CN109829258B - Main and auxiliary constant force spring cam profile curve design method considering roller radius - Google Patents
Main and auxiliary constant force spring cam profile curve design method considering roller radius Download PDFInfo
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Abstract
A main and auxiliary constant force spring cam profile curve design method considering roller radius belongs to the technical field of main and auxiliary constant force spring hangers and supports. The method is characterized by comprising the following steps: step 1001, determining an energy transfer relation in a motion process; step 1002, determining spring forces of a main spring and an auxiliary spring; step 1003, establishing a differential equation of the rotation angle of the knife-shaped cam and the vertical displacement of the load tube; step 1004, establishing a corresponding ellipse equation according to step 1003; step 1005-1006, respectively establishing a design equation of the knife-shaped cam profile curve of the support hanger without directly considering the roller radius and considering the roller radius; step 1007, obtaining the knife cam profile curve considering the roller radius. In the main and auxiliary constant force spring cam profile curve design method considering the roller radius, the quantitative influence of the roller radius on the knife-shaped cam profile curve is directly considered, so that an accurate and reliable knife-shaped cam profile curve is obtained, and the design level, reliability and support constancy of a support and hanger product are improved.
Description
Technical Field
A main-auxiliary constant force spring cam profile curve design method considering roller radius belongs to the technical field of main-auxiliary constant force spring supports and hangers.
Background
Thermal power plants, nuclear power plants, petrochemical and heating enterprises and the like all need conveying pipelines with short lengths of hundreds of meters and long lengths of hundreds of kilometers to realize the conveying of materials such as gas, water, smoke, wind and the like, and need to continuously and reliably work under the internal temperature, pressure and fluid load of complex alternation and external wind, rain and impact load. Due to the bearing fluctuation of the conveying pipeline and the expansion and contraction of the pipe wall, the pipeline can generate vertical deformation of dozens of even hundreds of millimeters. If a rigid support is adopted for supporting, the vertical deformation of the pipeline can be prevented, large additional primary and secondary stress and local stress concentration are generated, and the force is transmitted to a fixed support and connected equipment through a pipeline system, so that the safety of the equipment is damaged, and the safety of the pipeline equipment and the surrounding environment is seriously influenced; if the common spring is adopted for supporting, although the additional stress can be reduced to a certain degree, the pipeline fulcrum load is in direct proportion to the vertical displacement, and the additional stress of the pipeline cannot be eliminated fundamentally. At present, a large number of conveying pipelines are supported by various main and auxiliary constant-force spring hangers and supports, so that reasonable deformation of the pipelines is guaranteed, load transfer is avoided, and pipeline and interface stress is reduced.
At present, the main and auxiliary constant force spring support and hanger developed by LISEGA company in Germany is a typical form of the main and auxiliary constant force spring support and hanger with high precision in recent years. The knife-shaped cam is a core component of the main-auxiliary constant-force spring support and hanger, and the design precision of the curve of the knife-shaped cam directly influences the constancy of the support force of the support and hanger. At present, the design method for the profile curve of the knife-shaped cam is based on an ideal design without directly considering the radius of rollers at two ends of a load tube, however, in the actual working process of the main and auxiliary constant-force spring support and hanger, the left end and the right end of the load tube are in contact with the knife-shaped cam through the rollers in order to reduce friction and sliding between the load tube and the knife-shaped cam. The traditional design and processing method of the main and auxiliary constant force spring support and hanger basically does not directly consider the influence of the roller radius when calculating the cam profile curve, but adopts a post compensation strategy to correct the profile curve, and the method brings extra design errors, so that an accurate and reliable design method of the knife-shaped cam profile curve is established, a reliable technical method is provided for the design of the main and auxiliary constant force spring support and hanger knife-shaped cam profile curve, the design level, the reliability and the support constant degree of a support and hanger product are improved, and the technical problem to be solved urgently in the field.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: the design method overcomes the defects of the prior art, and provides the main and auxiliary constant force spring cam profile curve design method considering the roller radius, which directly considers the quantitative influence of the roller radius on the knife shape cam profile curve, obtains the accurate and reliable knife shape cam profile curve, ensures that the constant force spring support and hanger cam profile curve meets the design requirements, and improves the design level, reliability and support constancy of the support and hanger product.
