Formula It is generally accepted that the maximum available traction is dependent upon three major factors: i) angle of wrap of the ropes around the traction sheave; ii) shape of groove profile; and iii) coefficient of friction between rope and sheave material. e f = ratio between the greater and the smaller static force in the portions of rope situated on either side of the traction sheave in the following cases: - car stationary at the lowest landing level with a load equivalent to 125% of the rated load. - car stationary and unloaded at the highest landing level. = base of natural logarithms. = friction factor of the ropes in the grooves. = angle of wrap of the ropes on the traction sheave (radians).
Basic Types of Groove The friction factor of the ropes in the grooves is dependent upon the groove profile, and the three basic types to be considered are:- 'V' Full 'U' Undercut 'U' = coefficient of friction between steel ropes and cast iron pulleys = 0.09. = angle of the V grooves in the traction sheave (radians). = angle of the undercut U grooves in the traction sheave (radians).
Available Traction For given angles of wrap, eg 125 and 180, maximum available traction (T 1/T 2) for the three basic types of grooves is compared below: Angle of Wrap Groove Profile =35 =37 30 =90 =105 135 2.02 1.93 1.31 1.55 1.67 180 2.56 2.41 1.43 1.79 1.98 As expected, it can be seen that the V groove offers the greatest traction, whilst the full U groove offers the least amount for any given angle of wrap. However, it will be appreciated that under identical bending and loading conditions the fatigue life of a rope operating in a full U groove will be greater than that obtained in an undercut U groove which in turn will be greater than that obtained from a rope operating in a V groove. Although the V groove may be very satisfactory for the slower and medium speed elevators, its effect on rope performance may be significant at faster speeds, ie over 1.5 metres per second; hence, the necessity for a groove profile which will reduce the radial distortion of the rope at these higher speeds, eg undercut or full U groove. By introducing a double wrap system with a full U groove traction sheave, the traction capability of this type of groove can be greatly increased and the nett effect is a system capable of transmitting almost as much traction as a standard single wrap V groove installation. The effect of angle of wrap ( ) on the maximum available traction (T 1/T 2) of a single wrap drive can now be compared with a double wrap drive. Full U Groove Available Traction Single Wrap = 135 Double Wrap = 135 + 180 T 1/T 2 1.31 1.88
Determination of Required Traction When determining the actual T 1/T 2 value of any given installation, many factors have to be taken into consideration: - rated load - weight of car - weight of counterweight - weight of suspension rope - weight of compensating rope and pulley - weight of electric cables - angle of wrap around the traction sheave - shape of groove profile - coefficient of friction between rope and sheave material The above list of factors only takes care of the static condition but for required T 1/T 2 account must be taken of the dynamic effect due to acceleration and deceleration. Therefore, the following formula should be satisfied: Required Traction Available Traction C 1 = Coefficient taking account of acceleration, deceleration and specific conditions of the installation. g n = standard acceleration of free fall (m/s 2 ) a = braking deceleration of the car (m/s 2 ) The following minimum values of C 1 may be permitted: 1.10 for rated speeds 0.00 to 0.63 m/s 1.15 for rated speeds 0.63 to 1.00 m/s 1.20 for rated speeds 1.00 to 1.60 m/s 1.25 for rated speeds 1.60 to 2.50 m/s For rated speeds exceeding 2.50 m/s, C 1 should be calculated for each specific case but should not be less than 1.25. C 2 = coefficient taking account of the variation in profile of the groove due to wear. C 2 = 1 for full U and undercut U grooves. C = 1.2 for V grooves.
Specific Pressure Calculations Specific Pressure Calculations The specific pressure of the ropes in the grooves can be calculated using the following formulae: for full 'U' or undercut 'U' grooves. for V grooves. The specific pressure of the ropes should not exceed the following value, with the car loaded with its rated load. The following symbols apply: d = diameter of the rope (mm) D = diameter of the traction sheave (mm) n = number of ropes p = specific pressure (N/mm 2 ) T = static force in the ropes to the car at the level of the traction sheave, when the car is stationary at the lowest landing level with its rated load (N) vc = speed of the ropes corresponding to the rated speed of the car (m/s) Engineers should refer to the relevant standards dealing with the safety rules for the construction and installation of lifts.