CN101289146A - Method and device for friction compensation - Google Patents

Method and device for friction compensation Download PDF

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Publication number
CN101289146A
CN101289146A CNA2008101287198A CN200810128719A CN101289146A CN 101289146 A CN101289146 A CN 101289146A CN A2008101287198 A CNA2008101287198 A CN A2008101287198A CN 200810128719 A CN200810128719 A CN 200810128719A CN 101289146 A CN101289146 A CN 101289146A
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Prior art keywords
friction
procedure parameter
parameter
compensation
conditioning equipment
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CNA2008101287198A
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CN101289146B (en
Inventor
C·米勒
H·-J·多雷斯
S·舒尔特泽
R·克卢斯皮斯
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Robert Bosch GmbH
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Robert Bosch GmbH
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    • BPERFORMING OPERATIONS; TRANSPORTING
    • B65CONVEYING; PACKING; STORING; HANDLING THIN OR FILAMENTARY MATERIAL
    • B65HHANDLING THIN OR FILAMENTARY MATERIAL, e.g. SHEETS, WEBS, CABLES
    • B65H23/00Registering, tensioning, smoothing or guiding webs
    • B65H23/04Registering, tensioning, smoothing or guiding webs longitudinally
    • B65H23/18Registering, tensioning, smoothing or guiding webs longitudinally by controlling or regulating the web-advancing mechanism, e.g. mechanism acting on the running web
    • B65H23/195Registering, tensioning, smoothing or guiding webs longitudinally by controlling or regulating the web-advancing mechanism, e.g. mechanism acting on the running web in winding mechanisms or in connection with winding operations

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  • Controlling Rewinding, Feeding, Winding, Or Abnormalities Of Webs (AREA)
  • Braking Arrangements (AREA)
  • Winding Of Webs (AREA)

Abstract

The friction compensation device is fitted to a winding machine (1) by which material (70) is wound onto a winding drum (30) controlled by a controlling and regulating device (10). It has an additional process parameter (80) engaged on the input side for compensation of the friction moment in the friction compensation unit (14).

