METHOD FOR MONITORING THE OPERATION OF A TRANSMISSION SYSTEM EQUIPPED WITH PULLEYS AND A TRANSMISSION BELT

Abstract

Method for monitoring the operation of a transmission system (1) comprising a belt (10) mounted on driving (R) and receiving (N) pulleys, of given radii, the method comprising the following steps: determining a rotation speed of the pulleys; determining a receiving torque for the receiving pulley; determining tensions exerted on slack (11) and taut (12) strands of said belt; determining a sliding angle of said belt on one of said pulleys from step c); calculating an energy efficiency of said system from steps a) and b), calculating an abrasion rate of said belt from said given radii and from steps c) and d); comparing respectively the values ​​calculated in steps e) and f) with given threshold values; and generating a warning when one of said threshold values ​​is exceeded. Figure for abstract: Fig. 1

Description

Title of the invention: METHOD FOR MONITORING THE OPERATION OF A TRANSMISSION SYSTEM EQUIPPED WITH PULLEYS AND A TRANSMISSION BELT Technical field of the invention

[0001] The present invention relates to a method for monitoring the operation of a transmission system provided with pulleys and a transmission belt, in particular transmission systems used in the field of industrial machines. Technological background

[0002] Transmission systems are commonly used in various fields and industrial sectors to transmit mechanical energy from a power source to a tool or accessory. In these transmission systems, one can distinguish belt systems which comprise pulleys on which the transmission belt is mounted. The transmission belt is driven by a drive pulley and subsequently drives a receiving pulley which is generally connected to a tool or accessory via a drive shaft.

[0003] In such transmission systems, it is interesting to be able to monitor the evolution of given parameters to ensure the proper functioning of the transmission system.

[0004] These parameters may for example relate to the belt or the pulleys, in particular the respective rotation speeds which are used to determine a slip rate of the transmission belt on the pulleys. Other parameters may also relate to the aging of the transmission belt by focusing for example on cracks in the teeth of the belt, tearing of the cords of the belt or shear stresses of the teeth.

[0005] However, when such approaches are considered, they do not take into account the overall performance of the transmission system in terms of belt abrasion and energy efficiency.

[0006] Indeed, monitoring the abrasion level of a transmission belt on an industrial application generally requires shutting down the installation to dismantle the belt and weigh it to determine its mass loss before reassembling it on the installation. This procedure is complex, long and expensive.

[0007] As for monitoring the energy efficiency of the system, a complex protocol is generally put in place. This involves specific measuring devices, which are expensive due to their high precision and often complex to use, requiring advanced technical skills for optimal use. In addition, the time required for these measures is significant and does not allow for rapid reaction in the event of unfavorable performance.

[0008] Also, an objective of the invention is to propose an improved method for monitoring the operation of a belt transmission system which does not have at least one of the aforementioned drawbacks.

[0009] Another objective of the invention is to propose a solution providing a value of the abrasion level and the energy efficiency in real time using numerical models and simple algorithms.

[0010] Another objective of the invention is to propose a solution using easily quantifiable input quantities. Summary of the invention

[0011] A method is therefore proposed for monitoring the operation of a transmission system comprising at least two pulleys of given radii Rr, Rn and a transmission belt mounted on the pulleys, one of the at least two pulleys being a driving pulley and another of the at least two pulleys being a receiving pulley, the method comprising the following steps: a. determine a rotation speed coR, coN of each of the pulleys; b. determine a CN receiver torque for the receiver pulley; c. determine a tension t exerted on a slack strand of the belt transmission and a tension T exerted on a taut strand of the belt; d. determining a slip angle aG of the transmission belt on one of the pulleys from the data determined in step c); e. calculate an energy efficiency q of the transmission system from the data determined in steps a) and b); f. calculate an abrasion rate irab of the transmission belt from the radii of the pulleys and the data determined in steps c) and d); g. comparing the calculated value of the abrasion rate irab to at least a first given threshold value and comparing the calculated value of the energy efficiency q to at least a second given threshold value; and h. generate a warning when either of at least one first and at least one second threshold value is exceeded.

[0012] Thus, thanks to the invention, monitoring of the operation of the improved transmission system is ensured, by continuously monitoring the performance of the transmission system. Generally speaking, any belt mounted on pulleys wears over time, whether by friction or a reduction in its tension between the pulleys, and thus sees the performance of the transmission system decrease over time. The invention also makes it possible to detect an abnormal change in these performance

[0013]

[0014]

[0015]

[0016]

[0017]

[0018]

[0019] formances. Indeed, the input data, whether intrinsic to the transmission system such as geometric parameters such as the radii of the pulleys or dimensions of the belt, or variables such as the rotation speed of the pulleys, the tensions of the slack and tight strands of the belt or the angle of sliding of the belt on a pulley, are easily accessible by calculation, measurements or indication of the manufacturer. These input data make it possible to determine a level of abrasion of the belt and an energy efficiency of the transmission system which are important parameters to determine whether the transmission system is in normal operation or not, in other words whether it is necessary to plan maintenance or not of the transmission system by acting for example on the tension of the system or by replacing one or other of its elements such as the belt or a pulley.More generally, this allows an operator to intervene quickly in the event of a malfunction and to plan the necessary maintenance. The method according to the invention may comprise one or more of the features below, taken in isolation from each other or in combination with each other. In one embodiment of the invention, in step b), the receiving torque CN is calculated from the radius Rr, Rn of each of the driving and receiving pulleys, the rotation speeds coR, coN of each of the driving and receiving pulleys and a longitudinal module EA of the transmission belt. In another embodiment, when the drive pulley rotates in a clockwise direction, the CN receiver torque, being negative by convention, is defined by: _ OP PA In another embodiment, in step b), the CN receiver torque is measured by means of at least one torque sensor. In another embodiment, in step c), the tensions t, T exerted on the slack and taut strands of the transmission belt are calculated from the radius of the receiving pulley, the receiving torque CN, negative by convention, and a stabilized tension To of the transmission belt on the pulleys. In another embodiment, when the drive pulley (R) rotates according to a clockwise, the tension t exerted on the slack strand is defined by: + A a and the •HAS' tension T exerted on the taut strand is defined by: j1 _ t Cn ■ In another embodiment, the transmission system comprising a tensioner installed on the slack strand of the transmission belt to impose a tension t = To on the slack strand, the tension T exerted on the taut strand of the transmission belt is then calculated from the radius of the receiving pulley, the torque CN receptor, negative by convention, and the stabilized voltage To of the soft strand.