The technical scheme adopted by the invention for solving the technical problems is as follows: the design method of the main and auxiliary constant force spring cam profile curve considering the roller radius is characterized by comprising the following steps of:
1001, determining an energy transfer relation in the motion process of a main and auxiliary constant-force spring support hanger;
Preferably, the expression of the energy transfer relationship in step 1001 is:
wherein F is the output load, F 1 Is the spring force of the main spring, F 2 Is the spring force of the auxiliary spring, h is the vertical distance from the contact point of the auxiliary spring and the knife-shaped cam to the rotating shaft of the cam,
the turning angle from the global coordinate system XOY to the satellite coordinate system xi o eta along the clockwise direction is y, and the y represents the load tube plumbAnd (4) performing straight displacement.
Preferably, in step 1002, the expressions of the spring forces of the main spring and the auxiliary spring are respectively:
F 1 ＝k 1 (h-y)
wherein, F 1 Is the spring force of the main spring, F 2 To assist the spring force of the spring, k 1 Is the stiffness of the main spring, k 2 H is the vertical distance from the connecting point of the auxiliary spring and the knife-shaped cam to the rotating shaft of the cam, a is the compression length of the auxiliary spring when the rotating angle of the cam is zero,
y represents the load tube vertical displacement for the corner from the global coordinate system XOY in the clockwise direction to the satellite coordinate system ξ o η.
Preferably, the expression of the differential equation in step 1003 is:
wherein k is 1 Is the stiffness of the main spring, k 2 For stiffness of auxiliary spring, F h Is the sum of the horizontal forces of two auxiliary springs, F v Is the difference between the external load and the spring force of the main spring.
Preferably, the expression of the ellipse equation in step 1004 is:
wherein, F v Is the difference between the external load and the spring force of the main spring, F h Is the sum of the horizontal forces of the two auxiliary springs, gamma = k 1 /2k 2 The ratio of the rigidity of the main spring to the rigidity of the auxiliary spring is 2 times; k is a radical of formula 1 Is the stiffness of the main spring, k 2 To assist the stiffness of the spring, C 2 As an integration constant, C 2 ＝(1.1～1.5)max(F v 2 )。
Preferably, the design equation for the knife cam profile curve that does not directly consider the roller radius described in step 1005 is:
wherein (xi, eta) is the curve coordinate of the knife cam which is not directly considered with the radius of the roller,
the turning angle from the global coordinate system XOY to the satellite coordinate system xi o eta along the clockwise direction is shown as y, the vertical displacement of the load tube is shown as y, and d is the horizontal distance from the contact point of the load tube and the knife-shaped cam to the rotating shaft of the cam.
Preferably, the design equation of the knife cam profile curve considering the roller radius in step 1006 is:
wherein (xi) 1 ,η 1 ) Namely the coordinate of the profile curve of the knife-shaped cam considering the radius of the roller,
indicating the radius of the roller.
Compared with the prior art, the invention has the following beneficial effects:
in the main-auxiliary constant force spring cam profile curve design method considering the radius of the roller, the quantitative influence of the radius of the roller on the profile curve of the knife-shaped cam is directly considered, and the defect that in the prior art, the knife-shaped cam obtained by simplifying the design without directly considering the roller needs to adopt a post-compensation strategy to correct the profile curve during processing, so that extra errors are caused is overcome, the design error of the obtained result is smaller, and the use requirement of the constant force spring support and hanger can be met better. The method can obtain accurate and reliable profile curve of the knife-shaped cam, ensure that the profile curve of the constant-force spring support hanger cam meets the design requirements, and improve the design level, reliability and support constancy of the support hanger product.
Meanwhile, as can be seen from curve design and simulation analysis obtained by an example, the load deviation of the knife-shaped cam obtained by the main-auxiliary type constant force spring cam profile curve design method considering the radius of the roller is about 0.8%, compared with the prior art, the load deviation is about 6%, the precision is greatly improved, and the use requirement of the constant force spring support and hanger can be better met.
Drawings
FIG. 1 is a flow chart of a main-auxiliary constant force spring cam profile curve design method considering roller radius.
Fig. 2 is a schematic structural view of the main-auxiliary constant-force spring support and hanger.
FIG. 3 is a comparison graph of the profile curve design method of the main and auxiliary constant force spring cam in consideration of the radius of the roller and the profile curve of the prior art knife cam.
Fig. 4 is a comparison graph of the constant force effect of the main-auxiliary constant force spring support hanger in the prior art and the main-auxiliary constant force spring cam profile curve design method considering the roller radius.
Wherein: 1. the device comprises a load tube 2, a roller 3, a main spring 4, a knife-shaped cam 5, an auxiliary spring 6, a cam rotating shaft 7, a central load tube 8, a spring pressing plate 9 and a shell.
