如何正确测量扭矩-使用扭矩传感器

 

Rainer Schicker 和 Georg Wegener 博士在 272 页 的著作中对扭矩传感器的使用做了经典的描述。包括扭矩测量的基本原理以及如何设计和应用扭矩传感器(采用应变技术).

本书详细阐述了扭矩测量基本原理，以及基于应变原理的扭矩传感器的机械和电气配置要求， 并包含了大量如何解决应用中所遇到的问题，是扭矩测量工程师的必备工具书。

此书无论是对专家还是初学者都有很大帮助，包括传感器选择，配置，安装，调试以及振动过程分析，校准和测量原理等。

作者避免了对原理的大量讨论。同时也对振动工程学也进行了解释，并提供了大量的图表，并对 HBM 扭矩传感器进行了全面介绍。

本书内容：

扭矩测量原理

扭矩传感器结构

扭矩传感器选择与应用环境

扭矩传感器安装和使用

振动过程分析

扭矩传感器校准

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1 Introduction. . . . . . . . . . . . . . . . . . .. .. . . 9

The significance of torque as a measured quantity . .. . . . 10

1 Torque measurement methods. . . . . . . . .  . . . . . . . 13

Calculation from electrical power. . . . . . . . . . . . .. . 13

Measuring reaction torque................................... 13

Measuring the reaction force on a lever arm................. 13

Reaction torque transducers. . . . .. . . . . . . . . . . . . . 15

Measuring in-line torque. . . . . .  . . . . . . . . . . . . . 17

SGs in torque measurement.................................... 18

1 The structure of torque transducers. . . . . . . . . . . . 20

Mechanical structure. . . . . . . . . . .. . . . . .. . . . 20

Measuring body designs. . . . . . . . . . . . . . . . . . . 20

Torque connections. . . . . . . .  . . . . . . . . . . . . . 24

Torque shafts with bearings.................................. 25

Contactless and bearing-free torque transducers................ 26

Measurement signal transmission . . . . . . . . . . .... . . . . 26

Measurement signal transmission via slip rings. . . . . ..... . . 27

Contactless energy and measurement signal transmission . . . .. . 28

Measurement systems for speed and angle of rotation. . . . . . . . 31

Magnetic rotation speed acquisition. . . . . . . .. . . . . . . . . 32

Optical rotation speed and rotation angle acquisition............... 32

Reference pulse. . . . . . . . . . . . . . . . . . . . . . . . . . . 34

Electrical output signal types............................... 35

mV/V torque signal........................................... 35

Torque frequency signal. . . . . . . . . . . . . . . . . . . 35

Analog torque output ± 10 V. . . . . . .. . . . . . . . . . 39

Frequency output signal for speed and angle of rotation.. . . . 39

Selection criteria and application environment for torque transducers 41

Dimensions and basic mechanical properties. . . . . . . . . . . . . . . 42

Mechanical installation. . . . . . . . . . . . . . . . . . . . . . . . . . . 42

Mass, mass moments of inertia...................................... 42

Stiffness........................................................................ 44

Operating conditions and equipment features......................... 46

Maximum operating speed. . . . . . . . . . . . . . . . . . . . . . . . 46

Measuring the speed and angle of rotation. . . . . . . . . . . . 46

Maintenance requirements............................................. 46

Measuring range and maximum torque................................... 47

First rough estimate of the torque in an application. . . . . 47

Dynamic torque............................................................. 47

Parasitic loads. . . . . . . . . . . . . . . . .. . . . . . . 56

Accuracy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

Environmental influences. . . . . . . . . . . . . . . . . . . . . 60

Dust and foreign bodies................................ 61

Liquids.......................................................................... 61