[0020] In another embodiment, when the drive pulley (R) rotates in a clockwise direction, the tension T exerted on the taut strand (12) is defined by: y = t Cn •

[0021] In another embodiment, in step c), the tensions t, T exerted on the slack and taut strands are measured by means of at least one tension sensor integrated into the transmission belt or by means of at least one tension sensor external to the transmission belt.

[0022] In another embodiment, in step d), the sliding angle aG is calculated by the relation: Ç L ; p being a known dynamic friction coefficient of the transmission belt on the pulleys.

[0023] In another embodiment, in step f), the abrasion rate irab is defined by the relationship: _; m0 being an initial mass of the belt of '' ab mn transmission, mioss being a loss of mass of the transmission belt for a single turn of the belt on the pulleys and Ncycie being the number of turns made by the belt during a given operating time of the transmission system.

[0024] In another embodiment, the transmission belt being a belt provided with at least one tooth extending longitudinally, the mass loss mioss is defined according to the relationship: m • h being an abrasion height, nd being a number of teeth of the belt, hd being a height of the teeth, a being an angle formed by a vertex of a tooth, p being the density of the belt and L being the length of the belt.

[0025] In another embodiment, the abrasion height ha is defined by the relation: / ^ =.kd 10 6 — —__lr ; kR being the Archard coefficient, dG a RG' being a sliding distance of the transmission belt on a given pulley and p being a dynamic friction coefficient of the belt on the pulleys and R; being the radius Rr of the driving pulley or the radius RN of the receiving pulley, the given pulley being one of the at least two pulleys.

[0026] In another embodiment, the transmission belt being a flat belt, the mass loss mioss is defined according to the relation: = h(,.pLB ; ha being a abrasion height, p being the density of the belt, L being the length of the belt and B being the width of the flat belt.

[0027] In another embodiment, the abrasion height ha is defined by the relation: h — b P i J. -J- z ; kR being the Archard coefficient, dG being a sliding distance of the transmission belt on a given pulley, p being a dynamic friction coefficient of the belt on the pulleys, B being the width of the flat belt and R; being the radius Rr of the driving pulley or the radius RN of the receiving pulley, the given pulley being one of the at least two pulleys.

[0028] In another embodiment, the slip distance dG of the transmission belt is calculated, for a given pulley, from the radius of the pulley and the slip angle aG of the transmission belt on the pulley, so that the slip distance dG is defined by the relation: dG = Rj-ac-

[0029] In another embodiment, the transmission belt being a belt provided with teeth extending longitudinally, for each of the pulleys, a shear stress per tooth oR d, oN d of the transmission belt is calculated from the radius Rr, Rn of a given pulley, the tension t, T exerted on each of the slack and taut strands of the transmission belt, a winding angle [3R, |3N of the transmission belt on the given pulley and a number of teeth nd of the belt.

[0030] In another embodiment, the shear stress oN d of the belt on the receiving pulley is defined by the relation: _ 1 ; and the stress of ~ R .jp 'Pd tooth shear oRd of the transmission belt on the drive pulley is defined by the relation: _ _ (221 1 . °Rd~ -~r^~

[0031] In another embodiment, the calculated value of the shear stress per tooth oR d, oNd is compared to at least one predetermined threshold value, such that an alert is generated when the calculated value of the shear stress per tooth is greater than the at least one predetermined threshold value.

[0032] In another embodiment, in step e), the energy efficiency q is calculated from the radius RN, Rr of each of the pulleys, the rotation speed coR, coN of the pulleys and the receiving torque CN, so that the energy efficiency q is defined by: „ _ . r^r

[0033] In another embodiment, the transmission system comprising an electrical power sensor, the energy efficiency q is calculated, in step e), from an electrical consumption Peiec of the driving pulley, measured by said electrical power sensor, from an electromechanical efficiency peiec_motor of an electric motor rotating said driving pulley, from the rotation speed coN of the receiving pulley and the receiving torque CN, so that the energy efficiency q is defined by: _ IÇv-^vl 7 ~ np .

[0034] In another embodiment, for each of said pulleys, a sliding speed Vsiip R, Vsiip N of the transmission belt is distributed between said pulleys, said sliding speed Vsiip R, Vsiip N being calculated from the radius of each of the pulleys and the rotation speed coR, coN of each of the pulleys, so that that the sliding speed Vsiip N of the belt on the receiving pulley is defined by the relationship: v >. — RxMirRNMN VshpN~ 2 and the sliding speed Vsiip R of the belt on the drive pulley is defined by the relation: y R — -

[0035] The invention is part of a sustainable development approach by allowing including better control of the energy efficiency of a transmission system. Brief description of the figures

[0036] The invention will be better understood with the aid of the following description, given solely by way of example and with reference to the appended drawings in which:

[0037] [Fig.l] represents a schematic view of a transmission system provided with pulleys and a transmission belt,

[0038] [Fig.2] represents a schematic view of the transmission system of [Fig.l] in which a tensioner is used,

[0039] [Fig. 3] represents a schematic view of an example of a transmission belt, in particular a ribbed V-belt, used in the transmission system of [Fig. 1] or [Fig. 2],

[0040] [Fig.4] represents a block diagram of the method for monitoring the operation of a transmission system, according to the invention. Detailed description of the invention

[0041] [Fig.l] represents a transmission system 1 comprising at least two pulleys R, N of given radii Rr, Rn and a transmission belt 10 mounted on the pulleys R, N. One of the pulleys is a driving pulley R and another of the pulleys is a receiving pulley N (for the English terms “driveR” for motor and “driveN” for receiver).

