Eccentric clamping devices. DIY wooden clamp. Calculation of eccentric clamps

Easy to manufacture, with a high gain, fairly compact eccentric clamps, being a type of cam mechanisms, have another, undoubtedly, main advantage - speed.

The working surface of the cam is most often made in the form of a cylinder with a circle or Archimedes spiral at the base. In this article we will talk about the more common and more technologically advanced round eccentric clamp.

The dimensions of standardized round eccentric cams for machine tools are given in GOST 9061-68. The eccentricity of the round cams in this document is set to 1/20 of the outer diameter to ensure self-braking conditions over the entire operating range of rotation angles with a friction coefficient of 0.1 or more.

The figure below shows the calculated geometric diagram of the clamping mechanism. The fixed part is pressed against the supporting surface as a result of turning the eccentric handle counterclockwise around an axis rigidly fixed relative to the support.

The position of the mechanism shown is characterized by the maximum possible angle α , while the straight line passing through the axis of rotation and the center of the eccentric circle is perpendicular to the straight line drawn through the point of contact of the part with the cam and the center point of the outer circle.

If you turn the cam 90° clockwise relative to the position shown in the diagram, then a gap is formed between the part and the working surface of the eccentric equal in magnitude to the eccentricity e. This clearance is necessary for free installation and removal of the part.

CALCULATION FORMULAS

Find the friction angle (°) “part - eccentric”:

φ 1 = arctan (f 1),

Where,
f 1- coefficient of friction "part - eccentric";
0.15 - the value of the friction coefficient “part - eccentric” corresponding to the case “steel on steel without lubrication”.

Find the friction angle (°) "axis - eccentric":

φ 2 = arctan (f 2),

Where,
f 2- coefficient of friction "axis - eccentric";
0.12 - the value of the coefficient of friction “axle - eccentric” corresponding to the case “steel on steel with lubrication”.

Reducing friction in both places increases the power efficiency of the mechanism, but reducing friction in the contact area between the part and the cam leads to the disappearance of self-braking.

Find the maximum angle (°) of the circular wedge:

α = arctan (2 e / D),

Where,
e- cam eccentricity, mm;
To ensure self-braking on steel surfaces, it is desirable to fulfill the condition: D/e>15.
In GOST 9061-68: D/e=20.
D- eccentric diameter, mm.

Then the radius vector (mm) of the contact point will be equal to:

R = D / (2 cos (α)),

And the distance from the eccentric axis to the support (mm) will accordingly be:

A = s + R cos(α),

Where,
s- thickness of the clamped part, mm.

The condition for self-braking is the fulfillment of the relation:

e ≤ R f 1 + d/2 f 2,

If the condition is met, self-braking is ensured.

The clamping force (N) can be found using the formula:

F = P L cos (α) / (R tg (α + φ 1) + d/2 tg (φ 2)),

Where,
P- force on the handle, N;
L- handle length, mm.

The force transfer coefficient is:

k = F/P

The position of the eccentric clamp chosen for calculations and shown in the diagram is the most “unfavorable” from the point of view of self-braking and gain in strength. But this choice is not accidental. If in such a working position the calculated power and geometric parameters satisfy the designer, then in any other positions the eccentric clamp will have an even greater force transmission coefficient and better self-braking conditions.

When designing, moving away from the considered position towards reducing the size A if other dimensions are kept unchanged, it will reduce the gap for installing the part.

Increase in size A can create a situation where the eccentric wears out during operation and significant fluctuations in thickness s, when it is simply impossible to clamp the part.

GOST 9061-68 recommends using wear-resistant surface-cemented steel 20X with a surface hardness of 56...61 HRC at a depth of 0.8...1.2 mm as the material for making the cam. But in practice, an eccentric clamp is made from a wide variety of materials, depending on the purpose, operating conditions and available technological capabilities.

Using a small table in MS Excel created on the basis of these formulas, you can learn to quickly and easily determine the main parameters of clamps for cams made of any materials, just remember to change the values ​​of the friction coefficients in the initial data.

