Mechanisms of rectilinear motion, diagrams of cam mechanisms. Converting rotational motion into linear motion To convert rotational motion into linear motion, use

The invention relates to mechanical engineering and can be used as a screw device for converting rotational motion into translational motion. The device consists of a screw (1), a housing (2) with covers (3), threaded rollers (9) that engage with the threads of the screw (1). The threaded rollers (9) are secured against axial displacement relative to the body due to the balls (12) installed in the separators (11), which rest against the covers (3) of the body by means of a spherical undercut (D) made at the ends of each threaded roller, and an annular groove (B ), made on the inner end surface of each cover. Elastic rings (10) have the ability to rotate in the grooves (E) of the threaded rollers (9) relative to the screw axis. To ensure assembly of the device, the width L P of the groove “E” of the threaded rollers was greater than the width L K of the rings by at least 1.5...2 pitches of the screw thread. Two versions of the device are possible, in one of which the threaded rollers are additionally connected to the body by gears, and in the other they are not connected. Favorable kinematics at the points of contact of the ball with the cover and the roller, as well as the ability to roll the rings along the “E” grooves of the threaded rollers, provide high efficiency, low wear rate and high durability. 1 salary f-ly, 3 ill.

The invention relates to mechanical engineering and can be used as a mechanical screw transmission to convert rotational motion into translational motion.

A planetary roller screw gear is known (see Reshetov D.N. “Machine Parts,” a textbook for students of mechanical engineering and mechanical specialties at universities, 4th edition, M.: Mashinostroenie, 1989, p. 314), consisting of a screw, a nut and threaded rollers installed between them. The rollers with their end journals are installed in the separators. To prevent spontaneous unscrewing of the rollers, they are additionally connected at the ends to the nut by gears. The roller turns are in threaded engagement with the screw and nut turns. In this case, the screw has an external multi-start thread, and the nut has an internal multi-start thread.

The main disadvantage of this planetary roller screw is the technological complexity of manufacturing high-precision multi-start threads (usually five or six-start) on the inner surface of the nut, hardened to high hardness. Mainly for this reason, mastering the production of planetary roller screw gears, which in most operational parameters are superior to other gears for converting rotational motion into translational motion, is difficult. In the world, only a few companies have mastered the production of planetary roller screw gears.

In this case, the threaded nut of the planetary roller screw in question performs the following functions:

Receives axial force from the actuator and transmits it through the rollers to the screw;

Keeps the rollers from moving in the radial direction from the screw axis to the nut;

Participates in the transformation of rotational motion into translational motion.

Of the known technical solutions, the closest in technical essence to the claimed device is a device for converting rotational motion into translational motion (see Kozyrev V.V. Designs of roller screws and methods of their design: textbook / Vladimir State University - Vladimir : Editorial and Publishing Complex of VlGU, 2004. pp. 8-9, Fig. 1.7), which was chosen as a prototype. This device consists of a screw, a housing with covers that performs translational motion, threaded rollers that are installed in the housing with the ability to rotate around their own axes, two rings with internal conical chamfers and bearings installed between the rings and covers. On each threaded roller there is a thread cut, the turns of which are in engagement with the turns of the screw, and at the ends there are conical chamfers that interact with the internal conical chamfers of the rings. The device body does not have internal multi-start threads and internal gears, and the threaded rollers do not have external gears. In each bearing, the rolling elements are installed in a cage.

When the device operates, the screw rotates, the threaded rollers rotate only around their own axes (there is no rotational movement of the axes of the threaded roller around the screw axis), and the housing moves translationally along the screw axis. The working axial force of any direction is transmitted from the screw to the threaded rollers due to the engagement of the threads of these parts, from the threaded rollers to the corresponding bushing due to the contact of the conical chamfers of the threaded rollers and the bushing, and from the bushing to the corresponding cover through the corresponding bearing.

This device has the following disadvantages:

The neck of the threaded roller - the hole in the cover forms a plain bearing with low efficiency and high wear rate;

When the threaded roller rotates between its conical chamfers and the mating chamfers of the rings, sliding friction occurs due to different radii of the contact points;

Due to the small contact area between the mating conical chamfers of the threaded rollers and rings, the device has low contact strength, and due to sliding friction in the specified interface, low load capacity and durability;

The device has large radial dimensions;

Threaded rollers rotate only around their own axis, which reduces the transfer function of the device and the range of its change.