[0042] The transmission belt 10 being mounted between at least these two pulleys R, N, it comprises a slack strand 11 and a taut strand 12.

[0043] It is understood that the driving pulley R is the pulley which is rotated to drive the transmission belt 10 via a driving torque CR and the receiving pulley N is the pulley which is driven by the transmission belt 10 and which undergoes a receiving torque CN. Furthermore, the driving pulley R rotates with a rotation speed coR and the receiving pulley N rotates with a rotation speed coN.

[0044] In the following, it is considered that the driving pulley R rotates in a clockwise direction (arrow CW) and that the angles and torques are positive in this clockwise direction. In such a configuration, the taut strand 12 is located below the driving pulley R and the slack strand 11 is located above the driving pulley R.

[0045] In other words, we will consider that the receiving torque CN of the receiving pulley is negative when the power is taken from the transmission, thus braking the pulley. receptor N. As a result, the motor torque CR is positive.

[0046] In a configuration where the position of the slack 11 and taut 12 strands is reversed with respect to the configuration described above, it is understood that the receiving torque CN is positive and that the driving torque CR is negative. This configuration is not described in the following.

[0047] With reference to [Fig.2], the transmission system 1 may comprise a tensioner 20. This tensioner 20 is configured to be installed on the slack strand 11 of the transmission belt 10 in order to impose a quasi-constant tension on the slack strand 11 of the belt. This tension is generally considered to be equal to the stabilized tension To of the belt 10. The stabilized tension To is the tension which exists in the belt when the transmission system is not transmitting any torque.

[0048] In the following, it will be specified whether the tensioner 20 is considered to monitor the operation of the transmission system 1. In the absence of an indication, it must be understood that the tensioner 20 is not considered or that its presence has no impact, or a negligible impact, on the parameters mentioned.

[0049] The transmission belt 10 has different intrinsic parameters. These parameters can be the length L of the belt, the width B of the belt, the density p of the belt, the initial mass m0 of the belt or the height H of the belt.

[0050] The transmission belt 10 may be an elastomer-based belt. The belt 10 may be a multi-ribbed belt, of the poly-V ® type for example, a trapezoidal belt or even a flat belt. The belt 10 may comprise traction cords 16 embedded in the belt 10, these traction cords extending longitudinally in the belt 10.

[0051] Furthermore, for a given transmission belt 10 and whether it comprises traction cords 16 or not, a longitudinal modulus EA, specific to the belt, can be determined. This longitudinal modulus EA is homogeneous to the Young's modulus and to the section of the traction cords 16 or of the belt 10. In practice, this longitudinal modulus EA is determined on a test bench.

[0052] The transmission belt 10 may comprise a plurality of teeth 15 extending longitudinally of the belt 10. In such a case, additional parameters may be considered to define the belt 10. For example, the number of teeth nd, the height of the teeth hd or the angle a formed by the apex 17 of each of the teeth 15 may be considered.

[0053] For example, in the case of a poly-V ® type belt, the angle of the apex 17 of the teeth 15 is substantially equal to 40 degrees.

[0054] [Fig.4] represents a block diagram of a method 100 for monitoring the operation of a transmission system 1 as described previously, that is to say with at at least two pulleys R, N and a transmission belt 10 mounted on these pulleys R, N. It is understood that the number of receiving pulleys N is not limited.

[0055] The method 100 comprises the steps which are described below. It will be noted that the different steps are not necessarily carried out in the order presented below.

[0056] In a step a), or step 102, a rotation speed coR, coN of each of the pulleys R, N is determined.

[0057] In a step b), or step 104, a receiving torque CN for the receiving pulley N is determined. Step 104 can be carried out before, after or simultaneously with step 102.

[0058] In a step c), or step 106, a tension t exerted on a slack strand 11 of the transmission belt 10 and a tension T exerted on a taut strand 12 of the belt 10 are determined. Step 106 can be carried out before, after or simultaneously with one or other of steps 102 and 104.

[0059] In a step d), or step 108, a sliding angle aG of the transmission belt 10 on one of the pulleys R, N is determined from the data determined in step c), or step 106.

[0060] In a step e), or step 110, an energy efficiency q of the transmission system 1 is calculated from the data determined in steps a) and b), or in steps 102 and 104. Step 110 can be carried out before, after or simultaneously with steps 106 and 108 but after steps 102 and 104.

[0061] In a step f), or step 112, an abrasion rate irab of the transmission belt 10 is calculated from the radii Rr, Rn of the pulleys and the data determined in steps c) and d), or in steps 106 and 108. Step 112 can be carried out before, after or simultaneously with step 110 but after steps 106 and 108.

[0062] In a step g), or step 114, the calculated value of the abrasion rate irab is compared to at least one first given threshold value and the calculated value of the energy efficiency q is compared to at least one second given threshold value.

[0063] In a step h), or step 116, a warning is generated when one or other of the calculated values ​​of the abrasion rates irab and energy efficiency q is respectively greater than or less than the first and second threshold values. This warning may be an audible or visual alert. In particular, this warning may be the communication of a text alert through a computer system or network. The warning makes it possible to indicate to an operator the state of the system, whether its operation can be considered normal or not.