Chemicals. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

Thermal conditions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

Humidity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

Electromagnetic compatibility (EMC). . . . . . . . . . . . . . . 63

Vibration. . . . . . . . . . . . . . . . . .  . . . . . . . . . . . 64

Torsional vibration. . . . . . . . . . . . . . . . . . . . . . . 65

Bending vibration. . . . . . . . .  . . . . . . . . . . . . 77

Axial vibration........................................... 86

1 Using and installing torque transducers. . . . . . . . . .  . . . . . . . 87

Mechanical prerequisites.................................................... 87

Principles of installation. . . . . . . . . . . . . . . . . . . . . . . . . . 87

Checking torque transducers......................................... 90

Dimensions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

Types of mechanical connection. . . . . . . . . . . . . . . . . . . . 92

Balancing............................................................ 98

nstallation in the shaft train. . . . . . . . . . . . . . . . . . . . .100

Compensating elements in the shaft train. . . . . . . . .. . . . . . . .100

Effects of geometric errors in the shaft train . . . . . . . .. . . . . .107

Designing the shaft train to include torque transducers. . . . . . . . . 113

Aligning the shaft train. . . . . . . . . . . . . . . . . . . . . .. . . .119

Electrical connection. . . . . . . . . . . . . . . . . . . . . .  . . . . .121

Protection against electromagnetic interference. . . . . . . . . . . . . . .122

Shielding. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .123

5.4 Measuring amplifiers . . . . . . . . . . . . . . .. . . . . . . . . .124

Features of measuring amplifiers. . . . . . . . . . . . . . . . . .126

Combined frequency count/cycle duration method

from HBM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .127

Adjusting the measurement chain. . . . . . . . . . . . . . . .. . . . . .131

The aim of adjusting the measurement chain. . . . . . . .131

Basic measuring amplifier settings. . . . . . . . . . . . . . . . .131

Entering the characteristic curve for torque measurement . .. . .. . .134

Entering the characteristic curve for measuring the speed

and angle of rotation. . . . . . . . . . . . . . . . . . . . . . . . . . . .138

6 Analysis of vibrational processes. . . . . . . . . . . . . . . . . . . . . . . . . .140

The aim of vibration analysis. . . . . . . . . . . . . . . . . . . . . . . . . .140

Measuring vibrations in rotating machinery. . . . . . . . . . .. . . . . . . .141

Suitable transducer types and how to arrange them. . .. . . . . . . .141

Data conditioning and recording . . . . . . . . . . . . . . . . . . . . . . . .143

Data analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .146

Time domain. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .146

6.3.2 Frequency domain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .151

Diagnostic table for vibration problems. . . . . . . . . . . . . . . . . .160

Assessing vibration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .168

6 Calibrating torque transducers. . . . . . . . . . . . . . . . . . . . . . . . . . .169

Defining the concept. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .169

7.1.1 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .169

7.1.2 Terms that are often confused with calibration . . . . . . . .171

Calibration machine designs for torque transducers. . . . . . . . .172

Orders of rank in calibration – the calibration pyramid. . . . . .174

Test certificates and calibration certificates from the various orders of rank. . . . 177

Testing in production and the manufacturer’s test certificate . . . .. . . . . .177

Working standard calibration. . . . . . . . . . . . . . . . . . . .180

DKD calibration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .187

Calibration on the test bench . . . . . . . . . . . . . . . . . . . . . . . . . .201

Defining the task and approaches to a solution . . . . . . . .201

Calibration techniques and equipment for use on thetest bench . . . . . . . . . . . . . . . . . .203

