio. Therefore, AP and BP must be pitch radii and point P must be the pitch point. Path Of Contact And Contact Ratio The path of contact is the line described by the point of contact between two mating teeth during rotation. In involute gearing, the path of contact coincides with the line of action. It begins where the addendum circle of the driven sear intersects the line of action, and ends where the addendum circle of the driving gear intersects the line of action. This definition ignores possible interference conditions with pinions of small tooth numbers, which are outside the scope of this text
SCIENCE AND TECHNOLOGY ENGLIAH FOR MECHANICAL ENGINEERING The contact ratio (m) is a number indicating the average number of teeth in contact for a given pair of mating gears, and is found by dividing the length of the path of contact Z (theaction)by the base pitch, or m-length of action /base pitch Z/P 6.19 Cams cam 凸轮 A cam and its follower together form follower随动件 mechanism that converts rotary motion(often at constant speed) or oscillating motion, into a cyclical (repetitive) linear or angular motion
SCIENCE AND TECHNOLOGY ENGLISH FOR MECHANICAL ENGINEERING The contact ratio (mc ) is a number indicating the average number of teeth in contact for a given pair of mating gears, and is found by dividing the length of the path of contact Z (the “action”) by the base pitch, or mc = length of action / base pitch = Z / Pb 6. 19 Cams A cam and its follower together form a mechanism that converts rotary motion (often at constant speed) or oscillating motion, into a cyclical (repetitive) linear or angular motion. cam 凸轮 follower 随动件
SCIENCE AND TECHNOLOGY ENGLIAH FOR MECHANICAL ENGINEERING Plate Cams And Cylindrical Cams Plate cams are made in the shape of a flat plate with either a contoured periphery or a cylindrical periphery with a contoured groove in one face, and a hub. They rotate around an axis, which is perpendicular to the plane of the plate and they impart mainly radial motion to their followers 轮毂 Cylindrical cams consist of a cylindrical body designed to rotate around its axis, with either one end or a peripheral groove, shaped to impart the desired motion to a follower, and in a direction mainly parallel to the cylinder's axis There are other types of cams; these are, however outside the scope of this chapter
SCIENCE AND TECHNOLOGY ENGLISH FOR MECHANICAL ENGINEERING Plate Cams And Cylindrical Cams Plate cams are made in the shape of a flat plate with either a contoured periphery or a cylindrical periphery with a contoured groove in one face, and a hub. They rotate around an axis, which is perpendicular to the plane of the plate and they impart mainly radial motion to their followers. Cylindrical cams consist of a cylindrical body designed to rotate around its axis, with either one end, or a peripheral groove, shaped to impart the desired motion to a follower, and in a direction mainly parallel to the cylinder's axis. There are other types of cams; these are, however, outside the scope of this chapter. 轮毂
SCIENCE AND TECHNOLOGY ENGLIAH FOR MECHANICAL ENGINEERING Both plate and cylindrical cams have a wide field of application, and belong to the most efficient mechanisms known Cams of both types are used in both multispindle single and multispindle automatic screw machines and lathes for actuation of tool 多轴的 slides, in tool and die design, in internal automatic screw combustion engines for valve and machine Injector actuation, in various indexing 自动切丝机 devices, in packaging machinery, and in many other applications. Two plate cams acting on a single follower, one in the X direction. the other in the Y direction. can be designed to produce al most any follower path
SCIENCE AND TECHNOLOGY ENGLISH FOR MECHANICAL ENGINEERING Both plate and cylindrical cams have a wide field of application, and belong to the most efficient mechanisms known. Cams of both types are used in both single and multispindle automatic screw machines and lathes for actuation of tool slides, in tool and die design, in internal combustion engines for valve and injector actuation, in various indexing devices, in packaging machinery, and in many other applications. Two plate cams acting on a single follower, one in the X direction, the other in the Y direction, can be designed to produce almost any follower path. multispindle 多轴的 automatic screw machine 自动切丝机
SCIENCE AND TECHNOLOGY ENGLIAH FOR MECHANICAL ENGINEERING Plate cam followers may be radial, in which case the centerline of the follower intersects with the axis of rotation of the cam; offset when this is‖ofet偏 not the case, or swinging, when the follower is hinged around a point‖ hinge铰接 outside the cam's surface. so that the point of contact describes a circular arc The point of contact between cam and follower may be in the shape of a point a roller. or a flat or rounded surface Almost all followers are spring-loaded to make them follow the cam contour