[0064] In step 114, the abrasion rate irab can be compared, in addition to the first threshold value SI, to a third threshold value S3 so as to define three ranges of values ​​G1, G2, G3. The third threshold value S3 can be lower or higher than the first threshold value SL. For example, a first range of values ​​G1 includes values ​​which are higher than or equal to the first threshold value SI, so that SI < Gl. A second range of values ​​G2 comprises values ​​that are lower than the first threshold value SI but greater than or equal to the third threshold value S3, such that S3 < G2 < SI. Finally, a third range of values ​​G3 comprises values ​​that are lower than the third threshold value S3, such that G3 < S3. Thus, in step 116, a specific warning may be generated when the calculated value of the abrasion rate irab is included in one of the ranges of values ​​Gl, G2, G3.

[0065] The same may be applied for the energy efficiency q. That is, in step 114, the energy efficiency q may be compared, in addition to the second threshold value S2, to a fourth threshold value S4 so as to define three ranges of values ​​PI, P2, P3. The fourth threshold value S4 may be lower or higher than the second threshold value S2.For example, a first range of values ​​PI includes values ​​that are greater than or equal to the second threshold value S2, such that S2 < PL A second range of values ​​P2 includes values ​​that are less than the second threshold value S2 but greater than or equal to the fourth threshold value S4, such that S4 < P2 < S2. Finally, a third range of values ​​P3 includes values ​​that are less than the fourth threshold value S4, such that P3 < S4. Thus, in step 116, a specific warning may be generated when the calculated value of the energy efficiency q is included in one of the ranges of values ​​PI, P2, P3. .

[0066] Having multiple ranges or value ranges allows the warning to be declined according to multiple levels. These levels may, for example, depend on the severity of the system's dysfunctional state.

[0067] In step 102, the rotation speed coR, coN of each of the pulleys R, N can be measured by means of at least one speed sensor. It is understood that for each pulley R, N at least one speed sensor measures the rotation speed coR, coN. The rotation speed coR of the drive pulley R can be an input parameter of the transmission system 1, given, for example, by a control device of the transmission system 1.

[0068] In step 104, the receiving torque CN can be calculated from the radius Rr, Rn of each of the driving pulleys R and receiving pulleys N, the rotation speeds coR, coN of each of the driving pulleys R and receiving pulleys N and the longitudinal module EA of the transmission belt 10, so that, when the driving pulley R rotates in a clockwise direction, the receiving torque CN is defined by:

[0069] [Math.l] f — p P pA

[0070] In step 104, the receiver torque CN can, alternatively, be measured by means of at least one torque sensor.

[0071] At step 106, the tensions t, T exerted on the slack 11 and taut 12 strands of the transmission belt 10 can be measured by means of at least one tension sensor. This tension sensor can be integrated into the belt with for example a strain gauge or a pressure sensor, or be external to the belt with an instrumented roller for example present at the level of a tensioner.

[0072] In step 106, as an alternative, the tensions t, T exerted on the slack 11 and taut 12 strands of the transmission belt 10 can be calculated, when there is no tensioner 20, from the radius of the receiving pulley RN, the receiving torque CN, negative by convention, and a stabilized tension To of the transmission belt on the pulleys R, N, so that, when the driving pulley R rotates in a clockwise direction, the tension t exerted on the slack 11 is defined by:

[0073] [Math.2]

[0074] and the tension T exerted on the stretched strand 12 is defined by:

[0075] [Math.3] N

[0076] The tension t of the slack strand 11, the tension T of the taut strand 12 and the stabilized tension T0 of the belt 10 are expressed in Newton.

[0077] We now consider the embodiment in which the transmission system 1 comprises a tensioner 20 installed on the slack strand 11 of the transmission belt 10 to impose a quasi-constant tension t = To>, on the slack strand 11. For this embodiment, at step 106, the tension T exerted on the taut strand 12 of the transmission belt 10 can be calculated from the receiving torque CN, the radius of the receiving pulley RN and the stabilized tension To of the slack strand 11, so that, when the driving pulley R rotates clockwise, the tension T exerted on the taut strand 12 is defined by:

[0078] [Math.4] r= ÿ,

[0079] It will be noted that the tensioner 20 in the transmission system 1 influences the calculation of the tension t, T for each of the slack 11 or taut 12 strands of the belt 10. Also, in the calculations involving a tension, the tension t, T calculated with tensioner 20 is used when the transmission system 1 comprises a tensioner 20.

[0080] In step 108, the sliding angle aG is calculated by the relation:

[0081] [Math.5]

[0082] where p is a known dynamic friction coefficient of the transmission belt 10 on the pulleys R, N. Conventionally, the dynamic friction coefficient of the belt is determined by means of a test bench which simulates a transmission system

[0083] The sliding angle aG is expressed in radians (rad).

[0084] Generally, the coefficient of friction p and the tensions t, T of the slack 11 and taut 12 strands of the belt 10 are identical whether on the driving pulley R or on the receiving pulley N. Also, the sliding angle aG on each pulley R, N is the same. It is understood that the sliding angle aG is always, independently of the pulley considered, on the outgoing side of the belt 10. In other words, on the driving pulley R, the sliding angle aG is on the side of the slack 11 strand, while on the receiving pulley N, the sliding angle aG is on the side of the taut 12 strand.

[0085] It will be noted that, for a given pulley R, N, the sliding angle aG cannot be greater than a winding angle [3 of the belt 10 on the pulley R, N considered, nor be less than 0. The winding angle [3, like the sliding angle aG, is expressed in radians.

[0086] Furthermore, for each pulley R, N, a slip zone %G can be determined. This slip zone %G corresponds to the part of the winding angle [3 on which the belt 10 slides and can be defined as being a ratio between the slip angle aG and the winding angle [3, according to the relation:

[0087] [Math.6] % — / 0G~ P

[0088] The slip zone %G indicates over what proportion of the belt winding around the pulley, the belt slips. Thus, when the value of the slip zone %G exceeds a predetermined threshold, an alert can be generated. For example, a first predetermined threshold can be equal to 50% and a second predetermined threshold can be equal to 80% so as to define a first range of values ​​less than 50%, a second range of values ​​between 50% and 80% and a third range of values ​​greater than 80%. A specific alert can then be generated for each range of values.