Using transfer transducers and reference transducers in

an industrial environment. . . . . . . . . . . . . . . . . . . . .209

Dynamic calibration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .210

Definition. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .210

Defining the concepts of dynamic calibration . . . . . .211

Continuous calibration. . . . . . . . . . . . . . .212

ATerms and expressions for specifying torque transducers . . . . . .213

A.1 Metrological properties of the torque measuring system . . . . .213

A.2 Ambient conditions and load limits . . . . . . . .. . . . . . .223

BBrief summary of vibration engineering . . . . .  . . . . .230

B.1Examples of vibrating systems . . . . . .. . . . .230

B.2Free vibration . . . . . . . . . . . . . . . . . . . . . . . .232

B.2.1 Undamped free vibration . . . . . . . . . . . . .232

B.2.2 Damped free vibration . . . . . . . . . .  . . . . . . . . .234

B.3Forced vibration . . . . . . . . .  . . . .235

B.4Systems with multiple degrees of freedom . . . . . . . . . . . . . . . .240

B.4.1 Free vibration . . . . . . . . . . . . . . . . . .242

B.4.2 Forced vibration . . . . . . . . . . . . . . . .244

B.5Further excitation mechanisms for vibration . . . . . . . . . .244

B.5.1 Vibrations in non-linear systems . . . . . . .. . . . . . . .244

B.5.2 Parametrically excited vibrations . . . . . . . . . . . . .245

B.5.3 Self-excited vibrations . . . . . . . .. . . . . . . . .246

C Equations and tables . . . . . . . . . . . . . . . . . . . . .247

C.1Torque and moment . . . . . . . . . . . .. . . . . . . . . . . .247

C.2Power of a rotating shaft . . . . . . .  . . . . . . . . .248

C.3Mechanical efficiency coefficient . . . . . . . . . . . .248

C.4Torsional stiffness of elastic shafts or shaft sections . . . . . . . . .248

C.5Bending stiffness of elastic shafts . . . . . . . . . . . . . . . . . . . . . . .249

C.6Area moments of inertia and torsional moments of inertia . . . .251

C.7Mass moments of inertia . . . . . . . . . . . . . . . . . . .251

C.8Physical quantities and their units . . . . . . . . . . . . . . . .254

C.9Material constants of common materials . . . . . . . . . . . . . . . . . .255

Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .256

Index. . . . . . .. . . . . . . . . . . . . . . . . . . . . .259

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1 Introduction

Though torque is unquestionably an important mechanical quantity in the field of machine building, its significance is not confined to that area alone. The pre- cise measurement of torque, particularly that which occurs in rotating compo- nents, places heavy demands on manufacturers and users of test benches. The situation is further complicated by the trend towards improving the mechanical performance of modern engines by increasing their speed of revolution, coupled with a desire for greater accuracy in such areas as the measurement of efficiency.

This challenge is met by continuous development taking into account the ongo- ing advances in the application fields. Whilst torque shafts according to the original design principle are still used for certain applications, the full range of transducers now includes torque measurement hubs and torque flanges. Innova- tions in contactless torque transducers concern the transfer of power from the stator to the rotor and the transmission of measurement signals.

But even the most advanced measurement technology can only show its strength when specific rules are followed. This book is a comprehensive revi- sion of the 1989 HBM publication “The Proper Use of Torque Transducers”. It gives an overview of important aspects concerning the use of torque transducers and provides a source of reference for resolving issues affecting applications.

The information given can be adapted and applied by everyone who uses torque measurement devices. On the other hand it is not possible to put forward sug- gested designs for highly specialized problems. There are many torque mea- surement tasks which can be solved only after the problem has been clearly de- fined and all parameters have been taken into account. However, this does not come within the duties of a component supplier. This book can therefore give no assurances about specific characteristics or fitness for purpose in the legal sense, and no responsibility can be accepted for the use to which products are put.

This book describes the principal methods of torque measurement with particu- lar reference to the mechanical and electrical configuration of torque transduc- ers based on the strain gage principle (also called the SG principle) which are those most commonly in use at the present day.

The main fields covered by this publication are selection criteria, the environ- ment within which applications operate, installation, startup, vibration analysis, calibration, and the metrological principles applicable to measuring with torque transducers. It should be especially beneficial to those readers who do not have much practical experience in torque measurement.

Profound theoretical discussion has been avoided. However, for those approaching the subject afresh an appendix sets out the technical terms for the specification of torque transducers. There is also a brief outline of vibration engineering, together with the most important relationships in the form of tables and a collection of equations complete with short explanatory notes.

1.1 The significance of torque as a measured quantity

In a highly mechanized world, torque is among the most important of all the measured quantities. It plays a highly significant role not only in such products as gas turbines with 50 kN·m of nominal torque at 8000 min–1 and a mechanical output of over 40 MW, or Formula 1 test benches with nominal torque in the range 1 to 2 kN·m at 20,000 min–1, but in fact in virtually everything including screw caps on medicine bottles. And for many products the permitted tolerances are mandatory.

