Chapter 5 Force,Torque(转矩)，and Shaft Power(轴功率) Measurement by Yixin Ma 27/03/2013 2/50 Contents 1.Standards and Calibration 2.Basic methods of Force Measurement 3.Characteristics of Elastic Force Transducers 4.Resolution of Vector Forces and Moments into Rectangular Components 5.Torque Measurement on Rotating Shafts 6.Shaft Power Measurement(Dynamometers) 7.Vibrating-Wire Force Transducers
Chapter 5 Force, Torque(转矩), and Shaft Power(轴功率) Measurement by Yixin Ma 27/03/2013 Contents 1. Standards and Calibration 2. Basic methods of Force Measurement 3. Characteristics of Elastic Force Transducers 4. Resolution of Vector Forces and Moments into Rectangular Components 5. Torque Measurement on Rotating Shafts 6. Shaft Power Measurement (Dynamometers) 7. Vibrating-Wire Force Transducers 2/50
3/50 5.1 Standards and Calibration ■Force definition:F=M×A,inN=kgm/s2 M:mass is considered a fundamental quantity,in kg -International Kilogram Standards:cylinder of Platinum-Iridium,France A:acceleration,derived(from length and time,in m/s2 d2L A= dt2 ■Torque definition:T=F×R,inNm ■Shaft power definition:P=T×w,inw=Wm/s 4/50 5.1 Standards and Calibration The acceleration of gravity,g v=0U。=max v=0 U=max Fr=max KE=0 Fr=max KE =0 Fr=min Fr=min It is a convenient standard which can be determined with an accuracy of about 1/106 by 8=-8ma measuring the period and effective length of a 8=0 pendulum(摆锤)or by determining the change v=max U.=min with time of the speed of a freely falling body. F=0 KE max Fr=max >The actual value g varies with location and also slightly with time (in a periodic predictable fashion)at a given location.It may also change (slightly)unpredictable because of local T2m 6《1 geological activity. The so-called standard value of g refers to the value at sea level and 45 latitude and is numerically 9.80665m/s2
5.1 Standards and Calibration Force definition: ࡲ=ࡹ× ,in N=kg·m/s2 ¾ M: mass is considered a fundamental quantity, in kg - International Kilogram Standards: cylinder of Platinum-Iridium, France ¾ A: acceleration, derived(导出) from length and time, in m/s2 = ࡸࢊ ࢚ࢊ Torque definition: ࢀ=ࡲ×ࡾ , in N·m Shaft power definition: ࡼ=ࢀ×࣓ , in w=N·m/s 3/50 5.1 Standards and Calibration The acceleration of gravity, g ¾ It is a convenient standard which can be determined with an accuracy of about 1/106 by measuring the period and effective length of a pendulum (摆锤) or by determining the change with time of the speed of a freely falling body. ¾ The actual value g varies with location and also slightly with time (in a periodic predictable fashion) at a given location. It may also change (slightly) unpredictable because of local geological activity. ¾ The so-called standard value of g refers to the value at sea level and 45° latitude and is numerically 9.80665m/s2. 4/50
5/50 5.1 Standards and Calibration Basis of the "deadweight"calibration of force-measuring system: when the numerical value of g has been determined at a particular locality, the gravitational force (weight)on accurately known standard masses may be computed to establish a standard of force. Commercially available calibrating machine using deadweights,knife edges, and levers,covers the range of 0-50kN with an accuracy of +0.005%of applied load and a resolution of +0.0062%of applied load. Computerized calibration systems based on strain gage load cells and hydraulic load frames are also available. 6/50 5.2 Basic Methods of Force Measurement 1. Balancing it against the known gravitational force on a standard mass,either directly or through a system of levers(杠杆). >The analytical balance,which simple in principle, F requires careful design and operation to realize its Unknown Standard force maximum performance. mass Analytical balance >The beam deflection(梁的挠度)is a very sensitive Fig5.2(1)a indicator of unbalance.(due to its proper design) For the low end of a particular instrument's range,often the beam deflection is used as the output reading rather than attempting to null by adding masses or adjusting the arm length of a poise()weight.This approach is faster than nulling but requires that the deflection-angle unbalance relation be accurately known and stable. >Noise inputs:deformation of knife edges,buoyant force,temperature difference
5.1 Standards and Calibration Basis of the "deadweight" calibration of force-measuring system: ¾ when the numerical value of g has been determined at a particular locality, the gravitational force (weight) on accurately known standard masses may be computed to establish a standard of force. ¾ Commercially available calibrating machine using deadweights, knife edges, and levers, covers the range of 0-50kN with an accuracy of ±0.005% of applied load and a resolution of ±0.0062% of applied load. ¾ Computerized calibration systems based on strain gage load cells and hydraulic load frames are also available. 5/50 5.2 Basic Methods of Force Measurement 1. Balancing it against the known gravitational force on a standard mass, either directly or through a system of levers (杠杆). ¾ The analytical balance, which simple in principle, requires careful design and operation to realize its maximum performance. ¾ The beam deflection(梁的挠度) is a very sensitive indicator of unbalance. (due to its proper design) Fig 5.2 (1)a ¾ For the low end of a particular instrument’s range, often the beam deflection is used as the output reading rather than attempting to null by adding masses or adjusting the arm length of a poise(平衡) weight. This approach is faster than nulling but requires that the deflection-angle unbalance relation be accurately known and stable. ¾ Noise inputs: deformation of knife edges, buoyant force, temperature difference, … 6/50