[0089] Furthermore, for a given pulley R, N, a sliding distance dG of the transmission belt can be calculated from the radius Rr, Rn of the pulley considered and the sliding angle of the transmission belt on this pulley so that the sliding distance dG is defined by the relation:

[0090] [Math.7] ^G ~

[0091] where R; is the radius Rr of the driving pulley R or the radius RN of the receiving hen N.

[0092] We are now interested in calculating the energy efficiency q of the system of transmission 1 of step 110. Generally, we define the yield energy q as the ratio between the output power PN perceived by the receiving pulley N and the input power PR supplied by the driving pulley R, which translates according to the relationship:

[0093] [Math. 8]

[0094] The input powers PR and output powers PN are expressed in Watts (W), but for convenience they will be expressed more in kilowatts (kW). Although the torque CN exerted on the receiving pulley N is negative, these two powers PR and PN are positive.

[0095] Furthermore, when the output power PN perceived by the receiving pulley N is not measured directly, it can be calculated. Also, regardless of the type of configuration of the transmission system 1, the output power PN perceived by the receiving pulley N can be calculated according to the relationship:

[0096] [Math.9]

[0097] In some cases, the input power PR is not known, nor measured. In such a situation, an approximate energy efficiency qapp can be calculated from the radii Rr, Rn of the pulleys and the rotational speeds coR, coN of the pulleys, so that this efficiency q is defined by:

[0098] [Math. 10] _ ^app “ RrMr

[0099] This makes it possible to give an estimate of the energy efficiency in a simple manner. This information is not intended to be precise but to indicate an order of magnitude when the input powers PR and output powers PN are not known.

[0100] In other cases, the transmission system 1 may comprise an electrical power sensor configured to measure an electrical consumption PeieC, defined as being the product of the electrical voltage and the current. From this electrical consumption PeieC, the input power PR supplied by the drive pulley R can be measured according to the relationship:

[0101] [Math. 11] — Pelec_motor^elec

[0102] where peiec_motor is the electromechanical efficiency of an electric motor rotating the drive pulley R. The electromechanical efficiency peiec_motor of the electric motor is a known parameter, generally given by the motor manufacturer and which can depend on a number of other parameters such as the temperature or the speed of the drive pulley R.

[0103] Also, when the transmission system 1 comprises a power sensor electrical, the energy efficiency q can be calculated, in step 110, from an electrical consumption Peiec of the driving pulley R, measured by the electrical power sensor, from an electromechanical efficiency peiec_motor of an electric motor rotating the driving pulley R, from the rotation speed coN of the receiving pulley N, determined in step 102, and the receiving torque CN, determined in step 104, so that the energy efficiency q is defined by:

[0104] [Math. 12] — n P , “elec_motor mï

[0105] When the transmission system 1 comprises an electrical power sensor, the calculation of the energy efficiency is more precise than in the case previously described where the input power is not known.

[0106] In still other cases, the transmission system 1 may comprise a torque sensor on the driving pulley R or the pulley N configured to measure the driving torque CR of the driving pulley R or the torque CN of the pulley N. From this driving torque CR and the rotation speed coR of the driving pulley R, the input power PR supplied by the driving pulley R can be calculated according to the relationship:

[0107] [Math. 13] PR ~

[0108] Similarly, from this receiving torque CN and the rotation speed coN of the receiving pulley N, the output power PN exerted on the receiving pulley N can be calculated according to the relation:

[0109] [Math. 14] .P= Cjy.tÜY

[0110] Also, when the transmission system 1 comprises a torque sensor on the driving pulley R or on the receiving pulley N, in step 110, the energy efficiency q can be calculated from the rotation speed coR, coN of the pulleys R, N, determined in step 102, the driving torque CR and the receiving torque CN, determined in step 104, so that energy efficiency q is defined by: [YES] [Math. 15] C,v.Wy

[0112] We can define energy losses Pioss as being the difference between the input power PR supplied by the driving pulley R and the output power PN perceived by the receiving pulley N. This translates into the relationship:

[0113] [Math. 16] Ploss — Pr~ PN

[0114] From the energy loss Pioss, an economic loss C can be calculated on a period of time given by the relation:

[0115] [Math. 17] C = Plos.^lkW^y

[0116] where Cikwh represents the cost of one kilowatt-hour in monetary units and ty is the time expressed in hours. The economic loss C is expressed in monetary units for the duration ty.

[0117] Thus, at the end of step 110, the user can have an indication of the energy efficiency or the energy losses, or even economic losses, generated by the transmission system 1.

[0118] We are now interested in calculating the abrasion rate irab of the belt 10 of the transmission system 1 in step 112. Step 112 can be carried out simultaneously, before or after step 110.

[0119] In step 112, the abrasion rate irab is calculated as the ratio between the total mass loss mioss tot and the initial mass m0 of the belt 10 according to the relationship:

[0120] [Math. 18] ^ab— mè)

[0121] The total mass loss mioss tot is the product of the mass loss mioss of the belt 10 for a single turn of the belt 10 and the number of turns Ncycie made by the belt 10 during the duration tF of operation of the transmission system 1. The abrasion rate irab can therefore be defined according to the relation:

[0122] [Math. 19] ^ab— «A;

[0123] Thus, for a given pulley R, N, a mass loss mioss of the transmission belt 10 can be defined, when the belt 10 is provided with at least one tooth 15 extending longitudinally, according to the relation:

[0124] [Math.20]

[0125] where ha is an abrasion height, p is the density of the belt 10, L is the length of the belt 10, nd is the number of teeth 15, hd is the height of these teeth 15 and a is the angle of the apex 17 of tooth 15.