There are countless applications for torque measurement in test bench engineering, process monitoring and control, drive and conveyor engineering, quality assurance and R&D.

Recent years have seen rapid market growth. Faced with consumer demand for vehicles which offer lower fuel consumption, higher levels of comfort, greater operating safety and longer-lasting reliability, the automobile industry is highly oriented toward innovation. The industry’s requirement for metrological and test techniques to match this demand has therefore grown and is growing. This trend is being accelerated by ever stricter legal requirements for lower emissions.

Increasing importance is being attached to acquiring relevant data reliably and reproducibly. Torque is the key quantity in all investigations and refinement operations, particularly for the development of internal combustion engines and transmissions since, in combination with rotation speed, it provides the possibility to calculate mechanical power. Whereas at one time, particularly in the case of engine test benches, this measuring task was fulfilled by the use of braking devices with a measurement capability, nowadays the trend is toward in-line torque measurement with the aid of rotating torque transducers.

The main reasons for this are that the processes are always dynamic and the interplay between mechanisms such as the engine and the transmission is becom ing an increasingly important consideration when it comes to optimization. And in the matter of the torque transducers used in power and functionality test benches, HBM is the worldwide market leader.
HBM has over fifty years of experience in the electrical measurement of mechanical quantities. Production of the first transducer for measuring the torque in a rotating shaft train began over forty years ago. Fig. 1.1 shows a first generation torque shaft in comparison with modern torque transducers. Even today first generation transducers are still being sent to HBM for testing, overhaul or calibration, having been faithfully carrying out their tasks for more than thirty years. This is testimony to the quality and durability of HBM products.

Fig. 1.1 Different generations of torque transducers

HBM was accredited as a DKD calibration laboratory for the measured quantity force as long ago as 1977. This made HBM the first calibration laboratory to be accepted into the DKD (German Calibration Service). Accreditation for the measured quantity torque followed on July 13th, 1990. For many years HBM was the only calibration authority for torque in Germany and practically set the national standard.

HBM now offers calibration steps from 2 N·m up to 20 kN·m which is the widest range available in the DKD. The equipment used possesses an extremely high level of accuracy thanks to mass-lever systems in which the force is directly generated by the action of a mass in the earth’s gravitational field.

As a manufacturer of precision measuring instruments and also of sturdy indus- trial transducers, HBM takes its responsibilities for quality and reliability very seriously. Logically it was just a short step to a quality management system meeting the requirements of the relevant standards. In 1986 HBM was the first company in Germany to be accredited in accordance with ISO 9001. Then in 1996, in the context of a year-long active campaign for protection of the envi- ronment, HBM’s environmental management system was accredited to ISO 14001.

2 Torque measurement methods

2.1 Calculation from electrical power

Torque can be calculated from the electrical power and speed of rotation. Modern measuring equipment makes it easy to determine the electrical power and rotation speed of electrical machinery. However, when calculating torque there can be relatively large errors since dissipated power and the operating status of the machinery have considerable influence.

Today’s instruments with their advanced computerized features take an ever-increasing number of parameters into account in order to raise the level of accuracy and dynamic response. The key application areas, however, are more commonly to be found in process monitoring, such as mechanical agitators, rabblers and the like, since this is where it is important to monitor additional electrical parameters such as reactive power or efficiency. A significant advantage of determining torque by this method is that there is no need for any kind of mechanical intervention in the power train.

However, this method is suitable to only a limited extent for accurate, dynamic torque measurement. It cannot be used if the torque information is needed referring to another point on the train of mechanisms, for instance downstream of a transmission or some other power sink.

The uncertainty involved in measuring torque by purely computational means can be several factors worse than using torque transducers fitted with SG measuring systems. Due to the greater accuracy of SG transducers, they are also commonly used as transfer transducers when calibrating electrical machinery.