In the example shown in the screenshot, based on the given dimensions of the eccentric and the force applied to the handle, the mounting size from the axis of rotation of the cam to the supporting surface is determined, taking into account the thickness of the part, the self-braking condition is checked, the clamping force and the force transfer coefficient are calculated.

This calculation file can be found on the website www.al-vo.ru.

Related documents:

GOST 12189-66: Machine tools. Cams are eccentric. Design;
GOST 12190-66: Machine tools. Double eccentric cams. Design;
GOST 12191-66: Machine tools. Eccentric fork pads. Design;
GOST 12468-67 - Double-support eccentrics. Design.

They are the fastest of all manual clamping mechanisms. In terms of speed, they are comparable to pneumatic clamps. Eccentrics work on the wedge principle.

Two design types of eccentrics are used - circular and curved. Circular eccentrics are a disk or roller with a displaced axis of rotation. They are most widespread because they are easy to manufacture. Curvilinear eccentrics have a profile outlined along an Archimedean or logarithmic spiral.

Disadvantages of eccentric clamps:

Small stroke, limited by eccentricity.

Inconsistency of the clamping force in a batch of workpieces when secured with a circular eccentric.

Increased worker fatigue due to property.

Not suitable for impact or vibration applications due to the risk of self-detachment.

Despite these disadvantages, cam clamps are widely used in fixtures, especially for small-scale and mass production. This is due to the simplicity of the design, low manufacturing cost and high productivity.

The inconstancy of the clamping force of the circular eccentric is associated with the unevenness of the lifting angle of the curved wedge. The circular eccentric clamps the workpiece satisfactorily at working angles of rotation β=30...130. Even at such rotation angles, the clamping force fluctuates in value by 20...25%.

Practice has established that eccentrics with R/e 7 work well. They provide sufficient travel at a rotation angle β within 135 and ensure self-braking of the eccentric.

Curvilinear eccentrics ensure constant clamping force, since their lifting angle is constant. But these eccentrics are difficult to manufacture and therefore their use is limited.

Calculation of clamping force

The clamping force of a circular eccentric can be determined with sufficient accuracy for practical calculations by replacing the action of the eccentric with the action of a flat single-bevel wedge with an angle α in the gap between the trunnion and the surface of the workpiece. The diagram of such a replacement and the forces acting on the eccentric and fictitious wedge are shown in Fig. 4.79.

Rice. 4.79. Diagram of forces acting on the eccentric and fictitious wedge

In the diagram, the force W 1 is the force acting on the plane of the clamp PP at an angle α. The force T=W 1 α acts along the clamping plane. This force can be considered as external, acting on the KSR wedge with angle α. Using the formula for calculating a flat single-bevel wedge, we can write:

The force W 1 can be determined by considering the equilibrium of the eccentric:

Since, then.

Let us substitute the value of W 1 into formula (1) and omit α as a value close to unity at small angles α:

where R 1 and α are variable quantities.

The initial data for calculating the main dimensions of a round eccentric (Fig. 8.3) are: δ - tolerance on the size of the workpiece from its mounting base to the place where the fastening force is applied, mm; α - angle of rotation of the eccentric from the zero (initial) position; Q- workpiece fixing force, N.

Rice. 8.3. Eccentric clamps:

A - disk eccentric, b - eccentric with L-shaped clamp

If the angle of rotation of the eccentric is not limited, then

2e=s 1 +d+s 2 +

where s 1 is the gap for free entry of the workpiece under the eccentric; s 2 - eccentric power reserve, protecting it from passing through the dead center (takes into account eccentric wear); J- rigidity of the clamping device, N/mm.

The last term of the formula characterizes the increase in the distance between the eccentric and the workpiece as a result of elastic deformation of the clamping system. With s 1 = 0.2÷0.4 mm and s 2 = 0.4÷0.6 mm

e= +(0.3÷0.5) ​​mm

If the rotation angle α is significantly less than 180°,

e= (8.4)

We find the radius of the eccentric pin (mm) by taking the width d;

r=Q/2bσ cm, (8.5)

Where σ cm - permissible bearing stress (15-20 MPa).