Description

The method and apparatus that is used for friction compensation
Technical field
The present invention relates to a kind of method that is used at the up-coiler friction compensation, described up-coiler is wound to material on the winch spool, wherein, described winch spool is by the coiling driver drives of controlled/conditioning equipment control, wherein, predesignate the driving square of described coiling actuator in described control/conditioning equipment, wherein, the cireular frequency with described winch spool in the friciton compensation unit takes in as the input end procedure parameter.
The invention still further relates to a kind of device that is used at the up-coiler friction compensation, described up-coiler can be wound to material on the winch spool, wherein, described winch spool is by the coiling driver drives of controlled/conditioning equipment control, wherein, tension link and diameter calculating unit and/or the linearizing friciton compensation arrangements of cells that is used for described tension link are at described control/conditioning equipment, wherein, in described friciton compensation unit, the cireular frequency of described winch spool is taken in as the input end procedure parameter.
Background technology
Technical literature has been introduced the up-coiler that for example is used to reel for strip-shaped material such as fiber, paper, film, cloth, thin slice or metal wool or thread material fully.This machine is characterised in that, accuracy controlling tension force in winding process, thus avoid uneven or the coiling product of error is arranged.There is in batch document to describe the motor regulate and control method of actuator in this machine.
For example a kind of conditioning equipment that is used for up-coiler has been described, the tension force on it can regulate from conveying roller towards the product of coiling ingot among the DE OS 3919162A1.Conditioning equipment has high quick rotary speed controling unit, and it is used for the conveying motor speed of accuracy control conveying roller, and is used for the coiling motor speed at up-coiler glancing impact accuracy control coiling ingot.Thereby product can after same processes in remain under the tension force of predesignating.Can shorten to greatest extent by this conditioning equipment and to make up-coiler stop the required time.
Introduced a kind of up-coiler of the strip-shaped material that is used to reel among DE OS 10342020 A1, material especially is that lamination coating is rectangular, up-coiler has the air squeeze roll that can press to tambour (take up roll), can regulate the rotating speed and/or the moment of torsion of air squeeze roll when using this up-coiler according to the bar shaped pulling force of the rectangular material of present use.
Up-coiler uses the rotating speed control of torque limiting or restriction electric current usually.The limits value of moment of torsion or electric current is combined by a plurality of parts.These parts are the moment part of tension force, the moment partial sum friction square that is used to quicken.
Control/the conditioning equipment of up-coiler is also referred to as around the volume calculator, is made up of a plurality of functional elements, and these functional elements calculate the different moment parts of actuating device and correspondingly control the coiling actuator.
Except that tension link as original regulating loop major part; existing coiling calculator also has diameter calculating unit, acceleration compensation unit and friciton compensation unit usually; these unit are used for the controlled plant linearization with the original tension link of coiling calculator, thereby implement the adjusting of interference-free as far as possible amount influence.Single parts in the coiling calculator load different procedure parameters at input end, and these procedure parameter parts are obtained and calculated by model by corresponding sensor in the up-coiler.
Only considered friciton compensation in the prior art relatively simply.Usually only the rotating speed or the cireular frequency of axle volume are obtained the friciton compensation value as procedure parameter.Therefore can't regulate the required ginseng parameter of compensation usually.The only more known now system that can determine to have the characteristic curve of small number of nodes, wherein, characteristic curve is made of the rotating speed and the friction square of axle volume.This system for example appears in control/conditioning equipment of up-coiler REXROTH SYNAX 200, in this equipment with the form of the node of simple feature curve predesignated friction square when stopping, at minimized friction square under the regulation rotating speed and the maximum friction square under the velocity limit value.
Its defective is, does not consider main frictional influence when regulating.For example, because axle volume quality difference, bearing friction or power transmission loss are also inequality.In existing friciton compensation unit, do not consider the thrust of hold-down roller equally.In addition, the friction relevant or for example can produce inconstant frictional influence with the friction of temperature correlation with the position, it can appear under certain transmission configuring condition.
All friction shares of not considering can cause the controlled plant non-linearization.To cause and to regulate algorithm by optimal setting, perhaps when setting or trail run institute setting parameter, expend huge.Therefore increase the probability of failure of total system.
Summary of the invention
The objective of the invention is to, a kind of method is provided, described method can be considered the friction share in the winding process better and obtain compensating parameter better.The present invention also aims to, a kind of corresponding device thereof is provided.
The goal of the invention of described method reaches by following method, considers that promptly at least one additional procedure parameter is with the friction compensation square.Can when predesignating the driving square, different friciton compensation shares can be considered like this, thereby obviously better adjusting can be realized.