7/50 5.2 Basic Methods of Force Measurement 1.Balancing it against the known ∠∠∠∠∠/∠∠1 gravitational force Tape >The pendulum scale,is a deflection- type instrument in which the unknown force is converted to a torque that is Sector then balanced by the torque of a fixed standard mass arranged as a pendulum. >A practical version of this principle utilizes specially shoed sectors and steel tapes to linearize the inherently nonlinear torque-angle relation of a Counter- pendulum. weights Steel An electrical signal proportional to tapes force is easily obtained from any angular-displacement transducer Pendulum Fig 5.2(1)b scale attached to measure the angle. 8/50 5.2 Basic Methods of Force Measurement 1.Balancing it against the known gravitational force. Standard ma552 >The platform(托盘)scale,utilizes ("Poise weight") Standard mass I a system of levers to allow ☐n weigh"T measurement of large forces in terms Platform of much smaller standard weights The beam is brought to null by a proper combination of pan weights and adjustment of the poise-weight lever arm along its calibrated scales. Fig 5.2(1)c Platform Scale Self-balance:add an electrical displacement pickup for null detection and amplifier-motor system to position the poise weight to achieve null. When a/b=c/d,the reading of the scale is independent of the location of force on the platform.(why?)
5.2 Basic Methods of Force Measurement 1. Balancing it against the known gravitational force. ¾ The pendulum scale, is a deflectiontype instrument in which the unknown force is converted to a torque that is then balanced by the torque of a fixed standard mass arranged as a pendulum. ¾ A practical version of this principle utilizes specially shoed sectors and steel tapes to linearize the inherently nonlinear torque-angle relation of a pendulum. ¾ An electrical signal proportional to force is easily obtained from any angular-displacement transducer attached to measure the angle. Fig 5.2 (1)b 7/50 ¾ Self-balance: add an electrical displacement pickup for null detection and amplifier-motor system to position the poise weight to achieve null. ¾ When a/b=c/d, the reading of the scale is independent of the location of force on the platform. （why?） 5.2 Basic Methods of Force Measurement 1. Balancing it against the known gravitational force. ¾ The platform (托盘) scale, utilizes a system of levers to allow measurement of large forces in terms of much smaller standard weights. ¾ The beam is brought to null by a proper combination of pan weights and adjustment of the poise-weight lever arm along its calibrated scales. Fig 5.2 (1)c Platform Scale 8/50
9/50 5.2 Basic Methods of Force Measurement 2.Measuring the acceleration of a Accelerometer body of known mass to which the unknown force is applied. The use of an accelerometer for force measurement,is of somewhat limited application since the force determined is the resultant force(合力) on the mass. Fig 5.2(2)Force Measurement via Acceleration measurement Often several unknown forces are acting,and they cannot be separately measured by this method. 10/50 5.2 Basic Methods of Force Measurement 3.Balancing it against a magnetic force developed by interaction(相互作用)of a current-carrying coil(线圈)and a magnet.. It utilizes a photoelectric ()(or other displacement sensor)null detector,an amplifier and a torquing coil in a servo-system(伺服系统)to balance the difference between the unknown force and the gravity force on a standard mass Its advantages relative to mechanical balances are ease of use,less sensitivity to environment,faster response,smaller size,and ease of remote operation. The electric output signal is convenient for continuous recording and/or automatic-control applications. Fig 5.2(3)a&b shows a design available in range from 22 to 405 grams,with resolutions from 2 to 100 ug
5.2 Basic Methods of Force Measurement 2. Measuring the acceleration of a body of known mass to which the unknown force is applied. ¾ The use of an accelerometer for force measurement, is of somewhat limited application since the force determined is the resultant force(合力) on the mass. ¾ Often several unknown forces are acting, and they cannot be separately measured by this method. Fig 5.2 (2) Force Measurement via Acceleration measurement 9/50 5.2 Basic Methods of Force Measurement 3. Balancing it against a magnetic force developed by interaction (相互作用) of a current-carrying coil (线圈) and a magnet. ¾ It utilizes a photoelectric (光电) (or other displacement sensor) null detector, an amplifier and a torquing coil in a servo-system (伺服系统) to balance the difference between the unknown force and the gravity force on a standard mass. ¾ Its advantages relative to mechanical balances are ease of use, less sensitivity to environment, faster response, smaller size, and ease of remote operation. ¾ The electric output signal is convenient for continuous recording and/or automatic-control applications. ¾ Fig 5.2 (3) a&b shows a design available in range from 22 to 405 grams, with resolutions from 2 to 100 ug. 10/50