The objective of the invention is to increase the efficiency, load capacity and durability of a device for converting rotational motion into translational motion by replacing sliding friction with rolling friction at the interface between the device parts, as well as reducing the radial dimensions and expanding the range of changes in the transfer function of the device.

The task is achieved by the fact that the device is equipped with at least two rings, on the end surfaces of each threaded roller there are turnkey surfaces and spherical undercuts, the centers of which are located on the axis of the threaded roller, and on its cylindrical threaded surface there are ring grooves, the number of which equal to the number of rings, and on the inner end surface of each cover there is an annular groove, the profile of which is an arc of a circle, the rings are installed in the grooves of the threaded rollers, and the number of balls in each row is equal to the number of the last ones, while each ball in each row interacts on one side with spherical undercut of the threaded roller at the corresponding end, on the opposite side - with the annular groove of the corresponding cover, and the width of the annular grooves on the threaded rollers is greater than the width of the rings by at least 1.5...2 pitches of the screw thread. It is possible to design the device for which it is equipped with bushings with internal toothed rims fixed in the housing hole on its different sides, which engage with external gear rims made at the end sections of each threaded roller.

The invention is illustrated by the accompanying drawings, where:

Figure 1 shows a general view of the device;

Figure 2 shows a section A-A in Figure 1 for the 1st version of the device;

Figure 3 shows a section A-A in Figure 1 for the 2nd version of the device with additional gearing between the threaded rollers and the housing bushings.

The device for converting rotational motion into translational motion, see Fig. 1, consists of a screw 1 and a unit that makes translational movement with basic elements “B”, which are designed to connect the specified unit with the actuator. The specified unit, see Fig. 2, consists of a housing 2 and two covers 3, which are connected to the housing with screws 4 with spring washers 5. At least a set of shims or a compensator 6 is installed between one cover 3 and the housing 2. other versions of the specified unit, which ensure the assembly and operation of the device.

An L-shaped sleeve 7 is attached to the outer end surface of each cover 3, see Fig. 2, which holds the oil deflector 8 with axial and radial clearance, and on the inner end surface of the cover there is an annular groove “B”, the profile of which is an arc of a circle.

Inside the housing, see Fig. 2, threaded rollers 9 are installed, the number of which is usually selected from the neighborhood condition to increase the load capacity of the device (the minimum number of threaded rollers is three). The thread turns of the rollers 9 engage with the thread turns of the screw 1. At the ends of each threaded roller 9, see Fig. 2, spherical undercuts “G” are made, the center of which is located on the axis of the threaded roller, and turnkey holes “D”, and on the cylindrical threaded surface - grooves “E”, the number of which is at least two. Spring steel rings 10 are installed in the grooves “E” of the threaded rollers 9, which press the threaded rollers against the screw with little force. In this case, the width L P of the groove “E” is greater than the width L K of ring 10 by 1.5...2 thread pitches of the screw (threaded roller) to ensure assembly of the device.

Between each cover 3 and the threaded roller 9, see Fig. 2, there is one row of balls 12 installed in the separator 11, the number of which is equal to the number of threaded rollers. In this case, each ball 12 interacts on one side with the annular groove “B” of the cover 3, and on the opposite side with the spherical undercut “G” of the threaded roller 9.

In the device described above, the threaded rollers have two degrees of freedom: each roller can rotate around its own axis; all rollers together with separators can rotate relative to the screw axis. Hence, the device can have a non-constant axial movement of the housing with rollers and balls with uniform rotation of the screw (variable transfer function). Devices for converting rotary motion into translational motion with a variable transfer function can be used, for example, in locking mechanisms, jacks, and so on.

In order for the proposed device to have a constant transfer function, additional coupling is required between the threaded rollers and the housing, for example gears. This connection reduces the number of degrees of freedom of the threaded rollers to one. In this case, see Fig. 3, at the ends of each threaded roller 9 there are external gears “W”, and bushings 13 with internal gears “I” are fixed in the hole of the housing 2.