[0126] When the belt 10 is flat, in other words it does not have teeth 15, the mass loss mioss of the transmission belt 10 can be defined according to the relation:

[0127] [Math.21] mioss — ha.pLB

[0128] where B is the total width of the belt 10 which is flat.

[0129] The number of turns Ncycie is given in particular by the relation:

[0130] [Math.22] AT __ 'F-RR1''R cycle ~ --7--

[0131] The density p, the length L, the width B, the number nd of teeth 15, the height hd of these teeth 15 and the angle a of their apex 17 are intrinsic parameters of the transmission belt 10 and are known beforehand.

[0132] The abrasion height ha, or abraded height, of the belt 10 can be calculated from the relation:

[0133] [Math.23] ha — k^P .dG

[0134] where kR is the Archard coefficient which depends on intrinsic characteristics of the belt and the temperature and which is expressed in mmVN.m (cubic millimeter per Newton meter), P is the average contact pressure of the transmission belt 10 on a given pulley which is expressed in MPa (megapascal), and dG the sliding distance expressed in meters and already defined previously; the given pulley being one of the at least two pulleys R, N.

[0135] It should be noted that the abrasion height ha is calculated here for a single belt revolution.

[0136] The Archard coefficient kR is an empirical coefficient that is known for a given belt. This coefficient also generally depends on the temperature.

[0137] The average contact pressure P of the transmission belt 10 on the pulley R, N will depend on the type of belt installed.

[0138] For example, when the transmission belt 10 installed on the pulleys R, N of the transmission system 1 is a belt provided with longitudinal teeth 15, such as a poly-V ® type belt, the average contact pressure P on the sliding arc on a given pulley can be calculated from the sliding angle, the tensions exerted on the slack 11 and taut 12 strands of the belt 10 and the radius of the given pulley, so that the average contact pressure P is defined by the relation:

[0139] [Math.24] P = 1 (f6- -1--—---- -«G

[0140] where nd is a number of teeth 15 of the belt 10, hd is the height of the teeth 15, a is the angle formed by the apex 17 of the teeth 15, p is the coefficient of friction of the belt 10 on the pulley considered and R; is the radius Rr of the driving pulley R or the radius RN of the receiving pulley N.

[0141] When the transmission belt 10 installed on the pulleys R, N of the transmission system 1 is a flat belt, in other words without teeth, the contact pressure average P over the sliding arc on a given pulley can be calculated from the sliding angle, the tensions exerted on the slack 11 and taut 12 strands of the belt 10 and the radius of the given pulley, so that the average contact pressure P is defined by the relation:

[0142] [Math.25] p _ i n-6 1 1 Tt

[0143] where B is the width of the flat belt and R; is the radius Rr of the driving pulley R or the radius RN of the receiving pulley N.

[0144] Optionally, a sliding speed VsiiP_R, Vsiip_N of the transmission belt 10 can be calculated for each of the pulleys R, N. The sliding speed Vsiip_R, Vsiip N represents a relative tangential speed between the belt 10 and the pulley R, N considered. This sliding speed Vsiip_R, Vsiip N can be calculated from the radius Rr, Rn of each of the pulleys R, N and the rotation speed coR, coN of each of the pulleys R, N, determined in step 102, so that the sliding speed Vsiip N of the belt 10 on the receiving pulley N is defined by the relation:

[0145] [Math.26] \7 _ ~ 2

[0146] and so that the sliding speed Vsiip_R of the belt 10 on the drive pulley R is defined by the relation:

[0147] [Math.27] TT _ Pr-^'R^N^'N slip^R 2

[0148] The sliding speed Vsiip_R on the driving pulley R is negative because the belt 10 rotates more slowly than the driving pulley R while on the receiving pulley N, the belt 10 rotates more quickly than the receiving pulley N due to the negative receiving torque CN which will tend to brake the receiving pulley N, which explains the sliding and why the sliding speed Vsiip N is positive.

[0149] In the above, the slip is distributed equally and arbitrarily between the driving pulley R and the receiving pulley N.

[0150] Alternatively, the sliding can be entirely distributed over one of the two pulleys R, N. In other words, when the sliding is entirely distributed over the receiving pulley N, the sliding speed Vsiip N of the belt 10 on the receiving pulley N can be defined by the relation:

[0151] [Math.28] slipN — RrMr ~ Rn-P'n

[0152] and, when the slip is fully distributed over the drive pulley R, the slip speed Vsiip_R of the belt 10 on the drive pulley R can be defined by the relationship :

[0153] [Math.29] V slipR ~ " ^rwR "

[0154] The calculation of the sliding speed can be carried out before any of the steps 104 to 116 but after step 102.

[0155] Optionally, a slip rate rsiip_R, rsiip_N of the transmission belt 10 can also be calculated for each of the pulleys R, N. This slip rate rsiip_R, tshp_n can be calculated from the radius Rr, Rn of each of the pulleys R, N and the rotation speed coR, coN of each of the pulleys R, N, determined in step 102, so that the slip rate rsiiP_N of the belt 10 on the receiving pulley N is defined by the relation:

[0156] [Math.30] Tslip_N ~

[0157] and so that the slip rate rsiip_R of the belt 10 on the drive pulley R is defined by the relation:

[0158] [Math.31] _ _ fyafrlWfr Tslip_R ~ 2.Rrwr

[0159] As for the sliding speed, the sliding is distributed in the above in an equivalent and arbitrary manner between the driving pulley R and the receiving pulley N.

[0160] Alternatively, the slippage can be entirely distributed over one of the two pulleys R, N. In other words, when the slippage is entirely distributed over the receiving pulley N, the slippage rate rsiiP_N of the belt 10 on the receiving pulley N can be defined by the relation:

[0161] [Math.32] Tslip_N ~

[0162] and, when the slip is fully distributed over the drive pulley R, the slip rate rsiip_R of the belt 10 on the drive pulley R can be defined by the relation:

[0163] [Math.33] Tslip_R ~ Rrmr

[0164] The calculation of the slip rate can be performed before any of steps 106 to 116 but after step 104.