At b = 2r

Eccentric radius R we find from the self-braking conditions. From the diagram of forces acting on the eccentric (Fig. 8.4, A) it follows that the resultant T reactions Q and friction forces F should be equal to the reaction from the axle passing tangentially to the friction circle of radius ρ, and directed opposite to it:

where j = static friction angle.

At e≤ p R min = e+ r+ Δ, where Δ is the thickness of the jumper (Fig. 8.4, b).

Rice. 8.4. Scheme for power calculation of eccentrics

The radius ρ of the friction circle is determined from the equality ρ = f"r, Where f" - coefficient of static friction in the axle. Values ​​j and f"should be taken at the smallest limit. For semi-dry surfaces, j = 8° can be taken and f" = 0.12÷0.15.

Angle of rotation α 1 (see Fig. 8.4, A) for the least favorable position of the eccentric we will find using the formula α 1 = 90° - j.

Width of the working part of the eccentric IN we determine from the formula

σ=0.565

where σ is the permissible stress at the point of contact of the eccentric with the workpiece. For hardened steel, you can take σ = 800÷1200 MPa; E 1 E 2 - elastic moduli, respectively, of the materials of the eccentric and the element in contact with it (intermediate part or workpiece), MPa; µ 1, µ 2 - Poisson's ratios for the materials of the eccentric and the element in contact with it.

At E 1 =E 2 =E and µ 1 =µ 2 = 0.25 we get

from where (at R in mm)

B= 0.17 mm. (8.6)

Eccentric dimensions e, r, R And IN coordinated with GOST.

To establish the relationship between the fastening force Q and the moment on the eccentric handle at the end of securing the workpiece, we will use the diagram shown in Fig. 8.4, b. During the fastening process, three forces act on the eccentric: the force on the handle N, workpiece reaction T and the reaction of the axle S. Under the influence of these forces, the system is in equilibrium. Reaction T represents the resultant force Q and friction forces F. The sum of the moments of all acting forces relative to the eccentric rotation axis

Nl - Qe sin α" - fQ(R- e cos α") - Sρ = 0,

Where f- coefficient of friction between the eccentric and the workpiece.

Force S differs little in magnitude from normal force Q. Taking S" Q, we get the moment on the eccentric handle

Nl= Q[fR+ ρ + e(sin α" +f cos α")].

To simplify the resulting expression, we accept:

1) fR = tg j R"sin jR(at j= 6° the error is less than 1%);

2) expression sin α" +f cos α" replace sin (α" +j) (error 1%). After substitutions we get

Nl=Q(8.7)

Given the expression for R, we get

Nl= eQ. (8.8)

According to this formula, the moment Nl found with an accuracy of 10%.

Moving the point of contact of the eccentric with the plane when it is rotated through an angle α from the initial position (Fig. 8.5, a)

x = e- With= e- e cos α = e(1 - cos α).

Rice. 8.5. Schemes for calculating the movement of the point of contact of the eccentric with the plane when it rotates

In Fig. 8.5 b change shown X from α. Considering that

x=s 1 +d+ ,

cos α = 1- ; α "=180 o - α

Substituting the found value α " into formula (8.8), we can express the moment on the eccentric handle through the initial values.

Calculation of wedge clamps

Wedge clamps are used as an intermediate link in complex clamping systems. They are easy to manufacture, compact, easily placed in the device, and allow you to increase and change the direction of the transmitted force. At certain angles, the wedge mechanism has self-braking properties. For the most common single-bevel wedge in devices (Fig. 8.6, a) under the action of forces at a right angle, we have the following dependence obtained from the force polygon:

. . (8.9)

With a minus sign in the formula, we have a dependence for detaching the wedge. Self-braking occurs at α< φ 1 + φ 2 . Если φ 1 = φ 2 .= φ 3 = φ. то зависимость упрощается:

Rice. 8.6. Action of forces in the wedge mechanism:

a - with an angle of 90°; b - with an angle of more than 90°

When transmitting forces at an angle β > 90° (Fig. 8.6, b) the relationship between P and Q from the force polygon has the form (at 90 + α > β)

If the friction angle is constant and equal to φ, then

.