Let us consider, as a general case, the order of assembling a device in which the threaded rollers are additionally connected to the body by gears. The screw usually has a cylindrical “K” surface, which simplifies assembly, see Fig. 3. The right cover 3, see Fig. 3, with a row of balls 12 in the separator 11, is installed on the screw from its left end. Rings 10 are installed in the grooves “E” of the threaded rollers 9, and this unit is inserted from the left end of the screw, see Fig. 3, onto its cylindrical surface “K”. Using a wrench, the threaded rollers are alternately screwed onto the screw until their threads are completely engaged with the threads of the screw. Next, the screw is installed vertically in the fixture, and the base element of the fixture is placed under the cover 3, ensuring that the cover is perpendicular to the axis of the screw. The balls in the separator are installed in the annular groove “B” of the cover. Then, using a wrench, the threaded rollers are alternately screwed onto the screw until the undercut “G” of each roller interacts with the corresponding ball. Since when threaded rollers are screwed into a screw, they occupy different positions along its axis, it is necessary that the width L P of the groove “E” of the threaded rollers be greater than the width L K of rings 10 by at least 1.5...2 pitches of the screw thread. To fix the position of the threaded rollers relative to the screw and the right cover, a second row of balls with a separator is installed on top of the rollers and the assembled assembly is tightened with a special nut, which is screwed onto the screw. Then a housing is installed on top of the specified unit, in which the left sleeve 13 is fixed with an internal gear rim, the teeth of which are engaged with the outer teeth by a roller. The screw with the assembled assembly without the right cover and balls with a separator is removed from the device, and the right bushing 13 with an internal gear rim is inserted into the hole in the housing and onto the teeth of the rollers, and then this bushing is secured in the housing, for example, using a cylindrical pin. On the same side, balls with a separator and a right cover are connected to the rollers, which are connected to the body with a threaded connection. Then, having unscrewed the special nut, screws 4 with spring washers 5 connect the housing to the left cover through a compensator or a set of shims. By measuring the idle torque, it is determined whether the device needs to be adjusted using a compensator or a set of shims.

The device for converting rotational motion into translational motion operates as follows. Screw 1, see Fig. 3, rotating, sets in motion threaded rollers 6, which perform a planetary motion, rolling along the gear rims of bushings 13. The threaded rollers are secured against axial displacement relative to the housing due to balls resting against the housing covers. This is the mechanism for converting the rotational movement of the screw into the translational movement of the housing together with all the parts installed in it. In this case, the balls 12 will roll along the annular grooves “G” of the covers and perform additional rotation relative to the axis of the rollers under the influence of friction forces. Rings 10 will roll along the grooves of the threaded rollers, taking up the radial load from the screw to the rollers. The axial load will be transferred from the housing cover through the balls to the threaded rollers along their axes.

In the inventive device, the working axial force is transmitted from the housing cover directly through the balls to the rollers along their axes, almost like in a thrust bearing. In the prototype device, when transmitting axial force, there is an additional interface that works with sliding friction, and the installation of threaded rollers is carried out on plain bearings. Consequently, the inventive device provides higher efficiency, less wear of contacting surfaces and greater durability. In addition, the threaded rollers in the inventive device undergo planetary motion, for which a larger range of measurement of the transfer function can be obtained.

1. A device for converting rotational motion into translational motion, containing a screw installed in a housing having covers, with the ability to rotate around its own axis, threaded rollers that are threadedly engaged with the screw and on each side with their ends rest against the cover through a series of balls installed in separator, characterized in that the device is equipped with at least two rings, on the end surfaces of each threaded roller there are turnkey surfaces and spherical undercuts, the centers of which are located on the axis of the threaded roller, and on its cylindrical threaded surface there are ring grooves, the number of which equal to the number of rings, and on the inner end surface of each cover there is an annular groove, the profile of which is an arc of a circle, the rings are installed in the grooves of the threaded rollers, and the number of balls in each row is equal to the number of the last ones, while each ball in each row interacts on one side with spherical undercut of the threaded roller at the corresponding end, on the opposite side - with the annular groove of the corresponding cover, and the width of the annular grooves on the threaded rollers is greater than the width of the rings by at least 1.5...2 pitches of the screw thread.