[0165] For each of the pulleys R, N, the slip rate rsiip_R, Tsiip_N may be compared to a predetermined threshold value. When the value of the slip rate rsiip_R, Tsiip_N is greater than the corresponding threshold value, an alert may be generated in a manner similar to that implemented in step 116.

[0166] It has further been observed that at a slip rate greater than 10%, the transmission belt 10 will tend to heat up, accentuating its degradation.

[0167] Optionally, for each of the pulleys R, N, a shear stress per tooth oR d, oN d of the transmission belt 10 can also be calculated, when the belt 10 has teeth 15. This shear stress per tooth oRd, ox_(| can be calculated from the radius Rr, Rn of each of the pulleys R, N, the tension t exerted on the slack strand 11, the tension T exerted on the taut strand 12, the tensions t, T being determined in step 104, and the winding angle [3R of the belt 10 on the driving pulley R or the winding angle |3N of the belt on the pulley N, as well as the number of teeth 15 of the belt 10, so that the shear stress oN d of the belt 10 on the receiving pulley N is defined by the relationship:

[0168] [Math.34] (Tf)! RN.pN-"d

[0169] and so that the shear stress oRd of the belt 10 on the drive pulley R is defined by the relation:

[0170] [Math.35]

[0171] The calculation of the shear stress per tooth oR d, oNd can be carried out before any of the steps 106 to 116 but after step 104.

[0172] When the shear stress per tooth oR d, oNd becomes too great, the tooth or teeth 15 of the belt shear and a tooth tearing or cord tearing phenomenon may occur.

[0173] For each of the pulleys R, N, the shear stress per tooth oR d, oN d may be compared to at least one predetermined threshold value. When the value of the shear stress per tooth oR d, oN d is greater than the corresponding threshold value, an alert may be generated in a manner similar to that implemented in step 116. It will be noted that the predetermined threshold values ​​for the shear stress per tooth oR d, oN d are dependent on the belt 10, in particular on the type of profile of the teeth 15 of the belt 10.

[0174] Generally, it will be noted that all the calculations described in the above can be carried out by a control unit. This control unit can for example be a computer system.

[0175] The method according to the invention is particularly suitable for a transmission system of a high-power industrial machine. This industrial machine may be, for example, a crusher, a grinder, a ventilation / air conditioning system tisation or installation of a hydroelectric power plant. The method according to the invention is therefore of interest for industrial activities where shutting down an installation for breakdowns or maintenance is costly. The transmission systems of a motor vehicle or similar are, for example, little affected by the method according to the invention.

[0176] In light of the above, thanks to the method according to the invention, monitoring of the operation of the improved transmission system is ensured, by continuously monitoring the performance of the transmission system. Generally speaking, any belt mounted on pulleys wears over time, whether by a reduction in its tension between the pulleys which generates slippage of the belt on a pulley and therefore friction or excessive torque which also generates slippage, and thus sees the performance of the transmission system decrease over time. The invention also makes it possible to detect an abnormal change in these performances. Indeed, the input data, such as the radii of the pulleys, their respective rotation speed, the tensions of the slack and taut strands of the belt and the angle of slippage of the belt on a pulley, are easily accessible by calculation, measurements or indication from the manufacturer.These input data allow to determine in a simple way a level of abrasion of the belt and an energy efficiency of the transmission system which are important parameters to determine if the transmission system is in normal operation or not, in other words if it is necessary to plan a maintenance or not of the transmission system by replacing one or other of its elements like the belt or a pulley.

[0177] Another advantage of the method according to the invention is to provide a value of the abrasion level and the energy efficiency in real time using simple numerical models and algorithms.

Claims

Claims

1. Method (100) for monitoring the operation of a transmission system (1) comprising at least two pulleys (R, N) of given radii Rr, Rn and a transmission belt (10) mounted on said pulleys (R, N), one of said at least two pulleys being a driving pulley (R) and another of said at least two pulleys being a receiving pulley (N), the method comprising the following steps: a. determine (102) a rotation speed coR, coN of each of the pulleys (R, N); b. determine (104) a receiving torque CN for the receiving pulley (N); c. determining (106) a tension t exerted on a slack strand (11) of the transmission belt and a tension T exerted on a taut strand (12) of said belt; d. determining (108) a sliding angle aG of said transmission belt on one of said pulleys from the data determined in step c); e. calculating (110) an energy efficiency q of the transmission system (1) from the data determined in steps a) and b); f. calculating (112) an abrasion rate irab of said transmission belt from the radii (Rr, Rn) of the pulleys and the data determined in steps c) and d); g. comparing (114) the calculated value of the abrasion rate irab to at least a first given threshold value and comparing the calculated value of the energy efficiency q to at least a second given threshold value; and h. generating (116) a warning when either of said at least one first and at least one second threshold values ​​is exceeded.

2. Method according to claim 1, in which, in step b), the receiving torque CN is calculated from the radius Rr, Rn of each of the driving and receiving pulleys, the rotation speeds coR, coN of each of the driving (R) and receiving (N) pulleys and a longitudinal module EA of the transmission belt.

3. Method according to claim 2, in which, when the drive pulley (R) rotates in a clockwise direction, the receiving torque CN, being negative by convention, is defined by: _ nnr' A CN~ -

4. Method according to claim 1, wherein, in step b), the receiver torque CN is measured by means of at least one torque sensor.

5. Method according to any one of claims 1 to 4, in which, in step c), the tensions t, T exerted on the slack (11) and taut (12) strands of the transmission belt (10) are calculated from the radius of the receiving pulley (RN), the receiving torque CN, negative by convention, and a stabilized tension To of the transmission belt on said pulleys (R, N).