2.2 Measuring reaction torque

2.2.1 Measuring the reaction force on a lever arm

Measuring reaction force according to the principle that in-line torque equals reaction torque is a method very frequently used to determine power. Fig. 2.1 shows an industrial measurement configuration with a pendulum mounted braking device. The force acting on the end of the lever arm is measured using a force transducer. This solution calls for complex mechanical arrangements. To avoid measurement errors it is necessary to take due account of disturbing in14 fluences such as changes in the pendulum bearing over time, expansion of the lever arm due to temperature changes, and the different states of operation.

Fig. 2.1 Using a U2B force transducer to measure the reaction force acting on a lever arm

On the one hand, the inertia of the large masses involved make dynamic testing difficult. The mass moment of inertia acts as a mechanical low pass filter. On the other hand this characteristic can also be an advantage in cases where there is no necessity to measure dynamic moments. Dynamic torque components which are of no interest do not impinge on the force transducer. Another key application area for reaction force measurement is determining the viscosity of a medium for the purpose of process control via the supporting force of a motor in an agitator. Fig. 2.2 shows a simplified sketch of a suggested design.

Fig. 2.2 Measuring viscosity with the aid of a Z6F load cell

The HBM range includes many forms of force transducers and load cells suitable

for measuring reaction force by means of a lever arm. The main selection

criteria are:

• Stiffness: a high degree of stiffness allows higher mechanical natural frequencies. Lower stiffness results in greater displacement during measurement, which can be helpful if overload stops or damping techniques become necessary.
• Design
• Direction of force: tensile and/or compressive force
• Required accuracy
• Cost

2.2.2 Reaction torque transducers

Reaction torque transducers combine into one device the functionalities which the bearing and the force transducer have in the case of the lever arm-based torque measurement described in the previous section. Their main application is non-rotating torque acquisition. Typical examples are process monitoring in agitators, rabblers and similar types of mixing equipment. In such applications the transducer is located directly between the container and the drive on the agitator. The drive shaft goes right through the transducer. Fig. 2.3 shows a suggested configuration for measuring viscosity on the basis of reaction torque measurement.

Fig. 2.3 Reaction torque measurement using a TB1A torque measuringdisk between the motor housing and the container

The driving torque introduced into the agitator must be transmitted from the motor housing to the container flange in the form of a reaction torque. A TB1A torque measuring disk is fitted at precisely this point, between the motor housing and the container. The agitator shaft projects upward through the center hole and the motor is supported on the measuring disk. Interestingly enough the bearing friction in the motor, unlike the bearing friction on the bottom end of the agitator, does not give rise to measurement errors.

If a transmission is located between the transducer and the point on the drive train where the torque is actually intended to be acquired, the transmission ratio must be taken into account without fail in the choice of measuring range and in the scaling of the measuring amplifier. The torque that is actually to be measured will then be displayed with figures in the appropriate range. Torsion fatigue tests on components are yet another field of application. Fig. 2.4 shows a typical application of this kind.

Fig. 2.4 Using a TB1A to conduct torsion fatigue tests on a rod

2.3 Measuring in-line torque

This method acquires the torque in a rotating train of shafts and is commonly known as in-line torque measurement. Fig. 2.5 shows the principle by which inline torque measurement works. Torque transducers are conventionally divided into three product groups: torque shafts, torque hubs and torque flanges.

Fig. 2.5 The in-line torque measurement principle

Signals can be obtained by using a number of different physical principles:

• Hydraulic, pneumatic

• Translating an elastic deformation into a change in capacitance,

inductance, resistance, permeability or phase. Nowadays the most commonly used approach is to measure deformation with the aid of strain gages (SGs), which change their resistance in proportion to the

strain involved. All torque transducers in the HBM range are constructed on this principle. This technology, together with the core skills of HBM in the field of the development and manufacture of measurement bodies (spring elements), has fully proven its advantages by producing the highest levels of accuracy and dynamic response.

2.4 SGs in torque measurement

SG torque transducers consist mainly of spring elements combined with strain gages (SGs) and compensation elements as well as adaptation accessories for the torque connections to input and output sides. The main features of the strain gage principle mentioned in [1] as being of importance to torque measurement are set out in concrete terms below:

Strain gages used in the SG measuring bridge (or Wheatstone bridge circuit, named after the English scientist Sir Charles Wheatstone) together with their means of compensating for the effects of interference

variables, have excellent characteristics with regard to linearity, hysteresis and reproducibility.