If proofread and correct rated tension by the actual tension that records, then can directly obtain the deviation of predetermined value and make the driving square adaptive by tension link.
If realize the adjusting of tension force, just can avoid using the measuring equipment of measuring the tension force actual value, thereby realize a kind of simplification and the corresponding low structure of cost by control piece.
In control/conditioning equipment, predesignate the driving square of coiling actuator preferred enforcement in the flexible program by diameter calculating unit and/or friciton compensation unit.Thereby can calculate the accurate more predetermined value that drives square.
In another method for optimizing flexible program, in control/conditioning equipment, predesignate the driving square of coiling actuator by the acceleration compensation unit.Thereby can when predesignating the driving square, consider additional dynamic effect.
If use axle volume quality and/or temperature and/or roller thrust and/or motor angle actual value or axle volume angle actual value to take in as the procedure parameter of additional input end, thereby the friction compensation square, just can consider a friction relevant simultaneously with axle volume quality, the relevant friction with thrust, the friction of being correlated with the position and with the frictional influence of temperature correlation.The quality difference of axle volume, then for example bearing friction or power transmission loss are also different.In addition, because hold-down roller is optional accessory, so the thrust of hold-down roller can have different requirements to driving square.The friction relevant with the position for example can produce by pitch wheel, and the peripheral friction ring of these gears is constant.(that is to say that the gear number of teeth is very little) especially this situation can occur when miniature gears gear teeth calibration is big.Friction can occur in any transmission device between motor side, load-side (axle volume) or motor and the load.Friction with temperature correlation for example can appear when using tooth belt as the transfer zone between motor and the axle volume.The friction of described tooth belt and temperature correlation under high capacity, this is because the tooth belt heating makes friction change once more.Heating can make tooth belt expand usually, because tooth belt stress is less when expanding, so expansion can cause friction less.Use method of the present invention can obviously more preferably consider these effects.
In method flexible program of the present invention, stipulate, irrelevantly analyze mutually the single procedure parameter that uses for the friction compensation square, and its addition ground is combined into friction always compensates.Its advantage is, has also added extra friciton compensation value except that the existing friciton compensation value relevant with rotating speed, for example with the relevant friciton compensation value of axle volume quality, these friciton compensation values is carried out mutual incoherent processing, thereby can shortcut calculation.
Stipulate that in a kind of method flexible program compensation value is therefrom obtained at least two combinations mutually in the single procedure parameter that will use for the friction compensation square.This way especially helps obtaining of friciton compensation when having complex dependency relationship each other.
Especially favourable way is, the compensating parameter that will be used for determining the single procedure parameter of compensation value is handled with the form of one or more characteristic line clusters or family of characteristic curves, directly or obtain the compensation value of friction square by the interpolation method between the node in the family of characteristic curves.This way especially can be considered not to be without difficulty can be by the complex relationship of function with regard to representing.
Stipulate in the other method flexible program of the present invention, the compensating parameter of single procedure parameter before the winding process or during by determining that the repeatedly trail run under the condition obtains and store.This way can realize that automatic or manual obtains to calculating the required input end parameter of friciton compensation value.Thereby need not to carry out complicated input, the program of having minimized expends on the one hand, helps reducing wrong input on the other hand.Therefore, equipment can adapt to the different strip-shaped material with different take up rolls soon.
In being similarly the preferable methods flexible program, stipulate, the compensating parameter of single procedure parameter is used as safeguards that purposes is used and/or generate report when changing deviation and/or time occurring with respect to preset value.Can discern effectively like this and show fault, thereby support preventative maintenance, perhaps make it become possibility.
In said method, can stipulate, procedure parameter axle volume quality is determined as the function of axle coil diameter or radius, axle volume width and density of material, perhaps under the situation that the axle volume density can change according to diameter, determined by width of cloth band stress relevant or axle volume stiffness characteristics curve with diameter.Thereby can independently determine and the relevant compensation rate of axle volume quality, also need not to consider axle volume quality acceleration compensation amount known and that together carry out during the course.
Regulation calculates the deterministic process parameters of temperature by the temperature on the measurement coiling actuator or by thermal modeling in addition.Thereby can accurately determine the friction share with temperature correlation, and it is carried out corresponding compensation.
In a method flexible program, stipulate, measurement process parameters roller thrust, or calculate the roller thrust by other procedure parameter.This way is especially favourable when using hold-down roller.