Detailed Description
Fig. 1 to 4 show preferred embodiments of the present invention, and the present invention will be further described with reference to fig. 1 to 4.
In the structural schematic diagram of the main-auxiliary constant-force spring support and hanger (hereinafter referred to as a support and hanger) shown in fig. 2, a central load tube 7 penetrates out from the center of the bottom of a housing 9, a spring pressing plate 8 is fixed below the housing 9 through a plurality of bolts arranged around the central load tube, the bottom of the central load tube 7 simultaneously penetrates through the spring pressing plate 8 downwards, a load tube 1 is arranged at the top of the central load tube 7, and a main spring 3 is arranged between the load tube 1 and the spring pressing plate 8 and sleeved on the outer ring of the central load tube 7.
Two ends of the load tube 1 are respectively provided with a roller 2, the outer sides of the two rollers 2 are respectively provided with a knife-shaped cam 4, and the rollers 2 are in rolling contact with the inner surface of the knife-shaped cam 4. An auxiliary spring 5 is respectively hung on the outer side surface of the knife-shaped cam 4, the other end of the auxiliary spring 5 is fixed on the inner end surface of the shell 9, a cam rotating shaft 6 is respectively arranged at the bottom of the knife-shaped cam 4, and the knife-shaped cam 4 rotates by taking the cam rotating shaft 6 as a shaft.
In the motion process of the main-auxiliary type constant-force spring support hanger, the main spring 3 provides vertical supporting force, the auxiliary spring 5 provides vertical supporting force through the direction changing effect of the knife-shaped cam 4, and constant-force support is provided in a certain stroke range through the interaction of the main spring 3 and the auxiliary spring 5. The invention adopts a generating method to carry out linear transformation on the obtained cam profile curve without directly considering the radius of the roller, and establishes the profile curve of the main and auxiliary constant-force spring support and hanger knife-shaped cam with the radius of the roller taken into consideration.
In the main and auxiliary constant force spring cam profile curve design method considering the radius of the roller, a cam rotating shaft 6 is taken as an original point, the vertical direction is taken as a Y axis, a connecting line from the center of the cam rotating shaft 6 to the connecting point of an auxiliary spring 5 and a knife-shaped cam 4 is taken as an eta axis, a global coordinate system XOY and a following coordinate system xi o eta are established, the following coordinate system xi o eta rotates along with the knife-shaped cam 4 around the cam rotating shaft 6, and the included angle is formed by rotating along with the cam rotating shaft 6
Is the corner from the global coordinate system XOY to the following coordinate system xi o eta in the clockwise direction, F is the output load, F 1 Is the spring force of the main spring 3, F 2 Is the spring force of the auxiliary spring 5. k is a radical of 1 Is the rigidity, k, of the main spring 3 2 D is the horizontal distance from the contact point of the load tube 1 and the knife-shaped cam 4 to the cam rotating shaft 6, h is the vertical distance from the contact point of the auxiliary spring 5 and the knife-shaped cam 4 to the cam rotating shaft 6, a is the compression length of the auxiliary spring 5 when the rotation angle of the knife-shaped cam 4 is 0, and h is the rigidity of the auxiliary spring 5 1 The vertical distance from the upper end point of the main spring 3 to the rotating shaft 6 of the cam when the upper end point moves to the highest position is r, and the radius of the roller 2 is r.
As shown in fig. 1, the method for designing the profile curve of the main and auxiliary constant force spring cam considering the radius of the roller comprises the following steps:
1001, determining an energy transfer relation in the motion process of a main and auxiliary constant-force spring support hanger;
under the action of the output load F, the friction loss is not counted, the external load acting of the support hanger is the same as the energy variation of the main spring 3 and the auxiliary spring 5 inside the support hanger, and an energy transfer relational expression in the motion process of the support hanger is obtained:
wherein F is the output load, F 1 Is the spring force of the main spring 3, F 2 The spring force of the auxiliary spring 5 is shown, and h is the vertical distance from the connecting point of the auxiliary spring 5 and the knife-shaped cam 4 to the cam rotating shaft 6.