2. The device according to claim 1, characterized in that it is equipped with bushings with internal toothed rims fixed in the housing hole on its different sides, which engage with external gear rims made at the end sections of each threaded roller.

In construction machines, various mechanisms are used to convert rotational motion into other types of motion in order to transfer this motion to the working body.

Rack and pinion mechanism, screw and rocker

In construction machines, various types of motion are used to convert rotational motion into other types of motion in order to transfer this motion to the working body. mechanisms.

Rack and pinion mechanism
Design: drive gear and driven rack.

Used to convert rotational motion into translational motion.
Design: drive screw and driven nut.

Used to convert rotational motion into translational motion.
Design: driving cam and driven rod with spring.

Design: eccentric, connecting rod, slider.

Used to convert rotational motion into reciprocating motion.
Design: drive crankshaft with a curved pin, driven connecting rod, slider.

Used to convert rotational motion into swinging motion of the scenes.
Design: drive disk, slider, driven rocker.
Used in concrete pumps.

Maltese mechanism It is used to convert continuous rotating motion into intermittent rotating motion.
Design: driving disk with lever, driven maltissa.

Ratchet mechanism used to convert rotational motion into intermittent rotational motion, but with stopping and braking.
Design: the driving element is a ratchet, the driven element is a pawl (stopping element).

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1. Mechanisms for converting motion

The mechanical energy of many machine engines is usually the energy of a rotary shaft. However, not all machines and mechanisms have working bodies that also perform rotational motion. Often they need to communicate forward or reciprocating motion. The opposite picture is also possible. In such cases, mechanisms that transform movement are used. These include: rack and pinion, screw, crank, rocker and cam mechanisms.

1 .1 Rack and pinion mechanism

The rack and pinion mechanism consists of a cylindrical gear and a rack - a strip with teeth cut on it. Such a mechanism can be used for various purposes: by rotating a gear on a fixed axis, to move the rack translationally (for example, in a rack jack, in the feed mechanism of a drilling machine); When rolling a wheel on a stationary rack, move the wheel axis relative to the rack (for example, when performing longitudinal feed of a caliper in a lathe).

1 .2 Screw mechanism

To convert rotational motion into translational motion, a mechanism is often used, the main parts of which are a screw and a nut. This mechanism is used in various designs:

the nut (the internal thread is threaded in the body) is stationary, the screw rotates and at the same time moves forward;

the nut is stationary, the screw rotates and simultaneously moves forward with the slide. The slide is pivotally connected to the screw and can perform reciprocating movement depending on the direction of movement of the screw along the guides;

the screw is fixed so that it can only rotate, and the nut (in this case, the slide) is unable to rotate, since its lower (or other) part is installed between the guides. In this case, the nut (slide) will move forward.

The screw mechanisms listed above use threads. of various profiles, most often rectangular and trapezoidal (for example, in a bench vice, jacks, etc.). If the angle of elevation of the helix is ​​small, then the leading movement is rotational. With a very large helix angle, it is possible to convert translational motion into rotational motion, and a high-speed screwdriver can serve as an example of this.

1 .3 Crank mechanism

A crankpin is a link in a crank mechanism that can make a full revolution around a fixed axis. The crank (I) has a cylindrical protrusion - a spike 1 , the axis of which is displaced relative to the axis of rotation of the crank by a distance G, which can be permanent or adjustable. A more complex rotating part of the crank mechanism is the crankshaft. Eccentric (III) - a disk mounted on a shaft with eccentricity, that is, with a displacement of the axis of the disk relative to the axis of the shaft. The eccentric can be considered as a design variation of the crank with a small radius.

A crank mechanism is a mechanism that converts one type of movement into another. For example, uniform rotation - into translational, rocking, uneven rotation, etc. The rotating link of the crank mechanism, made in the form of a crank or crankshaft, is connected to the rack and the other link by rotational kinematic pairs (hinges). It is customary to distinguish such mechanisms into crank-rod, crank-rocker, crank-rocker, etc., depending on the nature of the movement and the name of the link with which the crank works.