For the friction share relevant with axle volume position compensated, can regulation will be relevant with procedure parameter motor angle actual value or axle volume angle actual value compensating parameter be stored in friciton compensation unit or the control/conditioning equipment with the form of data bank, for example it is saved as form.
The goal of the invention of relative assembly reaches by following method, considers in the input end of friciton compensation unit that promptly at least one additional procedure parameter is with the friction compensation square.Consider differently friciton compensation share during like this can be civilian especially in the use described method flexible program better.
In one embodiment, the acceleration compensation arrangements of cells is in control/conditioning equipment, and it especially can better be regulated when the speed of spoke continues to change.
Stipulate in a preferred embodiment, the friciton compensation unit has axle volume quality and/or temperature and/or roller thrust and/or motor angle actual value or axle volume angle actual value as additional input parameter, thus can predesignate consider when driving square relevant with axle volume quality, with temperature correlation, relevant and/or roll up the share of being correlated with in the position with hold-down roller in case of necessity with axle.
In order to determine simply that friciton compensation value, friciton compensation unit can have the family of characteristic curves unit that at least one is used to make up at least two procedure parameters.
In preferred implementing form, can in friciton compensation unit and/or control/conditioning equipment, determine the compensating parameter of single friction share, and it is stored to be used for subsequent analysis.Different service conditions be can adapt to neatly so on the one hand, preventive maintenance and maintenance mechanical device are easy on the other hand.
Description of drawings
Come the present invention is further specified by embodiment shown in the drawings below, wherein:
Fig. 1 is the up-coiler according to the band control/conditioning equipment of prior art; And
Fig. 2 is the up-coiler according to band control/conditioning equipment of the present invention.
The specific embodiment
Fig. 1 has shown up-coiler 1, and it has the vitals winch spool 30 that is driven by coiling actuator 20.Need the material 70 of coiling, it for example is the strip-type product, at first by first reversing arrangement 61, be designed to stationary roll in the embodiment shown, then by second reversing arrangement 62 at this, be designed to dancer at this, then guide for the 3rd reversing arrangement 63 of another stationary roll by form, the material 70 final winch spools 30 that lead to, wherein, hold-down roller 40 is rolled up the axle that material 70 is pressed on the winch spool 30 in the embodiment shown, thereby for example avoids occurring gas enclosure.
Reversing arrangement 62 is in mechanical action at this with dynameter 50 and is connected.Dynameter 50 1 sides firmly link to each other with up-coiler 1, and this dynameter for example may be embodied as force indicator, can determine the tension force of material 70 when reeling by this force indicator.The parameter that records is transported to (herein show) control/conditioning equipment 10 (coiling calculator), be integrated in tension control assembly 11 that being used in control/conditioning equipment 10 control coiling actuator 20 with this parameter as importing data.Instead also can only regulate pulling force.
According to prior art, control/conditioning equipment 10 also has other functional element, for example diameter calculating unit 12, acceleration compensation unit 13 and friciton compensation unit 14, these functional elements are used to make the controlled plant linearization of tension link 11, thereby implement the adjusting of interference-free as far as possible amount influence.This impels the regulating effect of total system better.With shown in identical, will in first combiner 15, be combined as a regulated value as the regulated value of the output signal of tension link 11 and correction regulated value as the output signal of diameter calculating unit 12 and acceleration compensation unit 13.Next in second combiner 16, another is flowed to the control signal of coiling actuator 20 in the embodiment shown as the correction regulated value of the output signal of friciton compensation unit 14.Usually friciton compensation and acceleration compensation are inserted as the pre-control to the driving square.Different procedure parameters offers the algorithm of single part in control/conditioning equipment 10, these algorithm controls coiling actuators 20.
According to the prior art regulation, only the cireular frequency 81 with winch spool 30 is transferred to friciton compensation unit 14 as procedure parameter 80.Usually in simple relatively model, calculate the compensation value of friction square by cireular frequency 81.
Fig. 2 has shown the design-calculated up-coiler 1 according to the present invention, and the difference of itself and form of implementation shown in Figure 1 is to have control/regulon 10, and the friciton compensation unit 14 in the control/regulon 10 has additional procedure parameter 80 at input end.
Except that the cireular frequency 81 of winch spool 30, also roll up angle actual value 85 as additional input value in the embodiment shown to temperature 83, roller thrust 84 and motor angle actual value or the axle of friciton compensation unit 14 transmission axles volume quality 82, coiling actuator 20.As shown in Figure 2, can also transmit other input value to friciton compensation unit 14.
Can stipulate that in a form of implementation mutual irrelevantly addition ground inserts the compensation value of single friction share.For example, except that the friciton compensation value relevant, also add the passage of a friciton compensation value relevant with axle volume quality with rotating speed.These two passages are uncorrelated mutually, that is to say, the access of the friciton compensation relevant with rotating speed irrespectively inserts with axle volume quality, and the access and the rotating speed of the friciton compensation relevant with axle volume quality are irrelevant.