when the load tube 1 of the constant-force spring support hanger moves to any position, the expressions of the spring force of the main spring 3 and the spring force of the auxiliary spring 5 are respectively as follows:
F 1 ＝k 1 (h-y)
wherein, F 1 Is the spring force of the main spring 3, F 2 Is the spring force, k, of the auxiliary spring 5 1 Is the rigidity, k, of the main spring 3 2 H is the vertical distance from the connecting point of the auxiliary spring 5 and the knife-shaped cam 4 to the cam rotating shaft 6, a is the compression length of the auxiliary spring 5 when the rotating angle of the knife-shaped cam 4 is zero,
y represents the vertical displacement of the load tube 1 for the rotation angle from the global coordinate system XOY in the clockwise direction to the satellite coordinate system ξ θ η.
according to the expression obtained in the steps 1001 to 1002, simultaneously carrying out variable substitution to enable F v ＝F-F 1 ，F h ＝2F 2 The angle of rotation of the blade cam 4 can be obtained
Differential equation with the vertical displacement y of the load tube 1, namely:
wherein k is 1 Is the rigidity, k, of the main spring 3 2 The rigidity of the auxiliary spring 5.
integrating the differential equation obtained in the step 1003 to obtain the rotation angle of the knife-shaped cam 4
Elliptic equation with vertical displacement y of the load tube 1:
wherein, F v The difference between the external load and the spring force of the main spring 3, namely the vertical force equivalently applied to the load tube 1 through the two auxiliary springs 5, is called the equivalent vertical force of the auxiliary springs 5 for short; f h The sum of the horizontal forces of the two auxiliary springs 5 is called the auxiliary spring horizontal force for short; γ = k 1 /2k 2 A ratio of the rigidity of the main spring 3 to the rigidity of the auxiliary spring 5 which is 2 times; c 2 Is an integration constant, generally taken as C 2 ＝(1.1～1.5)max(F v 2 )。
in the motion process of the constant force spring, the horizontal distance from the contact point of the knife shape of the load tube 1 and the cam 4 to the cam rotating shaft 6 is constant as d, and a design equation of a cam curve can be obtained through coordinate transformation:
where (ξ, η) are the determined coordinates of the curve of the knife cam 4 without directly considering the radius of the roller 2.
and (3) putting each coordinate point of the cam profile curve obtained in the step 1005 in a direction deviating from the load tube 1 along the normal direction of the cam profile curve, and retracting the radius of the roller 2 to obtain a design equation of the knife-shaped cam profile curve considering the radius of the roller:
wherein (xi) 1 ,η 1 ) I.e. the coordinates of the profile curve of the knife cam taking into account the radius of the roller 2,
indicating the radius of the roller.
and (3) giving the rigidity, the output load, the stroke range and the installation geometric parameters of the main spring 3 and the auxiliary spring 5, and solving the design equation obtained in the step 1006 to obtain the profile curve of the main-auxiliary constant-force spring support and hanger knife-shaped cam considering the radius of the roller.
The invention is illustrated in more detail below by way of examples:
if the external supporting load F of a main-auxiliary type constant-force spring support hanger is 10000N, the constant-force stroke of a load tube 1 is 400mm, and the rigidity k of a main spring 3 1 50N/mm, and the stiffness of the auxiliary spring 5 is k 2 75N/mm, the horizontal distance d from the contact point of the load tube 1 and the knife-shaped cam 4 to the cam rotating shaft 6 is 60mm, the vertical distance h from the connection point of the auxiliary spring 5 and the knife-shaped cam 4 to the cam rotating shaft 6 is 400mm, and the vertical distance h from the load tube 1 to the cam rotating shaft 6 when the main spring 3 is not stressed 1 600mm, the compression length a of the auxiliary spring 5 is 80mm when the rotation angle of the knife cam 4 is 0, and the radius r of the roller 2 is 20mm. According to the parameters, combining the steps 1001-1007 to carry out the main and auxiliary constant force spring supportThe hanger cam profile curve is calculated and the cam profile curve without directly considering the roller radius and the cam profile curve considering the roller radius are obtained through the above steps 1005 and 1006, respectively, and the comparative effect of the two curves is shown in fig. 3.
The constant force spring is modeled and analyzed in simulation software aiming at the cam profile curve which is obtained in the figure 3 and takes the radius of the roller into consideration, the comparison result of the constant force effects of the two models is shown in the figure 4, the curve shown in the figure 4 shows that the load deviation of the main and auxiliary type constant force spring support and hanger model obtained by the prior art is about 6%, and the load deviation of the main and auxiliary type constant force spring support and hanger model obtained by the technology of the specification is about 0.8%, so that the design precision is higher, and the use requirement of the main and auxiliary type constant force spring support and hanger can be better met.