Calculation of lever clamps

Lever clamps, similar to wedge clamps, are used in combination with other elementary clamps, forming more complex clamping systems. Using a lever, the magnitude and direction of the transmitted force are changed, and the workpiece is simultaneously and uniformly secured in two places.

Easy to manufacture, with a high gain, a fairly compact eccentric clamp, which is a type of cam mechanisms, has another, undoubtedly, main advantage...

... – instantaneous performance. If in order to “turn on and off” a screw clamp it is often necessary to make at least a couple of turns in one direction and then in the other, then when using an eccentric clamp it is enough to turn the handle only a quarter turn. Of course, they are superior to eccentric ones in terms of clamping force and working stroke, but with a constant thickness of the fastened parts in mass production, the use of eccentrics is extremely convenient and effective. The widespread use of eccentric clamps, for example, in stocks for assembling and welding small-sized metal structures and elements of non-standard equipment, significantly increases labor productivity.

The working surface of the cam is most often made in the form of a cylinder with a circle or Archimedes spiral at the base. Later in the article we will talk about the more common and more technologically advanced round eccentric clamp.

The dimensions of eccentric round cams for machine tools are standardized in GOST 9061-68*. The eccentricity of the round cams in this document is set to 1/20 of the outer diameter to ensure self-braking conditions over the entire operating range of rotation angles at a friction coefficient of 0.1 or more.

The figure below shows the geometric diagram of the clamping mechanism. The fixed part is pressed against the supporting surface as a result of turning the eccentric handle counterclockwise around an axis rigidly fixed relative to the support.

The position of the mechanism shown is characterized by the maximum possible angle α , while the straight line passing through the axis of rotation and the center of the eccentric circle is perpendicular to the straight line drawn through the point of contact of the part with the cam and the center point of the outer circle.

If you turn the cam 90˚ clockwise relative to the position shown in the diagram, then a gap is formed between the part and the working surface of the eccentric equal in magnitude to the eccentricity e. This clearance is necessary for free installation and removal of the part.

Program in MS Excel:

In the example shown in the screenshot, based on the given dimensions of the eccentric and the force applied to the handle, the mounting size from the axis of rotation of the cam to the supporting surface is determined, taking into account the thickness of the part, the self-braking condition is checked, the clamping force and the force transfer coefficient are calculated.

The value of the friction coefficient “part - eccentric” corresponds to the case “steel on steel without lubrication”. The value of the friction coefficient “axle - eccentric” is selected for the “steel on steel with lubrication” option. Reducing friction in both places increases the power efficiency of the mechanism, but reducing friction in the contact area between the part and the cam leads to the disappearance of self-braking.

Algorithm:

9. φ 1 =arctg (f 1 )

10. φ 2 =arctg (f 2 )

11. α =arctg (2*e /D )

12. R =D/ (2*cos (α ))

13. A =s +R *cos (α )

14. e ≤ R*f 1+ (d/2)* f 2

If the condition is met, self-braking is ensured.

15. F = P * L * cos(α )/(R * tg(α +φ 1 )+(d /2)* tg(φ 2 ))

1 6 . k = F/P

Conclusion.

The position of the eccentric clamp chosen for calculations and shown in the diagram is the most “unfavorable” from the point of view of self-braking and gain in strength. But this choice is not accidental. If in such a working position the calculated power and geometric parameters satisfy the designer, then in any other positions the eccentric clamp will have an even greater force transmission coefficient and better self-braking conditions.

When designing, moving away from the considered position towards reducing the size A if other dimensions are kept unchanged, it will reduce the gap for installing the part.

Increase in size A can create a situation where the eccentric wears out during operation and significant fluctuations in thickness s, when it is simply impossible to clamp the part.