Crank mechanisms are used in piston engines, pumps, compressors, presses, in driving movement of metal-cutting machines and other machines.

The crank mechanism is one of the most common motion conversion mechanisms. It is used both to convert rotary motion into reciprocating motion (for example, piston pumps), and to convert reciprocating motion into rotational motion (for example, internal combustion engines).

A connecting rod is a part of a crank-rod (slider) mechanism that transmits the movement of a piston or slider to the crankshaft crank. The part of the connecting rod that connects to the crankshaft is called the crank head, and the opposite part is called the piston (or slide) head.

The mechanism consists of a stand 1 ,crank 2, connecting rod 3 and slider 4. The crank performs continuous rotation, the slider performs a reciprocating movement, and the connecting rod performs a complex, plane-parallel movement.

The full stroke of the slider is equal to twice the length of the crank. Considering the movement of the slider from one position to another, it is easy to see that when the crank is turned at equal angles, the slider travels different distances: when moving from the extreme position to the middle, the sections of the slider’s path increase, and when moving from the middle position to the extreme, they decrease. This indicates that with uniform movement of the crank, the slider moves unevenly. So the speed of movement of the slider changes from zero at the beginning of its movement and reaches its greatest value when the crank and connecting rod form a right angle with each other, then decreases again to zero at the other extreme position.

The uneven movement of the slide causes inertial forces to appear, which have a negative impact on the entire mechanism. This is the main disadvantage of the crank-slider mechanism.

In some crank mechanisms, there is a need to ensure the straightness of the piston rod movement 4 . To do this, between the crank 1, connecting rod 2 and slider 5 use a so-called crosshead 3, absorbing the swinging movements of the connecting rod (4 - intermediate rod).

Eccentric mechanism. An eccentric mechanism works similar to a crank-slider mechanism, in which the role of a crank is played by an eccentric mounted on the drive shaft. Cylindrical surface of ex-centric 2 freely covered by a clamp 1 and yoke 3, to which the connecting rod is attached 4, transmitting translational motion to the slider during rotation of the drive shaft 5. Unlike the crank-slider mechanism, the eccentric mechanism cannot convert the reciprocating movement of the slider into the rotational movement of the eccentric due to the fact that, despite the presence of lubrication, sufficient friction remains between the clamp and the eccentric to impede movement.

For this reason, the eccentric mechanism is used only in those machines where it is necessary to convert rotational motion into reciprocating motion and create a small stroke for the executive body under significant forces. Such machines include stamps, presses, etc.

Crank-rocker mechanism. The rocker arm is a link in the lever mechanism and is a part in the form of a double-armed lever, swinging about the middle fixed axis on the stand. Crank 1 can perform rotational movement. Kinematic chain: crooked spike 1, connecting rod 2 and the rocker arm 3, connected by articulated joints, causes the rocker arm to perform rocking movements around a fixed axis on the stand.

The crank-rocker mechanism is used in spring suspensions of steam locomotives, carriages, in the designs of machines for testing materials, scales, drilling rigs, etc.

1 .4 Rocker mechanism

Backstage 1 - a link (part) of the rocker mechanism, equipped with a straight or arcuate slot in which a small slider moves - rocker stone 2 . Rocker mechanism - a lever mechanism that converts rotational or punitive movements into reciprocating movements and vice versa. According to the type of movement, the scenes are distinguished: rotating, swinging and rectilinearly moving (3 - hole through which the rocker stone is inserted and removed).

Crank mechanism. In Fig. 38, I shows that a crank 3 rotates around a fixed axis, pivotally connected at one end to a slider (rocker stone) 2. In this case, the slider begins to slide (move) in a longitudinal straight groove cut in the lever (slide) 1, and rotate it around a fixed axis. The length of the crank allows you to give the rocker a rotational movement. Such mechanisms serve to convert the uniform rotational movement of the crank into the uneven rotational movement of the rocker, but if the length of the crank is equal to the distance between the axes of the crank and rocker supports, then a crank mechanism with a uniformly rotating rocker is obtained.