The foregoing is directed to preferred embodiments of the present invention, other and further embodiments of the invention may be devised without departing from the basic scope thereof, and the scope thereof is determined by the claims that follow. However, any simple modification, equivalent change and modification of the above embodiments according to the technical essence of the present invention will still fall within the protection scope of the technical solution of the present invention.
Claims (2)
1. The main and auxiliary constant force spring cam profile curve design method considering the radius of the roller is characterized by comprising the following steps of:
1001, determining an energy transfer relation in the motion process of the main and auxiliary constant-force spring support hanger;
step 1002, respectively determining the spring force of a main spring and an auxiliary spring in the motion process of a main-auxiliary constant-force spring support hanger;
step 1003, establishing a differential equation of the rotation angle of the knife-shaped cam and the vertical displacement of the load tube;
step 1004, integrating the differential equation obtained in step 1003 to obtain an elliptic equation of the rotation angle of the knife-shaped cam and the vertical displacement of the load tube;
step 1005, establishing a design equation of the knife-shaped cam profile curve of which the roller radius is not directly considered by a supporting and hanging frame;
step 1006, establishing a design equation of the knife cam profile curve considering the radius of the roller;
step 1007, solving the design equation of the knife-shaped cam profile curve taking the roller radius into consideration established in step 1006 to obtain the knife-shaped cam profile curve taking the roller radius into consideration;
the expression of the energy transfer relationship in step 1001 is:
wherein F is the output load, F 1 Is the spring force of the main spring, F 2 Is the spring force of the auxiliary spring, h is the vertical distance between the contact point of the auxiliary spring and the knife-shaped cam and the rotating shaft of the cam,
the turning angle from the global coordinate system XOY to the satellite coordinate system xi o eta along the clockwise direction is shown as y, and the y represents the vertical displacement of the load tube;
in step 1002, the expressions of the spring forces of the main spring and the auxiliary spring are respectively:
F 1 ＝k 1 (h-y)
wherein, F 1 Is the spring force of the main spring, F 2 To assist the spring force of the spring, k 1 Is the stiffness of the main spring, k 2 H is the vertical distance from the connecting point of the auxiliary spring and the knife-shaped cam to the rotating shaft of the cam, a is the compression length of the auxiliary spring when the rotating angle of the cam is zero,
the rotation angle from the global coordinate system XOY to the satellite coordinate system xi o eta along the clockwise direction is shown, and y represents the vertical displacement of the load tube;
the expression of the differential equation in step 1003 is:
wherein k is 1 Is the stiffness of the main spring, k 2 For stiffness of auxiliary spring, F h Is the sum of the horizontal forces of two auxiliary springs, F v Is the difference between the external load and the spring force of the main spring;
the design equation for the knife cam profile curve that does not directly consider the roller radius described in step 1005 is:
wherein (xi, eta) is the curve coordinate of the knife cam which is not directly considered with the radius of the roller,
the angle is the corner from the global coordinate system XOY to the satellite coordinate system xi o eta along the clockwise direction, y represents the vertical displacement of the load tube, and d is the horizontal distance from the contact point of the load tube and the knife-shaped cam to the rotating shaft of the cam;
the design equation for the knife cam profile curve that takes into account the roller radius described in step 1006 is:
wherein (xi) 1 ,η 1 ) Namely the coordinate of the contour curve of the knife cam considering the radius of the roller,
indicating the radius of the roller.
2. Consideration roller according to claim 1The main and auxiliary type constant force spring cam profile curve design method of the wheel radius is characterized in that: the expression of the ellipse equation in step 1004 is:
wherein, F v Is the difference between the external load and the spring force of the main spring, F h Is the sum of the horizontal forces of the two auxiliary springs, gamma = k 1 /2k 2 The ratio of the rigidity of the main spring to the rigidity of the auxiliary spring is 2 times; k is a radical of 1 Is the stiffness of the main spring, k 2 To assist the stiffness of the spring, C 2 As an integration constant, C 2 ＝(1.1～1.5)max(F v 2 )。
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| CN110657312B (en) * | 2019-09-29 | 2021-05-25 | 山东理工大学 | Energy balance-based compact constant-force spring support and hanger cam curve design method |
| CN110737953A (en) * | 2019-09-29 | 2020-01-31 | 山东理工大学 | Force balance-based compact constant-force spring support and hanger cam curve design method |
| CN111062161B (en) * | 2019-12-11 | 2021-09-24 | 浙江大学 | Large-tension high-stability light and small constant force device |
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