Because SGs have negligible mass, the frequencies involved in processes under investigation can be very high (> 50 kHz). Centrifugal acceleration in excess of 10,000 m/s
is not critical.

Static and dynamic moments can be acquired.

SGs exhibit excellent strength in the presence of vibration, making them highly stable under alternating loads.

Torque transducers with SGs exhibit excellent long-term stability whensuitably configured for the application concerned.

Because of the way they are manufactured and the fact that they areproduced by the same company, SGs and measuring bodies (springelements) can be individually adapted to work with one another to optimum effect.

Due to the use of SGs specially adapted to show only minimal effects of temperature variation on the output signal, combined with the properties of the measuring bridge and the use of additional compensating elements, temperature has minimal effect on such devices. They can therefore be used in a wide range of temperatures.

Torque can be measured in positive and negative directions regardless of whether the shaft train is rotating.

The SG measuring bridge can compensate for the highly critical mechanical variables which can cause interference during torque measurement, namely bending moments, axial forces, lateral forces and rotational effects.

3 The structure of torque transducers

The following section describes the structure of torque transducers in which the measuring body forms part of the rotating transmission train and is elastically deformed by the torque being measured. The strain that occurs in these circumstances is acquired with the aid of strain gages.

A torque transducer of this kind principally consists of a rotating measuring body, known as the rotor, and a housing known as the stator. Torque transducers can differ structurally not only in the form of their signal transmission but also in their mechanical design.

Slip rings or contactless systems can be used to transmit the supply voltage and measurement signal. In addition some types of torque shafts have built-in bearings and others are without bearings. The design of the measuring body is important. A distinction is made between three types of torque transducers: torque shafts, torque hubs and torque flanges.

3.1 Mechanical structure

3.1.1 Measuring body designs

As a basic principle measuring bodies can take any shape. On the other hand they must have smooth surfaces on which the strain created by torque can be measured using strain gages.

Frequently used measuring bodies include versions with solid, hollow or square-section shafts. When these designs are used, torque produces torsionalstress only.

In contrast, tubular measuring bodies with the same load-bearing cross-sectional area provide higher bending stiffness. A solid square-section shaft is often used for especially high torque measurement ranges. It is very simple to manufacture and bonding of strain gages is easy.

In contrast, tubular measuring bodies with the same load-bearing cross-sectional area provide higher bending stiffness. A solid square-section shaft is often used for especially high torque measurement ranges. It is very simple to manufacture and bonding of strain gages is easy.

Such are the present-day demands on torque transducers for power test benchesthat they cannot be optimally met by the measuring body versions mentioned above. That is why in the mid nineteen-nineties HBM was the first manufacturer of torque transducers to introduce the shear principle for torque measurement [2]. Characteristic of this principle are features known as half beams, which can be used as shear elements for metrological purposes [3]. Four radial I-profile beams (shear spokes) are built into the T10F torque flange. Not only is this advantageous in terms of measurement technology, but it also gives excellent ratios for the lateral stiffness in directions perpendicular to the direction of measurement. Fig. 3.1 shows an overview of the measuring body shapes most commonly in use at the present day.

Fig. 3.1 Commonly used measuring body shapes

A careful choice of geometry for the strain gage application site and shear elements will make it possible to adjust the required properties of the torque flange within wide margins. Fig. 3.2 shows a series-manufactured T10F measuring body.

Fig. 3.2 T10F measuring body, 200 N⋅m

The measuring body of the T10FS torque flange represents yet a further development and modification of the above. In this case the U-profile shear elements are arranged axially rather than radially. The strain gages are fitted on the inside. This form of measuring body offers the possibility of a hermetically sealed version. HBM has applied for patents on the new radial shear principle and axial shear principle measuring body configurations. A number of patents have already been granted. Fig. 3.3 shows a series-manufactured T10FS measuring body.

Fig. 3.3 T10FS measuring body, 500 N⋅m

3.1.2 Torque connections