The crank mechanism with a swinging rocker (Fig. 38, II) is used to convert the rotational movement of the crank 3 into the rocking movement of the rocker 1 and at the same time there is a fast move when the slider moves in one direction and a slow move in the other. The mechanism is widely used in metal-cutting machines, for example: in cross-planing, gear shaping, etc.

A crank mechanism with a progressively moving rocker (Fig. 38, III) serves to transform the rotational movement of the crank 3 into the rectilinear translational movement of the scenes 1. In the mechanism, the link can be located vertically or obliquely. This mechanism is used for short stroke lengths and is widely used in calculating machines (sine mechanism)

1 .5 Cam mechanism

A cam is a part of a cam mechanism with a profiled sliding surface so that, during its rotational movement, it transmits motion to the associated part (pusher or rod) with a given law of speed change. The geometric shape of the cams can be different: flat, cylindrical, conical, spherical and more complex.

Cam mechanisms are transforming mechanisms that change the nature of movement. In mechanical engineering, cam mechanisms that convert rotary motion into reciprocating and reciprocating motion are widespread. Cam mechanisms (Fig. 39 and 40), like other types of mechanisms, are divided into flat and spatial.

Cam mechanisms are used to perform various operations in control systems for the operating cycle of technological machines, machine tools, engines, etc. The main element of the gas distribution system of an internal combustion engine is the simplest cam mechanism . The mechanism consists of a cam 1, rods 2, connected to the working body, and a rack that supports the links of the mechanism in space and provides each link with the corresponding degrees of freedom. Roller 3, installed in some cases at the end of the rod, does not affect the law of motion of the mechanism links. A rod that moves forward is called a pusher 2, & rotational - rocker 4 . With continuous movement of the cam, the pusher makes an intermittent translational movement, and the rocker arm makes an intermittent rotational movement.

A prerequisite for the normal operation of the cam mechanism is the constant contact of the rod and the cam (closing the mechanism). The closure of the mechanism can be forceful or geometric. In the first case, closure is usually provided by a spring 5 , pressing the rod to the cam, in the second - by the design of the pusher, especially its working surface. For example, a pusher with a flat surface touches the cam at different points, so it is used only when transmitting small forces.

In light industrial machines, to ensure very complex interconnected movement of parts,

In light industry machines, to ensure very complex interconnected movement of parts, along with the simplest flat ones, spatial cam mechanisms are used. In a spatial cam mechanism you can see a typical example of geometric closure - a cylindrical cam with a profile in the form of a groove into which the pusher roller fits.

When choosing the type of cam mechanism, they try to use flat mechanisms, which have a significantly lower cost compared to spatial ones, and in all cases where this is possible, they use a rod of a swinging design, since the rod (rocker arm) is convenient to install on a support using rolling bearings. In addition, in this case, the overall dimensions of the cam and the entire mechanism as a whole may be smaller.

The production of cam mechanisms with conical and spherical cams is a complex technical and technological process, and therefore expensive. Therefore, such cams are used in complex and precise instruments.

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Let's consider the transmission mechanisms with which you can transform rotational motion into translational or oscillatory motion(and vice versa).

Such mechanisms are characterized transfer function is the first derivative of movement functions 1 driven link by the angle of rotation or linear movement of the driving link.

Lever mechanisms . An example of a lever mechanism is hinged lever mechanism(see Fig. 1.2).

In Fig. Figure 1.11 shows the kinematic diagram of the crank-slider mechanism, which includes crank 1, connecting rod 2 and slider 3.

This mechanism serves to convert the rotational motion of the crank 1 into the reciprocating motion of the slider 3 (and vice versa).

Rice. 1.11. Crank-slider mechanism

The transfer function is the dependence of the speed of movement of the slider on the angular velocity of the crank: v 3 =f( 1) (and vice versa).

Screw-nut transmission . In Fig. Figure 1.12 shows a screw-nut transmission, which is designed to convert the rotational motion of one link into the translational motion of another.

The transfer function is the dependence of the speed of axial movement of the nut on the angular speed of the screw: v 2 =f( 1).