Stipulate that in another form of implementation addition ground forms total friciton compensation from the compensated part that is mutually related.Therefore at least two parameters that are mutually related are made up, thereby obtain compensation value.Draw characteristic line cluster or family of characteristic curves like this in model, it can be expressed as the face in the space when existing two to be mutually related parameter.Therefore for example can determine the friciton compensation value from the family of characteristic curves of forming by the cireular frequency 81 of axle volume quality 82 and winch spool 30.Also can serviceability temperature 83 in the characteristic family, roller thrust 84 and motor angle actual value or axle volume angle actual value 85 be as other dimensions.Characteristic line family is also nonessential known fully herein.For example can from characteristic line cluster, determine compensation value by corresponding interpolation method (for example linear interpolation), feasible equally when known minority node only.
According to the present invention, therefore the device among Fig. 2 has at least one characteristic family unit 14.1 in friciton compensation unit 14 or control/conditioning equipment 10, and it for example is stored in control/adjusting program with form of software.
Can also from a plurality of family of characteristic curves, determine different friction shares, and then its addition ground is made up.Also analysis method mentioned above can be used in combination.
Can stipulate procedure parameter axle volume quality 82 is determined as the function of axle coil diameter or radius, the function of axle volume width and the function of density of material, perhaps the axle volume density during according to vary in diameter a width of cloth band stress or the axle volume stiffness characteristics curve from the foundation vary in diameter come deterministic process parameter axle volume quality 82.Because axle volume width and density of material keep constant usually in process of production, so axle volume quality 82 only is the function of diameter or radius.Density of material also can change in process of production, reason be since width of cloth band stress according to vary in diameter (axle volume stiffness characteristics curve), an axle volume average density can change.Because width of cloth band stress or axle volume stiffness characteristics curve are normally known, so also can obtain density of material.
Can stipulate in addition, can deterministic process parameters of temperature 83 by measuring the temperature on the coiling actuator or calculating by thermal modeling.Thereby can accurately determine the friction share with temperature correlation, and it is carried out corresponding compensation.
In a kind of method flexible program, stipulate, measurement process parameters roller thrust 84, or calculate roller thrust 84 by other procedure parameter.This way is especially favourable when using hold-down roller.The function of corresponding compensation part as thrust or other procedure parameter (for example axle coil diameter) can be calculated, wherein, this compensated part is almost proportional with the product of thrust and axle coil diameter.
For the share relevant with axle volume position compensated, the form of the compensating parameter relevant with procedure parameter motor angle actual value or axle volume angle actual value 85 with data bank can be stored in friciton compensation unit or the control/conditioning equipment, for example it be saved as form.Can consider in addition between motor and winch spool 30, one or more gear stages to be set.
Because the mensuration complexity of compensating parameter continues to increase except simple compensation, and this mensuration is very important, so need carry out the trail run of automation aspect method and technology.
Can determine family of characteristic curves and it is stored in the control convenience by trail run, wherein, for example can determine and the relevant friciton compensation of axle volume quality, for example use empty reel spool, full up axle volume or half-full axle to involve in to go repeatedly trail run by trail run repeatedly.Each trail run can leave a plurality of velocity measurement points of obtaining compensating moment, for example by existing driving square in the coiling actuator 20, wherein, must deduct the driving square that forms pulling force from total driving square, thereby determine friciton compensation.
Can implement equally to be used to obtain with the compensating parameter of the compensating parameter of temperature correlation, roller thrust and with the position trail run of relevant compensating parameter.
Trail run also is of value to preventative maintenance.It is especially favourable to use empty axle to involve in capable trail run, because can ignore the characteristic of coiling thing like this.The limit of the maximum friction square that for example can stipulate the limit of starting friction square (starting torque) or occur when high revolution generates report in view of the above.This report can be used for the maintenance and the replacing of bearing.
Trail run can also be as the reference measurement that is used to check mechanical device.After changing mechanical part, for example change tooth belt after, can by these trail runs check its whether regulate correct (for example tooth belt stress) or its function whether normal.If tooth belt is very high, drives square and also can equally significantly improve.
Shown method flexible program and described device flexible program can allow to consider different friciton compensation shares better when control/regulation and control coiling actuator 20, thereby can realize obviously better adjusting.In addition, obtain to automation to a great extent and monitor different compensating parameters.Also can be advantageously used in the maintenance and the monitoring of up-coiler 1 at last.