6. A method according to claim 5, wherein, when the drive pulley (R) rotates in a clockwise direction, the tension t exerted on the slack strand (11) is defined by: and the tension T exerted on the taut strand (12) is defined by: T — T - Cn 1 - 1 0

7. Method according to any one of claims 1 to 4, in which the transmission system (1) comprising a tensioner (20) installed on the slack strand (11) of the transmission belt (10) to impose a tension t = To on said slack strand (11), the tension T exerted on the taut strand (12) of the transmission belt (10) is then calculated from the radius of the receiving pulley (RN), the receiving torque CN, negative by convention, and the stabilized tension To of the slack strand.

8. Method according to claim 7, in which, when the drive pulley (R) rotates in a clockwise direction, the tension T exerted on the taut strand (12) is defined by:

9. Method according to any one of claims 1 to 4, wherein, in step c), the tensions t, T exerted on the slack (11) and taut (12) strands are measured by means of at least one tension sensor integrated into said transmission belt (10) or by means of at least one tension sensor external to said transmission belt.

10. A method according to any one of claims 1 to 9, wherein, in step d), the sliding angle aG is calculated by the relation: aG = ±.ln(£) p being a known dynamic friction coefficient of the transmission belt on the pulleys (R, N).

11. Method according to any one of claims 1 to 10, wherein, in step f), the abrasion rate irab is defined by the relationship: ah — m0 m0 being an initial mass of the transmission belt (10), mioss being a loss of mass of the transmission belt for a single revolution of the belt on the pulleys and Ncycie being the number of revolutions made by the belt during a given operating time of the transmission system (1).

12. Method according to claim 11, wherein, the transmission belt being a belt provided with at least one tooth extending longitudinally, said mass loss mioss is defined according to the relation: 2hcrpUi .ai jm^= cos^)' ha being an abrasion height, nd being a number of teeth of the belt (10), hd being a height of said teeth, a being an angle formed by a vertex (17) of a tooth (15), p being the density of the belt and L being the length of the belt.

13. Method according to claim 12, wherein, the abrasion height ha is defined by the relation: h — kd ]()-6lJ__Id____ t- « « \ 2 7 kR being the Archard coefficient, dG being a sliding distance of the transmission belt on a given pulley and p being a dynamic friction coefficient of the belt on the pulleys and R; being the radius Rr of the driving pulley (R) or the radius RN of the receiving pulley (N), said given pulley being one of said at least two pulleys (R, N).

14. A method according to claim 11, wherein, the transmission belt being a flat belt, said mass loss mioss is defined according to the relationship: mlo,s = ha.pJLB ha being an abrasion height, p being the density of the belt, L being the length of the belt and B being the width of the flat belt.

15. Method according to claim 14, wherein, the abrasion height ha is defined by the relation: h» = hR.dG. 10 kR being the Archard coefficient, dG being a sliding distance of the transmission belt on a given pulley, p being a dynamic friction coefficient of the belt on the pulleys, B being the width of the flat belt and R; being the radius Rr of the driving pulley (R) or the radius RN of the receiving pulley (N), said given pulley being one of said at least two pulleys (R, N).

16. Method according to any one of claims 13 or 15, in which the sliding distance dG of the transmission belt (10) is calculated, for a given pulley, from the radius of said pulley and the sliding angle aG of the transmission belt on said pulley, so that the sliding distance dG is defined by the relation: dG — Ri.aG

17. A method according to any one of claims 1 to 13, wherein, the transmission belt being a belt provided with teeth extending longitudinally, for each of said pulleys (R, N), a shear stress per tooth oR d, oN d of the transmission belt (10) is calculated from the radius Rr, Rn of a given pulley (R, N), the tension t, T exerted on each of the slack (11) and taut (12) strands of said transmission belt, a winding angle [3R, |3N of said transmission belt on said given pulley and a number of teeth nd of the belt.

18. A method according to claim 17, wherein the shear stress oN d of the belt on the receiving pulley (N) is defined by the relation: -1ZÏ1 J. aN_d ~ RN.pv'nd and the shear stress per tooth oRd of the transmission belt on the driving pulley (R) is defined by the relation: (Tt) j ^R_d ~ ~

19. The method of claim 18, wherein the calculated value of the shear stress per tooth oR d, oNd is compared to at least one predetermined threshold value, such that an alert is generated when said calculated value of the shear stress per tooth is greater than said at least one predetermined threshold value.

20. Method according to any one of claims 1 to 19, wherein, in step e), the energy efficiency q is calculated from the radius RN, RR of each of the pulleys, the rotation speed coR, coN of said pulleys (R, N) and the receiving torque CN, so that the energy efficiency q is defined by:

21. Method according to any one of claims 1 to 19, in which, the transmission system comprising an electrical power sensor, the energy efficiency q is calculated, in step e), from an electrical consumption Peiec of the driving pulley (R), measured by said electrical power sensor, from an electromechanical efficiency peiec_motor of an electric motor rotating said driving pulley (R), from the rotation speed coN of the receiving pulley and the receiving torque CN, so that the energy efficiency q is defined by: r eiec^motor W'1-

22. A method according to any one of claims 1 to 21, wherein, for each of said pulleys (R, N), a sliding speed Vsiip_R, Vsiip_N of the transmission belt (10) is distributed between said pulleys, said sliding speed Vsiip_R, Vsiip N being calculated from the radius of each of the pulleys and the rotation speed coR, coN of each of the pulleys, so that the sliding speed Vsiip N of the belt on the receiving pulley (N) is defined by the relation: TZ _ 1shpN - 2 and so that the sliding speed Vsiip R of the transmission belt (10) on the driving pulley (R) is defined by the relation: T7 _ ' slip_R 2

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