Rice. 1.12. Screw-nut transmission: 1 – screw, 2 – nut

Cam mechanism . In Fig. 1.13 given cam mechanism(which includes cam 1 and pusher 2) and its kinematic diagram.

Rice. 1.13. Cam mechanism: 1 – cam, 2 – pusher

The transfer function is the dependence of the speed of axial movement of the pusher on the angular velocity of the cam: v 2 =f( 1).

In mechanical engineering, cam mechanisms are widely used that convert rotary motion into reciprocating or reciprocating motion: for example, to perform various operations in control systems for the operating cycle of technological machines, machine tools, engines, etc. 1 .

Examples for module 1 topics

Example 1 .

The machine diagram is shown in Fig. 1.1. Engine speed = 3000 rpm Angular speed of rotation of the actuator input shaft =2s -1. Select a worm gear, taking into account that the number of turns (approaches) worm is equal to one or two. Define And .

Solution.

1. Let us determine the angular speed of rotation of the motor shaft (see formula (1.4)):

2. Let's find the rotation transmission ratio (see formula (1.1)):

.

3. Let's select a worm gear.

Option 1. If the number of turns of the worm
, then the number of teeth of the worm wheel from formula (1.11)

.

Option 2. If the number of turns of the worm =2, then the number of teeth of the worm wheel

Example 2.

The gear drive should reduce the rotation speed of shaft 4 (see Fig. 1.4) by 3 times. Determine the number of wheel teeth , if the number of gear teeth = 25.

Solution.

Number of wheel teeth from formula (1.6)

.

Example 3.

Rice. 1.14. For example 3

Determine the gear ratio of the mechanism shown in Fig. 1.14, for a given number of wheel teeth: =22, =77, =25, =50. Find the angular velocity and rotation frequency of drive shaft 1 if shaft 3 rotates at a frequency =300 rpm.

Solution.

1. Let's determine the gear ratio of the gear mounted on shafts 1 and 2

2. Determine the gear ratio of the gear mounted on shafts 2 and 3

3. Gear ratio of the mechanism

4. Find the rotation speed of shaft 1:

5. Calculate the angular speed of rotation of shaft 1:

Answer: the gear ratio of the mechanism is 7, the rotation speed of shaft 1 is 2100 rpm, the angular speed is 219.8 s -1.

Crank mechanisms serve to convert rotational motion into reciprocating motion and vice versa. The main parts of the crank mechanism are: a crank shaft, a connecting rod and a slider, connected to each other by a hinge (a). The stroke length of the slider can be any length; it depends on the length of the crank (radius). If we denote the length of the crank by the letter A, and the stroke of the slider by B, then we can write a simple formula: 2A = B, or A = B/2. Using this formula, it is easy to find both the stroke length of the slider and the length of the crank. For example: the stroke of the slider B = 50 mm, you need to find the length of the crank A. Substituting a numerical value into the formula, we get: A = 50/2 = 25 mm, that is, the length of the crank is 25 mm.

a - the operating principle of the crank mechanism,
b - single-cranked shaft, c - multi-cranked shaft,
g - mechanism with eccentric

In a crank mechanism, a crankshaft is often used instead of a crank shaft. This does not change the essence of the mechanism. The crankshaft can have either one elbow or several (b, c).

A modification of the crank mechanism can also be an eccentric mechanism (d). The eccentric mechanism has no crank or knees. Instead, a disk is mounted on the shaft. It is not mounted in the center, but offset, that is, eccentrically, hence the name of this mechanism - eccentric.

In some crank mechanisms, it is necessary to change the stroke length of the slider. This is usually done with a crank shaft. Instead of a solid curved crank, a disk (faceplate) is mounted on the end of the shaft. The spike (the leash on which the connecting rod is put) is inserted into a slot made along the radius of the faceplate. By moving the tenon along the slot, that is, moving it away from the center or bringing it closer to it, we change the size of the slider's stroke.

The stroke of the slider in crank mechanisms is uneven. It is the slowest in places with backlash.

Crank-connecting rod mechanisms are used in engines, presses, pumps, and in many agricultural and other machines.