Claims (20)

1. method that is used at up-coiler (1) friction compensation, described up-coiler (1) is wound to material (70) on the winch spool (30), wherein, described winch spool (30) is driven by the coiling actuator (20) of controlled/conditioning equipment (10) control, wherein, in described control/conditioning equipment (10), predesignate the driving square of described coiling actuator (20), wherein, cireular frequency (81) with described winch spool (30) in friciton compensation unit (14) takes in as input end procedure parameter (80), it is characterized in that, consider that at least one additional procedure parameter (80) is with the friction compensation square.
2. method according to claim 1 is characterized in that, proofreaies and correct rated tension by tension link (11) with the actual tension that records.
3. method according to claim 1 is characterized in that, implements adjusting to tension force by control piece.
4. according to the described method of each claim in the claim 1 to 3, it is characterized in that, in described control/conditioning equipment (10), predesignate the driving square of described coiling actuator (20) with diameter calculating unit (12) and/or friciton compensation unit (14).
5. according to the described method of each claim in the claim 1 to 4, it is characterized in that, in described control/conditioning equipment (10), predesignate the driving square of described coiling actuator (20) with acceleration compensation unit (13).
6. according to the described method of each claim in the claim 1 to 5, it is characterized in that, use axle volume quality (82) and/or temperature (83) and/or roller thrust (84) and/or motor angle actual value or axle volume angle actual value (85) as additional input end procedure parameter (80), with the friction compensation square.
7. according to the described method of each claim in the claim 1 to 6, it is characterized in that, irrelevantly analyze mutually the single procedure parameter (80,81,82,83,84,85) that uses for the friction compensation square, and its addition ground is combined into friction always compensates.
8. according to the described method of each claim in the claim 1 to 6, it is characterized in that compensation value is therefrom obtained at least two combinations mutually in the single procedure parameter (80,81,82,83,84,85) that will use for the friction compensation square.
9. method according to claim 8, it is characterized in that, to be used for determining the single procedure parameter (80 of compensation value, 81,82,83,84,85) compensating parameter is handled with the form of one or more characteristic line clusters or family of characteristic curves, directly or obtain the compensation value of friction square by the interpolation method between the node of family of characteristic curves.
10. according to the described method of each claim in the claim 1 to 9, it is characterized in that, the compensating parameter of single procedure parameter (80,81,82,83,84,85) before the winding process or during under the condition of determining, repeatedly obtaining and storing in the trail run.
11. according to the described method of each claim in the claim 1 to 10, it is characterized in that, with single procedure parameter (80,81,82,83,84,85) compensating parameter is as safeguarding purposes and/or generating report when changing deviation and/or time occurring with respect to preset value.
12. according to the described method of any claim in the claim 6 to 11, it is characterized in that, described procedure parameter axle volume quality (82) is determined as the function of axle coil diameter or radius, axle volume width and material (70) density, perhaps under the situation that the axle volume density can change according to diameter, from width of cloth band stress relevant or axle volume stiffness characteristics curve, determined described procedure parameter axle volume quality (82) with diameter.
13. according to the described method of any claim in the claim 6 to 11, it is characterized in that, by measuring the temperature on the described coiling actuator (20) or calculating to determine described procedure parameter temperature (83) by thermal modeling.
14., it is characterized in that, measure described procedure parameter roller thrust (84), or calculate roller thrust (84) by other procedure parameter (80) according to the described method of any claim in the claim 6 to 11.
15. according to the described method of any claim in the claim 6 to 11, it is characterized in that compensating parameter that will be relevant with described procedure parameter motor angle actual value or axle volume angle actual value (85) is stored in described friciton compensation unit (14) or the control/conditioning equipment (10) with the form of data bank.
16. device that is used at up-coiler (1) friction compensation, described up-coiler (1) can be wound to material (70) on the winch spool (30), wherein, described winch spool (30) is driven by the coiling actuator (20) of controlled/conditioning equipment (10) control, wherein, tension link (11) and diameter calculating unit (12) and/or the linearizing friciton compensation unit (14) that is used for described tension link (11) are arranged on described control/conditioning equipment (10), wherein, cireular frequency (81) with described winch spool (30) in described friciton compensation unit (14) inserts as input end procedure parameter (80), it is characterized in that, in the input end of described friciton compensation unit (14), insert at least one additional procedure parameter (80), with the friction compensation square.
17. device according to claim 16 is characterized in that, acceleration compensation unit (13) are arranged in described control/conditioning equipment (10).
18. according to claim 16 or 17 described devices, it is characterized in that described friciton compensation unit (14) has axle volume quality (82) and/or temperature (83) and/or roller thrust (84) and/or motor angle actual value or the additional input end parameter of axle volume angle actual value (85) conduct.
19., it is characterized in that described friciton compensation unit (14) has at least one family of characteristic curves unit (14.1) that is used for described at least two procedure parameters of combination (80) according to the described device of each claim in the claim 16 to 18.
20. according to the described device of each claim in the claim 16 to 19, it is characterized in that, can in described friciton compensation unit (14) and/or control/conditioning equipment (10), determine the compensating parameter of single friction share, and it is stored to be used for subsequent analysis.
CN2008101287198A 2007-02-17 2008-02-15 Method and device for friction compensation Expired - Fee Related CN101289146B (en)

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DE102007007988.7 2007-02-17
DE102007007988A DE102007007988A1 (en) 2007-02-17 2007-02-17 Method and apparatus for friction compensation

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EP1958905A2 (en) 2008-08-20
CN101289146B (en) 2011-07-06

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