SCIENCE AND TECHNOLOGY ENGLISH FOR MECHANICAL ENGINEERING Plate cam followers may be radial, in which case the centerline of the follower intersects with the axis of rotation of the cam; offset when this is not the case, or swinging, when the follower is hinged around a point outside the cam's surface, so that the point of contact describes a circular arc. The point of contact between cam and follower may be in the shape of a point, a roller, or a flat or rounded surface. Almost all followers are spring-loaded to make them follow the cam contour. offset 偏心 hinge 铰接
SCIENCE AND TECHNOLOGY ENGLIAH FOR MECHANICAL ENGINEERING Sensitivity of Followers Not all followers have the same sensitivity to changes in cam contour. Only the pointed, specially shaped radial follower is able follow the sudden change in the particular cam profile shown The roller follower is next in sensitivity, while the flat follower is the least sensitive. Obviously, a cam outline should be based upon the shape of its follower to obtain the desired displacement and only that follower will provide the desired motion Determination Of The Contour of a Plate Cam To design the contour of a plate cam, we must first establish the motion requirements of the follower, which are most often record in the form of a displacement diagram, and sometimes as a displacement table or schedule. Such a diagram shows the desired displacements of the follower for a number of equal, sequential angular displacements of the cam, which are usually expressed in degrees
SCIENCE AND TECHNOLOGY ENGLISH FOR MECHANICAL ENGINEERING Sensitivity Of Followers Not all followers have the same sensitivity to changes in cam contour. Only the pointed, specially shaped radial follower is able to follow the sudden change in the particular cam profile shown. The roller follower is next in sensitivity, while the flat follower is the least sensitive. Obviously, a cam outline should be based upon the shape of its follower to obtain the desired displacement, and only that follower will provide the desired motion. Determination Of The Contour Of a Plate Cam To design the contour of a plate cam, we must first establish the motion requirements of the follower, which are most often record in the form of a displacement diagram, and sometimes as a displacement table or schedule. Such a diagram shows the desired displacements of the follower for a number of equal, sequential angular displacements of the cam, which are usually expressed in degrees
SCIENCE AND TECHNOLOGY ENGLIAH FOR MECHANICAL ENGINEERING Furthermore. we must establish the radius of the base circle which is numerically equal to the distance from the lowest point on the cam periphery to the center of rotation of the cam The base circle is the basis of the cam outline. to which are added the sequential distances the point of contact of the follower must travel, as indicated by the displacement diagram. The diameter of the base circle must at least be equal to the diameter of the hub. In the case of cams made integral with the shaft, the base-circle diameter must be at least equal to the shaft diameter The horizontal line 0-360 is the x axis of the displacement diagram for certain cam. Imagine that this line represents the base circle of that cam, flattened to a straight line. Any movements imparted to the follower are caused by the profile of the cam material outside the base circle, or, in the diagram above the baseline
SCIENCE AND TECHNOLOGY ENGLISH FOR MECHANICAL ENGINEERING Furthermore, we must establish the radius of the base circle, which is numerically equal to the distance from the lowest point on the cam periphery to the center of rotation of the cam. The base circle is the basis of the cam outline, to which are added the sequential distances the point of contact of the follower must travel, as indicated by the displacement diagram. The diameter of the base circle must at least be equal to the diameter of the hub. In the case of cams made integral with the shaft, the base-circle diameter must be at least equal to the shaft diameter. The horizontal line 0-360ºis the x axis of the displacement diagram for certain cam. Imagine that this line represents the base circle of that cam, flattened to a straight line. Any movements imparted to the follower are caused by the profile of the cam material outside the base circle, or, in the diagram, above the baseline