The article has deliberately not mentioned anything so far about the materials from which the cams can be made. GOST 9061-68 recommends using wear-resistant surface-cemented steel 20X to increase durability. But in practice, an eccentric clamp is made from a wide variety of materials, depending on the purpose, operating conditions and available technological capabilities. The calculation presented above in Excel allows you to determine the parameters of clamps for cams made of any materials, but you just need to remember to change the values ​​of the friction coefficients in the initial data.

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Eccentric clamps are easy to manufacture and for this reason they are widely used in machine tools. The use of eccentric clamps can significantly reduce the time for clamping a workpiece, but the clamping force is inferior to threaded clamps.

Eccentric clamps are made in combination with and without clamps.

Consider an eccentric clamp with a clamp.

Eccentric clamps cannot work with significant tolerance deviations (±δ) of the workpiece. For large tolerance deviations, the clamp requires constant adjustment with screw 1.

The materials used for the manufacture of the eccentric are U7A, U8A With heat treatment to HR from 50....55 units, steel 20X with carburization to a depth of 0.8... 1.2 With hardening HR from 55...60 units.

Let's look at the eccentric diagram. The KN line divides the eccentric into two? symmetrical halves consisting, as it were, of 2 x wedges screwed onto the “initial circle”.

The eccentric rotation axis is shifted relative to its geometric axis by the amount of eccentricity “e”.

Section Nm of the lower wedge is usually used for clamping.

Considering the mechanism as a combined one consisting of a lever L and a wedge with friction on two surfaces on the axis and point “m” (clamping point), we obtain a force relationship for calculating the clamping force.

where Q is the clamping force

P - force on the handle

L - handle shoulder

r - distance from the eccentric rotation axis to the point of contact With

workpiece

α - angle of rise of the curve

α 1 - friction angle between the eccentric and the workpiece

α 2 - friction angle on the eccentric axis

To avoid the eccentric moving away during operation, it is necessary to observe the condition of self-braking of the eccentric

where α - sliding friction angle at the point of contact with the workpiece ø - friction coefficient

For approximate calculations of Q - 12Р Let us consider the diagram of a double-sided clamp with an eccentric

Wedge clamps

Wedge clamping devices are widely used in machine tools. Their main element is one, two and three bevel wedges. The use of such elements is due to the simplicity and compactness of the designs, speed of action and reliability in operation, the possibility of using them as a clamping element acting directly on the workpiece being fixed, and as an intermediate link, for example, an amplifier link in other clamping devices. Typically self-braking wedges are used. The condition for self-braking of a single-bevel wedge is expressed by the dependence

α > 2ρ

Where α - wedge angle

ρ - the angle of friction on the surfaces G and H of contact between the wedge and the mating parts.

Self-braking is ensured at angle α = 12°, however, to prevent vibrations and load fluctuations during the use of the clamp from weakening the workpiece, wedges with an angle α are often used<12°.

Due to the fact that decreasing the angle leads to increased

self-braking properties of the wedge, it is necessary when designing the drive to the wedge mechanism to provide devices that facilitate the removal of the wedge from the working state, since releasing a loaded wedge is more difficult than bringing it into the working state.

This can be achieved by connecting the actuator rod to a wedge. When rod 1 moves to the left, it passes path “1” to idle, and then, hitting pin 2, pressed into wedge 3, pushes the latter out. When the rod moves back, it also pushes the wedge into the working position by hitting the pin. This should be taken into account in cases where the wedge mechanism is driven by a pneumatic or hydraulic drive. Then, to ensure reliable operation of the mechanism, different pressures of liquid or compressed air should be created on different sides of the drive piston. This difference when using pneumatic actuators can be achieved by using a pressure reducing valve in one of the tubes supplying air or liquid to the cylinder. In cases where self-braking is not required, it is advisable to use rollers on the contact surfaces of the wedge with the mating parts of the device, thereby facilitating the insertion of the wedge into its original position. In these cases, it is necessary to lock the wedge.